Critical magnetic behavior in [Ag8/Co0.5]x64, [Ag8/Co1]x32 and [Ag16/Co1]x32 epitaxial multilayers
Abstract
We investigate the low temperature magnetic behavior of three epitaxial Co/Ag multilayers, grown onto MgO (001) substrates, with a nominal content per period of either half a monolayer or one monolayer of Co, and either 8 or 16 Ag monolayers. The samples were studied by X-ray reflectivity and diffraction, transmission electron microscopy, magnetometry and ac susceptometry. The results indicated a well defined stacking sequence in the growth direction, the number of periods and of Ag monolayers per period being coincident with the nominal values for each sample. The Co layers were found to be discontinuous and corresponded to a quasi-monodisperse in-plane distribution of Co nanoparticles embedded in a Ag(001) matrix. The zero-field cooled and field cooled temperature variations of the low field magnetization indicated the presence of irreversibilities at temperatures below 20 K. The ac field frequency (f) and temperature (T) dependencies of the real part of the susceptibility (¿') corresponded to a Vogel-Fulcher behavior in the three samples, and indicated a frequency shift parameter (G) of the order of 4 x 10-2. For each sample, the experimental data corresponding to the variations of the imaginary part of the ac susceptibility (¿¿) with f and T were found to collapse into a single curve according to the dynamic scaling law. Taken together, these results allow us to conclude that the three multilayers experience a phase transition of the paramagnetic to superspin glass type, driven by the dipolar interactions between the Co nanoparticles. Regarding the influence of the multilayer features, we found a clear dependence of the order parameter of the transition on the nominal number of Co monolayers per period. Navarro, E.; Alonso, M.; Ruiz, A.; Magen, C.; Urdiroz, U.; Cebollada, F.; Balcells, L.; Martínez, B.; González, J.M.; Palomares, F.J.
Full text
## !"#$%" ##
7'
!"
## !"#$%"
&'()"*( +' ,'(-*-%.( ' ,
!"# $%&'( &$)"
$%%&'($)*
'(- /-"'-/ 0!)0!0 -
"'-/ 0!)0!0 -"'-/ 0!)
0!0 -"'-/ 0!)0!0 -"'-/
0!)0!0 -"'-/ 0!)0!0 -
+'(%&*,$-.,/&()'&+&*'&0()
1) ' /)! 2!-)
)! -!// ) -!
## !"#$%$
34) ' ' !-( !)'--,
1#5$ !"##%
&--!(,
-,3 ## !"#6
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
© Au ho (s) 2021
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 .
REFERENCES
1J. A. Mydosh, Spin Glasses: An Expe imen al In oduc ion (CRC P ess, London;
Washing on, DC, 1993).
2J. J. Hopfield, “Neu al ne wo ks and physical sys ems wi h eme gen collec i e
compu a ional abili ies,” PNAS 79, 2554–2558 (1982).
3H. Sompolinsky, “S a is ical mechanics o neu al ne wo ks,” Phys. Today 41(12),
70 (1988).
4D. W. Tank and J. J. Hopfield, “Collec i e compu a ion in neu onlike ci cui s,”
Scien ific Ame ican 257(6), 104–115 (1987).
5S. Kau man, The O igins o O de : Sel -O ganiza ion and Selec ion in E olu ion
(Ox o d Uni e si y P ess, New Yo k, 1993).
6J. D. B yngelson and P. G. Wolynes, “Spin glasses and he s a is ical mechanics
o p o ein olding,” PNAS 84(21), 7524–7528 (1987).
7W. Wang, M. Wallin, and J. Lidma , “Chao ic empe a u e and bond depen-
dence o ou -dimensional Gaussian spin glasses wi h pa ial he mal bounda y
condi ions,” Phys. Re . E 98, 062122 (2018).
8M. C. Alocén, P. Agudo, A. He nando, J. M. González, and P. C espo, “Two
ou es o diso de in a sys em wi h compe i i e in e ac ions,” J. Magn. Magn.
Ma e . 242-245, 879–881 (2002).
9E. Na a o, M. Alonso, A. Ruiz, C. Magen, U. U di oz, F. Cebollada, L. Balcells,
B. Ma ínez, F. J. Paloma es, and J. M. González, “Low empe a u e supe spin glass
beha io in a Co/Ag mul ilaye ,” AIP Ad ances 9, 125327 (2019).
10E. P. Wohl a h, Fe omagne ic Ma e ials (No h-Holland Publishing Company,
1980), Vol. 1.
11S. Sh ikman and E. P. Wohl a h, “The heo y o he Vogel-Fulche law o spin
glasses,” Physics Le e s A 85(8-9), 467–470 (1981).
12P. G. Debenede i and F. H. S illinge , “Supe cooled liquids and he glass
ansi ion,” Na u e 410, 259–267 (2001).
13P. C. Hohenbe g and B. I. Halpe in, “Theo y o dynamic c i ical phenomena,”
Re iews o Mode n Physics 49(3), 435 (1977).
14A. T. Ogielski, “Dynamics o h ee-dimensional Ising spin glasses in he mal
equilib ium,” Physical Re iew B 32(11), 7384 (1985).
15S. Gha a, B. G. Jeon, K. Yoo, K. H. Kim, and A. Sunda esan, “Reen an spin-
glass s a e and magne odielec ic e ec in he spi al magne BiMnFe2O6,” Physical
Re iew B 90(2), 024413 (2014).
16A. Malinowski, V. L. Bezusyy, R. Minikaye , P. Dziawa, Y. Sy yanyy, and
M. Sawicki, “Spin-glass beha io in Ni-doped La1.85S 0.15CuO4,” Physical Re iew
B84(2), 024409 (2011).
17J. Lago, S. J. Blundell, A. Eguia, M. Jansen, and T. Rojo, “Th ee-dimensional
Heisenbe g spin-glass beha io in S Fe0.90Co0.10O3.0,” Physical Re iew B 86(6),
064412 (2012).
18P. Beau illain, C. Dupas, J. P. Rena d, and P. Veille , “Expe imen al s udy o he
spin eezing in an insula ing spin-glass: S a ic and dynamical aspec s,” Physical
Re iew B 29(7), 4086 (1984).
AIP Ad ances 11, 025220 (2021); doi: 10.1063/9.0000086 11, 025220-5
© Au ho (s) 2021