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AIP Ad ances ARTICLE sci a ion.o g/jou nal/ad
C i ical magne ic beha io in [Ag8/Co0.5]x64,
[Ag8/Co1]x32 and [Ag16/Co1]x32 epi axial
mul ilaye s
Ci e as: AIP Ad ances 11, 025220 (2021); doi: 10.1063/9.0000086
P esen ed: 2 No embe 2020 •Submi ed: 16 Oc obe 2020 •
Accep ed: 22 Janua y 2021 •Published Online: 8 Feb ua y 2021
En ique Na a o,1Ma ía Alonso,1Ana Ruiz,1Cesa Magen,2Unai U di oz,1Fede ico Cebollada,3Lluís Balcells,4
Benjamín Ma ínez,4Jesús M. González,1,a) and F. Ja ie Paloma es1
AFFILIATIONS
1Nanos uc u es and Su aces, Ins i u o de Ciencia de Ma e iales de Mad id, 28049 Mad id, Spain
2Depa amen o de Ma e iales Magné icos, Ins i u o de Ciencia de Ma e iales de A agón, 50009 Za agoza, Spain
3POEMMA-CEMDATIC, Uni e sidad Poli écnica de Mad id, 28040 Mad id, Spain
4Magne ic Ma e ials and Func ional Oxides, Ins i u de Ciència de Ma e ials de Ba celona, 08193 Ba celona, Spain
No e: This pape was p esen ed a he 65 h Annual Con e ence on Magne ism and Magne ic Ma e ials.
a)Au ho o whom co espondence should be add essed: [email p o ec ed]
ABSTRACT
We in es iga e he low empe a u e magne ic beha io o h ee epi axial Co/Ag mul ilaye s, g own on o MgO (001) subs a es, wi h a nominal
con en pe pe iod o ei he hal a monolaye o one monolaye o Co, and ei he 8 o 16 Ag monolaye s. The samples we e s udied by X-
ay eflec i i y and di ac ion, ansmission elec on mic oscopy, magne ome y and ac suscep ome y. The esul s indica ed a well defined
s acking sequence in he g ow h di ec ion, he numbe o pe iods and o Ag monolaye s pe pe iod being coinciden wi h he nominal
alues o each sample. The Co laye s we e ound o be discon inuous and co esponded o a quasi-monodispe se in-plane dis ibu ion o
Co nanopa icles embedded in a Ag(001) ma ix. The ze o-field cooled and field cooled empe a u e a ia ions o he low field magne iza ion
indica ed he p esence o i e e sibili ies a empe a u es below 20 K. The ac field equency ( ) and empe a u e (T) dependencies o he eal
pa o he suscep ibili y (χ′) co esponded o a Vogel–Fulche beha io in he h ee samples, and indica ed a equency shi pa ame e (Γ)o
he o de o 4 x 10-2. Fo each sample, he expe imen al da a co esponding o he a ia ions o he imagina y pa o he ac suscep ibili y (χ′′ )
wi h and T we e ound o collapse in o a single cu e acco ding o he dynamic scaling law. Taken oge he , hese esul s allow us o conclude
ha he h ee mul ilaye s expe ience a phase ansi ion o he pa amagne ic o supe spin glass ype, d i en by he dipola in e ac ions be ween
he Co nanopa icles. Rega ding he influence o he mul ilaye ea u es, we ound a clea dependence o he o de pa ame e o he ansi ion
on he nominal numbe o Co monolaye s pe pe iod.
©2021 Au ho (s). All a icle con en , excep whe e o he wise no ed, is licensed unde a C ea i e Commons A ibu ion (CC BY) license
(h p://c ea i ecommons.o g/licenses/by/4.0/). h ps://doi.o g/10.1063/9.0000086
INTRODUCTION
Quenched diso de and compe ing in e ac ions coexis ing in
a sys em cons i u e he necessa y ing edien s o he occu ence o
he so-called spin glass beha io .1Tha beha io is la gely ubiq-
ui ous and has been iden ified in many di e en fields,1like he
analysis o he human b ain unc ionali y,2neu al ne wo ks,3,4 p e-
bio ic e olu ion5o p o ein olding.6Ne e heless, he pa adigm o
he spin glass phenomenology and o i s heo e ical unde s anding
a e magne ic momen s sys ems including dis ibu ed in e ac ions.
Ac ual ealiza ions o magne ic spin glass sys ems include om he
simple canonical spin glass me allic phases (whe e dilu ed, an-
domly dis ibu ed, localized momen s in e ac h ough he spa ially
oscilla o y RKKY in e ac ion), o mo e complex magne ic ma e i-
als inco po a ing di e en in e -momen s in e ac ions ( om supe -
and double-exchange o dipola coupling). The magne ic spin glass
sys ems also encompass a b oad ange o dimensionali ies, diso de
ypes and diso de pa ame e s dis ibu ions.1,7,8 In a p e ious wo k9
AIP Ad ances 11, 025220 (2021); doi: 10.1063/9.0000086 11, 025220-1
© Au ho (s) 2021
AIP Ad ances ARTICLE sci a ion.o g/jou nal/ad
on a Co/Ag mul ilaye wi h g anula mo phology a he Co laye s,
we ha e shown he occu ence a low empe a u e o a supe spin
glass phase ansi ion go e ned by he dipola in e ac ions be ween
he eezing Co nanopa icles. He e we ex end he analysis o he low
empe a u e magne ic beha io o a se ies o Co/Ag mul ilaye s also
including a educed Co con en pe pe iod and explo e he influence
o a ying he Co o Ag con en pe pe iod.
SAMPLE PREPARATION AND EXPERIMENTAL
TECHNIQUES
The h ee mul ilaye s ([Ag8/Co0.5]x64, [Ag8/Co1]x32 and
[Ag16/Co1]x32) ha e been g own by molecula beam epi axy (MBE),
al e na ing Ag and Co deposi ion on clean MgO(001) su aces.
Samples we e co e ed by a 3 nm Ag capping laye , and, in he ol-
lowing, will be e med X/Y, X being he nominal numbe o Co
monolaye s (ML) pe pe iod, and Y ha o Ag ones. He e X is ei he
0.5 o 1 Co ML, while Y is ei he 8 o 16 Ag ML. In o de o deposi
he same o al nominal numbe o Co a oms pe su ace uni a he
h ee samples, he pe iod was epea ed 32 o 64 imes depending
on he X alue (1 o 0.5). The s acking, s uc u e and mo phol-
ogy o he samples we e in es iga ed by means o X- ays eflec i i y
(XRR), di ac ion (XRD) and scanning ansmission elec on
mic oscopy (STEM). The magne ic cha ac e iza ion was pe o med
by using ib a ing sample and SQUID magne ome e s (fields o up
o 90 kG) and an ac suscep ome e , co e ing he ange o ac field e-
quencies ( ) om 10−1up o 104Hz, and empe a u es (T) om 2 K
up o 290 K.
FIG. 1. a) XRR esul s o he 1/8 and
1/16 samples, indica ing also he nomi-
nal alues o he pe iod hickness (black
figu es) and hose de i ed om he XRR
analysis (g een/blue figu es); b) High
esolu ion c oss sec ion STEM image o
he 1/16 sample showing Co NPs (da k)
embedded in a Ag (001) ma ix; da a co -
espond o wo consecu i e Co laye s
sepa a ed by 16 Ag monolaye s (num-
be s in blue); c) ZFC/FC cu es o he dc
low field magne iza ion s T o he 1/8
sample.
TABLE I. Values o di e en pa ame e s de i ed om he magne ic analysis o each sample (de ails in he ex ). Ti : i e e sibili y empe a u e obse ed
a he ZFC/FC low field magne iza ion cu es; Vpa a and Øpa a: pa amagne ic a e age olume and diame e es ima ed o he Co nanopa icles om
he Cu ie–Weiss fi s; Γ: equency shi pa ame e ; T0and Ea/kB: magni ude o he in e ac ions and ac i a ion ene gy o sys em elaxa ion, espec i ely
(Vogel–Fulche model); Zν(c i ical exponen ) and Tg(phase ansi ion empe a u e o an infini e obse a ion ime) ob ained om he fi o he ac suscep ibili y
o he scaling law a he c i ical egime.
Co/Ag
sample Ti (K)
pa a ×10−21
(cm3)Ø
pa a (nm) Γ×10−2T0(K) Ea/kB(K) ZνTg(K)
0.5/8 11.0 1.2 1.3 ±0.2 4.0 7.1 37.6 9.0 8.1
1/8 17.8 3.4 1.9 ±0.2 4.9 10.3 45.7 9.6 15.5
1/16 14.0 3.3 1.9 ±0.2 4.7 14.3 62.1 6.7 12.0
AIP Ad ances 11, 025220 (2021); doi: 10.1063/9.0000086 11, 025220-2
© Au ho (s) 2021
AIP Ad ances ARTICLE sci a ion.o g/jou nal/ad
RESULTS AND DISCUSSION
The XRD, XRR, and STEM esul s indica ed ha he MBE
deposi ed films exhibi ed good c ys allini y, cc(001) s uc u e and
clea supe la ice pe iodici ies, he numbe o pe iods in each sam-
ple being coinciden wi h he nominal ones (see e.g., he XRR da a
shown in Figu e 1a o he 1/8 and 1/16 samples). The STEM images
also e ealed ha , as epo ed inRe . 9, he Co laye s we e no
con inuous (see Fig. 1b), bu exhibi ed a close- o-monodispe se in-
plane dis ibu ion o Co nanopa icles (NPs) embedded in a Ag(001)
ma ix. The cha ac e is ic size and shape o he Co NPs o he 1/16
sample can be seen in Figu e 1b, which also shows he p esence o
16 Ag MLs be ween wo consecu i e Co laye s. The STEM analysis
o he di e en samples indica ed a diso de ed dis ibu ion o he
Co NPs posi ions wi hin each laye , and confi med he nominal Ag
pe iodici y. Fo he 1/8 and 1/16 samples, he dis ance be ween he
la e al su aces o wo neighbo ing NPs in a Co laye is o he o de
o 1.5 nm, simila o he a e age NPs diame e .
The ze o field-cooling (ZFC) and field-cooling (FC) a ia ions
wi h T o he dc low field magne iza ion indica ed he occu ence o
i e e sibili ies a empe a u es (Ti ) lowe han 20 K (see Fig. 1c o
he 1/8 sample, and Ti alues o each sample in Table I). Below
Ti , he mul ilaye s exhibi ed hys e esis wi h dc coe ci i ies o up
o 350 Oe a 2 K. Abo e Ti , he ZFC ini ial dc suscep ibili y (χ)
beha ed acco ding o he Cu ie–Weiss law,10 1/χ=(T - θ)/C, in he
h ee samples. The alues ob ained om he fi s o he Cu ie–Weiss
law yielded pa amagne ic momen s wo o de s o magni ude la ge
han he Co a omic momen . They app oxima ely co espond o he
clus e ing o cc coo dina ed Co momen s in a NP wi h a diame-
e be ween 1 and 2 nm. Since his is consis en wi h he g anula
mo phology o he Co laye s e ealed by STEM, hese Cu ie–Weiss
pa amagne ic momen s can be associa ed o he Co NPs and we used
FIG. 2. Tempe a u e dependencies o he eal (χ′) and imagina y (χ′′ ) componen s o he ac suscep ibili y measu ed a he indica ed equencies, by using a SQUID
magne ome e (le panels) o an ac suscep ome e ( igh panels); a)-a′) display da a o 0.5/8 sample, b)-b′) o 1/16 sample, and c)-c′) o 1/8 sample.
AIP Ad ances 11, 025220 (2021); doi: 10.1063/9.0000086 11, 025220-3
© Au ho (s) 2021
AIP Ad ances ARTICLE sci a ion.o g/jou nal/ad
hem o es ima e he a e age olumes (Vpa a) and diame e s (Øpa a)
o he NPs (assumed sphe ical); see alues in Table I.
Figu e 2 shows he empe a u e dependencies o he eal (χ′)
and imagina y (χ′′ ) pa s o he ac suscep ibili y1measu ed a ac field
equencies ( ) in he ange om 1 Hz up o 10 kHz. Maxima on χ′
a e obse ed a empe a u es (Tp_ac) o he o de o Ti .T
p_ac and
hei associa ed peak magni udes inc ease and dec ease, espec i ely,
as inc eases. The a ia ions o Tp_ac, wi h a e pa ame e ized1by
conside ing he ela i e inc ease o Tp_ac pe decade, acco ding o
Γ=(ΔTp_ac/Tp_ac)/Δlog10 , and aking as e e ence =1 Hz.
The Γ alues hus ob ained (see Table I) a e clea ly lowe han hose
associa ed o supe pa amagne ic elaxa ion p ocesses (which in a
la ge majo i y o ma e ials a e abo e 0.21). These esul s sugges ha ,
like in ou p e ious epo ,9 he magne ic p ope ies o hese mul i-
laye s a e associa ed o he Co NPs o he nominal Co laye s, and ha
such NPs could exhibi a Ti a phase ansi ion om a pa amagne ic
o a magne ically o de ed sa e.
In o de o assess he ac ual occu ence o in e ac ions be ween
he Co NPs, we ha e fi ed he expe imen al da a o he e-
quency a ia ion o Tp_ac o he Vogel–Fulche model.11 Tha model
desc ibes he empe a u e dependence o he cha ac e is ic imes
o he spin glass-like eezing12 acco ding o ω=ω0exp [- Ea/kB
(Tp_ac -T
0)], whe e ωis he ac field angula equency and ω0,
Ea, and T0fi ing pa ame e s: ω0is he y equency, Ea he
ac i a ion ene gy o he elaxa ion, and T0 he magni ude (in em-
pe a u e uni s) o he in e ac ions p esen in he sys em; Table I
shows he T0and Ea/kB alues ob ained om he fi s. Fo he h ee
samples, ω0 alues a e in he ange o 5 x 109s-1, whe eas T0 alues
a e o he o de o he co esponding Ti . Thus, hese esul s clea ly
endo se he p esence o in e ac ions whose magni ude could be on
he o igin o an o de ed magne ic s a e a empe a u es below Ti ,
ansi ioning o a supe pa amagne ic phase abo e Ti .
To analyze ha beha io we will conside wo di e en
app oaches. Fi s , we will s udy he ela ionship o he empe a-
u e elaxa ion ime τ(T) wi h he Tp_ac expe imen ally de e mined
alues.1,13,14 Tha ela ionship can only be s ablished a he c i ical
s a e, ha is, a T nea he phase ansi ion a which he dis ibu-
ion o he magne ically co ela ed egions ( h ough he in e ac ions
p esen in he sys em) spans all he possible dimensions compa ible
wi h he elemen al in e ac ing en i ies and he sys em sizes. The li e-
imes o he co ela ed egions should also each he cha ac e is ic
ime o he measu emen . In his c i ical s a e, he spin elaxa ion
ime di e ges wi h he educed co ela ion leng h (ξ) acco ding o
τ=τ∗
0ξZ(whe e Z is he dynamic scaling exponen ). ξis ela ed
o Tp_ac h ough he law ξ=ε-ν(whe e νmeasu es he di e gence
o he co ela ion leng h, and ε=[(Tp_ac/Tg)-1]; Tgbeing he em-
pe a u e a which he phase ansi ion occu s when he measu ing
ime is infini e. In e ms o he equency , he scaling law akes
he o m: = ∗[(Tp_ac/Tg)-1]Zνo equi alen ly, ln =ln ∗-Zν
ln [(Tp_ac/Tg)-1] (Zνis he exponen linked o he collec i e s a e
occu ing below Tg). Figu e 3a) displays, o he h ee mul ilay-
e s, he dependence o he loga i hm o he equency on he
FIG. 3. a) Dependence o he loga i hm o he ac field equency ( ) on he quan i y ln[(Tp_ac/Tg)-1] o each sample; b) Collapse o he expe imen al da a om he and T
dependencies o he abso p ion componen o he ac suscep ibili y (χ′′ ) acco ding o he dynamic scaling law (see ex ).
AIP Ad ances 11, 025220 (2021); doi: 10.1063/9.0000086 11, 025220-4
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AIP Ad ances ARTICLE sci a ion.o g/jou nal/ad
quan i y ln[(Tp_ac/Tg)-1]; he ∗ alues conside ed o he h ee sam-
ples we e o he o de o 109s-1; hose o he Zνand Tgpa ame e s
a e shown in Table I. As i is eadily seen, in all he cases he e is a
good ag eemen be ween he expe imen al da a and he scaling law.
I is in e es ing o ema k ha he Tg alues a e sligh ly lowe han
he Ti ones (as expec ed om he fini e measu ing imes). Also,
and impo an ly, he alues o he c i ical exponen he e ob ained
( a ying om Zν=6.7 o 9.6; see Table I) a e clea ly wi hin he ange
iden ified in he li e a u e as co esponding o he occu ence o spin
glass-like sys ems eezing.15–17
Ou second app oach o elucida e i a eezing ansi ion occu s
in hese samples a Ti , is based on he dynamic scaling o he
imagina y (abso p ion) componen o he ac suscep ibili y (χ′′ ).18
Tha scaling p edic s he collapse o he expe imen al da a co e-
sponding o he and T a ia ions o χ′′ , in a single cu e G(x),
e i ying: T χ′′ ( , T) =[(T/Tg)–1]
βG(x); in his exp ession
x= [(T/Tg)−1]−Zν(whe e Zνis he c i ical exponen and Tgis he
ansi ion empe a u e a ze o equency); βis he o de pa ame e
o he ansi ion.1Figu e 3b) displays he scaling beha io ob ained
o ou h ee samples, which is in ag eemen wi h he exis ence
o a eezing ansi ion a empe a u es close o Ti . No e ha he
β alues, ob ained om he collapse in Figu e 3, a e in he ange
co esponding o spin glass-like sys ems.18 In e es ingly, in hese
samples he β alues a e only ound o a y wi h he nominal numbe
o Co monolaye s pe pe iod.
CONCLUSIONS
The abo e esul s allow us o conclude ha he h ee mul i-
laye s expe ience a phase ansi ion o he pa amagne ic o supe -
spin glass ype a empe a u es Ti . The eezing en i ies a e he Co
nanopa icles p esen a he nominal Co laye s. The magni ude o
he momen s o hese Co NPs, as well as ha o he a e age in e pa -
icle dis ance, indica e he occu ence o high dipola in e ac ions.
We hus p opose ha such in e ac ions, oge he wi h he in-plane
diso de o he NP posi ions, a e on he o igin o he spin glass-like
magne ic o de .9The size and in-plane concen a ion o he Co NPs
can be also co ela ed wi h he a ia ions obse ed in Ti depend-
ing on he nominal numbe o Co and Ag monolaye s pe pe iod.
I can be seen ha he 0.5/8 sample exhibi s a lowe Ti han he
1/8 and 1/16 samples; his is due o he smalle olume and in-plane
concen a ion o he Co NPs p esen in he 0.5/8 sample, and he
consequen ly lowe magni ude o he in e pa icle dipola in e ac-
ions. On he o he hand, ou esul s indica e ha he 1/8 sample
expe iences he phase ansi ion a a highe empe a u e han he
1/16 sample; his can be explained by conside ing he hickness o
he Ag space , which o he 1/16 sample is la ge enough o signi -
ican ly educe he in e laye Co NPs in e ac ions; in con as , hose
in e laye in e ac ions measu ably con ibu e o he phase ansi ion
in he 1/8 sample. Finally, he alues o he βexponen in he scal-
ing ela ionship a e only ound o a y (in hese samples) wi h he
numbe o Co monolaye s pe pe iod.
ACKNOWLEDGMENTS
This wo k has been de eloped wi h unds co esponding
o p ojec MAT2016-80394-R financed by he Spanish Resea ch
Agency (AEI). We also acknowledge he Spanish Minis e io de Cien-
cia e Inno ación and Consejo Supe io de In es igaciones Cien íficas
o financial suppo and o p o ision o synch o on adia ion a
beamline BM25-SpLine (ESRF).
DATA AVAILABILITY
The da a ha suppo he findings o his s udy a e a ailable
om he co esponding au ho upon easonable eques .
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AIP Ad ances 11, 025220 (2021); doi: 10.1063/9.0000086 11, 025220-5
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