Document [original]

Element-Speciﬁc Magnetization Damping in Ferrimagnetic

DyCo

Alloys Revealed by Ultrafast X-ray Measurements

Radu Abrudan, Martin Hennecke, Florin Radu, Torsten Kachel, Karsten Holldack,

Rolf Mitzner, Andreas Donges, Sergii Khmelevskyi, András Deák, László Szunyogh,

Ulrich Nowak, Stefan Eisebitt, and Ilie Radu*

1. Introduction

Manipulation and control of magnetism by

light is one of the key concepts of modern

research in magnetism with direct and

far-reaching implications for magnetic data

recording.

[1,2]

Of particular interest for both

fundamental and applied science is the

use of femtosecond (fs) laser pulses to fully

control the orientation of a spin ensemble

on ultrashort timescales. A cornerstone in

this respect was the discovery of thermally

induced magnetization switching in ferri-

magnetic GdFeCo via a single fs laser pulse

excitation. This ultrafast spin switching

process was mediated by an unexpected

transient ferromagnetic-like state (TFLS),

which has been identiﬁed as the driving

microscopic mechanism behind thermally

induced switching in ferrimagnetic alloys.

[3]

The existence of the TFLS is related to

the different demagnetization rates of the

transition metal (TM) and rare-earth (RE)

constituents in the alloy.

[3,4]

This is com-

monly linked to the larger magnetic moment

of the RE spins, e.g., μGd ¼7.63 μB

Dr. R. Abrudan, Dr. F. Radu, Dr. T. Kachel, Dr. K. Holldack, Dr. R. Mitzner

Helmholtz-Zentrum Berlin für Materialien und Energie

BESSY II

Albert-Einstein-Str. 15, Berlin 12489, Germany

Dr. M. Hennecke, Prof. S. Eisebitt, Dr. I. Radu

Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy

Max-Born-Strasse 2A, Berlin 12489, Germany

E-mail: [email protected]e

Dr. A. Donges, Prof. U. Nowak

Fachbereich Physik

Universität Konstanz

Universitätsstraß e 10, Konstanz 78457, Germany

The ORCID identiﬁcation number(s) for the author(s) of this article

can be found under https://doi.org/10.1002/pssr.202100047.

published by Wiley-VCH GmbH. This is an open access article under the

terms of the Creative Commons Attribution License, which permits use,

distribution and reproduction in any medium, provided the original work is

properly cited.

DOI: 10.1002/pssr.202100047

Dr. S. Khmelevskyi

Research Center for Computational Materials Science and Engineering

Vienna University of Technology

Karlsplatz 13, Vienna A-1040, Austria

Dr. A. Deák, Prof. L. Szunyogh

Department of Theoretical Physics

Budapest University of Technology and Economics

Budafoki út 8, Budapest H-1111, Hungary

Dr. A. Deák, Prof. L. Szunyogh

MTA-BME Condensed Matter Research Group

Budapest University of Technology and Economics

Budafoki út 8, Budapest H-1111, Hungary

Prof. S. Eisebitt

Institut für Optik und Atomare Physik

Technische Universität Berlin

Straße des 17. Juni 135, Berlin 10623, Germany

Dr. I. Radu

Fachbereich Physik

Freie Universität Berlin

Arnimallee 14, Berlin 14195, Germany

The dynamic response of magnetically ordered materials to an ultrashort external

stimulus depends on microscopic parameters, such as magnetic moment,

exchange, and spin–orbit interactions. Whereas it is well established that, in

multicomponent magnetic alloys and compounds, the speed of demagnetization

and spin switching processes has an element-speciﬁc character, the magnetization

damping was assumed to be a universal parameter for all constituent magnetic

elements irrespective of their different spin–orbit couplings and electronic struc-

ture. Herein, experimental and theoretical evidence for an element-speciﬁcmag-

netic damping parameter is provided by investigating the ultrafast magnetization

response of a high-anisotropy ferrimagnetic DyCo

alloy to femtosecond laser

excitation. Strikingly different demagnetization and remagnetization dynamics of

Dy and Co magnetic moments is revealed by employing femtosecond laser pump–

X-ray magnetic circular dichroism probe measurements combined with atomistic

spin dynamics (ASD) simulations using ab initio calculated parameters. These

observations, fully corroborated by the ASD simulations, are linked to the element-

speciﬁc spin–orbit coupling strengths of Dy and Co, which are incorporated in the

phenomenological magnetization damping parameters. These ﬁndings can be

used as a recipe for tuning the speed and magnitude of laser-driven magnetic

processes and consequently allow control over various dynamic functionalities in

multicomponent magnetic materials.

RESEARCH ARTICLE

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compared with μFe ¼1.92 μB,

[4]

leading to slower spin dynamics

with respect to the TM spins. However, the demagnetization

times τi

[5]

τiμi

2αiγikBT(1)

do not only depend on the magnetic moments μibut also on the

spin–orbit coupling strength of the respective elements, which,

in atomistic spin models, is contained in the damping parameter

αi;

[6–8]

γidenotes the gyromagnetic ratio, kBis the Boltzmann

constant, and Tdenotes the temperature of either the electronic

or phononic subsystems—see also Equation (4) and (5). Previous

studies on ultrafast switching often assumed that the damping

parameter αiis universal for all spins in the compound, and

despite this approximation, these models provided reasonable

agreement with experimental observations so far.

[3,4,9,10]

Yet,

as we will show in the following, a quantitative understanding

of ultrafast spin dynamics in complex multi-sublattice ferrimag-

nets requires a more detailed knowledge of the damping mech-

anisms on an atomistic level.

In this work, we present an element- and time-resolved study of

ferrimagnetic DyCo

alloy with a focus on the demagnetization

processes of the constituent Dy and Co elements. The choice of

DyCo

alloy has been motivated by the existence of large and dif-

ferent elemental spin–orbit coupling strengths and magnetic

moments at Dy and Co sites, with the former being expected to

presumably generate different magnetic damping behaviors of

the constituent elements. The experimental observations reveal

distinctly different demagnetization times and remagnetization

behaviors for Dy and Co. To understand the time evolution of these

processes, we use atomistic spin dynamics (ASD) simulations

using an ab initio calculated spin Hamiltonian.

[11]

Simulation

results and the X-ray magnetic circular dichroism (XMCD) meas-

urements are compared in a quantitative manner to determine the

distinct, element-speciﬁcdampingcoefﬁcients of Dy and Co spins.

The experimental XMCD data can only be described using largely

different elemental magnetic damping constants for Co and Dy.

These ﬁndings provide the ﬁrst direct experimental and theoretical

evidence for an element-speciﬁc damping in ferrimagnetic alloys.

2. Results and Discussion

2.1. Ferrimagnetic DyCo

and Time-Resolved XMCD Method

The DyCo

sample is an intermetallic stoichiometric phase of

1x

alloys and a highly anisotropic magnetic system with

remarkably strong magnetocrystalline anisotropies per sublat-

tice, which are, e.g., comparable with the Dy–Co intra- and inter-

atomic exchange interaction energies (see the previous study

[11]

and the following). Dy and Co sublattices are aligned in a ferri-

magnetic structure, as sketched in Figure 1b. DyCo

exhibits

both, a magnetization compensation and a spin-reorientation

transition, and it has attracted increased attention recently as

a prototype ferrimagnetic alloy.

[11–15]

Polycrystalline DyCo

ﬁlms

of 25 nm thickness with perpendicular magnetic anisotropy

were grown by magnetron sputtering in an ultraclean argon

atmosphere at room temperature. The stoichiometry of the fer-

rimagnetic alloy was controlled by varying the deposition rate of

separate chemical elements during cosputtering. Aluminum

membranes (500 nm thick) have been used as substrates due

to their large transmission in the soft X-ray spectral range and

to ensure maximum stability during laser pumping experiments.

Detailed sample characterization was performed prior to the

pump–probe experiments using the ALICE diffractometer

[16]

at BESSY II synchrotron and has been reported elsewhere.

[11]

To measure the element-speciﬁc magnetization dynamics at Dy

and Co absorption edges in DyCo

, we used time-resolved XMCD

at the fs-slicing facility of the BESSY II electron storage ring, which

provides 100 fs soft X-ray pulses with circular polarization.

[17]

XMCD measurements were performed in transmission geometry

(Figure 1a), recording the intensity of the transmitted X-ray beam

with an avalanche photodiode (APD) upon ﬂipping the external

magnetic ﬁeld direction (250 mT). Stroboscopic laser pump/

X-ray probe measurements were performed using 40 fs (full width

at half maximum) laser pulses of 1.5 eV photon energy; the sub-

sequent laser-induced magnetization dynamics was measured by

recording the XMCD signal using 100 fs X-ray pulses tuned to the

edge of the Co (778 eV) and the M

edge of Dy (1295 eV).

Element selectivity, provided by the X-ray transitions involving

core electrons, allows us to probe separately the dynamics of

the 3d and 4f magnetic moments of Co and Dy, respectively.

Measurements were performed at two different incident laser ﬂu-

ences of 9.4 and 14.1 mJ cm

. The sample temperature was kept at

150 K during the pump–probe measurements, i.e., above the com-

pensation temperature Tcomp ¼125 K and below the spin-reorien-

tation transition region TSR1,2 ¼320–360 K.

[11]

2.2. ASD Simulations

Figure 1b shows the crystallographic CaCu

-type structure of the

DyCo

alloy with the Dy and Co spins being antiferromagneti-

cally coupled and parallel with the ab basal plane of the unit cell;

this spin conﬁguration is retained up to the spin-reorientation

temperature TSR1,2 ¼320–360 K. To model the ultrafast demag-

netization of DyCo

, we use our previously developed multiscale

model of ab initio calculations and ASD simulations (see the pre-

vious study

[11]

). Self-consistent ﬁeld calculations were performed

in terms of the scalar-relativistic Korringa–Kohn–Rostoker (KKR)

method within the atomic sphere approximation

[18,19]

and the

local spin-density approximation (LSDA), where the nine 4f elec-

trons of Dy were treated within the frozen-core approximation.

The isotropic exchange couplings were then calculated in the spirit

of the magnetic force theorem.

[20]

The magnetic anisotropy ener-

gies were obtained from the relativistic local density approxima-

tion (LDA) þUmethod used within the KKR formalism

[21,22]

in terms of the magnetic force theorem as a difference of the band

energies corresponding to different spin quantization axes.

The spin Hamiltonian for the normalized magnetic moments

Si¼μi=μireads

H¼

i,j

JijSi⋅SjB⋅X

μiSiþX

2,isin2ϑi

þX

6,isin6ϑicosð6φiÞ

(2)

accounting for the exchange interaction, Zeeman interaction

with an external magnetic ﬁeld, and the elemental magnetic

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anisotropies, respectively; Jij are the Heisenberg exchange inter-

actions, dz

2,Dy ¼1.4 mRy and dz

2,Co ¼þ0.1 mRy are the compet-

ing uniaxial anisotropy energies of Dy and Co spins, respectively,

6,Dy ¼0.17 mRy is a basal-plane anisotropy, and ϑi,φiare the

polar coordinates of spin Si. As the laser excitation will heat

the sample beyond the spin reorientation temperature, the long

delay times simulations, shown in Figure 2c, require an external

ﬁeld B¼15 T to keep the magnetization aligned along the b-axis

(i.e., the ﬁlm normal). This magnetic ﬁeld is larger than experi-

mentally required ﬁelds to magnetically saturate the sample

but much smaller than the effective exchange ﬁelds acting in

the magnetically ordered state on the sublattice (calculated

JCoCo ¼1.1 mRy and JDyCo ¼0.23 mRy, see the previous

study,

[11]

correspond to effective exchange ﬁelds of about 100 T

for Dy and 1000 T for Co) and, thus, is not affecting the ultrafast

demagnetization behavior. Moreover, ASD simulations with a

reduced magnetic ﬁeld of 100 mT instead of 15 T show a similar

transient demagnetization behavior—see Supporting Information.

Using the spin Hamiltonian deﬁned in Equation (2), we inte-

grate the stochastic Landau–Lifshitz–Gilbert (LLG) equation of

motion

[23]

∂

t¼γi

ð1þα2

iÞμi

SiðHiþαiSiHiÞ(3)

where γi¼giμB=ℏis the gyromagnetic ratio (with gDy ¼4=3 and

gCo ¼2), and αi¼αel

iþαph

iis the atomistic Gilbert damping

coefﬁcient. The effective ﬁeld is

Hi¼

∂

þζiel þζiph (4)

with ζiνbeing Gaussian white noise with

hζiνi¼0, ζiλð0Þζν

jðtÞ†¼2αν

ikBTνμi

γi

δðtÞδijδνλ (5)

The separation of the thermal noise ζiνand damping αν

iinto

the electronic and lattice contributions, denoted by index

ν¼el, ph, is rationalized by the different electronic structures

of the TM and RE metals;

[24]

δij and δνλ denote the Kronecker

deltas, and δðtÞis the delta distribution function. It is worth not-

ing that the atomistic Gilbert damping parameter αν

idetermines

the amount of energy and angular momentum dissipated per ele-

mental spin (or sublattice magnetization) precessional cycle into

the heat bath, which acts here as an external reservoir.

In general, for the delocalized 3d moments of the TM, the

demagnetization is due to scattering with hot conduction elec-

trons, and thus, it is sufﬁcient to couple the Co spins only to

the electronic temperature via αel

Co,

[5]

i.e., αph

Co ¼0. The 4f states

Co 2c

Co 3g

X-rays

Laser

DyCo5

APD

Detector

(c)

(b)

(a)

-5

-10

DOS (states/eV f.u.)

-8 -6 -4 -2 0 2 4

E-EF (eV)

Co 3g

Co 2c

Figure 1. a) Schematic illustration of the time-resolved XMCD measurement geometry. The fs X-rays and laser pulses are collinearly impinging on DyCo5

sample in a transmission pump–probe geometry; thin Ta ﬁlms (blue sheets) are used as buffer and capping layers. The transmitted X-ray intensity is

measured using an APD detector. b) Representation of the ferrimagnetic spin structure of DyCo5for an out-of-plane magnetization conﬁguration, as used

in the XMCD experiments; the basal plane of the hcp unit cell is perpendicular to the DyCo5sample surface. c) Element- and spin-resolved density of

states (DOS) for DyCo5alloy obtained from ab initio calculations showing the antiferromagnetic coupling of Dy and Co. The spin-up and spin-down DOS

states are depicted by solid and dashed lines, respectively.

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of Dy are located well below Fermi level (Figure 1c); hence,

there is only a weak coupling αel

Dy to the electronic temperature

stemming from the spin-polarized 5d6sp electrons, whereas

the 4f moments only interact with the less excited lattice via

αph

Dy.

[4,24,25]

However, due to the large 4f orbital moment of Dy,

we expect that this 4f contribution to the Gilbert damping still

plays a fundamental role in the demagnetization process; see,

e.g., the previous studies.

[24,26]

Finally, we obtain the time-

dependent electron and phonon temperatures Tνin Equation (5)

by solving the two-temperature model (2TM)—the details about

the 2TM parameters can be found in the Supporting Information.

2.3. Element-Speciﬁc Magnetization Dynamics

The results of the laser-induced demagnetization of ferrimag-

netic DyCo5measured element-speciﬁcally at the incident laser

ﬂuences of 9:4 and 14:1mJcm

2(corresponding to demagneti-

zation degrees of 40% and 80%, respectively) are shown in

Figure 2. For both ﬂuences, a clearly distinct demagnetization

and remagnetization dynamics is visible for both Co and Dy sub-

lattices. At Co sites, the demagnetization reaches its maximum in

about 0.5 ps (depending on the laser ﬂuence), whereas Dy needs

3–4 ps to achieve the same demagnetization amplitude. Such a

disparity of the RE and TM demagnetization times has previously

been observed in other RE-TM ferrimagnets.

[3,27,28]

Moreover, it

is clear that in the temporal range where the Co magnetization

has started to recover, Dy is not even fully demagnetized yet. For

a better overview on the remagnetization processes, the transient

XMCD data measured on longer pump–probe delays are shown

in Figure 2c. We observe that around 50 ps time delay, Co is

almost fully remagnetized, with about 80–90% of its initial

XMCD values, whereas the Dy magnetization is still 40–60%

demagnetized.

To retrieve the time constants of the demagnetization (τD) and

remagnetization (τR) processes from the transient XMCD data,

we use a biexponential ﬁt function convolved with a Gaussian g(t)

accounting for the time resolution of the measurement of 110 fs

fðtÞ¼gðtÞ⊗8

A,t≤0

ABexpt

τDCexpt

τR,t>0(6)

where Adescribes the XMCD signal before the pump pulse

arrival, whereas Band Care the amplitudes of the two exponen-

tials describing the initial magnetization quenching and the

subsequent relaxation processes, respectively. The retrieved time

constants for the demagnetization and remagnetization pro-

cesses of Co and Dy are listed in Table 1. The ﬁtting curves

of Dy and Co XMCD data are shown in the Supporting

Information.

The elemental demagnetization times τDcoincide for both

applied ﬂuences within our experimental error: Co demagnetizes

within 200 fs, whereas for Dy, it takes about 1 ps. This is dif-

ferent for the respective remagnetization time τR, where we

clearly observe a slowing down of the Co recovery with increasing

ﬂuence. Unfortunately, the relaxation time behavior at Dy sites is

inconclusive due to large error bars, and therefore, an accurate

comparison of Dy versus Co remagnetization times is difﬁcult.

We note, however, that the remagnetization time is more inﬂu-

enced by the values of the exchange integrals, which are respon-

sible for the occurrence of the magnetic order, as well as by the

maximum degree of spin disorder generated during the initial

demagnetization process. Comparing our demagnetization

times with recent measurements on amorphous CoDy alloys,

we ﬁnd, however, similar values for τD.

[29]

Now, we turn to the comparison of the experimental and the-

oretical results. We obtain distinct, element-speciﬁc damping

parameters of αel

Co ¼0.004 and αDy ¼0.03 by minimizing the

mean squared error between the combined Dy and Co XMCD

data and the ASD simulation results, both displayed in

Figure 2. Here, we assumed that the electronic contribution

43210

-1.0

-0.5

0.0

0.5

1.0

43210

-1.0

-0.5

0.0

0.5

1.0

43210

Delay (ps)

5040302010

Delay (ps)

Co Co

(c)

Normalized XMCD

(b)(a)

Figure 2. Time-resolved XMCD data showing the demagnetization behav-

ior of Co (blue dots) and Dy (red dots). a,b) The data measured for the

incident laser ﬂuences of 9:4 and 14:1mJcm

2, respectively. The ASD sim-

ulations performed for various magnetization damping parameters αiare

shown as continuous black and gray lines. The dark and light colored areas

represent 25% and 50% variation of αifrom the optimum αivalues

(αCo ¼0.004 and αDy ¼0.03) describing the best match with the experi-

mental data (black solid line). c) Long-time behavior of demagnetization

and remagnetization dynamics measured for the two ﬂuences shown in

(a,b); the solid lines are the results of the corresponding ASD simulations.

Table 1. Demagnetization τDand remagnetization τRtime constants of

Co and Dy as determined by ﬁtting the time-resolved XMCD data

shown in Figure 2.

F[mJ cm

2

]τD[fs] τR[ps]

Dy Co Dy Co

9.4 980 120 175 45 18.0 9.3 1.85 0.5

14.1 900 160 210 35 12.1 6.7 4.20 0.7

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to the atomistic damping is similar for both elements and set

αel

Dy ¼αel

Co ¼0.004, thus leading to αph

Dy ¼0.026. This procedure

gives us nearly identical values for both ﬂuences, indicating the

robustness of the theoretical model. In Figure 2a,b, the output of

atomistic simulations is shown for variations of 25% and

50% of the αiparameters for both elements and laser ﬂuences.

The best data match of the simulations is depicted by the thick

black line, corresponding to αel

Co ¼0.004 and αDy ¼0.03 damp-

ing parameters.

To further highlight the importance of an element-speciﬁc

damping, we tried to reproduce the demagnetization data with

the more common approach, namely, a single, universal damp-

ing constant αel for both elements and with αph

Dy set to zero. The

results are displayed in Figure 3 with the dotted and dashed lines

representing simulations for different values of αel ¼0.004,

0.005, and 0.006. It becomes evident that a single damping con-

stant does not reproduce simultaneously both the Dy and Co

experimental data: while one could obtain a satisfactorily descrip-

tion of Co behavior using αel ¼0.004, this is obviously not the

case for Dy. Only upon introducing an extra damping term at Dy

sites αph

Dy, and thus using an element-speciﬁc damping for Co and

Dy, the ASD simulations can reproduce the experimental data

with high accuracy (blue and red solid lines in Figure 3).

The ASD simulations describe the experimental results only

by choosing clearly different values of the magnetic damping

parameters for each element, namely, αCo ¼0.004 and

αDy ¼αel þαph ¼0.03. This is a surprising observation, because

the ASD simulations are based on an ab initio-parametrized spin

Hamiltonian with the elemental magnetic moment, magnetic

anisotropy, and the exchange interaction being ab initio calcu-

lated; i.e., these are not variable parameters. The only free param-

eters in our spin model in Equation (2) and (3) are the magnetic

damping parameters that can be adjusted to match the experi-

mental data.

At this point, it is important to note the major differences

between the atomistic Gilbert damping parameters used in

our ASD simulations and a macroscopic damping parameter,

as obtained, for instance, from ferromagnetic resonance meas-

urements (FMR). Typically, an FMR-derived damping parameter

contains both extrinsic (i.e., sample-speciﬁc damping due to

spin scattering with defects, magnetic/structural inhomogenei-

ties, two-magnon scattering, etc.) and intrinsic (e.g., due to

electron–spin, lattice–spin interactions) contributions to magne-

tization relaxation and, hence, can be considered as an effective,

macroscopic damping parameter. The atomistic Gilbert damp-

ing, on the other hand, accounts only for intrinsic spin relaxation

effects at the microscopic level describing the local exchange of

energy and angular momentum between the spins, the electronic

system, and the crystal lattice.

To understand these observations, we ﬁrst consider the micro-

scopic origin of the damping parameters of Dy and Co spins

in ferrimagnetic DyCo5in more detail, based on the different

electronic structure of the RE and TM atoms.

The Co magnetic moment stems from 3d electrons that

are hybridized with the delocalized 4sp electrons, which can

be considered as a single magnetic moment coupled predomi-

nantly to the electronic thermal reservoir of the system. The

spin-relaxation mechanism in such an itinerant, metallic 3dfer-

romagnet is dominated by ultrafast transversal spin excitation in

the form of electron-magnon scattering,

[5,30]

quantiﬁed by αel

Co.

Additional longitudinal Stoner excitations and Elliott–Yaffet

spin-ﬂip scattering

[31,32]

are not considered in our extended

Heisenberg formalism, but recent studies suggest that they play

only a secondary role in ultrafast demagnetization.

[30,33]

Dy atoms, on the other hand, exhibit highly localized 4f

moments, which couple via intraatomic exchange to the itinerant

5d6sp electrons.

[4,25]

As such, their magnetization damping can

be described by an s–f model,

[34]

where the RE spin relaxation can

occur via different channels. First, there is direct coupling of the

4f spins to the lattice due to spin–lattice interaction mediated by

their large orbital moments

[35–37]

—in our model incorporated as

αph

Dy. Second, the intraatomic exchange of the Dy 4f moments to

its delocalized 5d6sp electron spins provides an indirect coupling

to the hot conduction electrons. This opens a relaxation channel

in terms of spin pumping, where angular momentum is trans-

ferred from the 4f to the 5d6sp orbitals

[34,38]

and subsequently

dissipated via electron-magnon-scattering (αel

Dy) analogous to

the damping of the Co 3d moments.

The magnitude of the spin-relaxation rates αν

iis, hereby,

highly sensitive to the elemental spin–orbit coupling. In fact,

it was found that the damping αν

iscales quadratically with the

spin–orbit coupling parameter

[6,7,39]

in the high temperature

-1.0

-0.5

0.0

0.5

1.0

43210

Delay (ps)

el = 0.004

el = 0.005

el = 0.006

Co best match Fig. 2

Dy best match Fig. 2

Normalized XMCD

Figure 3. Comparison of the time-resolved XMCD measurements (solid

dots) with the ASD simulations (green lines) performed using a single

magnetic damping parameter αel for both Dy and Co. Variation of the

αel values, as labeled in the ﬁgure, does not reproduce the transient

XMCD data for both elements. The best match with the experimental data

is obtained for clearly different magnetic damping parameters at Co and

Dy sites, namely, αCo ¼0.004 and αDy ¼0.03; the corresponding ASD

simulation curves (blue and red solid lines) are taken from Figure 2.

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regime, as used in our fs XMCD experiments. As the atomic-like

Dy 4f electrons obey Hund’s rules, they exhibit a large orbital

moment of L5μBin DyCo5,

[11]

which leads to strong spin–

orbit coupling and, hence, to: 1) large single-ion magnetic aniso-

tropy and to 2) large magnetization damping in the Dy sublattice.

This is, for instance, in contrast to the S-ion state with L¼0 that

is found in pure Gd and Gd-based ferrimagnets. In these sys-

tems, there is only a weak intrinsic magnetic anisotropy and

damping stemming from the Gd 5d moments.

[26,37,40,41]

The orbital moments of the 3d electrons of the Co sublattice

are almost fully quenched, due to their itinerant character, with

residual moments of only 0.1–0.2 μB.

[42,43]

This reduces the

effective spin–orbit interaction in the TM sublattice signiﬁcantly

compared with the RE (L≫0) sublattice, and thus, magnetic

damping and anisotropy of the TM sublattice are, in general,

much weaker. This discrepancy in the elemental spin–orbit

coupling strengths (λDy ¼235 meV vs λCo ¼70 meV, see the

previous study

[44]

) in combination with the different origins of

magnetic damping in the RE and TM sublattices supports the

choice for our spin model and can, therefore, explain the differ-

ences in magnetic damping retrieved from our data.

3. Conclusion

To conclude, we have performed an fs laser pump—XMCD probe

study of the ultrafast demagnetization and the subsequent remag-

netization in a highly anisotropic ferrimagnetic DyCo5alloy. The

transient dynamics of the system is described by an ultrafast

and distinct demagnetization of the elemental constituents.

ASD simulations using ab initio model parameters can reproduce

the experimental results only using largely different values of

the magnetic damping parameters for each element, namely,

αCo ¼0.004 and αDy ¼αel þαph ¼0.03. These combined theo-

retical and experimental results provide clear evidence for an

element-speciﬁc magnetization damping in a strongly exchange-

coupled magnetic alloy, with far reaching consequences for

modeling various ultrafast magnetic phenomena, such as ultra-

fast demagnetization,

[28,29,45]

helicity-dependent all-optical switch-

ing,

[46,47]

or thermally induced magnetization reversal.

[3,9,48,49]

As,

microscopically, the damping parameter is connected to the spin–

orbit coupling strength, we expect these ﬁndings to apply to all

compounds with strongly distinct spin–orbit coupling of the con-

stituent elements. Hence, future modeling approaches, which

rest on ASD for the treatment of dynamic magnetic phenomena,

such as demagnetization, switching, etc., will have to consider

this for an accurate description of the transient spin dynamics.

Supporting Information

Supporting Information is available from the Wiley Online Library or from

the author.

Acknowledgements

I.R. acknowledges funding from the Federal Ministry of Education

and Research (BMBF) through project 05K16BCA (Femto-THz-X) and

European Research Council through project TERAMAG (Grant No.

681917). R.A. acknowledges funding from BMBF through project

05K10PC2. U.N. acknowledges ﬁnancial support from the Deutsche

Forschungsgemeinschaft via SFB 1432. A.D. and L.S. are grateful for

the support by the Hungarian National Scientiﬁc Research Fund

(NKFIH) under project Nos. K131938 and PD134579, as well as by the

NRDI Fund (TKP2020 IES, Grant No. BME-IE-NAT). The authors thank

Christian Schüßler-Langeheine and Niko Pontius for their help with the

slicing measurements and Helmholtz-Zentrum Berlin for the allocation

of synchrotron radiation beam time.

Open access funding enabled and organized by Projekt DEAL.

Conﬂict of Interest

The authors declare no conﬂict of interest.

Data Availability Statement

The data that support the ﬁndings of this study are available from the

corresponding author upon reasonable request.

Keywords

atomistic spin dynamics simulations, femtosecond X-ray spectroscopy,

ferrimagnets, magnetization damping, ultrafast magnetism

Received: January 22, 2021

Revised: March 9, 2021

Published online: May 6, 2021

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