Magnetic coupling in (GaMn)As ferromagnetic
semiconductors - studied by soft x-ray
spectroscopy
vorgelegt von
Diplom Physiker
Florian Kronast
von der Fakult¨at II - Mathematik und Naturwissenschaften
der Technischen Universit¨at Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
- Dr.rer.nat. -
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. E. Sedlmayr
Berichter: Prof. Dr. W. Eberhardt
Prof. Dr. W. Thomsen
Tag der wissenschaftlichen Aussprache 20. Dezember 2005
Berlin 2006
D 83
2
.
Dedicated to my family
Contents
1 Introduction 1
2 Soft x-ray absorption spectroscopy 5
2.1 The dipole transition . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 X-ray magnetic circular dichroism . . . . . . . . . . . . . . 7
2.2 Analysis of XAS and XMCD spectra . . . . . . . . . . . . . . . . 11
2.2.1 Sumrules ........................... 11
2.2.2 Multiplet structure . . . . . . . . . . . . . . . . . . . . . . 14
3 Ferromagnetism in dilute magnetic semiconductors 17
3.1 Introduction.............................. 17
3.2 Magnetic ordering in dilute magnetic semiconductors . . . . . . . 18
3.2.1 Zenermodel.......................... 18
3.2.2 RKKY coupling . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.3 Magnetic polarons . . . . . . . . . . . . . . . . . . . . . . 20
3.2.4 Double exchange . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Experimental considerations 25
4.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.1.1 Annealing ........................... 26
4.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3 Datarecording ............................ 28
4.3.1 Total electron yield . . . . . . . . . . . . . . . . . . . . . . 28
4.3.2 Fluorescence yield . . . . . . . . . . . . . . . . . . . . . . . 28
4.3.3 Self absorption effects . . . . . . . . . . . . . . . . . . . . 30
4.4 Resonant reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . 34
5 Chemical and magnetical depth profile of Ga1−xMnxAs films 39
5.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.1.1 Surface magnetization deficit . . . . . . . . . . . . . . . . . 40
5.1.2 Chemical depth profile probed by resonant x-ray reflectivity 45
5.2 Discussion............................... 50
3
CONTENTS i
5.3 Conclusion............................... 53
6 Mn 3dhybridization 55
6.1 Influence of the surface . . . . . . . . . . . . . . . . . . . . . . . . 55
6.2 pd-hybridization of ferromagnetically coupled Mn . . . . . . . . . 57
6.3 Saturation magnetization . . . . . . . . . . . . . . . . . . . . . . . 60
6.4 Evidence for antiferromagnetic coupling of Mn . . . . . . . . . . . 62
6.5 Discussion............................... 66
6.6 Conclusion............................... 67
7 Orbital magnetic moment anisotropy 69
7.1 Introduction.............................. 69
7.2 Results................................. 69
7.2.1 Orbital magnetic moment anisotropy . . . . . . . . . . . . 69
7.2.2 Angular dependence the of ground state hybridization . . . 71
7.3 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . 73
7.4 Outlook ................................ 76
8 Summary 81
Bibliography 84
Danksagung 91
.
Chapter 1
Introduction
ferromagnetic semiconductors a new material class designed for
spintronic applications
The term ”spintronics” refers to electronic devices that utilize not only the charge
of the carriers but also their magnetic moment the so called spin. The huge po-
tential of this combination was impressively demonstrated by the discovery of
the giant magneto resistance (GMR) effect in 1988. The GMR effect exploits the
spin dependent scattering of conduction electrons in a structure of two ferromag-
netic layers separated by a non magnetic spacer layer [75, 76]. Depending on its
magnetic direction, a single-domain magnetic material will scatter electrons with
”up” or ”down” spin differently. Thus electrons become spin polarized if they
pass through a magnetic layer. When the two magnetic layers in GMR structures
are aligned anti-parallel, the resistivity is high because conduction electrons po-
larized by the first magnetic layer will find a reversed magnetization direction if
they enter the second magnetic layer and undergo additional spin-flip scattering
[76]. When the layers are aligned in parallel less spin flip scattering occurs, yield-
ing a lower resistance of the GMR structure [76]. Today the effect is widely used
in magnetic sensors and read heads for hard drives. It is a prominent example for
the benefit of industrial applications from fundamental research. The interest to
incorporate such effects in integrated circuits, e.g. as magneto resistive random
access memory devices, is huge. But the implementation is hampered by the
choice of the right material. Electronic devices are mainly made of semiconduc-
tors whereas only transition metals or rare earth metals show ferromagnetism e.g.
spontaneous magnetic ordering with a net spin polarization. It is rather difficult
to combine these two material classes in functional heterostructures [77]. On the
one hand metal films can not easily be integrated in the production process of
semiconductor plants on the other hand the injection of spin polarized carriers
across a metal-semiconductor interface is rather inefficient. The large difference
in the density of states and the resulting band structure will cause scattering at
the interface that destroys the spin polarization [77].
1
2Introduction
This explains why the discovery of ferromagnetism in III −Vand II −V I
dilute magnetic semiconductors (DMS) attracted such a large interest. These sys-
tems are promising candidates for spintronic devices since the above described
interface problem is avoided in a very elegant way. Spin polarized carriers are
provided by magnetic ions integrated in the semiconductor host matrix. Exper-
iments performed on DMS so far show new and fascinating physical properties
that have not been observed in other systems yet. It has been demonstrated that
the magnetic properties can be changed isothermally by light or electric fields in
(In,Mn)As/(Al,Ga)Sb heterostructures [30]. The anisotropy in Ga1−xMnxAs can
be tailored by the choice of temperature and carrier concentration [54]. Also spin
injection from Ga1−xMnxAs into a (InGa)As has been demonstrated. Unfortu-
nately up to now all dilute magnetic semiconductor materials suffer from a Curie
temperature far below room temperature. At the moment the world record Curie
temperature for Ga1−xMnxAs is at 173K[83]. But nevertheless these materials
are an ideal test ground to study the interplay of quantization effects, magnetism,
carrier dynamics and transport properties. The prospects of spintronic devices
that allow to incorporate data processing and storage in a single chip is more
than encouraging. Thus the community investigating the magnetic properties of
DMS’s is steadily growing.
In this thesis the origin of the ferromagnetic ordering in Ga1−xMnxAs , the
most prominent member of the III −Vseries of ferromagnetic DMS, is investi-
gated by x-ray spectroscopy (XAS) in combination with x-ray magnetic circular
dichroism (XMCD). The ferromagnetism in (Ga1−xMnx)As is based on two coop-
erative effects caused by replacing the trivalent Ga atoms with Mn. Mn provides
a local spin magnetic moment and as an acceptor it creates itinerant holes, which
mediate the long range ferromagnetic order [1]. But despite the existence of
various theoretical models the physics underlying the magnetic properties is still
under discussion [2, 3]. This is partially due to the high degree of dissorder in
these systems caused by the limited solubility of Mn. The formation of As an-
tisites and interstitial Mn were predicted [4]. Both defects act as double donors
partially compensating the effect of the Mn acceptors [4]. For the understanding
of the ferromagnetic ordering the electronic configuration of the Mn impurities
and the number of Mn atoms contributing to the long range ferromagnetic order
are of major interest. These parameters can be probed directly by x-ray ab-
sorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD). At
the Mn 2p- 3dresonance the XAS and MXCD line shapes are characteristic for
the Mn 3delectronic and magnetic ground state configuration respectively [51].
This is a major advantage of the x-ray spectroscopy compared to the widely used
SQUID measurements.
This work starts with a short introduction to the principles of x-ray absorption
spectroscopy. In the following chapter we give an overview on the various theoret-
ical models describing the origin of ferromagnetic coupling in Ga1−xMnxAs. After
presenting the experimental details the chemical and magnetic depth profiles of
3
different Ga1−xMnxAs layers are investigated. The main question at this point is
the diffusion of interstitial Mn during the growth and annealing process and its
influence on the ferromagnetic coupling. The signature of Mn 3d5-3d6mixed va-
lence acceptor states responsible for long-range ferromagnetic order is identified
with x-ray magnetic circular dichroism at all Mn concentrations. In chapter 6 we
demonstrate that an additional non-ferromagnetic Mn species with an electron
count close to 3d4is observed at high Mn concentrations. We discuss a model
in which the latter is due to Mn-Mn antiferromagnetic nearest neighbor pairs.
The last chapter deals with the orbital magnetic moment anisotropy present
in Ga1−xMnxAs films. The microscopic origin of the orbital magnetic moment
anisotropy is probed by x-ray magnetic circular dichrosim spectroscopy. It pro-
vides first evidence for an anisotropic pd-hybridization and, therefore, anisotropic
exchange coupling.
4Introduction
Chapter 2
Soft x-ray absorption
spectroscopy
The fundamental interactions of x-rays with matter are the photoelectric ab-
sorption, scattering processes like Thompson (elastic) and Compton (inelastic)
scattering and the formation of electron positron pairs (above a threshold of 1,022
MeV photon energy). In the regime of soft x-rays (below 10keV photon energy)
the cross section of photoelectric absorption is two to three orders of magnitude
larger than that of the scattering processes. This effect refers to the absorption
of an incoming photon by a core electron exciting the electron to a bound state
or into the continuum if the photon energy is higher than the binding energy
and the work function of the solid. The photoelectric effect was discovered by
Heinrich Hertz in 1887 and could not be explained within the classical theory
at this time. Albert Einstein succeeded to explain the photoelectric effect by
the quantum nature of light and received in 1921 the Nobel price for his find-
ings. Today the photoelectric effect is one of the most popular tools to study
the electronic structure in solid state and surface science. Measuring the x-ray
absorption coefficient as a function of photon energy near the absorption edge of
the element of interest is a widely used technique to obtain information on the
chemical environment of the probed element, its valency, its spin state and so on.
Synchrotron sources like BESSY provide soft x-rays at high brilliance, an energy
resolution below 0.2eV and with full polarization control. The latter is especially
important for the analysis of magnetic samples by x-ray spectroscopy. Similar
to the Faraday-Kerr effect in the optical regime, the x-ray absorption coefficient
for polarized x-rays depends on the magnetization vector which also allows to
study magnetic properties by x-ray spectroscopy. The most popular effect is the
x-ray magnetic circular dichroism (XMCD) i.e. the difference of the x-ray ab-
sorption coefficient between two helicities of a circular polarized incident photon
beam. The combination of x-ray absorption spectroscopy and x-ray magnetic cir-
cular dichroism is ideally suited to study the 3dshell of transition metals like Ni
or Mn since electronic configuration and magnetic moments can be investigated
5
6Soft x-ray absorption spectroscopy
simultaneously.
2.1 The dipole transition
The absorption cross section σis defined as the number of excited electrons per
time unit divided by the photon flux Iph:
σ(E) = Pi,f Wi→f
Iph
(2.1)
Whereby Wi→fdenotes the probability per unit time to promote a core electron
from the initial state |i > into the final state < f|by the absorption of a photon
of the energy E= ¯hω. This transition probability is given by Fermi’s golden rule.
It describes the transition probability from the initial state |i > in to the final
state < f|under the influence of the perturbation H0as
Wi→f=2π
¯h|< f|H0|i > |2δ(Ef−Ei−¯hω).(2.2)
The δ- function represents the energy conservation; transitions are only possible
if the energy interval between initial and final state corresponds to the energy of
the absorbed photon. The electromagnetic field of the photons can be described
by the vector potential A(r, t) = A0ei(ky−ωt)in terms of an electromagnetic
plane wave. With the wave vector k, frequency ωand the polarization vector
ε.0corresponds to linear and −1(+1) to left (right) circular polarization with
a polarization vector +1 = 1/√2(x+iy) (−1= 1/√2(x−iy) ). Circular
polarized photons carry an angular momentum which is parallel (antiparallel) to
the wave vector kfor left (right) circular polarization. The Hamiltonian becomes
[38]
H=1
2m[P−e
cA(r, t)]2+V(r)−e
mcS·(∇×A(r, t)).(2.3)
The last term describes the interaction of the magnetic moment of the electrons
with the oscillating field of the electromagnetic wave. A decomposition in the
undisturbed Hamiltonian of the atom and the perturbation results in:
H=H0−e
mcP·A(r, t)
| {z }
HI
−e
mcS·(∇×A(r, t))
| {z }
HII
+e2
2mc2A2(r, t)
| {z }
HIII
(2.4)
In a first order approximation the term quadratic in Acan be neglected. The
matrix elements of term II are in the order of ¯h·kA0and compare to those of the
term Ilike the impulse if the absorbed photon to the momentum of the electron:
HII
HI≈¯hk
p1.(2.5)
2.1 The dipole transition 7
In the energy range below 1000eV that we are interested in the momentum of the
photon can be neglected. In this approximation the transition probability can be
expressed by a dipole transition:
Wi→f=2π
¯h
e
mc|< f|A·P|i > |2δ(Ef−Ei−¯hω).(2.6)
According to the Wigner-Eckart theorem the dipole selection rules for linear
polarized light are:
∆j= 0,±1; ∆l=±1; ∆m= 0; ∆s= 0.(2.7)
And for circular polarized light:
∆j= 0,±1; ∆l=±1; ∆m=±1; ∆s= 0.(2.8)
By the selection rules we find that the dipole transitions are spin conservative
and orbital selective as ∆mis determined by the polarization of the photon
(∆m= 1 (−1) for left circular (right circular) polarization. The total absorp-
tion cross section in the dipole approximation is given by the sum of all initial
and final states. With the incident photon flux written as the energy flux of
the electromagnetic field divided by the photon energy Iph =E2
0c
2π¯hω =A2
0ω
2π¯hc , the
photoabsorption cross section in the dipole approximation reads:
σ(¯hω) = 4π2α¯hω X
i,f |< f|·r|i > |2δ(Ef−Ei−¯hω).(2.9)
Whereby αis the fine structure constant (α= 1/137). The electronic and mag-
netic properties of the transition metals are determined by the occupation of the
3dshell. Such they are ideally accessible to soft x-ray spectroscopy at the 2p−3d
resonance. But the conservation of orbital angular momentum (∆l=±1) allows
transitions from the 2plevel into 3das well as into 4sstates. The absorption
cross section that we measure at the 2p−3dresonance is, therefore, a mixture
of two transition channels as shown in Fig. 2.1. Transitions into continuum 4s
states cause a step like background whereas the intensity of the resonance peaks
in the absorption spectrum is proportional to the unoccupied 3dstates.
2.1.1 X-ray magnetic circular dichroism
The x-ray magnetic circular dichroism (XMCD) is defined as the difference in
the absorption cross section between left and right circularly polarized x-ray
light with the wave vector kparallel to the magnetization M(the x-ray helicity
±is collinear with the propagation direction). This effect is the analogue to
the magneto optical Faraday effect in the soft x-ray regime. In 1845 Faraday
discovered a rotation of the polarization vector of linearly polarized light upon
8Soft x-ray absorption spectroscopy
Figure 2.1: X-ray absorption spectra recorded at the Mn L3/ L2edges of a
Ga1−xMnxAs sample. The resonance peaks are due to transitions in unoccupied
3d levels as indicated by the inset. Transition into continuum states (represented
by the parabola) cause a step-like background.
2.1 The dipole transition 9
the transmission through silicon borate in an applied magnetic field. Due to
the exchange spitted valence states the absorption coefficient for the two circular
components of the incident light is different. This effect also causes a rotation of
the linear polarization into elliptically polarized light after the transmission.
The XMCD effect occurring at the L3and L2edge of 3d transition metals
can be explained within a qualitative picture. The circular polarized photon gets
absorbed generating a hole in the 2p shell. The p states are split into the 2p3/2
and 2p1/2level by the spin orbit interaction. This interaction couples the spin of
the 2pelectrons to the orbital moment. At the 2p3/2and the 2p1/2level the orbital
angular momentum land the spin angular momentum sare coupled parallel and
antiparallel, respectively. The spin-orbit coupling allows to excite electrons of
the 2pshell by circular polarized light spin selective into the valence shell even if
the dipole operator does not act on the spin. The spin polarization arises from
the selction rule for the orbital magnetic moment depending on the polarization
on the absorbed x-ray photon. Because of the parallel coupling of land sat the
2p3/2level and the antiparallel at the 2p1/2level, transitions from the 2p3/2and
the 2p1/2levels into the valence shell occur with different spin polarization.
Possible final states for the photoexcitation are the unoccupied 3dand 4s
states above the Fermi level. The dipole transition is spin conservative which
means that and spin up electron can only be promoted in to a spin up empty
state and vice versa. In a ferromagnetic transition metal there is an imbalance
of unoccupied spin-up and spin-down states in the d-band due to the exchange
coupling (Stoner model). If the orientation of the magnetization Mis parallel to
the photon wave vector kthis imbalance of empty d-states leads to a spin selec-
tive excitation process, i.e. the probability of an electron transition excited by a
circular polarized photon is proportional to the unoccupied d-states. It causes an
asymmetry in the absorption cross sections for left and right circular polarized
light which is proportional to the difference in the unoccupied spin-up and spin-
down states, i.e. the spin magnetic moment. But the photoelectron also probes
the orbital magnetic moment of the valence band. Due to the conservation of
angular momentum the change in the quantum number mis determined by the
polarization of the photon. Left circular polarized photons with the magnetic
moment +¯hcan cause only transitions with ∆m= 1 and accordingly right circu-
lar polarized photons can cause only transitions with ∆m=−1. If the valence
states with quantum numbers ±mlare unequally occupied the absorption of pho-
tons with opposite helicity will be different. An example of the XMCD effect is
given in Fig. 2.2. For a magnetically almost saturated Ga1−xMnxAs sample at
10K we find a huge difference between the absorption spectra recorded with left
and right circular polarized x-rays. The XMCD signal changes sign between the
L3and L2edge because of the parallel and antiparallel coupling of land sat the
2p1/2and 2p3/2levels, respectively.
10 Soft x-ray absorption spectroscopy
Figure 2.2: The upper panel displays x-ray absorption spectra recorded at the
Mn 2p−3dresonance exciting with left (blue line) and right (red line) circular
polarized x-rays. The sample was a Ga1−xMnxAs (x=0.017) at 10K and in 4T
external magnetic field. A schematic picture of the absorption process is given in
the inset. The lower panel shows the XMCD spectrum (difference spectrum).
2.2 Analysis of XAS and XMCD spectra 11
2.2 Analysis of XAS and XMCD spectra
2.2.1 Sum rules
The sum rules allow under certain approximations to extract from the XAS and
XMCD spectra quantitative information on the ground state spin and orbital
magnetic moments of the atomic shell into which the core electron is excited.
The sum rules presented here were derived for dipole transitions from the levels
j±=c±1/2 of the spin-orbit splitted core state ctowards a valence level lwith n
electrons [58]. The first sum rule was derived by Thole et al. [58]. It states that
the integral over the XMCD signal (the difference in the absorption cross section
between left (σ−) and right (σ−) circularly polarized x-ray light with the wave
vector kparallel to the magnetization M) normalized to the integral over the
unpolarized absorption cross section is proportional to the average expectation
value of the orbital momentum operator Lzacting on the shell in which the
photoelectron is excited [58].
Rj++j−σ+−σ−dω
Rj++j−σ++σ−+σ0dω =l(l+ 1) + 2 −c(c+ 1)
2l(l+ 1)(4l+ 2) −n)< Lz>(2.10)
A second sum rule that relates the integrated XMCD signal to the average ex-
pectation value of the spin momentum operator Szwas derived by Carra et al.
later on [59].
Rj+σ+−σ−dω −c+1
cRj−σ+−σ−dω
Rj++j−σ++σ−+σ0dω =l(l+ 1) −2−c(c+ 1)
3c(4l+ 2) −n)< Sz>(2.11)
+l(l+ 1)[l(l+ 1) + 2c(c+ 1) + 4] −3(c−1)2(c+ 2)2
6lc(l+ 1)(4l+ 2 −n)< Tz>
Whereby < Tz>is the expectation value of the magnetic dipole operator, which
measures the asphericity of the spin magnetization. Such anisotropy can be
caused by distortions of the valence shell due to the spin-orbit interaction or the
crystal field. It is defined as:
~
T=~
S−3~r(~r ×~
S) (2.12)
In principle the sum rules are only applicable to a single transition channel.
Whereas the spectra recorded at the 2p−3dresonance also contain contributions
from transitions into 4sstates. Such a mixture of transition channels contributing
to the XMCD spectra is problematic for the application of the sum rules since
the sum rules would be different for the two channels. But fortunately the ratio
of the radial dipole matrix elements for the 2p→4sand the 2p→3dtransitions
is rather small, and the 2p→4stransitions can be neglected.
|<4s||r||2p > |2
|<3d||r||2p > |2≈0.02 (2.13)
12 Soft x-ray absorption spectroscopy
If we take only the transitions into 3dfinal states (l=2) with the number of
holes n3d= 4l+ 2 −ninto account the sum rules read [60]:
mL=µB
¯h< Lz>=−4RL3+L2(σ+−σ−)dω
3RL3+L2(σ++σ−)dω(10 −n3d) (2.14)
ms=2µB
¯h< Sz>=−6RL3(σ+−σ−)dω −4RL3+L2(σ+−σ−)dω
RL3+L2(σ++σ−)dω (2.15)
×(10 −n3d)(1 + 7< Tz>
2< Sz>)
Whereby the relative cross-section for linearly polarized light, σ0, was replaced by
(σ++σ−)/2. This is justified since usually the x-ray linear magnetic dichroism is
much smaller than the XMCD effect [79]. An example for the application of the
sum rules is given in Fig. 2.3. It shows the unpolarized absorption spectrum and
the XMCD spectrum obtained from a Nickel film. The integrals over the XMCD
spectrum and the isotropic spectrum after subtraction of the step like background
(to remove the contributions from transitions into continuum states) are indicated
by dashed lines. The presence of an orbital moment can be estimated directly
from the non vanishing integral over the XMCD spectrum (RL3+L2σ+−σ−).
A negative (positive) value corresponds to a parallel (antiparallel) alignment of
orbital and spin moment.
For the derivation of the spin sum rule it is assumed that the L3and the L2
edge are well separated. This assumption is only correct if the spin-orbit-splitting
of the core hole is large compared to the coulomb interactions between the core
hole and the final states that lead to a coupling of the two L2,3absorption edges.
Such coulomb interactions with the final state affects directly the ratio between
the absorption coefficients at the L3and the L2edge, the so called branching
ratio. It was predicted that the intermixing of the L2and L3absorption edges is
mainly present towards the early transition metals [64] where the electron core
hole interaction increases while the spin-orbit splitting decreases. For such metals
(e.g. Mn) the application of the spin sum rule can produce an error up to 30%.
Whereas the determination of the orbital moment by the sum rules is not affected
by such intermixing.
A further assumption is that the radial matrix element can be taken as con-
stant due to the normalization to the isotropic absorption cross-section. Wu et
al. calculated for Ni that the radial part of the matrix elements of the d band
|<3d||r||2p > |2varies linearly with the photon energy by ≈30% and is propor-
tional to the spin-orbit coupling in the 3d shell [63]. Since the dichroic signal is
proportional to the radial part of the matrix elements and Lzis proportional to
the spin-orbit coupling in the 3d shell this approximation does not have any ef-
fect on the orbital sum rule. Whereas the spin sum rule is affected by the energy
dependent radial matrix elements [63]. However the sum rules are normalized
2.2 Analysis of XAS and XMCD spectra 13
Figure 2.3: Application of the sum rules to Ni XAS and XMCD spectra. The
dotted line in the upper panel shows the two step function that was subtracted
from the XAS sum spectrum (solid line) prior to the integration to remove the
contributions due to transition into continuum states. The integrals that are used
for sum rule analysis are indicated by the arrows.
14 Soft x-ray absorption spectroscopy
to the isotropic absorption cross-section which is proportional to the number of
holes in the d-shell. But also sand p(continuum states) states contribute to
the measured absorption cross-section. To eliminate these contributions a dou-
ble step function is fitted below the absorption cross-section and subtracted as
shown in Fig. 2.3. This procedure is likely to introduce a systematic error in the
determination of the number of holes in the final state.
It has been shown by ref. [60] that for the transition metals Iron and Cobalt
the spin and orbtial moments determined by the application of the sum rules are
in good agreement with those obtained from Einstein de Haas gyromagnetic ratio
measurements.
2.2.2 Multiplet structure
Electronic and magnetic properties of the transition metals are characterized by
the 3dstates which are successively filled across the series, the Fermi surface
is mainly formed by these states. Compared to the sp bands, with almost free
electron character, the 3dbands with a bandwidth of 5 −10eV are less itinerant.
Coulomb and exchange interaction split the 3d shell into a magnitude of energy
levels corresponding to the possible combinations of the orbital and spin quan-
tum numbers mland msof the residing electrons. The multiplet terms for the
different occupation of the 3d shell are shown in Fig. 2.4 (taken from [65]). The
lowest energy states can be found at the top of Fig. 2.4. In this ground state
configuration the multiplet is occupied according to Hund’s rules. This means
that first the spin moment is maximized, then the orbital angular momentum
and then both are coupled to lowest (highest) possible total angular momentum
for a less (more) than half filled shell [82]. The multiplet terms of the 3dshell
have a strong influence on the hybridization and the magnetic coupling of the
transition metals. In Nickel for example the hybridization of the 3d-shells of
atomic neighbors leads to an admixture of d10 and d8contributions in the ground
state configuration [82]. Thus two adjacent Nickel atoms with two holes can have
either a
d9+ (↑) + d9 + (↑)←→ d8+ (↑↑) + d10 (2.16)
or a
d9+ (↑) + d9 + (↓)←→ d8+ (↑↓) + d10 (2.17)
configuration. In Nickel metal it is not the d8+ (↑↓) singlet state that has the
lowest energy but the d8+ (↑↑) configuration with parallel arrangement of the
spins [82]. Thus the electron correlation causes the ferromagnetic spin alignment
of adjacent Ni atoms which fluctuate between d9+d9and d8+d10 [82].
A strong advantage of the x-ray spectroscopy at the L2,3edges is that, provided
the experimental resolution is high enough, these multiplet splitting of the 3d shell
can be resolved in the 2p−3dabsorption spectra. Because of the large Coulomb
interaction between the 2pand the 3dlevels the dipole transitions depend strongly
2.2 Analysis of XAS and XMCD spectra 15
Figure 2.4: Energy distribution of the terms in the initial state configuration
3dn. The terms are collected in spin manifolds, where the labels give the values
of 2S+1 and L. The lowest energy state is at the top of the diagram. (taken from
[65])
16 Soft x-ray absorption spectroscopy
on the local electronic structure [82]. Van der Laan et al. used a localized
description for the 3dnto 2p53dn+1 excitation that includes the 3d-3dand 2p-
3dCoulomb and exchange interactions, the 2pand 3dspin-orbit interactions
and the crystal field acting on the 3dstates to calculate the L2,3absorption
spectra of different transition metals [51]. It was demonstrated that the multiplet
structure at the L2,3edges can act as an fingerprint of a particular electronic
ground state configuration of the 3d-shell [52]. For the case of Nickel experimental
XAS and XMCD spectra are displayed in Fig. 2.3. XAS and XMCD lineshapes
are dominated by the d9→2p53d10 transitions. But due to the d8admixture in
the Ni ground state configuration also d8→2p53d9transitions should contribute.
It has been demonstrated that those transitions cause the satellite structure in
the XMCD signal at ≈3.3eV above the L3peak [72].
Also the XAS branching ratio, BR= RL3σ0
RL3+L2σ0, is strongly influenced by the
interactions in the 3dshell. In absence of spin-orbit coupling and electrostatic in-
teractions between core hole and valence electrons on the final state the branching
ratio would be statistical, BR=2/3, as expected from the quantum degeneracy
2j+ 1 of the 2plevel. Besides a systematic change in the branching ratio for less
than half filled 3d-shells, it has been shown that a branching ratio larger than the
statistical value is typical for high spin states [65]. Depositing Mn on Cu(110)
it has been demonstrated that the multiplet structure and the branching ratio
in the Mn 2p−3dabsorption spectra change with the atomic coordination [50].
At low coverage detailed multiplet structures are visible which are characteristic
for an atomiclike d5ground state accompanied by a large branching ratio of 0.8
[50]. With increasing Mn coverage up to 4 monolayers the XAS spectrum be-
comes smoother and the XAS spectrum approaches the statistical value of 2/3
[50]. Thus in transition metals we can study the hybridization of the 3dshell
and its ground state configuration by analyzing the multiplet structure and the
branching ratio of the 2p−3dXAS spectra.
Chapter 3
Ferromagnetism in dilute
magnetic semiconductors
3.1 Introduction
Magnetic ordering is a result of the interplay between the Coulomb interaction
and exchange interaction due to the Pauli principle. A simple model demon-
strating this effect is given by Heitler and London for the H2molecule with two
electrons. In this molecule the exchange interaction favors ferromagnetic coupling
whereas the kinetic energy is favored in antiferromagnetic coupling. When both
spins are parallel the electrons are localized at one atom each and can not jump
to the neighboring site. Such antibonding state is energetically not favored. The
configuration with the lowest energy is the bonding state with antiferromagnetic
coupling. But delocalization of electrons does not generally lead to antiferro-
magnetic coupling. The coupling of magnetic moments by hybridization depends
strongly on the electronic and magnetic ground state which is shown for the tran-
sition metals in Fig. 2.4. In the already mentioned case of Nickel, for instance,
the hybridization of the d-shells between atomic neighbors leads to an admixture
of d10 and d8contributions in the otherwise 3d9ground state configuration. The
d8state with the lowest energy is a 3F configuration with parallel arrangement of
spins that causes a ferromagnetic coupling between adjacent Nickel atoms [82].
Itinerant metals require approximations to model the spin-spin interactions.
A relatively simple approach to handle the spin-spin interactions in solids with
itinerant spins is the mean field approximation. It is based on the phenomeno-
logical assumption that the elusive spin-spin interaction between electrons can be
replaced by the interaction of the spins with a very strong magnetic field. The
molecular field will tend to line up the magnetic moments. In such models e.g. the
Stoner model ferromagnetism is described as an extreme case of paramagnetism.
So far we considered only the case of direct exchange interaction, where the
orbital in which the magnetic moments reside overlap. If direct exchange is
17
18 Ferromagnetism in dilute magnetic semiconductors
not possible, e.g. the magnetic orbitals are separated too far from each other
to overlap, the magnetic moments are able to sustain magnetic interactions via
exchange interactions mediated by conduction electrons or valence holes. This
indirect exchange coupling is responsible for the magnetism in the rare earth
metals, the interlayer exchange coupling in GMR systems or the magnetism in
semiconductors doped by transition metals. For the latter we will discuss the
possible coupling mechanisms in detail.
3.2 Magnetic ordering in dilute magnetic semi-
conductors
The magnetic coupling of Mn ions in different types of semiconductors has been
studied extensively in the recent years. In II-VI host materials, like ZnTe, Mn
is divalent and assumes a d5high spin configuration (S=5/2) [43]. Since the
Mn doping in II-VI host materials does not introduce any carriers, the intrinsic
carrier density is rather low and the localized Mn spins order paramagnetically.
Antiferromagnetic coupling between Mn nearest neighbors, due to short range
antiferromagnetic super exchange interactions, has been observed [73]. For highly
p-doped Zn1−xMnxTe also carrier mediated ferromagnetic interactions between
the Mn magnetic moments have been found [73].
In III-V host materials like GaAs where the Mn replaces trivalent Ga atoms
it can be present either in a d4configuration or a d5configuration with a weakly
bound hole, h. In GaAs it is commonly agreed that Mn is present in a d5+h
configuration providing not only localized spins but also acting as an acceptor [1].
The pd-hybridization of the Mn 3dshell with the dangling bonds of As neighbors
induces a spin dependent coupling between the localized Mn spins and the holes
[43]. The mobility of holes in the p-doped Ga1−xMnxAs changes strongly with the
Mn concentration, as the system undergoes a metal to insulator transition (MIT).
Impurity bands start to occur at Mn concentrations of x= 0.01 −0.02 [43]. The
interest to find a theoretical description of the ferromagnetism in Ga1−xMnxAs,
which occurs on both sides of the MIT, is huge (especially the calculation of Tc).
But however, there is no consensus on a common model yet. In the following
sections we give a short overview over the different models in literature, describing
the ferromagnetic ordering in Ga1−xMnxAs .
3.2.1 Zener model
In the metallic regime attempts have been made to describe the ferromagnetism
by the Zener model [43]. Zener first proposed this model of ferromagnetism
driven by the local exchange coupling between carriers and localized spins. Ac-
cording to the model, polarization of localized spins leads to band splitting. In
this spin split band structure carriers become spin polarized to lower their free
3.2 Magnetic ordering in dilute magnetic semiconductors 19
energy. At sufficiently low temperature the lowering of the free energy overcom-
pensates the energy that is necessary to polarize the localized spins. Below that
temperature the ferromagnetic alignment becomes energetically more favorable.
For the description of ferromagnetism in metals the Zener model has been aban-
doned because it does not include the quantum oscillations of the carrier spin
polarization around localized spins (Friedel oscillations). For the description of
ferromagnetism in dilute magnetic semiconductors the Zener mean field theory
has been reconsidered. In Ga1−xMnxAs the carrier concentration is often found
to be significantly lower than the Mn concentration; in that case oscillations in
the carrier spin polarization can be neglected. Within these limitations the Zener
mean field theory has been successfully used to describe the Tcin dilute mag-
netic semiconductors [43] as a function of the Mn concentration, x, and the carrier
density, p. The results of these calculations indicate that the Curie temperature
of Ga1−xMnxAs should scale with the number of substitutional Mn atoms and
the number of carriers like Tc∝x·p1/3. This led to a large experimental ef-
fort devoted to increasing the hole density, which is usually much smaller than
x due to compensation effects. But more recent calculations [41], taking explic-
itly into account spatial disorder and a finite mean free path in RKKY theory,
showed that this simple relation between Tcand the carrier density will not hold
for high carrier densities when h is of the order of x. In that case the oscilla-
tory character of the RKKY coupling can no longer be neglected and will cause
magnetic frustration limiting Tc. The authors also consider the adverse effect of
antiferromagnetic exchange between Mn-Mn nearest neighbors on Tc.
3.2.2 RKKY coupling
The most prominent type of indirect exchange is known as the RKKY interaction,
named after the people who developed this theory (Ruderman, Kittel, Kasuya
and Yosida). The basic idea behind this mechanism is that the interaction of
carriers and localized magnetic moments will establish a non uniform spin density
that leads to a oscillatory behavior of the coupling. For p-dhybridization, like
in Ga1−xMnxAs, the sign of the interaction between magnetic impurities and
valence band carriers is typically antiferromagnetic, as the carriers attempt to
screen the spin of the impurity. Rather than forming a negative spin -5/2 at
the impurity site, the holes instead spin-polarize in concentric rings around the
impurity. The source of the rings of alternating polarization is that a true delta-
function in space would require, in Fourier k-space, all the k-vectors from 0
to infinity to be equally weighted. However, there are only k-vectors from 0
to the Fermi wave vector available. The system thus cannot form a localized
screening of the impurity spin, but does the closest alternative possibility, which
results in an oscillatory spin density surrounding the impurity spin. A second Mn
magnetic moment will interact with this oscillatory spin density, and hence will
couple ferromagnetically or antiferromagnetically, depending on the sign of the
20 Ferromagnetism in dilute magnetic semiconductors
spin density at that point. The oscillatory character of the RKKY coupling can
be neglected as long as the average distance between carriers rc= (4πp/3)−1/3
is much larger than that between the magnetic impurities rs= (4πxN0/3)−1/3.
The RKKY function changes sign the first time at r≈1.17rc. Interestingly the
ferromagnetism does not break down at Mn concentrations below the metal to
insulator transition as one would expect from RKKY theory. To explain the origin
of ferromagnetism in this regime a magnetic polaron model has been proposed
[3].
In the Zener model and the RKKY scheme the pd-hybridization is usually
assumed to be spherically isotropic [2]. Only recently Mahadevan et al. predicted
a strongly anisotropic pd-hybridization in Ga1−xMnxAs, taking into account the
symmetry of the Mn 3dlevels hybridizing with the As porbitals [71]. By the
tetrahedral crystal field the Mn 3dlevels are split into eglevels with lower energy
and t2glevels with higher energy, respectively. Fully occupied t2gand eestates
inside the valence band have mainly Mn dcharacter whereas the partially filled t2g
states at the valence band are formed of Mn 3dand As porbitals [71]. Assuming
spin conserving hopping interactions between those partially occupied levels the
exchange interaction between Mn pairs at various distances along different lattice
orientations has been studied by total energy ab initio calculations [71]. The
main result of these calculations is a significant orientation dependence of the pd-
hybridization and therefore of the exchange coupling [71]. The exchange coupling
of Mn pairs oriented along the <110 >axis remains higher in strength compared
to that of Mn pairs oriented along other directions even if their separation is
smaller [71].
3.2.3 Magnetic polarons
Contrary to the Zener model that assumes itinerant carriers (holes) in Ga1−xMnxAs,
the idea of magnetic polarons is based on localized holes [74]. Such scenario ap-
plies to Ga1−xMnxAs samples with Mn concentrations that are below the metal
to insulator transition. The hole wave function is assumed to fall off exponen-
tially from the localization center with the decay length aB[74]. Within the
localization radius of the hole (aB≈1nm in Ga1−xMnxAs ) exchange interac-
tion with the Mn impurities lead to the formation of a bound magnetic polaron
[74]. At low enough temperatures neighboring polarons begin to overlap and
interact with each other. When the cluster of correlated polarons reaches the
percolation limit the ferromagnetic transition occurs. A schematic picture of two
magnetic polarons is given in Fig. 3.1. The exponential decay of the two hole
wave functions defines a lens shaped region in between the two polarons which is
important for the ferromagnetic coupling of the two polarons (indicated by the
hatched area in Fig. 3.1). The polaron model predicts the existence of magnetic
clusters (magnetic polarons) above the Curie temperature.
3.2 Magnetic ordering in dilute magnetic semiconductors 21
Figure 3.1: Interaction of two bound magnetic polarons. Within the polaron
radius impurity spins (small arrows) interact with the hole spin (large arrow).
(taken from ref. [74])
3.2.4 Double exchange
Also the double exchange mechanism between Mn ions of different valency has
been considered as an origin of ferromagnetism. Double exchange is a mechanism
for spin coupling between magnetic ions of different valency that arises from
electron delocalization. The term double exchange was introduced by Zener to
explain the magneto-conductive properties of mixed-valence solid, notably doped
Mn perovskites. The ferromagnetic alignment of Mn spins due to double exchange
is demonstrated in Fig. 3.2. If the spin down electron of the right Mn atom is
allowed to delocalize to the left Mn the hopping can only occur into an orbital that
contains a spin up electron (Pauli principle). Since the hopping does not involve
spin flips (because the interaction leading to delocalization is spin-independent),
the hopping of the electron forces the spins of both metal sites into parallel
alignment, resulting in nine unpaired spins.
The difficulties to describe the ferromagnetic ordering in Ga1−xMnxAs by an
exact model are partially due to the high degree of disorder in this system. The
distribution of substitutional Mn, the carrier density and the carrier mobility are
strongly influenced by the presence of defects like interstitial Mn or As antisites.
Both of them act as double donors [4] and the experimentally observed carrier
densities well below the Mn concentration have been assigned to their presence
[34]. Furthermore it was proposed that the interstitial Mn tends to align an-
tiferromagnetically with substitutional Mn effectively canceling their moments
[10]. Such reduction of the average magnetic moment per Mn atom was observed
experimentally [22, 18, 11] but the origin is not clear. It could arise from anti-
ferromagnetic coupling between interstitial and substitutional Mn but it could
be also due to antiferromagnetic coupling between substitutional Mn-Mn near-
est neighbors. Also magnetic frustration as predicted by [41] could cause such a
reduction of the observed magnetic moment. This would explain why this effect
22 Ferromagnetism in dilute magnetic semiconductors
Figure 3.2: Ferromagnetic coupling between Mn2+ and Mn1+ due to double ex-
change. Hopping of the spin down electron is only possible for parallel alignment
of the localized Mn spins.
was found to remain at Mn concentrations of x=0.06 [22] even if compensat-
ing defects such as interstitial Mn donors are removed by post-growth annealing
techniques [78].
3.3 Magnetic anisotropy
Ferromagnetic materials exhibit intrinsic easy and hard directions of magnetiza-
tion. This magnetic anisotropy is from a technological and from a fundamental
point of view one of the most important properties of magnetic materials. Differ-
ent applications require different anisotropy. For instance magnetic data storage
requires a large magnetic anisotropy barrier between opposite magnetization di-
rections to prevent the loss of information due to thermal magnetic fluctuations.
However in magnetic sensors a weak magnetic anisotropy is advantageous so that
the magnetization direction can follow external magnetic fields easily. But not
only the strength also the symmetry properties of the magnetic anisotropy are of
major interest to align the magnetization axis along a preferred direction. In that
respect Ga1−xMnxAs is a very interesting material since it allows tailoring of the
anisotropy by the eptiaxial strain, temperature and hole concentration [43, 54].
Depending on these parameters configurations with an out-of-plane or a cubic
in-plane magnetic anisotropy have been predicted and experimentally observed
[43, 54]. Recently also the combination of a cubic in-plane magnetic anisotropy
superposed by an additional uniaxial in-plane magnetic anisotropy has been ob-
served [84]. The complexity of magnetic anisotropy in Ga1−xMnxAs indicates al-
ready its microscopic origin since the magnetic shape anisotropy term would cause
an isotropic in-plane easy axis for lateraly extended thin film samples. Usually
3.3 Magnetic anisotropy 23
a strong magneto-crystalline anisotropy originating in the electronic structure is
characterized by a directional dependence of the orbital magnetic moment. This
has been predicted by Bruno [56] and experimentally verified by different groups
[66, 67]. The difference of the orbital moments along easy and hard magneti-
zation axis is directly proportional to the magneto-crystalline anisotropy energy
[66, 67]. However for Ga1−xMnxAs the situation is more complex. The long
range ferromagnetic coupling of the Mn impurity 3dspins is mediated by valence
holes with a non-zero spin polarization. Strain effects due to a lattice mismatch
between the Ga1−xMnxAs and the substrate can cause a large valence hole spin
anisotropy due to the strong spin-orbit coupling in the GaAs valence band. Thus
the out-of-plane or cubic in-plane magnetic anisotropy of Ga1−xMnxAs films is
explained by the presence of uniaxial tensile or biaxial compressive strain, re-
spectively [54, 84]. E.g. under tensile uniaxial strain the valence band splits
into heavy-hole mj=±3/2 and light hole mj=±1/2 subbands. Following a
simplified model described in ref. [54] the heavy or light hole character of the
carriers depending on the occupation of the two subbands determines the in- or
out-of-plane orientation of sample magnetization at remanence. The exchange
coupling of valence holes and the Mn 3dimpurity spins via the pd-hybridization
transfers these complexity into the Mn 3dsubsystem.
It is obvious that in Ga1−xMnxAs a detailed understanding the Mn 3d config-
uration is the crucial part to separate the influence of different Mn configurations
on the magnetic coupling. This information is not available to standard tech-
niques like SQUID or anomalous Hall current measurements that are commonly
used to characterize the magnetic properties. These methods can even not dis-
tinguish between contributions from holes or Mn atoms to the magnetization.
Soft x-ray spectroscopy is an ideal tool to investigate the electronic and magnetic
configuration of the Mn 3d shell. The following chapters will demonstrate that
this method is sensitive enough to separate the different Mn species occurring in
Ga1−xMnxAs and investigate their influence on the ferromagnetic coupling.
24 Ferromagnetism in dilute magnetic semiconductors
Chapter 4
Experimental considerations
4.1 Sample preparation
The challenge of growing Ga1−xMnxAs by molecular beam eptiaxy (MBE) is to
overcome the limited solubility of Mn in GaAs. At the usual growth temperatures
of GaAs ( 600K), the coevaporation of Mn would lead to the formation of a second
phase with MnAs clusters [1]. The formation of MnAs can only be avoided at
lower growth temperatures (180 - 300K) in the so called low-temperature MBE.
Whereby the actual growth temperature varies with the Mn concentration [1].
The samples presented here were grown at the university of W¨urzburg at the
institute of Prof. L.W. Molenkamp [9] using a GaAs (001) surface as substrate
with 80nm low-temperature GaAs layer deposited as a buffer prior to the growth
of the Ga1−xMnxAs layer. The Mn concentration x for each sample has been
determined from the lattice constant as described in ref. [9]. In the present work
samples with Mn concentrations ranging from x=0.007 to x=0.062 that have
been investigated as listed in table 4.1. Most of the Ga1−xMnxAs films are rather
thick compared to literature. Samples that reach a Tcabove 140K after annealing
usually have a thickness of 50nm or less. This is ascribed to the diffusion of defects
like interstitial Mn to the surface during the annealing which is less efficient in
thicker samples [15]. Results from ref. [80] indicate that also in the as grown state
thinner samples can reach a higher Tc. For the x-ray spectroscopy and especially
the fluorescence measurements a thicker Ga1−xMnxAs layer ensures that the bulk
properties can be probed with not too much disturbance from the surface layer.
The surface of the Ga1−xMnxAs layer was characterized in situ by RHEED
measurements showing a nice epitactic growth and a (2 x 1) surface reconstruction
[9]. In addition the roughness of the surface has been analyzed ex-situ by atomic
force microscopy (AFM). This topographic information is a valuable input for
the evaluation of reflectivity spectra as explained at the end of this chapter. A
typical AFM image of the x=0.017 sample is shown in Fig. 4.1. On a length scale
of several 100nm the surface shows a sinusoidal corrugation with an amplitude
25
26 Experimental considerations
of 6 ±2nm. Very similar corrugations were present in all other samples except
the x=0.062 sample which had a flatter surface. This corrugation is most likely
caused by thickness variations of the low-temperature GaAs buffer layer [70]. In
addition to the buffer layer corrugation all samples have a rms surface roughness
of 0.6 ±0.2nm that we assign to thickness variations of the Ga1−xMnxAs layer.
Mn concetration x: 0.008 0.017 0.051 0.062
Curie temperature Tc: 12K 25K 55K 65K
thickness : 350nm 300nm 500nm 180nm
4.1.1 Annealing
A disadvantage of the low-temperature growth is the large number of defects
that are introduced. In literature mainly interstitial Mn and As antisites are
discussed, because both defects act as double donors and compensate the effect
of the Mn acceptors [4]. To remove such defects the samples have to undergo a
post growth annealing procedure [15]. The optimum annealing temperature is
below the activation threshold of substitutional Mn diffusion but above that of
interstitial Mn (≈180oC). Most of the annealing experiments in the literature
have been performed ex situ in air [15]. It has been demonstrated that by low-
temperature annealing the carrier concentration and thus Tccan be raised [15]. It
is generally agreed that this is due to the removal of interstitial Mn by diffusion.
The record values of Tc, so far, were obtained by the annealing of samples thinner
than 50nm. It is still an open question whether the annealing of thicker samples
is inefficient because of the limited diffusion length, or whether the formation of
a layer of interstitial Mn at the surface, passivated by oxidation prevents the out-
diffusion of the remaining interstitial Mn. The interest of x-ray spectroscopy is
to distinguish interstitial Mn from substitutional Mn by its different ground state
hybridization. To keep the influence of surface oxidation as small as possible the
x= 0.062 sample was annealed at 185oCfor 24h in vacuum.
4.2 Experimental setup
The experiments described here were performed at the BESSY UE46 Hahn-
Meitner-Institute beamline and at the high field magnet at ID8 at the ESRF.
A schematic view of the experimental setup inside the ultra high vacuum cham-
ber at BESSY is given in Fig. 4.2. The sample was mounted on a He cryostat
that allowed for temperatures between 10 and 300K. At BESSY the sample holder
was equipped with small permanent magnet applying a field of 100- 200 Oe along
the horziontal inplane direction of the sample to align the magnetization by field
cooling. The fluorescence diode was mounted inside the cold shield collecting the
fluorescence photons at an fixed angle of 30ofrom above with respect to the sam-
ple surface. Scattered x-rays were detected by a diode mounted on a scattering
4.2 Experimental setup 27
Figure 4.1: Atomic force microscopy (AFM) image of the x=0.017 sample. On
a length scale of several 100nm we find sinusoidal surface corrugations with an
amplitude of 6nm ±2nm as shown by the line scan. Besides this long distance
corrugation a rms roughness of 0.6 ±0.2nm is present.
28 Experimental considerations
arm in the plane of the incident x-rax beam. The polar angle of the sample and
the scattering arm were movable to measure reflectivity spectra and fluorescence
at different incidence angles. For the high field measurements a similar setup was
realized at ID8. In this setup fields up to 4.5T could be applied along the axis of
the incoming x-ray beam. The fluorescence diode was mounted in the scattering
plane at fixed 90oangle with respect to the incident x-ray beam.
4.3 Data recording
Due to the thickness of the samples a direct absorption measurement in trans-
mission geometry was not feasible. Instead we recorded the total electron yield
and the fluoresecence yield which are related to the decay of photoinduced 2p
core holes. The two involved decay channels are radiatonless Auger decay and
the emission of a fluorescent photon. By the Auger process the core hole is re-
occupied by an electron of the d-shell, accompanied by the emission of a second
electron of the d-shell that compensates energy and momentum. The fluores-
cent decay is the reversal of the excitation process, the 2pvalence is filled by an
electron of the d-shell under the emission of a photon that compensates energy
and momentum. Within the limitations discussed below both signals the total
electron yield and the total fluorescence yield are proportional to the absorption
cross section σ(E). To account for intensity variations in the exciting x-ray beam
both signals were normalized to the photocurrent of the refocussing mirror.
4.3.1 Total electron yield
The total electron yield signal represents all electrons that escape from the sample
surface. A large fraction of these electrons are not Auger electrons generated in
the initial x-ray absorption event, but result from inelastic scattering processes
along the trajectories of Auger electrons in the sample. The average energy of
these secondary electrons is very low with an energy distribution ranging from
zero to several 10 eV. This yield of secondary electrons is proportional to the
absorption cross section times the photon energy. Since the spin-orbit splitting
of the Mn L2,3edges is small compared to the energy of the L2,3thresholds, the
approximation by a direct relation between the total electron yield (TEY) and
the absorption cross section σis well justified. As shown by Fig. 4.3 the drain
current signal is very surface sensitive due to the limited escape depth of Auger
electrons and secondary electrons of typically 1-2nm.
4.3.2 Fluorescence yield
The escape depth of fluorescence photons is in general much larger than that
of electrons. As shown in Fig. 4.4 the calculated escape depth for a typical
4.3 Data recording 29
Figure 4.2: Schematic view of the experimental setup at BESY.
Figure 4.3: Energy dependence of the escape depth for electrons. The energies
covered by our experiment are marked by red circles.
30 Experimental considerations
Ga1−xMnxAs sample is around 200nm. This makes the fluorescence yield (FY)
detection a bulk sensitive signal, but it can also give rise to self absorption effects.
In absence of self absorbtion effects the current recorded from the fluorescence
diode is proportional to the absorption cross section σ(E) times the photon en-
ergy.
4.3.3 Self absorption effects
If the probing depth (escape depth) of the fluoresecence yield (FY) or total elec-
tron yield (TEY) is of the same order or larger than the attenuation length of
the incident x-rays (1/σ(E)), the proportionality between the recorded signal
and the absorption cross section σ(E) is likely to be destroyed by self absorption
effects. Therefore especially FY detection suffers often from saturation or self
absorption effects. These effects arise from the absorption of exciting photons on
their way in the sample and from the absorption of fluorescence photons or Auger
electrons on their way out of the sample. These effects depend strongly on the
experimental geometry as indicated by Fig. 4.5. At grazing incidence angles the
attenuation length normal to the surface decreases according to 1/σeff =sinα/σ.
In the worst case, e.g. for fluorescence detection normal to the sample surface
and grazing incidence of the x-ray beam, all the incoming photons get absorbed
in a region within the probing depth of the detector. In that case the signal
becomes nearly independent of the absorption cross section and proportional to
the intensity of the incoming x-ray beam. For a flat sample of the thickness d we
can calculate the expected fluorescence intensity Ix(E). Photons of the energy E
enter the sample under an incident angle αand get absorbed causing core hole
in the level X according to their energy. If this core hole decays via the emission
of a fluorescence photon at the energy EFand this photon leaves the sample it
can be detected at the takeoff angle β. The partial fluorescence intensity excited
by the incoming x-ray intensity at the depth d is proportional to [39]:
dIx
d(E)∝I0(E)exp[−(σ(E)
sinα +σ(Ef)
sinβ )·d]σx
sinαdd(4.1)
We obtain the expected fluorescence signal by an integration over the sample
thickness D:
Ix(E)∝ZD
0dIx
d(E)dd(4.2)
All samples investigated in this work consist of a Ga1−xMnxAs layer deposited
on a GaAs substrate in this case the integral can be substituted by the sum over
two discrete layers:
4.3 Data recording 31
Figure 4.4: Calculated attenuation length for fluorescence photons emitted from
a sample with a manganese concentration of x=0.06.
Figure 4.5: This figure illustrates the dependence of saturation effects on the
experimental geometry. The x-ray beam enters the sample under the glancing
angle αand the fluorescence photons are detected at an detection angle β. Strong
self absorption effects are expected for grazing incidence of the x-ray beam and
the fluorescence detection under β= 90o. In that case the way of the fluorescence
photons to the detector is short compared to the penetration length. The other
extrem is the normal incidence of the x-ray beam and the fluorescence detector
at a grazing angle. In this geometry fluorescence photons from deeper levels that
experienced self absorption effects can not reach the detector.
32 Experimental considerations
Ix(E)∝I0(E)·hσx(E)
sinα ×(1 −e−(σtot(E)
sinα +σtot(Ef)
sinβ )d)
σtot(E)
sinα +σtot(Ef)
sinβ
(4.3)
+σsub(E)
sinα ×(e−(σtot(E)
sinα +σtot(Ef)
sinβ )d)
σsub(E)
sinα +σsub(Ef)
sinβ i
Where σxis the absorption coefficient related to the production of a core hole
in the investigated level Xof the Mn impurities and σtot is the total absorption
coefficient of the Ga1−xMnxAs layer which is the sum of σXand σother the lat-
ter describe the absorption due to shallower core levels, valence levels and other
atomic species. The absorption coefficient of the GaAs substrate enters as σsub
and IOdenotes the intensity of the incoming x-ray light. To identify the presence
any self absorption effects in our FY signal we compared spectra recorded at
different experimental geometries (i.e. varying the incidence angle of x-ray beam
with fixed geometry between sample and detection diode as shown in Fig. 4.2).
Fig. 4.6 shows two XAS spectra of the x=0.062 sample recorded with the flu-
orescence diode in a fixed detection geometry (constant acceptance angle), only
the incidence angle of the exciting x-ray beam was changed. The spectra are
normalized to a constant step edge before and after the L2,3absorption edges.
This step in the absorption cross section is caused by transition into continuum
states. Comparing the XAS spectrum recorded at an incidence angle of 70o(red
triangles) to that obtained at an incidence angle of 10o(black circles) we find a
decreased peak intensity. This indicates that the fluorescence signal is no longer
proportional to the absorption cross section σ(E) due to the presence of self ab-
sorption effects. The dependence of the self absorption effects on the incidence
angle of the x-ray beam is demonstrated in the inset of Fig. 4.6. It displays
the measured L3peak intensity for various incidence angles of the x-ray beam
(solid squares). If we scale the measured fluorescence intensities to absolute ab-
sorption cross sections, according to the literature data provided by the Center
of X-ray Optics [14], we can use equation 4.3 to calculate the intensity seen by
the fluorescence diode in dependence on the absorption cross section of the Mn
species, the sample thickness and the experimental geometry [39]. We assumed
that σother and σsub are constant within the probed energy interval (from 620eV
to 670eV). Thus the energy dependence of saturation effects is determined by the
Mn absorption cross section. The calculated reduction of the L3peak intensity
due to self absorption effects indicated by the red line in the inset of Fig. 4.6
agrees well with the measurements.
To correct for the saturation effects we can use an iterative algorithm. In the
first step we apply equation 4.3 to the measured absorption cross sections and
calculate the ratio of measured and saturation reduced intensities at different
detection angles. If the ratio is always one no saturation effects are present, if not
4.3 Data recording 33
Figure 4.6: This figure displays XAS spectra of the x=0.062 sample recorded in
fluorescence at the L2,3edge of Mn. The sample was kept at room temperature
(non magnetic). The fluorescence detector was fixed in respect to the sample
surface, pointing on the sample at an angle of 300in respect to the sample surface.
The spectrum displayed by black open circles was recorded with the x-ray beam at
an incidence angle of 10o. Whereas for the spectrum displayed by red triangles the
incidence angle of the x-ray beam was changed to 70o. The spectra are normalized
to a constant step function to visualize the influence of the self absorption effects
on the peak intensities. Using an iterative algorithm the spectrum recorded at
70oincidence angle was corrected for saturation effects. The corrected spectrum
is displayed as black line. The inset shows the calculated change of the L3peak
height due to saturation effects in dependence of the incidence angle of the x-ray
beam using equation 4.3. The measured L3peak intensities for various incidence
angles of the x-ray beam are shown as black squares.
34 Experimental considerations
the measured absorption cross sections multiplied by the ratio are used as input
for the next iteration. The iterations are stopped if the calculated saturation of
the input intensities is identical with the measured absorption intensities. Now
each point in the measured spectra is multiplied by a intensity dependent factor
determined by the algorithm. To confirm the result of our saturation correction
we compared the corrected spectra to those recorded at geometries or sample
thicknesses for which no saturation effects have been found. In Fig. 4.6 we
find excellent agreement between the spectrum of the x=0.06 sample measured
at normal incidence and the calculated correction (solid line) of the spectrum
recorded at 70oincidence angle (solid triangle).
4.4 Resonant reflectivity
In order to obtain structural information on the Mn distribution in our samples
we recorded x-ray resonant reflectivity spectra at the Mn 2p→3dresonance.
The reflectivity is given by:
I∝| X
i
fi×exp(iqri)|2(4.4)
where fiis the complex scattering amplitude of the atom iat the position riand
qthe scattering vector. To calculate the reflected intensity we need to know the
complex scattering amplitude of the Mn atoms present in our sample. The imag-
inary part Im(f), which describes the attenuation, corresponds to the measured
absorption signal. The real part, Re(f), can be obtained by a Kramers-Kronig
transformation of Im(f) as explained in the paragraph below. The different line
shape of Re(f) and Im(f), shown in Fig. 4.7, implies a phase shift between inci-
dent and scattered x-rays. This phase shift depends on the chemical composition
of the individual layers and leads to interferences as a function of q, i.e. the
incidence angle and the photon energy. Since we detect only the intensity and
not the phase of the reflected x-rays the measured reflectivity spectra contain
not all the information that is needed to determine the chemical depth profile.
To extract information from the measured spectra we need to compare them to
spectra calculated from a model system. This requires an additional assumption
on the structure e.g. the existence of an surface layer, interface roughness, etc..
The calculations were done employing the IMD code [7] which is based on
a modified Fresnel coefficient formalism, that takes interface imperfections into
account [8]. The Fresnel equations describe the amplitude of the reflected (E0
i)
and transmitted (Ej) electric fields of a plane electromagnetic wave at an ideal
interface of two semi-infinite media with the complex indices of refraction niand
nj. For an incidence angle θithey read:
|E0
i|
|Ei|=nicosθi−njcosθj
nicosθi+njcosθj
=rij (4.5)
4.4 Resonant reflectivity 35
|Ej|
|Ei|=2nicosθi
nicosθi+njcosθj
=tij (4.6)
Where θjis the angle of refraction and rij and tij are the Fresnel reflection and
transmission coefficients, respectively. Interface imperfections like roughness or
diffuseness are included in the Fresnel equations following a formalism developed
by Stearns [8]. In this formalism the interface is described by a profile function
p(z) (z along the surface normal). The profile function is defined as the normalized
average value of the dielectric function (x) (with n=√) along the z-direction.
P(z) = R R (x)dxdy
(i−j)R R dxdy (4.7)
As demonstrated in ref. [8] the loss in specular reflectivity resulting from interface
imperfections can be approximated by multiplying the Fresnel coefficients with
the Fourier transform of the function wz=dp/dz. The new Fresnel coefficients
are now:
r0
ij =rij ˜w(si),(4.8)
with si= 4πθi/λ and λthe wavelength of the light. Four different profile functions
have been developed in ref. [8], describing the interface profile by a error function,
exponential function, linear function or sinusoidal function. The explicit terms
are given in ref. [8]. The width of the interface is described by the parameter σ,
for a purely rough interface σcorresponds to the rms roughness.
In the case of a multilayer system consisting of Nlayers and N+ 1 interfaces
in which the i-th layer has the thickness dithe roughness σiand the index of
refraction ni, the net reflection and transmission coefficients of the i-th layer are
given by [40]:
ri=rij +rje2iβi
1 + rij rje2iβi;with βi= 2πdiniθi/λ (4.9)
ti=tij tje2iβi
1 + rij rje2iβi(4.10)
To compute the net reflection and transmission coefficients of the multilayer the
IMD code applies equations 4.9 and 4.10 recursively, starting at the bottom layer.
Kramers Kronig Transformation
The imaginary part of the scattering factor Im(f) can be determined from the
total absorption cross section σ(ω) that is proportional to the measured total elec-
tron yield and fluorescence yield signal. Their relation is given by: Im(f)(ω) =
ωσ(ω)/4πr0c. Where r0is the classical electron radius, c the speed of light and ω
the incident x-ray frequency. To obtain the absolute absorption cross section the
normalized absorption spectra were multiplied by a scaling factor. We choose a
36 Experimental considerations
Figure 4.7: The figure shows the real (panel A) and the imganinary (panel B)
part of the optical constants for substitutional Mn (black line) and Mn in a 3d5
configuration (red line). The imagninary part was determined by x-ray absorption
spectroscopy, the real part was calculated by a Kramers Kronig relation using
equation 4.11.
4.4 Resonant reflectivity 37
scaling factor that forced the measured absorption cross section before and af-
ter the L2,3resonances to be identical with the data provided by the Center of
X-ray Optics at the Berkley Lab [14]. Then we calculated the real part of the
scattering factor Re(f) from the imaginary part using a Kramers Kronig relation.
These dispersion relations couple the real and the imaginary part of the atomic
scattering amplitude by a Hilbert transformation:
Re(f)(ω0) = 1 + 2
πPZ∞
0
ω Im(f)(ω)
ω2
0−ω2dω. (4.11)
Two obstacles for the practical application of the Kramers-Kronig relations exist.
First we need to know the absorption coefficient at all energies to determine the
real part. And second a singularity in the Cauchy principal value integral occurs.
In our experiment we measure the absorption coefficient only in a short energy
range from 620 −670eV photon energy covering the L2,3absorption edges of Mn.
To calculate the real part of fwith the above formula we extended the energy
range of the measured data set to several hundred eV. We did this by adding
literature data obtained from the Center of X-ray Optics on the low and the high
energy side of the measured data set. Values outside the integration limits are
replaced by a constant.
The presence of the singularity at ω0in the cauchy intrgal requires that the
equation is manipulated to allow numerical integration. The integral can be split
into three parts with the singulatity in the second part, where aand bdenote the
adjacent points below and above the singularity.
38 Experimental considerations
2
πPZ∞
0
ω·Im(f)(ω)
ω2
0−ω2=2
πZa
0
ω·Im(f)(ω)
ω2
0−ω2(4.12)
+2
πPZb
a
ω·Im(f)(ω)
ω2
0−ω2+2
πZ∞
b
ω·Im(f)(ω)
ω2
0−ω2
The integral containing the singulatity can be rewritten as:
2
πPZb
a
ω·Im(f)(ω)
ω2
0−ω2=1
π−PZb
a
Im(f)(ω)
ω0−ω−PZb
a
Im(f)(ω)
ω−ω0(4.13)
Hoyt et al. [5] deomstrated that if we expand Re(f)(ω) in a Taylor series about
ω0the integral on the interval a→bbecomes numerically calculable. It reads
now [5]:
2
πPZb
a
ω·Im(f)(ω)
ω2
0−ω2=1
πhPZb
a−Im(f)(ω)
ω0+ωdω (4.14)
−nln|b−ω0|−ln|a−ω0|o−d Im(f)
dω ω0(b−a)
−
∞
X
n=2
1
(n)n!
dnIm(f)
dωnω0(b−ω0)n−(a−ω0)ni
By substituting 4.14 into 4.12 we can now use equation 4.11 to calculate the real
part of the atomic scattering factor. Results obtained from the Kramers Kronig
transformation are shown in Fig. 4.7. In this case we applied the transformation
to two differnt Mn electronic configurations present in our Ga1−xMnxAs samples.
The figure displays the index of refraction nwhich we used as input for the IMD
code. The index of refraction can be calculated from the atomic scattering factor
by (Re(n) + iIm(n))(ω) = 1 −Nr0(c/ω)2·(Re(f) + iIm(f))(ω)/2π. Where Nis
the number of atoms per unit.
Chapter 5
Chemical and magnetical depth
profile of Ga1−xMnxAs films
For the understanding of the ferromagnetic ordering the electronic configura-
tion of the Mn impurities and the number of Mn atoms contributing to the
long range ferromagnetic order are of major interest. These parameters can be
probed directly by x-ray absorption spectroscopy (XAS) and x-ray magnetic cir-
cular dichroism (XMCD). At the Mn 2p- 3dresonance the XAS and MXCD line
shapes are characteristic for the Mn 3delectronic and magnetic configuration
respectively [51]. Although these techniques have been applied to Ga1−xMnxAs
previously [11, 18, 13, 16, 21] the results are in some points inconsistent. The
first experiments [11, 18] found a pronounced multiplet structure in the Mn XAS
spectra characteristic of a highly localized state. The weak XMCD signal indi-
cated that only a fraction of 13% of the Mn atoms participate in the long range
ferromagnetic ordering. Changes in the line shape of the Mn XAS spectra be-
fore and after annealing have been observed indicating that more than one Mn
species must be present in Ga1−xMnxAs [13]. More recently XAS spectra with
less pronounced multiplet structure have been reported [16] in combination with
remarkably high numbers (66%) of ferromagnetically aligned Mn impurities in
Ga1−xMnxAs [16]. It has been proposed very recently [21] that this discrepancy
may be caused by a Mn rich surface layer.
In this chapter we study the chemical depth profile of as-grown and anneled
Ga1−xMnxAs samples. As-grown refers to MBE grown samples that were trans-
ported through air and measured in our UHV setup without surface preparation.
The annealing was done in a separate vacuum chamber with a short exposure to
air during the transfer into the measurement chamber. The presented XAS and
XMCD experiments exploit the different probing depth of flourescence and elec-
tron yield detection to resolve bulk and surface properties of the Mn impurities.
Comparing bulk and surface sensitive XAS and XMCD spectra two Mn species
can be identified. The bulk is dominated by ferromagnetic Mn in a mixed valence
3d5- 3d6electronic configuration. This has been assigned to substitutional Mn
39
40 Chemical and magnetical depth profile of Ga1−xMnxAs films
hybridizing with the GaAs host [11]. At the surface substitutional Mn and a
second non-ferromagnetic Mn species in a localized 3d5configuration is observed.
The contributions of both Mn species to the spectra are clearly discernible by
their different multiplet structure and a 0.6eV core level shift of the 2p- 3dreso-
nance. The depth profile of both Mn species in the Ga1−xMnxAs films is obtained
by x-ray resonant reflectivity measurements. The results show a non-homogenous
depth profile of two Mn species wich is present in all as-grown samples with var-
ious Mn concentrations ranging from x=0.01 to 0.062. To explore the origin of
this Mn distribution we tested the effect of low temperature annealing on the
Mn depth profile. The x=0.062 sample was annealed for 24h at 185oC ex-situ
in vacuum. A strongly enhanced surface accumulation of the non-ferromagnetic
Mn species after low-temperature annealing is observed, indicating that the non-
ferromagnetic species at the surface could be due to diffusion of interstitial Mn
out of the bulk. Finally the quantified Mn concentrations can be used to evaluate
the effect of the two Mn species on the ferromagnetic coupling.
5.1 Experimental results
5.1.1 Surface magnetization deficit
Fig. 5.1 shows XAS and XMCD spectra of the as-grown x=0.017 sample recorded
with total electron and fluorescence yield detection at the Mn 2p- 3dresonance.
The spectra display two pronounced edges due to transitions into localized 3d
states producing 2p3/2and 2p1/2core holes. The XAS spectra are normalized
to a constant step like background caused by transitions into continuum states.
The XAS multiplet structure obtained with bulk sensitive fluorescence yield (open
circles) is very different from that seen with surface sensitive total electron yield
(solid circles) detection. In addition the 2p-3dresonance maximum in total elec-
tron yield is shifted to 0.6eV higher photon energy compared to the fluorescence
spectrum. In contrast the XMCD lineshape in remanence is very similar for both
detection methods as shown in Fig. 5.1 B. With an applied field of 2.5T the am-
plitude of the bulk XMCD spectra increases, but the line shape is still identical
with the spectrum taken at remanence. In the surface sensitive XMCD spectra
a second peak appears with the applied field as shown in Fig. 5.1 C. The second
peak is shifted to 0.6eV higher photon energy compared to the XMCD spectrum
recorded at remanence and it corresponds to the 2p-3dresonance maximum in
total electron yield XAS (see Fig. 5.1 A). The maximum asymmetry, i.e. the
ratio of maximum XMCD and XAS intensity, in the fluorescence yield channel is
22 ±1.4% in remanence and 49 ±1.3% with an applied magnetic field of 2.5T.
In the total electron yield we obtain an asymmetry of 5.6 ±1.8% in remanence
and 14.9 ±1.3% with an applied field of 2.5T. This is much less than in the
fluorescence yield spectra.
5.1 Experimental results 41
Figure 5.1: A) Normalized XAS spectra of (Ga1−xMnx)As with x=0.017 recorded
at x-ray incidence of Θ = 23ousing fluorescence yield (open circles) and total
electron yield (solid squares) detection. B) shows the corresponding XMCD spec-
tra in remanence and C) at an external field of 2.5T applied along the photon
incidence direction.
42 Chemical and magnetical depth profile of Ga1−xMnxAs films
XAS and XMCD line shapes at the 2p-3dresonance are characteristic for the
3dvalence configuration [51]. The very different XAS line shapes in Fig. 5.1
A, therefore, point to different Mn species in the bulk and at the surface of the
Ga1−xMnxAs films. The bulk XAS lineshape corresponds to that observed in
ref. [21] after removing a surface layer. It was assigned to a single Mn species
in a hybridized ground state with 16% 3d4, 58% 3d5and 26% 3d6character (see
chapter 6). The observed bulk XMCD line shape is identical to that reported
previously [11, 16]. It was assigned to a 80% 3d5, 20% 3d6hybridized Mn ground
state [11] in good agreement with the XAS results. In the following the bulk XAS
and XMCD line shapes are assigned to one species named MnI.
The identical XMCD signal at remanence in the bulk and at the surface
demonstrates that MnIcontributes to the surface signal, too. Therefore the
surface signal must result from more than one Mn species since the XAS spectrum
is obviously dominated by a different Mn species. Further evidence is provided
by the XAS line shape changes that are observed upon annealing as shown in
Fig. 5.2. Typical spectra of the x=0.062 sample are shown before (lines) and
after (symbols) annealing. In the total electron yield we find a reduced intensity
for the low photon energy shoulder of the XAS spectrum after annealing (see Fig.
5.2 A). This shoulder corresponds to the main XAS peak observed in the bulk
sensitive fluorescence yield data (see Fig. 5.2B). Similar changes are also visible in
the total electron yield XMCD spectra recorded with an applied field of 2.5T (see
Fig. 5.2 C). The shoulder corresponding to the bulk XMCD spectrum is reduced
in intensity by annealing. In addition the maximum XMCD asymmetry is reduced
by a factor of 3.1 as shown in Fig. 5.2 C. In the fluorescence yield spectra an
additional multiplet structure appears in the XAS spectra of the annealed sample
(see open circles in Fig. 5.2 B). This structure is identical to the one observed with
electron yield. It is absent in the spectra after removing the surface layer by Ar-
ion sputtering as shown by the crosses in Fig. 5.2 B. Interestingly the additional
multiplet structures do not contribute to the XMCD signal in the fluorescence
yield, i.e. they correspond to non-ferromagnetically ordered Mn. The XMCD
spectra recorded in fluorescence yield before and after annealing have almost
identical line shapes. The XMCD asymmetry in the fluorescence yield is reduced
by about 14% in the annealed spectrum. This means that annealing enhances the
surface segregation of a second Mn species that is paramagnetic at the surface,
which is probed by the total electron yield, but in buried layers, that are probe
by the fluorescence yield, the second Mn species has either no magnetic moment
or is antiferromagentically coupled.
The measured total electron yield XAS spectrum of Fig. 5.1 A) can be decom-
posed if we assume that the low photon energy shoulder at a photon energy of
640eV visible in Fig. 5.2 A is caused by the MnIcontribution. Such an assignment
is strengthened by the observed annealing dependence of the spectral line shape.
Following this idea also the total electron yield XMCD spectrum recorded at 2.5
T external magnetic field can be decomposed into contributions of two different
5.1 Experimental results 43
Figure 5.2: A) Total electron yield XAS and B) fluorescence yield XAS spectra
of the as-grown (solid line) and annealed (symbols) x=0.062 sample. C) The cor-
responding XMCD spectra for both signals, recorded at 2.5T external magnetic
field.
44 Chemical and magnetical depth profile of Ga1−xMnxAs films
Figure 5.3: Spectra of the x=0.017 sample are displayed. A) shows the decompo-
sition of the electron yield XAS spectrum (solid line) into the bulk species MnI
(open circles) and the remaining MnII (crosses) contributions as described in the
text. The decomposition of the corresponding XMCD spectrum recorded at 2.5T
is demonstrated in B). A comparison between the MnII (crosses) line shape and
calculated Mn 3d5XAS and XMCD spectra [51, 6] (black lines) is displayed in
the inset of panel A). The magnetization curves for the two species are shown in
the inset of panel B).
5.1 Experimental results 45
Mn species, since only in the surface sensitive spectrum an external magnetic
field causes a dramatic change in the line shape. This decomposition was done
according to that of the XAS spectrum by assuming that the low photon energy
shoulder in the XMCD signal recorded at 2.5T corresponds to the bulk XMCD
peak of MnIatoms (see Fig. 5.2 C). The results of this analysis are displayed in
Figs. 5.3 A and B. The remaining surface XAS and XMCD lineshapes agree with
multiplet calculations for a 3d5configuration [51] as shown in the inset of Fig.
5.3 A. No other decomposition gives a similar agreement. This Mn 3d5species
is denoted as MnII in the following. The magnetization curves versus applied
magnetic field for the two Mn species are shown in the inset of Fig. 5.3 B. For
the MnIspecies we find a mixture of ferromagnetic and paramagnetic moments.
The ferromagnetic coupling increases at higher Mn concentrations (magnetiza-
tion curves for different Mn concentrations are shown in the next chapter in Fig.
6.5). Atoms of the MnII species have an uncompensated magnetic moment only
at the surface (probed only by total electron yield) which is paramagnetic in all
samples.
5.1.2 Chemical depth profile probed by resonant x-ray
reflectivity
So far the XAS spectra demonstrated the existence of two Mn species. MnII ob-
viously accumulates at the surface and can be distinguished from the bulk MnI
species by XAS. The aim is now to obtain more detailed information on the depth
profile of the two Mn species. This was done by using x-ray resonant reflectivity
at the Mn 2d−3dresonance. Reflectivity spectra for the x= 0.017 sample are
displayed in Fig. 5.4 A. The spectral line shape differs from the XAS spectra
measured by fluorescence and total electron yield since the reflected intensity is
modulated by interference between incident and reflected photons. As indicated
by equation 4.4 the scattering phase shifts and the resulting interference are de-
termined by the spatial Mn distribution and the scattering vector i.e. the photon
energy and the incidence angle. The dependence on the latter is demonstrated in
Fig. 5.4 A. With decreasing incidence angle we observe a decreasing resonance
peak height and the development of a dip on its low energy side. The sensitiv-
ity to changes in the Mn distribution is obvious if we compare the signal of the
as-grown and the annealed x=0.062 sample in Fig. 5.4 B. At identical incidence
angle we find a change in the reflectivity spectrum caused by a rearrangement of
interstitial Mn during annealing.
As mentioned in chapter 4 the reflectivity spectra cannot be transformed
directly into a distribution of Mn atoms, since only the reflected intensity is
recorded while the phase information is lost. For the evaluation a fitting algo-
rithm is used, comparing the measured reflectivity spectra to those calculated
from a model structure, using the Mn distribution as a fit parameter. Because
46 Chemical and magnetical depth profile of Ga1−xMnxAs films
Figure 5.4: A) X-ray resonant reflectivity spectra of the x=0.0175 sample (open
circles) recorded at incidence angles of (a=27o,b=23o,c=19o). For clarity a ver-
tical offset has been applied to the spectra. The fits to the spectra are shown as
black lines. B) Reflectivity spectra of the x=0.062 sample before (open triangles)
and after (solid squares) annealing. The fits to the spectra are shown as black
lines. The inset shows the enlarged the pre edge part of the spectra.
5.1 Experimental results 47
the specular reflectivity is sensitive only to the vertical Mn distribution, it is
reasonable to model the reflectivity data by a system of different layers that are
assumed to be homogenous in the lateral directions. The model describes the
sample by three layers, the simplest configuration that is in agreement with the
absorption measurements. As shown in the inset of Fig. 5.6 A) the three lay-
ers are: (i) the low-temperature GaAs substrate with semi-infinite thickness, (ii)
the bulk Ga1−xMnxAs layer with given thickness and MnIconcentration (x) and
(iii) a surface layer with variable thickness and concentrations of MnII and MnI.
Predetermined input parameters of the model are the bulk MnIconcentration,
the thickness of the Ga1−xMnxAs layer, the interface roughness, and the index of
refraction for both Mn species and the GaAs substrate. The rms roughness for
the investigated samples was determined by atomic force microscopy as shown in
Fig. 4.1. The index of refraction for two Mn species was determined from the
absorption coefficient as explained in chapter 4. The explicit energy dependence
of the indices of refraction for MnIand MnII used in the calculations are shown in
Fig. 4.7. The index of refraction of the GaAs substrate was taken from literature
[14]. The thickness of the surface layer and the concentrations of MnIand MnII
in the surface layer were used as fit parameters. For the calculations and fitting
of the reflectivity spectra the IMD code [7] was employed.
Within the model two scenarios are possible. The simplest case would be that
the surface layer is formed only by MnII atoms. But if MnIis excluded from the
surface layer the resulting fit is of very poor quality indicating that this model
is incorrect. The measured reflectivity spectra can only be fitted if we assume
that MnII and MnIcoexist in the surface layer. In this case we find a perfect
agreement between the measured spectra and the fit at all measured angles and
photon energies as demonstrated in Fig. 5.4 B. An example how sensitive the
calculated reflectivity spectrum depends on the the MnIconcentration in the
surface layer is given by Fig. 5.5. It shows the measured reflectivity spectrum of
the x=0.62 sample recorded at an incidence angle of θ= 22o(open circles). By
the fit the MnIsurface concentration was determined to be x=0.09 (solid line).
Keeping the MnIconcentration fixed at a value of 20% away from the optimum
causes a rather large error in the fit, as visible by the line shapes obtained with
the MnIconcentration fixed at x=0.11 (dashed line) or x=0.07 (dotted line).
Such tests were preformed for each of the three fit parameters to estimate the
error of this method.
The thickness of the surface layer and the Mn concentrations, that were de-
termined by the fit, are summarized for all samples in Fig. 5.6. All as-grown
samples have a surface layer of similar thickness (1.5 - 2nm). The MnIconcen-
tration in the surface layer (solid circles in Fig. 5B) is found to be slightly higher
than in the bulk. As expected from the XAS data we find additionally a high
concentration of MnII atoms in the surface layer, which is well above the bulk
concentration of MnIatoms in all samples. As mentioned above MnIand MnII
coexist in the surface layer which means that the total density of Mn in the sur-
48 Chemical and magnetical depth profile of Ga1−xMnxAs films
Figure 5.5: The confidence interval for the Mn concentrations determined from
the fit to the reflectivity spectra (shown is the reflectivity spectrum of the x=0.62
sample recorded at θ= 22o). By the best fit the MnIsurface concentration
was found to be x=0.09. Significantly worse results are obtained if the MnI
concentration is fixed at x=0.11 (dashed line) or x=0.07 (dotted line)
5.1 Experimental results 49
Figure 5.6: Summary of results for all samples shown as a function of Mn con-
centration. Solid symbols refer to the as-grown, open symbols to the annealed
samples. A) displays the thickness of the surface layer. B) shows the concen-
trations of MnI(circles) and MnII (square) in the surface layer derived from fits
to the reflectivity signal. The lower two panel show the MnIXMCD asymme-
try in the bulk (triangles) and at the surface (diamonds) normalized to the MnI
concentration. The values in C) are obtained in remanence and in D) at 2.5T
external magnetic field applied along the in-plane direction.
50 Chemical and magnetical depth profile of Ga1−xMnxAs films
face layer is more than two times above the bulk value. After annealing we find
the MnII concentration in the surface layer strongly enhanced accompanied by an
increase in thickness of the surface layer from below 2nm to around 6nm (see Fig.
5.6). Obviously the total amount of MnII at the surface has strongly increased,
whereas the MnIdistribution is hardly affected by the annealing process.
It is important to note that the measured and calculated reflectivity spectra
are influenced by interface roughness. This is demonstrated by the reflectivity
spectra of the x= 0.062 sample, recorded before and after annealing, which are
displayed in the inset of Fig. 5.5 B. In the as-grown state (open triangles) rela-
tively smooth interfaces lead to interference fringes caused by the finite thickness
of the Ga1−xMnxAs layer. This is visible as intensity oscillations in the inset
of Fig. 5.5 B. The oscillations can be fitted for an interface roughness of 0.65
±0.1nm and a bulk layer thickness of 171 ±8nm. These values are in perfect
agreement with the surface roughness of 0.6 ±0.2nm obtained by atomic force
microscopy and the Ga1−xMnxAs layer thickness known from the growth param-
eters, respectively. After annealing these oscillations disappear (solid squares).
This can only be reproduced by our model if we assume an interface region
between Ga1−xMnxand the LT GaAs layer with a gradual change of the Mn
concentration. To suppress the oscillations completely, as observed in the ex-
periment, the width of this region has to be 3nm or more. This indicates that
diffusion of interstitial Mn during the low temperature annealing does not only
take place towards the surface but also into the substrate.
5.2 Discussion
The experimental results presented in this chapter are summarized in Fig. 5.6.
Panels A and B contain results from the reflectivity measurements while panels C
and D summarize the XMCD results. Although the Ga1−xMnxAs layer thickness
differs from sample to sample, the thickness of the surface layer of 1.5 - 2nm
is quite uniform for all as-grown samples (see Fig. 5.6 A). After annealing the
surface layer thickness increases strongly. All samples exhibit a coexistence of
MnIand MnII in the surface layer. The total Mn concentration in the surface is
more than two times higher than that in the bulk. Even the MnII concentration
itself (solid squares in Fig. 5.6 B) is higher than the bulk MnIconcentration
for all samples (dotted line in Fig. 5.6 B). Low-temperature annealing leads to
a strong enhancement of the MnII surface concentration (see Fig. 5.6 B). No
significant changes in the MnIsurface concentration are observed (open circle in
Fig. 5.6 B). The ratio of MnIand MnII in the surface layer obtained from the
reflectivity data (Fig. 5.6 B) agrees with that obtained from decomposition of
the electron yield XAS spectra. Also the changes upon annealing are reflected
in the total electron and fluorescence yield XAS spectra displayed in the Fig.
5.2 A and B, respectively. The change in the ratio between MnIand MnII
5.2 Discussion 51
at the surface reduces the weight of the MnIpeak in the surface signal. The
shoulder corresponding to the MnI2p-3dresonance peak (marked by the arrow
in Fig. 5.2 A) is less pronounced in the annealed electron yield spectrum. The
fluorescence yield signal averages over a large probing depth compared to the
total electron yield. In the as-grown sample the surface layer is obviously only a
minor contribution to the fluorescence signal and below the detection limit. After
annealing the MnII surface concentration is enhanced by six times and becomes
visible in the annealed fluorescence yield XAS spectrum (open circles) as a second
peak that corresponds to the MnII 2p-3dresonance peak.
The XMCD results for MnIare summarized in Figs. 5.6 C and D. The bulk
XMCD asymmetries (triangles) were directly taken from the fluorescence yield
data. The surface XMCD values (diamonds) correspond to the measured total
electron yield XMCD asymmetries normalized to the fraction of surface MnI. In
remanence we observe a decline of the bulk magnetization (solid triangles in Fig.
5.6 C) with lower Mn concentration. This is most likely due to the reduction of
the magnetic ordering temperature. At an external magnetic field of 2.5T the low
concentration samples exhibit the highest asymmetry of 0.49 ±0.013 as shown
in Fig. 5.6 D. Using the calculated XMCD asymmetries in ref. [11] this would
correspond to 83 ±4 % of the Mn atoms that are magnetically orderd if every
Mn atom carries a magnetic moment of 4.6µB. Interestingly the bulk saturation
magnetization of the x=0.062 sample in the as-grown state is smaller than this
value of the low concentration sample. Annealing causes a somewhat lower bulk
magnetic moment (open triangle) even though it raises the Curie temperature of
this sample by 13K. A lower magnetic moment per Mn atom in high concentration
samples and its reduction upon annealing has also been observed in ref. [22]. The
origin of this effect is discussed in detail in chapter 6. In remanence and with an
external magnetic field we find a clearly reduced magnetic moment of surface MnI
(solid diamonds in Fig. 5.6 C and D) which is further reduced after annealing
(open diamond). The ferromagnetic exchange coupling of MnIatoms is obviously
weaker in the presence of MnII. Possible mechanisms that could cause this effect
are discussed below.
The XAS data of Fig. 2 and the resonant reflectivity data summarized in Fig.
5.6 B show an inhomogeneous distribution of two Mn species. From its ferromag-
netic and electronic configuration MnIcan be clearly identified as substitutional
Mn replacing the Ga atoms. MnIis the dominant species in the bulk of all films.
The consistently higher surface concentration of substitutional Mn points to a
non-equilibrium MBE growth process as the reason for disorder. Possible site
exchanges are then energetically more favorable [20]. Post growth annealing pro-
duces hardly any change in the MnIsurface species (open and solid circles in of
Fig. 5.6 B).
It is tempting to assign the second observed Mn species, MnII , character-
ized by a 3d5electronic configuration to interstitial Mn. The growth process is
known to provide pathways for the generation of interstitial Mn [20], i.e. the
52 Chemical and magnetical depth profile of Ga1−xMnxAs films
concentration of interstitial Mn at the surface should be significantly higher. In
addition the diffusion of interstitial Mn from bulk to the surface during anneal-
ing has been observed [15]. This is consistent with the increased accumulation of
MnII at the surface of the x=0.062 sample after annealing. Assuming that the
accumulation of MnII at the surface is due to diffusion of interstitials out of the
bulk one can estimate that 5 ±1 % of interstitial Mn was present in the bulk of
the as-grown sample. Such an amount of interstitial Mn is less than the value of
17% recently obtained from ion channeling in the bulk of a Ga1−xMnxAs sample
[19]. However, the number of interstitial Mn in the bulk may strongly depend on
the growth conditions. On the other hand the reflectivity data indicate that Mn
diffuses not only to the surface but also into the substrate. The accumulation
of MnII in the surface layer is accompanied by magnetization deficit of the MnI
residing in that layer. It has been proposed that interstitial Mn should couple an-
tiferromagnetically with substitutional Mn and hybridize less with the substrate
[10]. The latter seems to be reflected in the 3d5configuration of MnII which is
more localized than that of substitutional Mn (MnII ). But the XMCD spectra
provide only little evidence of antiferromagnetic coupling between MnII and sub-
stitutional Mn. Only a small change in the XMCD lineshape that is present in
the as-grown x=0.062 sample and dissappears after the annealing is visible in
Fig. 6.3. It is more likely that the double exchange between substitutional Mn
is influenced via interstitial Mn acting as electron donor. This could lead to a
reduced carrier concentration in the surface layer, thus reducing Tc.
The presence of MnII at the surface and its enhancement upon annealing is
clearly due to the diffusion of interstitial Mn, but the observed lineshape can
not be unambiguously identified as interstitial Mn since one can not rule out the
influence of surface oxidation as reported previously [15]. In some publication
it is argued that the complete out diffusion of interstitial Mn is only possible in
the presence of oxygen or nitrogen passivating intersitial Mn at the surface [62].
The annealing of the x=0.062 sample was done under vacuum. Following this
argument would mean that possibly not all interstitial Mn was removed, because
of the limited amount of oxygen that was present at the surface. Interestingly the
data indicate that two different magnetic configurations of the MnII species are
present in the surface layer after the annealing. The outer MnII atoms accessible
to the electron yield, which are probaly oxidized, carry a paramagnetic moment.
But the buried MnII atoms visible in the fluorescence yield after annealing have
no paramagnetic moment or are strongly antiferromagnetically aligned even at
2.5T external field. This and the coexistence of ferromagnetically ordered MnIat
the same depth below the surface indicates that the surface layer is not completely
oxidized.
Also the Mn bulk spectra could possibly answer the question whether the
MnII configuration is formed at the surface or is also present in the bulk in a very
dilute form. If we assume that the MnII atoms were homogenously distributed
in the bulk before the annealing, we can estimate the change of the bulk XAS
5.3 Conclusion 53
lineshape upon their removal. The FY spectrum of the as-grown sample and that
of the annealed sample after removing the surface layer by Ar sputtering should
show a slight difference due to the missing MnII in the bulk. These two FY
spectra are displayed in Fig. 5.7 (normalized to the same step like backgound).
They are compared to a reference spectrum (opens squares) that was generated by
subtracting the MnII lineshape from the as-grown bulk XAS spectrum, according
to a spectral weight of 5% MnII. As indicated by the reference signal the removal
of 5% MnII from the bulk should cause a small change in the FY signal at the
high energy side of the MnI2p−3dresonance which is above the detection limit.
Interestingly the experimental data show an obvious deviation in the spectral
lineshape between the as-grown and the annealed and sputtered sample on the
low energy side of the MnI2p−3dresonance. This effect will be discussed in the
next chapter in detail. But the expected change on the high energy side of the
MnI2p−3dresonance is not observed. This points to the influence of surface
oxidation. But still, the surface could be altered by sputtering or the MnII not
completely removed.
It is interesting to compare this results to recent neutron scattering experi-
ments [12] which studied depth dependent the magnetic and structural properties
of Mn in a x=0.073 sample as-grown and after annealing. The XAS and reflec-
tivity data demonstrate an increased Mn surface concentration in the as-grown
samples which is strongly increased upon annealing. By neutron scattering such
surface accumulation of Mn could only be found after annealing. In contradic-
tion to the neutron scattering data the XMCD measurements can not confirm
a zero magnetic moment of the Mn surface atoms. Their magnetic moment is
only reduced compared to the bulk Mn. In addition the bulk magnetic moment
measured by XMCD was found to decrease slightly after annealing whereas an
increase was seen by neutron scattering. The inconsistent results that both meth-
ods obtain for the surface layer may be due to the limited sensitivity of neutron
scattering experiments to layers of a few nm. Whether the bulk magnetic moment
of Mn is increased or decreased by annealing may also depend on the annealing
conditions as time and temperature and the presence of ambient gases. In that
respect the annealing conditions were not identical. However, the decrease upon
annealing has been also observed by SQUID measurements [22].
5.3 Conclusion
The analysis of the chemical and magnetical depth profile of the Ga1−xMnxAs
samples revealed the presence of two different Mn species with different XAS
and XMCD line shapes in our samples. The bulk of the Ga1−xMnxAs samples
is dominated by substitutional Mn. This species can easily be identified by its
ferromagnetic properties and a mixed valence 3d5- 3d6electronic configuration
which is characteristic for the hybridization with GaAs valence orbitals. At the
54 Chemical and magnetical depth profile of Ga1−xMnxAs films
Figure 5.7: Lineshape analysis of the fluorescence yield spectrum obtained from
the x=0.062 sample in the as-grown state (solid line)and after annealing and Ar
sputtering (crosses). The reference signal (open squares) was generated by sub-
tracting the MnII lineshape (dotted line) from the as-grown bulk XAS spectrum
according to 5% MnII in the sample volume.
surface we find an accumulation of non-ferromagnetic Mn in a 3d5electronic
configuration. The enhanced surface segregation of this second Mn species upon
annealing of the as-grown samples and the pronounced surface magnetization
deficit of substitutional Mn provides strong evidence that the second Mn species
is related to interstitial Mn. We can not exclude the influence of oxidation on the
measured 3d5ground state configuration but the coexistence of both Mn species
in the surface layer excludes that the surface layer is formed only by oxidation.
Chapter 6
Mn 3dhybridization
In this chapter the hybridization of Mn 3dwith Ga/As 4sp valence orbitals is
studied systematically using high resolution XAS and XMCD spectroscopy for
samples with different Mn concentrations. The spectral XAS and XMCD line-
shape is known to be characteristic for the electronic 3dnvalence configuration
[11, 50, 51, 6, 21]. Most models of exchange coupling presently discussed in the
literature are based on a localized Mn 3d5electronic configuration which interacts
with holes via impurity states consisting of mainly Ga/As 4sp orbitals [45, 46, 44].
Population analysis indicates that the number of Mn 3delectrons is actually be-
tween 3d5and 3d6[47]. This is in agreement with experimental investigations
using x-ray magnetic circular dichroism (XMCD) [11, 21]. However, there are
also experimental reports that Mn is present in a 3d4configuration [61]. In ref.
[61] the 3d4component was even considered essential to establish ferromagnetic
order. The presence of Mn interstitials close to clusters of substitutional Mn
was theoretically predicted to strongly modify the exchange coupling between
the latter as well as their charge state [20, 49]. Finally, in contrast to II-VI based
magnetic semiconductors no antiferromagnetic exchange between Mn-Mn nearest
neighbors has been considered for Ga1−xMnxAs due to a lack of experimental ev-
idence despite its possibly adverse effect on a high ferromagnetic Tc[2]. Here we
present experimental evidence for antiferromagnetic exchange between Mn-Mn
nearest neighbors in Ga1−xMnxAs at high Mn concentrations.
6.1 Influence of the surface
As demonstrated before, using the fluorescence yield detection in XAS and XMCD
is the ideal choice to probe the bulk properties of dilute Ga1−xMnxAs samples.
But of course also the surface contributes to some extend to the signal. To elimi-
nate or minimize the influence of any modified surface layer (see chapter 5) on the
bulk measurements the sample surfaces were prepared by in situ Ar-ion sputter-
ing to remove the surface layer and any contaminants. The surface preparation
55
56 Mn 3dhybridization
Figure 6.1: A) After Ar-ion sputtering the electron yield signal (blue squares)
and the fluorescence signal (black circles) of the x=0.008 sample become more
similar but not identical. The corresponding XMCD spectra in B were recorded
at 4K and 2.5T external magnetic field. They demonstrate that by sputtering
also the contributions of the paramagnetic d5species to the electron yield XMCD
signal are removed. The inset displays the electron yield XAS before (blue line)
and after (blue squares) sputtering.
6.2 pd-hybridization of ferromagnetically coupled Mn 57
can be monitored in XAS and XMCD by total electron yield detection. Typical
XAS spectra before and after sputtering are shown in the inset of Fig. 6.1 A) The
d5multiplet (solid line in the inset) characteristic for the as grown sample (see
Fig. 5.1) disappears after the surface layer is removed (blue squares in the inset).
As visible in Fig. 6.1 A) the lineshape of the total electron yield spectrum (solid
squares) is then similar to that of the fluorescence yield (open circles). But a
distinct broadening of the electron yield XAS spectrum remains compared to the
fluorescence yield data. The origin of that broadening could be due to disorder at
the surface which is of course increased by the Ar-ion sputtering. Also the total
electron yield XMCD signal (solid squares in Fig. 6.1 B) is broadened compared
to the fluorescence XMCD signal (open circles in Fig. 6.1 B) and the surface
XMCD amplitude is reduced compared to that of the bulk. For an external mag-
netic field of 4T the slight broadening at the high energy side of the L3peak,
visible in Fig. 6.1 B), indicates the presence of paramagnetic Mn atoms which are
absent in the bulk. A difference in the fluorescence yield spectra before and after
removing the surface layer was only observed in case of the annealed x=0.062
sample where the Mn d5containing surface layer was (5.8±0.9)nm thick, i.e.
much thicker than in the as-grown state. In all other cases the influence of the
surface layer to the bulk spectra was negligible. In the literature also HCl etching
is used to remove the surface layers from Ga1−xMnxAs samples [21]. The results
of this method are very similar to sputtering. Fig. 6.2 presents the electron yield
spectrum of a sample prepared by HCl etching taken from ref. [21] (red line)
compared to that of a sputtered sample (blue squares). Both spectra are iden-
tical indicating the same influence of disorder. This underlines the advantage of
the fluorescence signal probing the undisturbed bulk properties.
6.2 pd-hybridization of ferromagnetically coupled
Mn
Typical Mn L3,2XAS and XMCD spectra for two different Mn concentrations,
the x=0.008 sample (black line) and the x=0.062 sample after annealing (red
line) are shown in Fig. 6.3 A) and b), respectively. The spectra were recorded
at 10K with saturation magnetic fields (see Fig. 6.5) of 4.5T (x=0.008) and
2.5T (x=0.062) applied along one of the two equivalent in-plane hard magnetic
<110 >axes. The spectra are normalized to a constant step like background
caused by transitions into continuum states. The observed XMCD lineshape is
identical to the one reported previously [11, 21, 17]. Only the as-grown x=0.062
XMCD spectrum (green line in the inset of Fig. 6.3 B)) displays lineshape changes
which, however, disappear after interstitial Mn atoms are removed by annealing
(see red line in the inset of Fig. 6.3 B)).
At low Mn concentrations of x=0.008 and x=0.017 (not displayed in Fig. 6.3)
58 Mn 3dhybridization
Figure 6.2: Samples prepared by Ar sputtering (blue squares) and by HCl etch-
ing (red line) have almost identical surface XAS (electron yield) spectra. The
spectrum of the HCl etched sample was digitized from ref. [21] and stems from
a sample with almost the same Mn concentration (x=0.067) as the sputtered
sample (x=0.062) studied in this work.
6.2 pd-hybridization of ferromagnetically coupled Mn 59
Figure 6.3: XAS (A) and XMCD (B) spectra of the x=0.008 (black line) and the
x=0.062 sample after annealing in vacuum (red symbols). The XMCD lineshape
of the as grown x=0.062 sample (green symbols) is shown in the inset. The
spectra were recorded at 10K for an incidence angle of 20orelative to the sample
surface with the photodiode positioned at 90orelative to the incident x-rays.
60 Mn 3dhybridization
there is excellent agreement between the experimentally observed lineshape and
Anderson impurity calculations [51] of the XAS [21] and XMCD [11] spectra.
A comparison between the calculated XAS [21] and XMCD [11] spectra (red
line) and the measured spectra for the x=0.008 sample (open circles) is shown in
Fig. 6.4 A) and B), respectively. The Mn 3delectronic configuration fluctuates
mainly between 3d5and 3d6with an average 3delectron count at all Mn sites
near n=5.1 [21] or 5.2 [11]. We note that the XAS and XMCD lineshapes cannot
be reproduced by an incoherent superposition of 3d5and 3d6configurations [51].
This implies that all Mn atoms have the same mixed valence 3d5-3d6ground state
and there is no phase separation e.g. in 3d5and 3d6-like Mn sites.
However, at higher Mn concentrations the asymmetric broadening of the XAS
lineshape (red line in Fig. 6.3) indicates that there is more than one Mn species
present. Whereas the unaltered XMCD lineshape present in all samples demon-
strates that the Mn 3dvalency is intimately linked to the observed exchange
coupling in Ga1−xMnxAs . Only a mixed valence Mn 3d5-3d6ground state is
responsible for ferromagnetic coupling at all Mn concentrations! Obviously the
second species of Mn atoms with a different 3dconfiguration contributes only to
the asymmetrically broadened XAS lineshape at x=0.062 but not to the XMCD
spectrum. This is only possible if the second species is non-ferromagnetic. Please
note that this lineshape change cannot be caused by a phase separation and the
formation of MnAs clusters as reported in ref. [48]. MnAs is known to display a
large chemical shift and a significantly different lineshape than the one observed
in Fig. 6.3 [16].
6.3 Saturation magnetization
The XMCD intensity depends strongly on Mn concentration and annealing. This
can be seen by the magnetization curves displayed in Fig. 6.5. The magnetization
curves were recorded by the XMCD signal on the L3peak at a sample temperature
of 10K. For x=0.008 sample (black symbols) and the 0.018 (magneta symbols) the
magnetization curves show signs of coexisting ferromagnetic and paramagnetic
regions. With increasing Mn concentration TCincreases and the ferromagnetic
regions develop into percolation networks eventually covering the whole sample
at x=0.062. This behavior is also reflected in an increase of XMCD intensity with
x at remanence as observed previously [17]. The saturation magnetization for the
different samples can be obtained directly from the magnetization curves. Before
evaluating the XMCD signal at the L3peak all spectra have been normalized
to a constant step edge. For the x=0.008 and the x=0.017 samples (black and
magenta line in Fig. 6.5) the saturated XMCD signal reaches at the L3peak an
value of 65% asymmetry, i.e. the difference of the two XAS spectra recorded with
opposite x-ray helicity divided by the sum of both. Following the calculations
of ref. [11] such dichroic asymmetry corresponds to fully aligned Mn magnetic
6.3 Saturation magnetization 61
Figure 6.4: XAS (A) and XMCD (B) spectra of the x=0.008 (open circles) com-
pared to Anderson impurity calculations [51] of the XAS [21] and XMCD [11]
assuming a Mn 3delectronic 3d5configuration with an admixture of 3d6contri-
butions. The average 3delectron count at all Mn sites was set to n=5.1 [21] or
5.2 [11] (red line).
62 Mn 3dhybridization
moments with an average magnetic moment of 4.6µBper Mn atom [11]. The
average magnetic moment per Mn atom in saturation for the x=0.062 sample is
significantly reduced in the as grwon state (green lines) and the 24h annealing in
vacuum reduced it even further as can be seen by the red line in Fig. 6.5. The
inset in Fig. 6.5 demonstrates that the concentration dependent XMCD reduction
at saturation (orange symbols) scales approximately with the calculated number
of Mn atoms that have a Mn nearest neighbor (blue symbols).
6.4 Evidence for antiferromagnetic coupling of
Mn
It is very likely that the reduced saturation magnetization observed in the x=0.062
sample and the asymmetric broadening of its XAS lineshape have the same ori-
gin. As shown in Fig. 6.6 after annealing of the x=0.062 sample the saturation
magnetization is reduced further. This is accompanied by a stronger asymmetric
broadening of the XAS lineshape. This effect is clearly visible at the low photon
energy side of the L3peak enlarged in the inset of Fig. 6.6. The easiest expla-
nation of the observed effect would be that the asymmetric broadening is caused
by an admixture of non-ferromagnetic Mn that leads to the observed reduction
in the average magnetic moment per Mn atom. This would mean that the XAS
spectrum of the x=0.062 sample can be decomposed into a ferromagnetic species
with a lineshape identical to the XAS spectrum for the x=0.008 sample accord-
ing to the observed XMCD intensity. The remaining part of the spectrum would
be characteristic for the non-ferromagnetic species. Such a decomposition of the
XAS spectra for the x=0.062 sample into spectra for non-ferromagnetic (red sym-
bols and green symbols) and ferromagnetic Mn species (black lines) is shown in
Fig. 6.7. The lineshape of the XAS spectrum for the ferromagnetic species was
assumed to be identical to that for x=0.008. Its intensity was rescaled accord-
ing to the measured XMCD ratios for x=0.008 and x=0.062 as shown in the
inset (black line). This corresponds to the fraction of ferromagnetically aligned
Mn atoms in the sample. The lineshapes of the resulting XAS spectra of the
non-ferromagnetic Mn species for as-grown (green symbols) and annealed (red
symbols) x=0.062 sample are identical. This lends credibility to the quality of
the decomposition procedure.
The observed XAS lineshape displays much less pronounced multiplet fea-
tures than that of the ferromagnetic species. Such an effect is characteristic for
increased valence electron fluctuations [50, 51] possibly due to increased elec-
tronic hopping between 3dshells of adjacent Mn-Mn pairs. A detailed lineshape
analysis similar to the 3d5-3d6Mn species is not available yet. However, informa-
tion about the ground state properties can be extracted using the integral XAS
intensities after subtracting a step like background [50] shown in Fig. 6.7 B).
6.4 Evidence for antiferromagnetic coupling of Mn 63
Figure 6.5: The XMCD signal at a photon energy of 640eV is used to probe the
sample magnetization versus applied magnetic field for as-grown (Ga1−xMnx)As
samples with x=0.008, 0.017 and 0.062 (solid black, solid magenta, and solid
green symbols). The magnetization curve for the annealed x=0.062 sample is
displayed by open red symbols. All spectra were taken at 10K which is only
slightly below TCfor the x=0.008 sample. The upper inset shows the relative
saturation magnetization, Msat (orange symbols) and the calculated number of
Mn atoms that have nearest neighbors, NMn−Mn, (blue symbols) vs x.
64 Mn 3dhybridization
Figure 6.6: The bulk XAS and XMCD spectra of the x=0.008 sample (black line)
are compared to those of the x=0.062 sample at different stages of annealing: as
grown (green) and after annealing under vacuum (red). As demonstrated in A)
the XAS lineshapes are not identical, especially at the low energy side of the L3
peak (enlarged in the inset) differences between the x=0.008 sample (black line)
and the x=0.062 (red symbols) are obvious. The saturation magnetization of the
x= 0,062 sample annealed under vacuum is reduced by a factor of 0.54 compared
the x=0.008 sample, but the XMCD lineshapes of both are exactly identical as
demonstrated in B). The inset in A) visualizes how the XAS lineshape of the
x= 0,062 sample varies with the stage of annealing. This corresponds to a
change of the saturation magnetization that is shown in the inset of B). The
XAS and XMCD spectra of the x=0.017 sample (not shown) were identical to
the x=0.008 case.
6.4 Evidence for antiferromagnetic coupling of Mn 65
Figure 6.7: A) XAS spectra representing ferromagnetic (black line) and non-
ferromagnetic Mn species for as-grown (green symbols) and in vacuum annealed
x=0.062 (red symbols). The inset illustrates the decomposition of the annealed
x=0.062 XAS spectrum (red line) as described in the text. B) Integral of the
XAS spectra in A) after subtraction of a step like background [50]. The integral
intensity corresponds to the number of unoccupied Mn 3dstates for the respective
species.
66 Mn 3dhybridization
Sum rules relate the total L3,2intensity to the average number of unoccupied 3d
levels, nh=10-n [51, 50, 11, 21]. For the non-ferromagnetic species we find a 20%
reduced 3delectron count close to 3d4compared to that of ferromagnetic Mn
atoms. Even if the lineshape in Fig. 6.7 A) shows that this is not a pure atomic
3d4configuration [51]. Interestingly there is hardly a change in the branching ra-
tio, BR=I(L3)/[I(L3)+I(L2)], of the integral L3,2intensities, I(L3,2). We find BR
values of 0.72±0.01 and 0.75±0.01 for the ferromagnetic and non-ferromagnetic
Mn species, respectively. Branching ratios so much larger than the statistical
value of 2/3 are typical for high-spin ground state configurations [65, 50]. This
result together with the zero XMCD spectrum is conclusive evidence that the 3d4-
like Mn species is present as clusters of two or more Mn atoms with their high-spin
atomic magnetic moments compensated by antiferromagnetic coupling.
6.5 Discussion
The concentration dependent XMCD reduction scales approximately with the
calculated number of Mn atoms that have a Mn nearest neighbor (blue symbols
in the upper inset of Fig. 6.5). The observed XMCD lineshape is characteristic
for a high-spin 3d5ground state configuration with a small 3d6admixture [11].
The characteristic 3d5atomic multiplet is still discernible as peaks in the XMCD
and the XAS spectra of Fig. 6.6 [51] but the structures are attenuated by the
3d6ground state weight [11, 21]. The latter is caused by hybridization of Mn 3d
and ligand Ga/As 4sp-states. It is characterized by an extra Mn 3delectron and
a hole on the ligand atoms. Delocalized ligand holes mediate the ferromagnetic
exchange between localized Mn impurities in dilute magnetic semiconductors [2].
For a high-spin 3d5configuration only an extra electron with opposite spin ori-
entation can be accommodated [50]. Therefore, the 3d6weight leads to anti-
ferromagnetic alignment between Mn and As magnetic moments as observed in
ref. [17]. The mixed valence 3d5-3d6configuration is characterized by an average
number of n=5.2 Mn 3delectrons on all sites [11]. Similar values of n=5.3 and 5.1
were obtained from photoemission measurements and cluster model calculations
[53] and XAS data (see below) [21]. The unaltered XMCD lineshape at all Mn
concentrations demonstrates an identical local Mn 3delectronic configuration of
the ferromagnetic Mn species [11, 50]. It also implies that the local magnetic
moments are identical for the ferromagnetic Mn species at all concentrations.
Together with the reduced XMCD signal at saturation this shows that the frac-
tion of Mn atoms participating in the long-range ferromagnetic order is reduced
at larger concentrations. Part of this effect could be caused by non-collinear ar-
rangements of Mn magnetic moments due to a RKKY-like magnetic interaction
[46]. However, since the Mn XMCD lineshape is known to be very sensitive to
changes in the magnetic exchange coupling [50] the latter effect should play a
minor role. The presence of Mn interstitials in the as-grown x=0.062 sample
6.6 Conclusion 67
causes a slightly different XMCD lineshape. This is a strong indication that sub-
stitutional and interstitial Mn occupy neighbor sites and form magnetic clusters
[49, 10].
Ferromagnetism is connected only to the d5-d6Mn species as, for instance,
evidenced by the temperature dependent hysteresis loop changes in Fig. 6.5. In
this case the exchange of holes mediates ferromagnetic coupling and long range
ferromagnetic order sets in as the Mn concentration increases [45, 46, 49]. On av-
erage there is much less than one hole per ferromagnetic Mn acceptor [2, 45, 20].
Theoretical models indicate that compensation of the negative charge for neigh-
boring Mn-Mn acceptor pairs by up to two holes can lead to antiferromagnetic
interaction between Mn neighbors [20]. It is tempting to explain the identified
antiferromagnetic d4-like Mn clusters by this scenario. The observed increase in
the number of d4-like Mn atoms by removal of Mn interstitials is in agreement
with first principles calculations which predict interstitial Mn to cluster with two
or more substitutional Mn atoms [49]. This proximity of interstitial and sub-
stitutional Mn is also thought to affect the ferromagnetic coupling between the
latter [49]. We surmise that this could explain the observed 10% change in Mn
magnetization upon the removal of 5% Mn interstitials (described in the previous
chapter). We can presently only speculate that the electric charge of substitu-
tional Mn-Mn acceptor clusters might be screened by valence holes. The results
could then indicate that some of these holes are tightly bound around antiferro-
magnetic Mn-Mn pairs and may even hop onto the Mn 3dshell as reflected in
the experimentally observed 20% reduced Mn 3delectron count for this species.
It will be interesting to see a first-principles description of such an effect develop
in the future.
6.6 Conclusion
The signature of Mn 3d5-3d6mixed valence acceptor states, responsible for long-
range ferromagnetic order, was identified with x-ray magnetic circular dichroism
at all Mn concentrations. With increasing Mn content an increasing amount of
Mn atoms is observed exhibiting a significantly reduced number of 3delectrons of
close to 3d4. Their number scales approximately with the number of Mn nearest
neighbor pairs expected for a statistical Mn distribution. Both observations can
be explained by the presence of Mn-Mn nearest neighbor pairs. We also find
a corresponding reduction of the number of ferromagnetic Mn atoms at high
Mn concentrations. Contrary to II-VI based materials this represents the first
observation of antiferromagnetic order in III-V dilute magnetic semiconductors
with possibly a similar adverse effect to the ferromagnetic ordering temperature.
68 Mn 3dhybridization
Chapter 7
Orbital magnetic moment
anisotropy
7.1 Introduction
The local exchange coupling between the GaAs valence states and the Mn dstates
is very important for the understanding of the long range ferromagnetic coupling
in Ga1−xMnxAs. The valence holes are exchange coupled to the Mn impurity 3d
spins by pd-hybridization. In this chapter we present angle dependent XMCD
measurements that show a variation of the Mn 3dorbital moment with the in-
plane azimuthal lattice direction. Correlated spectroscopic lineshape changes in
the XMCD spectra can be interpreted as an anisotropy in the spatial overlap of
Mn 3dand As 4sp states that is probed by the spin-orbit coupling, present in
the Mn 3dshell. This interpretation is in agreement with recent calculations pre-
dicting a strongly anisotropic pd-hybridization [71]. This is the first experimental
evidence for an orientation dependent pd-hybridization in Ga1−xMnxAs.
7.2 Results
7.2.1 Orbital magnetic moment anisotropy
In this chapter we will focus on the annealed sample with x=0.062. At low
temperature (5-10K) this sample exhibits two in-plane easy-axis of the mag-
netization which are oriented along the equivalent <100 >lattice directions
as determined by SQUID measurements [68]. Analyzing the magnetization by
XMCD spectroscopy we find an obvious difference between XMCD spectra that
were recorded with the magnetization aligned along the equivalent <100 >and
the equivalent <110 >lattice directions. The Fig. 7.1 B). shows two XMCD
spectra that were recorded in magnetic saturation with an external magnetic field
of 4T applied. For the red spectrum the magnetic field and the incoming x-ray
69
70 Orbital magnetic moment anisotropy
Figure 7.1: This figure displays spectra of the annealed x=0.062 sample recorded
at 5K and an incidence angle of 20orelative to the surface. In panel B) two
XMCD spectra are displayed: for the red XMCD spectrum the magnetization
was saturated along a hard magnetic <110 >axis whereas the black spectrum
was recorded with the magnetization saturated along an easy magnetic <100 >
axis. The integrals over the XMCD spectra are shown as dashed lines. Panel A)
shows the corresponding isotropic XAS spectra (solid lines) and their integrals
(dashed lines) after subtraction of the indicated step function (dotted line). Only
the XAS spectra were normalized to an identical height of the step edge.
7.2 Results 71
beam were aligned along the <110 >lattice direction (hard axis) whereas for
the black XMCD spectrum the azimuth of the sample was rotated by 45oso that
the magnetization was aligned along the <100 >direction (easy axis). The
incidence angle was in both cases 20oand the sample temperature 5K.
By sum rule analysis (see chapter 2) we find for both directions a non-zero
orbital moment residing on the Mn 3dshell. In both cases the orbital moment
is positive, which means that spin and orbital moment are aligned parallel. Ac-
cording to Hund’s rule this is expected for a more than half filled 3dshell and
agrees very well with a d6admixture to the mainly d5ground state (see chapter
2). As described in chapter 2 only the d6contribution carries an orbital moment
which is zero for a high-spin d5configuration. Our experimental data demon-
strate that the size of the orbital moment strongly depends along which axis the
magnetization is aligned. The absolute orbital moments were calculated using
equation 2.14. Where the occupation of the d-shell was assumed to be 5.2 elec-
trons as determined from the ground state hybridization analysis in chapter 6.
From the integrated XMCD and XAS spectra shown in Fig. 7.1 we obtain orbital
moments of 0.02 ±0.01µBper Mn atom if the magnetization is aligned along the
easy axis which is significantly lower than the value of 0.055±0.01µBobtained for
the magnetization aligned along the hard axis. This is in contradiction with an
increased orbital moment along the easy axis as described by Bruno’s model due
to magneto crystalline anisotropy [56]. This contradiction points to a different
origin of the orbital moment anisotropy. In the next section we will demonstrate
that the orbital magnetic moment anisotropy is correlated to clear differences
in the XMCD lineshape. The two observed XMCD lineshapes provide a direct
access to a different ground state hybridization.
7.2.2 Angular dependence the of ground state hybridiza-
tion
The XMCD lineshapes measured with the magnetization saturated along the
<110 >lattice directions (red line) and the <100 >lattice directions (black
line) are different. This is shown in Fig. 7.2. The insets show enlarged regions
of the spectra with the distinct lineshape changes. The two XMCD spectra were
not scaled relative to each other. They match each other perfectly except for
the regions enlarged in the insets. Inset a) shows that the small positive peak
at the high energy side of the negative XMCD L3main peak is increased if the
magnetization is saturated along a <100 >lattice direction. In this configuration
also the low energy side of the L2doublet is increased in combination with a
sharpening of the rising edge as shown in the inset b).
Fig. 7.3 A) demonstrates that this effect depends only on the alignment
of the magnetization and is not due to any artifact introduced by the sample
rotation. The figure shows two XMCD spectra measured along the <110 >hard
72 Orbital magnetic moment anisotropy
Figure 7.2: A) This figure compares XMCD spectra of the annealed x=0.062
sample recorded at 5K and 4T magnetic field applied along two different lattice
directions to calculated XMCD spectra. For the red XMCD spectrum displayed
in panel A) the magnetization was saturated along a <110 >direction (hard
magnetic axis) whereas the black spectrum was recorded with the magnetization
saturated along a <100 >direction (easy magnetic axis). The insets enlarge
parts of the two spectra which exhibit lineshape variations. The XMCD spectra
displayed in panel B) were calculated for a pure Mn 3d5configuration (blue line)
and for a Mn 3d5configuration with an admixture of 3d6(magenta line) (taken
from [51, 11])
7.3 Discussion and conclusions 73
magnetization direction. The spectra are normalized to equal XMCD intensity
at the negative L3peak. In remanence, i.e. with no external magnetic field
applied, the spectrum (black line) corresponds to that with the spins aligned
along the easy <100 >and equivalent directions, although attenuated by the
incomplete alignment of x-ray polarization and magnetization direction. In an
applied magnetic field of 2.5T (red line) the spins rotate into the hard <110 >
direction. The spectra in Fig. 7.3 A) are identical to the one shown in Fig. 7.2
A) with the same lineshape changes. However this procedure of forcing the spins
away from the easy direction gives far more accurate results and it is, for instance,
possible now to study the temperature dependence of the lineshape changes. This
is shown in Fig. 7.3 B) where the difference spectra of the XMCD data of Fig.
7.3 A) are displayed together with spectra measured at elevated temperatures of
15K (green line) and 50K (black line). The integrals over the spectra are shown
in the inset. The effect decreases rapidly with the temperature and is very small
at 50K which is 22K below the critical temperature.
Unfortunately no calculations have been carried out so far to reproduce these
XMCD lineshape variations. For a qualitative evaluation we can compare the
observed XMCD lineshapes to the calculated XMCD spectra for a pure d5ground
state [51] (blue line) and the hybridized ground state of 80% d5with a 20% d6
admixture [11] (magenta line) shown in Fig. 7.2 B). The regions enlarged in the
insets a) and b) are the same as in panel A). Comparing the enlarged regions in
panels A) and B) we find obvious similarities that allow us to correlate the change
in the measured XMCD lineshape with a trend in the ground state hybridization.
The stronger positive peak in inset a) and the sharp rise at the onset of the L2edge
shown in inset b) are obviously fingerprints of a more localized 3d5configuration
with less admixture of a d6configuration. In this simplifying and qualitative
picture the Mn 3dground state turns out to be less hybridized with the GaAs sp
orbitals if the magnetization is aligned along the easy axis.
Finally it should be noted that these changes are obvious only in the XMCD
signal. Within the experimental error the isotropic lineshape does not depend on
the magnetization orientation. Thus the XMCD lineshape is either much more
sensitive to changes in the Mn 3dground state hybridization than the isotropic
XAS spectrum or the total 3delectron count and, therefore, the charge transfer
between the Mn dorbitals and the As ligands does not change with the orientation
of the magnetization vector.
7.3 Discussion and conclusions
We have shown above that the XMCD lineshape varies if the magnetization is
saturated along an easy (<100 >) or hard magnetic (<110 >) axis. Analyzing
the two different XMCD lineshapes in a simplified way we obtained qualita-
tive information about the corresponding ground state configurations. With the
74 Orbital magnetic moment anisotropy
Figure 7.3: A) XMCD lineshape of the x=0.062 sample recorded at two different
magnetic fields of 2.5T (red line) and 0.01T (black line) applied along the <110 >
direction (hard axis). The spectra are scaled to identical amplitude at the L3edge.
The difference of the two XMCD spectra is displayed in B) for temperatures of
5K (blue line), 15K (green line) and 50K (magenta line). The inset displays the
integral of the difference spectra.
7.3 Discussion and conclusions 75
magnetization oriented along an easy axis the XMCD lineshape indicates a more
localized d5like configuration whereas for the magnetization aligned along a hard
axis the corresponding ground state configuration appears to be more hybridized
i.e. it shows stronger mixing of d5and d6configurations. Evaluating the orbital
moment with sum rules we found that the change in the XMCD lineshape is cor-
related with a change in the orbital moment. Surprisingly for the magnetization
aligned along the hard magnetic axis the orbital moment is found to be larger
than for an alignment along the easy axis. From that observation it can be ex-
cluded that the anisotropy of the orbital magnetic moment is caused by magneto
crystalline anisotropy effects which should result in a different variation of the
orbital moment. To understand the observed effect it is important to consider the
Mn 3dorbitals involved in the pd-hybridization. The Mn 3dlevels are split by the
tetrahedral crystal field into an E-symmetric doublet and a T2-symmetric triplet
[69]. Fully occupied t2gand egstates inside the valence band have mainly Mn d
character whereas the partially filled t2gstates at the valence band are formed of
Mn 3dand As porbitals [71]. The absolute values of the t2gwave functions are
shown in Fig. 7.4. Assuming spin conserving hopping interactions between those
partially occupied orbitals the exchange interaction Jij(R) between Mn pairs at
the distance Ralong different lattice orientations has been studied [71]. In con-
trast to RKKY calculations assuming a spherical pd-hybridization the exchange
intensities were found to depend on the specific lattice orientation [71]. A scheme
of the t2genergy levels of two interacting Mn atoms is given at the top of Fig.
7.5. Spin-up and spin-down states of the Mn atoms interact by spin conserving
hopping and form a set for bonding and antibonding states. The results of the
ab initio total energy calculations are shown in the lower panel of Fig. 7.5. The
ferromagnetic stabilization energy EAF M −EF M is found to be highest if the
hopping interaction occurs along the <110 >lattice direction [71]. Calculations
using large cells of up to 256 atoms could demonstrate a significant domination
of the orientation dependence over the distance dependence in the exchange cou-
pling [71]. The exchange coupling of Mn pairs oriented along the <110 >axis
Figure 7.4: Absolute values of the Mn 3dt2gwave functions in respect to the
crystallographic axes. Open circles indicate the As ligands of the central Mn
atom.
76 Orbital magnetic moment anisotropy
remains higher in strength compared to Mn pairs oriented along other directions
even if their separation Ris smaller [71]. In the previous chapters it has been
demonstrated that the pd-hybridization introduces a 20% d6admixture to the
Mn 3d5ground which is characteristic for substitutional Mn. This admixture
of d6is also the origin of the orbital magnetic moment residing on the Mn 3d
shell ( a pure d5high-spin state is spherically symmetric and possesses no orbital
moment). The angular dependence of the orbital moment and the change in the
ground state hybridization indicated by the XMCD lineshape are obviously not
due to magneto-crystalline anisotropy but reflect the spatial anisotropy of the
hybridization between Mn dstates and the dangling sp3hybrids of neighboring
As atoms. The ab initio total energy calculations based on pd-hopping interac-
tions predicted that a significant feature of the Jij exchange-coupling strength
is a pronounced orientation dependence [71]. Dominant contributions stabilizing
the ferromagnetic state are maximal along the <110 >directions and minimal
along the <100 >directions i.e. the hopping strength along the <110 >di-
rection is found to be larger than along the <100 >direction. It is tempting
to correlate this predicted anisotropy of the pd-hybridization with the directional
dependence of the d6ground state weight observed in XMCD. As an effect of the
Mn 3dspin-orbit coupling XMCD, therefore, is sensitive to the directional depen-
dence of valence fluctuations. In agreement with the preferred hopping along the
<110 >directions we observe the higher XMCD d6ground state weight along
this direction.
The conclusion of the above described effect is that due to the spin-orbit cou-
pling in the Mn 3dshell XMCD spectroscopy is able to map the spatial anisotropy
of the pd-hybridization in Ga1−xMnxAs. By XMCD spectroscopy we can identify
distinct spectroscopic features that are related to the spatial overlap of Mn 3d
and As sp states influencing the ferromagnetic ordering. This is exactly what
is needed for a detailed understanding of the origin of ferromagnetism in these
systems. In future this effect could be used to test theoretical models.
7.4 Outlook
So far we studied the effect of the anisotropic pd-hybridization on the XMCD
lineshape by changing the orientation of the magnetization axis. Within the
experimental uncertainty the isotropic XAS signal was not affected by that. This
indicates that we probe the anisotropy of the pd-hybridization via the spin-orbit
interaction but the charge transfer between the Mn dorbitals and the As ligands
does not change with the magnetization direction or the changes are too small
to be resolved in our experiment. As an outlook on future projects we present
data that possibly indicate changes in the charge transfer between the Mn d
orbitals and the As ligands occurring between the ferromagnetic state at low
temperature and an non ferromagnetic state above the critical temperature. The
7.4 Outlook 77
Figure 7.5: A) Schematic energy levels for two interacting Mn atoms with their
spins ferromagnetically and antiferromagnetically aligned. B) Distance and ori-
entation dependence of EF M and EAF M for two Mn atoms in a 64 atom GaAs
cell obtained by ab initio total energy calculations. The direction of the vector
connecting the two Mn atoms is given by the upper x-axis. (both taken from
[71])
78 Orbital magnetic moment anisotropy
data were recorded on the x=0.017 sample which exhibited the same anisotropy
and the same the dependence of the XMCD lineshape on the magnetization axis
but less pronounced than the x=0.062 sample. In Fig. 7.6 A) the isotropic XAS
of the x=0.017 spectrum is displayed and in Fig. 7.6 C) the difference of two
XMCD spectra comparable to that in Fig. 7.3 is shown. As for the x=0.062
sample one XMCD spectrum was recorded in remanence and the other one with
4T magnetic field applied along the hard axis. Prior to subtraction both spectra
were normalized to identical L3peak height. The shown XAS data are the average
of more than fifty single spectra, thus we could reduce the noise to less 0.5 permil
of the peak intensity. The interesting result is, that the isotropic XAS spectrum
recorded at 5K differs from XAS spectra recorded at 40K which is above the
critical temperature. The difference of these two XAS spectra (high minus low
temperature) is shown in Fig. 7.6 B). It was of course tested that these minimal
variations can not originate from a small energy shift between the two spectra.
Most interestingly the changes in the XAS intensity occur mainly at positions of
the spectrum where the XMCD lineshape was found to be sensitive to the spatial
structure of the pd-hybridization. This coincidence makes it possible that the
observed changes in the XAS lineshape reflect a general change pd-hybridization
at the onset of ferromagnetism. By the positive integral of the difference spectrum
shown as a dashed line in Fig. 7.6 B) we can determine that the number of dholes
is larger at 40K than at 5K. This would mean that the charge transfer between
the Mn dorbitals and the ligands is reduced above the critical temperature. It
will be the purpose of future projects to study these promising observations in
more detail.
7.4 Outlook 79
Figure 7.6: This figure displays spectra of the x=0.017 sample normalized to
the mirror current without any self absorption correction. A) XAS spectrum
recorded at 5K. B) Difference of two XAS spectra recorded below and above the
Curie temperature(40K - 5K). The integral of the difference is shown as a dashed
line. C) Difference of two XMCD spectra recorded in remanence(0.01T) and in
saturation(4T) both at 5K.
80 Orbital magnetic moment anisotropy
Chapter 8
Summary
In the recent years a large field of research emerged, exploring the possibilities
how to introduce and handle spin polarized carriers in semiconductor materials.
One of the goals is to incorporate spintronic devices in conventional semiconduc-
tor technology. Very promising systems are the dilute magnetic semiconductors,
where the spin polarized carriers arise from magnetic ions doped into the semi-
conductor host.
In this thesis we studied the origin of the ferromagnetic ordering in Ga1−xMnxAs,
the most prominent member of the III −Vseries of ferromagnetic DMS. The
ferromagnetism in Ga1−xMnxAs is based on two cooperative effects, caused by
replacing the trivalent Ga atoms with Mn. Mn provides a local spin magnetic
moment and as an acceptor it creates itinerant holes, which mediate the long
range ferromagnetic order [1]. But the limited solubility of Mn can lead to a high
number of defects e.g. As antisites and interstitial Mn [4]. Due to the complexity
of Ga1−xMnxAs and the high degree of disorder, the physics underlying its mag-
netic properties is still under discussion, even if various theoretical models exist
[2, 3]. For further understanding of the ferromagnetic ordering the electronic
configuration of the Mn impurities and the number of Mn atoms contributing
to the long range ferromagnetic order are of major interest. We probed these
parameters directly by x-ray absorption spectroscopy (XAS) and x-ray magnetic
circular dichroism (XMCD). The spectral XAS and XMCD lineshape is known to
be characteristic for the electronic 3dnvalence configuration [11, 50, 51, 52, 21].
In contrast to previous attempts we combined surface and bulk sensitive de-
tection methods with additional reflectivity measurements to resolve a chemical
and magnetical depth profile of the (GaMn)As layer. This analysis revealed the
presence of two different Mn species with different XAS and XMCD line shapes
in our samples. The bulk of the Ga1−xMnxAs samples is dominated by substi-
tutional Mn residing at the Ga sites. This species can easily be identified by
its ferromagnetic properties and a mixed valence 3d5- 3d6electronic configu-
ration which is characteristic for the hybridization with GaAs valence orbitals.
At the surface we find an accumulation of non-ferromagnetic Mn in a 3d5elec-
81
82 Summary
tronic configuration. The enhanced surface segregation of this second Mn species
upon annealing, causing a large surface magnetization deficit of substitutional
Mn, provides strong evidence that the second Mn species is related to intersti-
tial Mn. Acting as a double donor interstitial Mn should strongly reduce the
carrier density and, therefore, also the ferromagnetic coupling between substitu-
tional Mn. Our results demonstrate that XAS and XMCD spectra representing
the bulk properties of Ga1−xMnxAs can only be obtained if the influence of the
surface layer is excluded.
Using the bulk sensitive XAS and XMCD spectra we studied the hybridiza-
tion of Mn 3dwith GaAs 4sp valence orbitals systematically for samples with
different Mn concentrations. We find a signature of Mn 3d5-3d6mixed valence
acceptor states responsible for long-range ferromagnetic order at all Mn concen-
trations. This is in agreement with previous experimental investigations [11, 81]
and with theoretical models based on a localized Mn 3d5electronic configuration
which interacts with holes via impurity states, consisting of mainly GaAs 4sp
orbitals [45, 46, 44]. In addition we find experimental evidence for an antiferro-
magnetic exchange between Mn-Mn nearest neighbors in (GaMn)As at high Mn
concentrations. With increasing Mn concentration an increasing amount of Mn
atoms not participating in the ferromagnetic ordering is observed. Their number
scales approximately with the number of Mn nearest neighbor pairs expected for
a statistical Mn distribution. For the Mn atoms not participating in the ferro-
magnetic ordering we also find a reduced number of 3delectrons of close to 3d4.
Both observations can be explained by the presence of Mn-Mn nearest neighbor
pairs. It has been predicted theoretically that the exchange coupling and the
charge state of Mn in clusters of substitutional Mn can be strongly modified by
the presence of interstitial Mn [20, 49]. Contrary to II-VI based materials this
represents the first observation of antiferromagnetic order in III-V dilute mag-
netic semiconductors with possibly a similar adverse effect to the ferromagnetic
ordering temperature.
In angle resolved XMCD measurements we studied the hybridization of the
Mn 3dshell with GaAs valence orbitals. The pd-hybridization is usually assumed
to be spherically isotropic [2]. But we find a variation of the Mn 3dorbital
moment with the in-plane azimuthal lattice direction that is correlated with dis-
tinct spectroscopic features. The observed dependence of the orbital magnetic
moment on the lattice directions is contrary to what is expected from the mag-
neto crystalline anisotropy contribution. Thus the magneto crystalline anisotropy
can be ruled out to cause this effect. The spectroscopic features in the XMCD
spectra and the correlated change in the orbital moment can be interpreted by
an anisotropy in the spatial overlap of Mn 3dand As 4sp states influencing the
ferromagnetic ordering. This interpretation is in agreement with recent calcu-
lations predicting a strongly anisotropic pd-hybridization [71]. This is the first
experimental indication for an anisotropic pd-hybridization in (GaMn)As and,
therefore, magnetic exchange coupling. The spectroscopic features related with
83
this effect could be used in future to test theoretical models.
84 Summary
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Danksagung
Diese Arbeit wurde bei BESSY in Berlin durchgef¨uhrt. Ich m¨ochte allen BESSY
Mitarbeitern f¨ur die gute Arbeitsatmosph¨are danken und speziell denen, die am
Zustandekommen der Arbeit beteiligt waren.
Mein besonderer Dank gilt Herrn Prof. Dr. W. Eberhardt, der es mir erm¨oglicht
hat diese Arbeit anzufertigen und der jederzeit f¨ur fruchtbare Diskussionen zur
Verf¨ugung stand.
Ganz besonders m¨ochte ich Herrn Dr. H.A. D¨urr f¨ur seine ausdauernde und fre-
undschaftliche Unterst¨utzung danken. Er hat mir bei der Arbeit mit Anregungen
und Ideen stets zur Seite gestanden.
An den in der Arbeit vorgestellten Messungen waren insbesondere Frau Dr.
A. Vollmer und Herr R. Ovsyannikov beteiligt. Ich m¨ochte mich f¨ur ihre Un-
terst¨utzung bedanken.
Auch den Beamline- und Experiment-Betreuern, Frau Dr. C. Boegelin, Herrn Dr.
D. Schmitz, Herrn Dr. P. Imperia und Herrn Dr. J. Cezar, die mich bei meinen
Messungen bei BESSY und an der ESRF nach Kr¨aften unterst¨utzt haben geb¨uhrt
mein besonderer Dank.
Ich m¨ochte weiterhin Herrn Prof. Dr. C. Thomsen f¨ur die ¨
Ubernahme des Ko-
referats danken.
Zuletzt ein ganz grosses Dankesch¨on an meine Familie f¨ur ihre Unterst¨utzung in
allen Lebenslagen.
