Ci a ion: Po o, J.M.; Villa , A.;
Redondo, C.; Río-López, N.A.;
Lashe as, A.; Salaza , D.; Mo ales, R.;
Fe nández-Ma ín, E. Compe i ion o
Magne ic Aniso opies in Pe malloy
An ido La ices. Magne ochemis y
2022,8, 55. h ps://doi.o g/10.3390/
magne ochemis y8050055
Academic Edi o s: Jean Ebo héand
Zheng Gai
Recei ed: 2 Ap il 2022
Accep ed: 5 May 2022
Published: 10 May 2022
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
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Copy igh : © 2022 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
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dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
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magne ochemis y
A icle
Compe i ion o Magne ic Aniso opies in Pe malloy
An ido La ices
Jose M. Po o 1,2,* , A i z Villa 1, Ca olina Redondo 3, Na alia A. Río-López 1, Andoni Lashe as 4,
Daniel Salaza 1, Ra ael Mo ales 1,2,3 and Edua do Fe nández-Ma ín1
1BCMa e ials, Basque Cen e o Ma e ials, Applica ions and Nanos uc u es, 48940 Leioa, Spain;
[email p o ec ed] (A.V.); [email p o ec ed] (N.A.R.-L.);
[email p o ec ed] (D.S.); [email p o ec ed] (R.M.);
[email p o ec ed] (E.F.-M.)
2Ike basque, Basque Founda ion o Science, 48009 Bilbao, Spain
3Depa men o Chemical-Physics, Facul y o Science and Technology, Uni e si y o he Basque Coun y
UPV/EHU, 48940 Leioa, Spain; ca olina. [email p o ec ed]
4Depa men o Physics, Facul y o Science and Technology, Uni e si y o he Basque Coun y UPV/EHU,
48940 Leioa, Spain; [email p o ec ed]
*Co espondence: jm.po [email p o ec ed]
Abs ac :
An ido la ices made o magne ic hin ilms a e good candida es o be employed in u u e
magne ic eco ding media. In his manusc ip we p esen a s udy on he e ec o shape and ield-
induced magne ic aniso opies on he magne iza ion e e sal o 10 nm and 50 nm hick pe malloy
an ido la ices. Rounded an ido squa e la ices we e ab ica ed using a combina ion o elec on
beam e apo a ion and lase in e e ence li hog aphy, co e ing su aces o a ew cm
2
. We demons a e
ha a magne ic aniso opy induced in he samples, as a consequence o an applied magne ic ield
du ing g ow h, compe es wi h he shape aniso opy ha domina es he esponse o he pa e ned
hin ilms, and ha he e ec o he ield-induced magne ic aniso opy scales wi h he hickness
o he an ido hin ilms. Finally, we ha e quan i ied he aniso opy cons an a ibu able o he
uniaxial ield-induced magne ic aniso opy in ou an ido la ices. These indings a e suppo ed by
mic omagne ic simula ions pe o med using MuMax3.
Keywo ds: an ido la ices; magne ic aniso opy; magne iza ion e e sal
1. In oduc ion
Many cu en echnological de elopmen s ela ed o eco ding media a e ied o he
s udy and gene a ion o no el magne ic ma e ials in he o m o hin ilms. These include
loa ing solid-s a e hin ilms o dynamically econ igu able unc ional nanode ices [
1
],
hin ilms unde going all-op ical swi ching phenomena o magne ic eco ding media [
2
],
hin ilms unde going magne ic phase ansi ions [
3
], and he exploi a ion o s a ic and
dynamic magne ic p ope ies o Heusle alloy hin ilms owa ds hei implemen a ion in
eco ding media [
4
,
5
]. Pa e ned magne ic hin ilms a e a pa icula subg oup o in e es -
ing magne ic ma e ials being de eloped o cu en and u u e echnological applica ions,
including he s udy o magne ic memo ies h ough pa e ned opological insula o ma e i-
als [6], magne ic sky mions [7], and a i icially us a ed nanos uc u ed sys ems [8,9].
An ido la ices a e a pa icula ly a ac i e subg oup o pa e ned magne ic hin ilms,
as hese p o ide scien is s wi h a ple ho a o pa ame e s o expe imen wi h in o de o
change he ma e ial’s p ope ies. In pa icula , he shape, size, la e al dimensions, choice o
ma e ials, and la ice geome ies a e enginee able a iables ha allow a ine uning o he
an ido la ice p ope ies. Speci ically, changes in geome ical pa ame e s esul in a change
in he s eng h and p o ile o he s ay ields [
10
] ac oss he an ido s, which leads o di e en
pinning and mo ion o he domain walls h ough he la ice [
11
–
13
]; whe eas changes in
Magne ochemis y 2022,8, 55. h ps://doi.o g/10.3390/magne ochemis y8050055 h ps://www.mdpi.com/jou nal/magne ochemis y
Magne ochemis y 2022,8, 55 2 o 9
he hin ilm composi ion and/o hicknesses lead o di e en coupling s eng hs be ween
magne ic domains [14–17].
To da e, an ido hin ilms ha e been s udied a ge ing speci ic scien i ic ad ances in
hei p ope ies and unc ionali ies, such as enginee ing hei pe pendicula aniso opy
h ough ma e ial p ope ies uning [
16
,
18
–
20
]; combining so and ha d magne ic ma e ials
in mul ilaye ed an ido la ices o enginee hei coe ci i y [
12
,
13
,
21
]; s udying he p opaga-
ion o magnons and spin wa es h ough he an ido la ices [
15
,
17
,
22
–
33
]; nuclea ing and
p opaga ing sky mions h ough he la ices [
34
]; enabling he an ido a ays as pla o ms o
spin onic applica ions [
13
,
19
]; enabling he an ido a ays o use as monoli hic mic owa e
band-pass il e s [
25
] o high densi y s o age e oelec ic memo ies [
35
]. None heless,
he e is s ill oom o imp o emen in e ms o enginee ing he p ope ies o he magne ic
ma e ials om which he an ido s a e made, as his c ucially a ec s hei p ope ies, and,
he e o e, hei a ge applica ions. In his ega d, uning he magne ic aniso opy o a
widely s udied ma e ial o an ido la ices, such as pe malloy, eme ges as a p omising way
o use a cheap and so magne ic ma e ial wi h aniso opy landscapes common o o he
ha de and mo e expensi e magne ic elemen s.
We s udied he e ec o induced compe ing magne ic aniso opies, namely shape-
and ield-induced, on he magne iza ion e e sal o ounded an ido squa e la ices made
o pe malloy (Py, composi ion Ni
80
Fe
20
). An ido la ices wi h ounded geome ies and
wi h wo di e en hicknesses, 10 nm and 50 nm, we e g own simul aneously alongside
non-pa e ned sis e hin ilms o compa ison pu poses. The an ido la ices and non-
pa e ned hin ilms we e g own wi h and wi hou an in si u applied magne ic ield on
he subs a e du ing g ow h. We demons a ed ha he magne ic aniso opy induced in
he samples as a consequence o he applied ield du ing g ow h is ans e ed on o he
an ido la ices, e en hough he shape aniso opy domina es he magne ic esponse o he
pa e ned hin ilms. These esul s a e accompanied by mic omagne ic simula ions ha
quali a i ely esemble he expe imen ally obse ed beha io o he an ido la ices, which
also p o ides in o ma ion abou he magne ic domain con igu a ions upon magne iza ion
e e sal o he an ido s.
2. Ma e ials and Me hods
The samples we s udied we e ab ica ed using elec on beam e apo a ion in he case
o he non-pa e ned hin ilms, and a combina ion o elec on beam e apo a ion and lase
in e e ence li hog aphy in he case o he an ido ilms [
36
]. Fo he esis empla e, an
an i e lec i e coa ing laye (WIDE-8B, app oxima ely 80 nm hick, comme cially a ailable
om B ewe Science Inc., Rolla, MO, USA) ollowed by a nega i e esis (TSMR-IN027,
app oxima ely 200 nm hick, comme cially a ailable om Tokyo Ohka Koygo Co., L d.,
Tokyo, Japan) we e bo h spun-coa ed on op o Si (100) subs a es. Subsequen ly, hey we e
double-exposed o a He:Cd lase wi h a wa eleng h o 325 nm, ollowed by a de eloping
p ocess o he esis on AZ726 MIF. Py hin ilms wi h hicknesses o 10 nm and 50 nm
we e deposi ed using elec on beam e apo a ion, ollowed by a 4 nm hick Al capping
laye o p e en oxida ion. A li -o p ocess including ul asound ba h sonica ion du ing
imme sion in N-Me hyl-2-py olidone (NMP) a 120
◦
C esul ed in an ido la ices co e ing
su aces o a ew cm
2
. The esul ing an ido la ices a e shown in Figu e 1. Du ing he
hin ilm deposi ion p ocess esis - ee Si (100) subs a es we e also co e ed wi h Py and
Al, esul ing in non-pa e ned hin ilms wi h he same hicknesses as hose o he an ido
la ices; i.e., 10 nm Py/4 nm Al, and 50 nm Py/4 nm Al.
Magne ochemis y 2022,8, 55 3 o 9
Magne ochemis y 2022, 8, x FOR PEER REVIEW 3 o 9
masks wi h simila shapes, allowing a a mo e ealis ic simula ion p ocess. Bo h he 10
nm and he 50 nm hick Py an ido la ices we e simula ed using 2D pe iodic bounda y
condi ions (PBC) wi h he ollowing pa ame e s: magne iza ion sa u a ion MS = 860 × 103
A/m, exchange coupling cons an A = 13 × 10−12 J/m, damping cons an α = 0.02, PBCs
(2,2,0), pe iodici y 1200 nm, and uni cell size 5 × 5 × 5 nm3, smalle han he exchange
leng h o Py [38]. The in en ional in oduc ion o edge oughness using a mask ex ac ed
om he SEM images p esen ed in Figu e 1 does no esul in c i ical changes in he sim-
ula ion esul s, while hey signi ican ly inc ease he equi ed compu a ion imes. The ap-
plied ield was simula ed o be 1° o he la ice axis o accoun o impe ec ield align-
men in he eal expe imen s. A ield-induced uniaxial magne ic aniso opy wi h a alue
o Ku = 500 J/m3 was employed o he simula ions. The choice o his alue is jus i ied in
he Resul s and Discussion sec ion o his manusc ip .
3. Resul s and Discussion
SEM images o he an ido la ices s udied in he p esen manusc ip a e shown in
Figu e 1. Figu e 1a,b a e SEM images o he 10 nm hick an ido la ices; Figu e 1c,d co -
espond o images o he 50 nm hick ones. Bo h la ices possess pe iodici ies o 1.2 μm
om cen e - o-cen e o neighbo ing an ido s. The diame e s o he an ido s a e app oxi-
ma ely 750 nm. The black shadowed egions o he inside o he an ido s co espond o
non-magne ic polyme ic esis le o e s; hei p esence does no in luence he beha io o
he an ido la ices. The di e ence in he an ido oundness is a ibu ed o sligh ly di e -
en exposi ion and de eloping imes du ing he nano ab ica ion p ocesses. Ve y small
a ia ions in he exposu e ime o he lase beam and/o he de eloping ime o he esis
a e exposu e can a ec pa e n sizes and shapes [36,39].
Figu e 1. SEM images o he an ido la ices s udied, including he 10 nm hick an ido la ices (a,b)
and he 50 nm hick an ido la ices (c,d). Panels (b) and (d) a e il ed SEM images aken a an angle
o 30 deg ees wi h espec o he elec on beam di ec ion. The ed a ows deno e he di ec ions along
which he hys e esis loops a e measu ed. The di ec ion o he applied ield du ing g ow h co e-
sponded o 0°.
As men ioned in he Ma e ials and Me hods sec ion, when he Py and Al laye s we e
deposi ed du ing he nano ab ica ion p ocess o he an ido la ices, pa e ned and non-
Figu e 1.
SEM images o he an ido la ices s udied, including he 10 nm hick an ido la ices (
a
,
b
)
and he 50 nm hick an ido la ices (
c
,
d
). Panels (
b
,
d
) a e il ed SEM images aken a an angle
o 30 deg ees wi h espec o he elec on beam di ec ion. The ed a ows deno e he di ec ions
along which he hys e esis loops a e measu ed. The di ec ion o he applied ield du ing g ow h
co esponded o 0◦.
The shapes and sizes o he an ido la ices we e analyzed using scanning elec on
mic oscopy (SEM) using a JEOL JSM-7000F (JEOL, Tokyo, Japan). Vib a ing sample mag-
ne ome y was used o eco d oom empe a u e hys e esis loops using a Mic osense EZ
VSM (Mic oSense, Lowell, MA, USA).
Mic omagne ic simula ions we e pe o med using MuMax3 so wa e [
37
]. Simula ed
hys e esis loops a oom empe a u e we e ob ained o an ido shapes esembling hose o
he la ices obse ed in he SEM images p esen ed in Figu e 1, by making simula ion masks
wi h simila shapes, allowing a a mo e ealis ic simula ion p ocess. Bo h he 10 nm and
he 50 nm hick Py an ido la ices we e simula ed using 2D pe iodic bounda y condi ions
(PBC) wi h he ollowing pa ame e s: magne iza ion sa u a ion M
S
= 860
×
10
3
A/m,
exchange coupling cons an A = 13 ×10−12 J/m, damping cons an α= 0.02, PBCs (2,2,0),
pe iodici y 1200 nm, and uni cell size 5
×
5
×
5 nm
3
, smalle han he exchange leng h
o Py [
38
]. The in en ional in oduc ion o edge oughness using a mask ex ac ed om
he SEM images p esen ed in Figu e 1does no esul in c i ical changes in he simula ion
esul s, while hey signi ican ly inc ease he equi ed compu a ion imes. The applied ield
was simula ed o be 1
◦
o he la ice axis o accoun o impe ec ield alignmen in he eal
expe imen s. A ield-induced uniaxial magne ic aniso opy wi h a alue o K
u
= 500 J/m
3
was employed o he simula ions. The choice o his alue is jus i ied in he Resul s and
Discussion sec ion o his manusc ip .
3. Resul s and Discussion
SEM images o he an ido la ices s udied in he p esen manusc ip a e shown in
Figu e 1. Figu e 1a,b a e SEM images o he 10 nm hick an ido la ices; Figu e 1c,d co e-
spond o images o he 50 nm hick ones. Bo h la ices possess pe iodici ies o 1.2
µ
m om
cen e - o-cen e o neighbo ing an ido s. The diame e s o he an ido s a e app oxima ely
750 nm. The black shadowed egions o he inside o he an ido s co espond o non-magne ic
polyme ic esis le o e s; hei p esence does no in luence he beha io o he an ido la -
Magne ochemis y 2022,8, 55 4 o 9
ices. The di e ence in he an ido oundness is a ibu ed o sligh ly di e en exposi ion
and de eloping imes du ing he nano ab ica ion p ocesses. Ve y small a ia ions in he
exposu e ime o he lase beam and/o he de eloping ime o he esis a e exposu e can
a ec pa e n sizes and shapes [36,39].
As men ioned in he Ma e ials and Me hods sec ion, when he Py and Al laye s we e
deposi ed du ing he nano ab ica ion p ocess o he an ido la ices, pa e ned and non-
pa e ned hin ilms we e g own wi h a magne ic ield o 500 Oe applied pa allel o one
side o he subs a es, and, consequen ly, o one la ice axis. This will allow o a di ec
compa ison be ween he magne ic p ope ies o he an ido la ices and o p is ine hin ilms
wi h iden ical composi ions, so ha any changes can be di ec ly a ibu ed o compe ing
aniso opies in he an ido la ices.
Room empe a u e hys e esis loops o he con inuous hin ilms eco ded using VSM
magne ome y a e p esen ed in Figu e 2. To analyze any possible aniso opy induced in
he samples, he hys e esis loops we e eco ded a h ee di e en angles (0
◦
, 45
◦
, and 90
◦
)
om he di ec ion o he applied ield du ing g ow h. Figu e 2a shows he hys e esis loops
co esponding o he 10 nm hick ilm; Figu e 2b, shows he hys e esis loops co esponding
o he 50 nm hick ilm. As deduc ed om he measu emen s p esen ed in Figu e 2,
he applica ion o a magne ic ield du ing hin ilm g ow h induces a ha d axis a 90
◦
,
pe pendicula o he di ec ion o he applied ield du ing g ow h. While he coe ci e ield
(H
C
) emains una ec ed in he 10 nm hick ilm, i espec i e o he applied ield di ec ion,
he 50 nm hick ilm p esen s a educ ion in H
C
o abou 25% om he one along he
ha d axis ( om H
C,0◦
=4Oe oH
C,90◦
= 3 Oe), on he easy axis. This is consis en wi h
obse a ions in Py hin ilms, whe e he de eloped aniso opy as a consequence o he
applied ield du ing hin ilm g ow h dec eases wi h he ilm hickness, and anishes a
hicknesses o app oxima ely 10 nm [
40
]. We can es ima e he uniaxial aniso opy cons an
o he ield-induced aniso opy by calcula ing he a ea o he hys e esis loops measu ed
along he induced ha d axes. Acco ding o he S one –Wohl a h model o cohe en o a ion
o domains [
41
], knowing ha M
s
= 860
×
10
3
A/m o pe malloy, and using he sa u a ing
ield o ha hys e esis loop as inpu , we ob ain a ield-induced uniaxial aniso opy cons an
Ku≈430 J/m3.
Magne ochemis y 2022, 8, x FOR PEER REVIEW 4 o 9
pa e ned hin ilms we e g own wi h a magne ic ield o 500 Oe applied pa allel o one
side o he subs a es, and, consequen ly, o one la ice axis. This will allow o a di ec
compa ison be ween he magne ic p ope ies o he an ido la ices and o p is ine hin
ilms wi h iden ical composi ions, so ha any changes can be di ec ly a ibu ed o com-
pe ing aniso opies in he an ido la ices.
Room empe a u e hys e esis loops o he con inuous hin ilms eco ded using VSM
magne ome y a e p esen ed in Figu e 2. To analyze any possible aniso opy induced in
he samples, he hys e esis loops we e eco ded a h ee di e en angles (0°, 45°, and 90°)
om he di ec ion o he applied ield du ing g ow h. Figu e 2a shows he hys e esis loops
co esponding o he 10 nm hick ilm; Figu e 2b, shows he hys e esis loops co espond-
ing o he 50 nm hick ilm. As deduc ed om he measu emen s p esen ed in Figu e 2,
he applica ion o a magne ic ield du ing hin ilm g ow h induces a ha d axis a 90°,
pe pendicula o he di ec ion o he applied ield du ing g ow h. While he coe ci e ield
(HC) emains una ec ed in he 10 nm hick ilm, i espec i e o he applied ield di ec ion,
he 50 nm hick ilm p esen s a educ ion in HC o abou 25% om he one along he ha d
axis ( om HC,0°= 4 Oe o HC,90°= 3 Oe), on he easy axis. This is consis en wi h obse a ions
in Py hin ilms, whe e he de eloped aniso opy as a consequence o he applied ield
du ing hin ilm g ow h dec eases wi h he ilm hickness, and anishes a hicknesses o
app oxima ely 10 nm [40]. We can es ima e he uniaxial aniso opy cons an o he ield-
induced aniso opy by calcula ing he a ea o he hys e esis loops measu ed along he
induced ha d axes. Acco ding o he S one –Wohl a h model o cohe en o a ion o do-
mains [41], knowing ha Ms = 860 × 103 A/m o pe malloy, and using he sa u a ing ield
o ha hys e esis loop as inpu , we ob ain a ield-induced uniaxial aniso opy cons an Ku
≈ 430 J/m3.
Figu e 2. Room empe a u e hys e esis loops eco ded om (a) 10 nm hick and (b) 50 nm hick
pe malloy hin ilms g own using elec on-beam e apo a ion wi h an applied ield o 500 Oe. The
angles indica ed in he legend co espond o he ield di ec ion wi h espec o he applied ield
du ing g ow h. Inse s a e zoomed egions a ound HC o each plo .
The oom empe a u e hys e esis loops eco ded om he an ido la ices a e p e-
sen ed in Figu e 3 as a unc ion o he applied ield angle wi h espec o he di ec ion o
he applied ield du ing g ow h. Figu e 3a shows he 10 nm hick an ido la ice hys e esis
loops, while Figu e 3b shows he 50 nm hick an ido la ice hys e esis loops. The i s
ema kable di e ence is ha he an ido s p esen a c osso e in he aniso opy o easy and
ha d axis con igu a ion, om a 90° angle be ween hem in he hin ilms o a 45° angle in
he an ido la ices. This beha io is a ibu ed o he o igin o he main magne ic aniso -
opy con ibu ion. While in he hin ilms he ield-induced aniso opy domina es, hus
esul ing in a magne ic easy axis along he g ow h ield di ec ion (0°) and a ha d one pe -
pendicula o i (90°), in he an ido la ices he magne ic shape aniso opy akes o e he
ield-induced one, hus modi ying he easy and ha d axis con igu a ion landscape, and
Figu e 2.
Room empe a u e hys e esis loops eco ded om (
a
) 10 nm hick and (
b
) 50 nm hick
pe malloy hin ilms g own using elec on-beam e apo a ion wi h an applied ield o 500 Oe. The
angles indica ed in he legend co espond o he ield di ec ion wi h espec o he applied ield
du ing g ow h. Inse s a e zoomed egions a ound HC o each plo .
The oom empe a u e hys e esis loops eco ded om he an ido la ices a e p esen ed
in Figu e 3as a unc ion o he applied ield angle wi h espec o he di ec ion o he
applied ield du ing g ow h. Figu e 3a shows he 10 nm hick an ido la ice hys e esis
loops, while Figu e 3b shows he 50 nm hick an ido la ice hys e esis loops. The i s
ema kable di e ence is ha he an ido s p esen a c osso e in he aniso opy o easy
and ha d axis con igu a ion, om a 90
◦
angle be ween hem in he hin ilms o a 45
◦
angle in he an ido la ices. This beha io is a ibu ed o he o igin o he main magne ic
Magne ochemis y 2022,8, 55 5 o 9
aniso opy con ibu ion. While in he hin ilms he ield-induced aniso opy domina es,
hus esul ing in a magne ic easy axis along he g ow h ield di ec ion (0
◦
) and a ha d one
pe pendicula o i (90
◦
), in he an ido la ices he magne ic shape aniso opy akes o e
he ield-induced one, hus modi ying he easy and ha d axis con igu a ion landscape,
and esul ing in he obse ed 45
◦
angle be ween axes. This is in good ag eemen wi h
p e iously s udied an ido squa e la ices, whe e he easy and ha d axes display a 45
◦
pe iodici y [
42
]. None heless, he p esence o he ield-induced magne ic aniso opy is s ill
no iceable in he an ido la ices; he 50 nm hick sample has H
C,90◦
= 30 Oe when he ield is
applied a 90
◦
, while H
C,0◦
= 24 Oe when i is applied along 0
◦
. This is a educ ion o ~20%
in H
C
due o he ield-induced magne ic aniso opy. The coe ci e ields measu ed a 0
◦
and
90
◦
in he 10 nm hick an ido la ice a e indis inguishable, which is in good ag eemen
wi h he esul s obse ed o he non-pa e ned sis e hin ilm wi h simila hickness.
Magne ochemis y 2022, 8, x FOR PEER REVIEW 5 o 9
esul ing in he obse ed 45° angle be ween axes. This is in good ag eemen wi h p e i-
ously s udied an ido squa e la ices, whe e he easy and ha d axes display a 45° pe iodic-
i y [42]. None heless, he p esence o he ield-induced magne ic aniso opy is s ill no ice-
able in he an ido la ices; he 50 nm hick sample has HC,90° = 30 Oe when he ield is
applied a 90°, while HC,0° = 24 Oe when i is applied along 0°. This is a educ ion o ~20%
in HC due o he ield-induced magne ic aniso opy. The coe ci e ields measu ed a 0°
and 90° in he 10 nm hick an ido la ice a e indis inguishable, which is in good ag eemen
wi h he esul s obse ed o he non-pa e ned sis e hin ilm wi h simila hickness.
As de i ed om a di ec inspec ion o he hys e esis loops p esen ed in Figu e 3, he
magne iza ion e e sal on bo h an ido la ices akes place in a wo-s ep p ocess, indica ed
by he jumps obse ed in he hys e esis loops. The e is a no iceable di e ence be ween
he 10 nm and 50 nm hick an ido la ices. Fo he 10 nm hick la ice, he jumps on he
hys e esis loops a e sha pe ; he 50 nm hick la ice p esen s smoo he jumps. This is a -
ibu ed o shape aniso opy, which a ec s he pinning o domains and domain walls
wi hin he an ido s: he 10 nm hick la ice p esen s a sha pe and uni o m an ido geom-
e y, hus esul ing in a na owe dis ibu ion o he domain pinning and depinning ields,
whe eas he 50 nm hick la ice p esen s a mo e ounded and less uni o m an ido geom-
e y, leading o a wide dis ibu ion o domain pinning and depinning ields [43]. The
magne iza ion e e sal mechanism obse ed in ou an ido la ices is simila o ha ob-
se ed in bicomponen an ido s [44] o s adium shaped an ido s [43].
Figu e 3. Room empe a u e hys e esis loops eco ded om (a) 10 nm hick and (b) 50 nm hick
pe malloy an ido la ices g own by elec on-beam e apo a ion wi h an applied ield o 500 Oe pa -
allel o one la ice axis (0°). Inse s a e zoomed egions a ound Hc o each plo .
To be e unde s and he magne iza ion e e sal p ocess in ou an ido la ices, as
well as o quan i y he ield induced aniso opy du ing g ow h, mic omagne ic simula-
ions ha e been pe o med using MuMax3 [37]. De ails abou he speci ic simula ion pa-
ame e s and me hodology ollowed a e desc ibed in he Ma e ials and Me hods sec ion.
The simula ed hys e esis loops o he wo an ido la ices s udied in he p esen wo k a e
shown in Figu e 4, oge he wi h inse s o speci ic in e es ing magne ic con igu a ion
s a es a applied ields ma ked on he hys e esis loops. As obse ed om he calcula ed
loops, he simula ions on he an ido la ices a e in good quali a i e ag eemen wi h he
expe imen ally measu ed hys e esis loops p esen ed in Figu e 3. The di e gences be-
ween he shapes o he simula ed and eco ded hys e esis loops, which a e e iden o
he 50 nm hick an ido la ice, co espond o much smoo he magne iza ion jumps on he
expe imen al loops wi h espec o he simula ed ones. By inspec ing he me as able mag-
ne iza ion s a es ha a ise om he simula ions o he hys e esis loops, we can con i m
ha hey a e ela ed o he shape aniso opy o he la ices induced by he eal shape o
he an ido s; sha p jumps in he simula ion a e due o pe ec shapes o he an ido s,
whe eas smoo h jumps in he hys e esis loops o igina e in he non-uni o mi y o he
shapes o he an ido s wi hin he la ices. This esul s in a smoo h se ies o domain wall
Figu e 3.
Room empe a u e hys e esis loops eco ded om (
a
) 10 nm hick and (
b
) 50 nm hick
pe malloy an ido la ices g own by elec on-beam e apo a ion wi h an applied ield o 500 Oe
pa allel o one la ice axis (0◦). Inse s a e zoomed egions a ound Hc o each plo .
As de i ed om a di ec inspec ion o he hys e esis loops p esen ed in Figu e 3, he
magne iza ion e e sal on bo h an ido la ices akes place in a wo-s ep p ocess, indica ed
by he jumps obse ed in he hys e esis loops. The e is a no iceable di e ence be ween
he 10 nm and 50 nm hick an ido la ices. Fo he 10 nm hick la ice, he jumps on he
hys e esis loops a e sha pe ; he 50 nm hick la ice p esen s smoo he jumps. This is
a ibu ed o shape aniso opy, which a ec s he pinning o domains and domain walls
wi hin he an ido s: he 10 nm hick la ice p esen s a sha pe and uni o m an ido ge-
ome y, hus esul ing in a na owe dis ibu ion o he domain pinning and depinning
ields, whe eas he 50 nm hick la ice p esen s a mo e ounded and less uni o m an ido
geome y, leading o a wide dis ibu ion o domain pinning and depinning ields [
43
].
The magne iza ion e e sal mechanism obse ed in ou an ido la ices is simila o ha
obse ed in bicomponen an ido s [44] o s adium shaped an ido s [43].
To be e unde s and he magne iza ion e e sal p ocess in ou an ido la ices, as well
as o quan i y he ield induced aniso opy du ing g ow h, mic omagne ic simula ions
ha e been pe o med using MuMax3 [
37
]. De ails abou he speci ic simula ion pa ame e s
and me hodology ollowed a e desc ibed in he Ma e ials and Me hods sec ion. The
simula ed hys e esis loops o he wo an ido la ices s udied in he p esen wo k a e
shown in Figu e 4, oge he wi h inse s o speci ic in e es ing magne ic con igu a ion s a es
a applied ields ma ked on he hys e esis loops. As obse ed om he calcula ed loops, he
simula ions on he an ido la ices a e in good quali a i e ag eemen wi h he expe imen ally
measu ed hys e esis loops p esen ed in Figu e 3. The di e gences be ween he shapes o
he simula ed and eco ded hys e esis loops, which a e e iden o he 50 nm hick an ido
la ice, co espond o much smoo he magne iza ion jumps on he expe imen al loops
wi h espec o he simula ed ones. By inspec ing he me as able magne iza ion s a es ha
a ise om he simula ions o he hys e esis loops, we can con i m ha hey a e ela ed
Magne ochemis y 2022,8, 55 6 o 9
o he shape aniso opy o he la ices induced by he eal shape o he an ido s; sha p
jumps in he simula ion a e due o pe ec shapes o he an ido s, whe eas smoo h jumps in
he hys e esis loops o igina e in he non-uni o mi y o he shapes o he an ido s wi hin
he la ices. This esul s in a smoo h se ies o domain wall depinning p ocesses, while
in he ideal case o pe ec uni o m an ido shapes (which is he simula ed one), a sha p
all-a -once depinning p ocess o he domains akes place, which is e iden om he sha p
magne iza ion jumps on he hys e esis loops. Simila o he beha io o he an ido la ices,
simula ions also accoun o he highe H
C
when he ield is applied a 45
◦
. No e ha
M/M
S
along he 45
◦
di ec ion is a ac o o 0.70 imes lowe han ha along he 0
◦
and 90
◦
di ec ions. This is because wha is ob ained om he simula ions a 45
◦
is he p ojec ion o
M along MX, which is a an angle o 45◦wi h espec o M.
Magne ochemis y 2022, 8, x FOR PEER REVIEW 6 o 9
depinning p ocesses, while in he ideal case o pe ec uni o m an ido shapes (which is
he simula ed one), a sha p all-a -once depinning p ocess o he domains akes place,
which is e iden om he sha p magne iza ion jumps on he hys e esis loops. Simila o
he beha io o he an ido la ices, simula ions also accoun o he highe HC when he
ield is applied a 45°. No e ha M/MS along he 45° di ec ion is a ac o o 0.70 imes lowe
han ha along he 0° and 90° di ec ions. This is because wha is ob ained om he simu-
la ions a 45° is he p ojec ion o M along MX, which is a an angle o 45° wi h espec o
M.
In addi ion o he unde s anding o he magne iza ion e e sal p ocess in he an ido
la ices, simula ions also p o ide us wi h a me hod o quan i y he ield-induced aniso -
opy in he la ices as a consequence o he applica ion o a magne ic ield du ing he hin
ilm g ow h p ocess. This can be accomplished by a ying he uniaxial aniso opy con-
s an , Ku, wi hin he pa ame e s o he mic omagne ic simula ions. We ound ha highe
coe ci e ields a 90° away om he di ec ion o he ield applied du ing g ow h s a o
de elop o Ku alues o app oxima ely 450–500 J/m3 o he 50 nm hick an ido la ices.
This esul s in an inc ease in HC on he 90° hys e esis loop o app oxima ely 20% o HC
along 0°. A simila Ku alue employed in he simula ion o he 10 nm hick an ido la ices
does no yield any di e ence in HC a 0° and 90°. This is in good ag eemen wi h ou
expe imen al obse a ions, hus concluding ha he ield-induced uniaxial aniso opy
cons an alue in ou an ido la ices is simila o he one calcula ed om ou expe imen al
measu emen s (Ku ≈ 430 J/m3).
Figu e 4. Hys e esis loops simula ed on (a) 10 nm and (b) 50 nm hick an ido la ices wi h simila
an ido shapes o hose obse ed in hei co esponding nano ab ica ed samples p esen ed in Figu e
1. The hys e esis loops p esen ed we e simula ed wi h ields applied a simila angles o hose p e-
sen ed in Figu e 2. The inse s co espond o ele an ep esen a i e magne iza ion s a es ob ained
om he mic omagne ic simula ions in speci ic ields o he 0° hys e esis loops. The colo scale de-
pic ing he di ec ions o he magne iza ion ec o s p esen ed in he inse s is shown in he bo om
cen al pa o he igu e.
Figu e 4.
Hys e esis loops simula ed on (
a
) 10 nm and (
b
) 50 nm hick an ido la ices wi h simila
an ido shapes o hose obse ed in hei co esponding nano ab ica ed samples p esen ed in Figu e 1.
The hys e esis loops p esen ed we e simula ed wi h ields applied a simila angles o hose p esen ed
in Figu e 2. The inse s co espond o ele an ep esen a i e magne iza ion s a es ob ained om he
mic omagne ic simula ions in speci ic ields o he 0
◦
hys e esis loops. The colo scale depic ing he
di ec ions o he magne iza ion ec o s p esen ed in he inse s is shown in he bo om cen al pa o
he igu e.
In addi ion o he unde s anding o he magne iza ion e e sal p ocess in he an ido
la ices, simula ions also p o ide us wi h a me hod o quan i y he ield-induced aniso opy
in he la ices as a consequence o he applica ion o a magne ic ield du ing he hin ilm
g ow h p ocess. This can be accomplished by a ying he uniaxial aniso opy cons an , K
u
,
wi hin he pa ame e s o he mic omagne ic simula ions. We ound ha highe coe ci e
ields a 90
◦
away om he di ec ion o he ield applied du ing g ow h s a o de elop o
Ku alues o app oxima ely 450–500 J/m3 o he 50 nm hick an ido la ices. This esul s
in an inc ease in H
C
on he 90
◦
hys e esis loop o app oxima ely 20% o H
C
along 0
◦
. A
simila K
u
alue employed in he simula ion o he 10 nm hick an ido la ices does no
yield any di e ence in H
C
a 0
◦
and 90
◦
. This is in good ag eemen wi h ou expe imen al
Magne ochemis y 2022,8, 55 7 o 9
obse a ions, hus concluding ha he ield-induced uniaxial aniso opy cons an alue in
ou an ido la ices is simila o he one calcula ed om ou expe imen al measu emen s
(Ku≈430 J/m3).
4. Conclusions
We in es iga ed he e ec o a ield-induced uniaxial magne ic aniso opy on he
aniso opy landscape, and he magne iza ion e e sal p ocesses o an ido la ices o di -
e en hicknesses made o pe malloy. The hys e esis loops o he an ido la ices show a
c osso e in he aniso opy axes landscape, om a 90
◦
ield-induced easy- o-ha d axis angu-
la dis ibu ion in Py hin ilms o a 45
◦
axis angula dis ibu ion one in he an ido la ices.
Al hough he 45
◦
angula di e ence be ween easy and ha d axes is well known in squa e
an ido la ices, he e we obse e ha a 90
◦
om he di ec ion o he applied ield du ing
g ow h o he la ices, which should co espond o an easy axis in a s anda d squa e an ido
la ice, he coe ci e ield measu ed om he hys e esis loops is app oxima ely 20% highe
han he one measu ed a 0
◦
. This is due o he con ibu ion o he ield-induced aniso opy
o he o al magne ic aniso opy o he sample. Simula ions on an ido la ices wi h simila
shapes and dimensions a e in good ag eemen wi h he expe imen al esul s, and p o ide
us wi h in o ma ion abou magne ic domain con igu a ions du ing he magne iza ion
e e sal p ocess. Finally, we ha e quan i ied he ield-induced uniaxial aniso opy cons an
o be K
u≈
430 J/m
3
, which is in good ag eemen wi h he aniso opy cons an employed
in simula ions ha esemble he ob ained expe imen al esul s. These esul s p esen a
p omising pa h owa ds magne ic aniso opy enginee ing o an ido la ices in o de o
une hei magne ic esponses so ha hey can mee speci ic u u e echnology demands.
Au ho Con ibu ions:
Concep ualiza ion, J.M.P., A.L., R.M. and E.F.-M.; me hodology, J.M.P., R.M.
and E.F.-M.; samples g ow h: A.V. and C.R.; measu emen s, J.M.P., A.V., N.A.R.-L. and D.S.; mic o-
magne ic simula ions, J.M.P. and E.F.-M.; in e p e a ion, J.M.P., R.M. and E.F.-M.; w i ing—o iginal
d a p epa a ion, J.M.P.; w i ing— e iew and edi ing, J.M.P., A.V., C.R., N.A.R.-L., A.L., D.S., R.M.
and E.F.-M. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding:
We acknowledge inancial suppo om he depa men o Educa ion o he Basque
Go e nmen h ough he PIBA p ojec call (PIBA_2021_1_0051). A.V. and N.A.R.-L. acknowledge
unding om he Basque Go e nmen P e-doc o al ellowship p og am. R.M. and C.R. acknowledge
unding om MCIN/ AEI/10.13039/501100011033/ unde g an no. PID2019-104604RB-C33.
Da a A ailabili y S a emen : Da a a e a ailable om he au ho s upon easonable eques .
Acknowledgmen s:
The au ho s would like o hank he echnical and human suppo p o ided
by SGIke uni s o Elec on mic oscopy and Magne ic measu emen s (UPV/EHU/ERDF, EU). We
g a e ully acknowledge he suppo o NVIDIA Co po a ion wi h he dona ion o he NVIDIA
QUADRO P6000 GPU used o his esea ch.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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