Ci a ion: S alo , A.V.; Go ko enko,
A.N.; La añaga, A.; Volochae , M.N.;
Ku lyandskaya, G.V. S uc u al and
Magne ic P ope ies o FeNi Films
and FeNi-Based T ilaye s wi h
Ou -o -Plane Magne iza ion
Componen . Senso s 2022,22, 8357.
h ps://doi.o g/10.3390/s22218357
Academic Edi o : Rosa Ga iga
Recei ed: 16 Oc obe 2022
Accep ed: 28 Oc obe 2022
Published: 31 Oc obe 2022
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senso s
A icle
S uc u al and Magne ic P ope ies o FeNi Films and
FeNi-Based T ilaye s wi h Ou -o -Plane
Magne iza ion Componen
And ey V. S alo 1, Alexand N. Go ko enko 1, Ai o La añaga 2, Mikhail N. Volochae 3
and Galina V. Ku lyandskaya 1,4,*
1Ins i u e o Na u al Sciences and Ma hema ics, U al Fede al Uni e si y, 620002 Eka e inbu g, Russia
2Ad anced Resea ch Facili ies (SGIKER), Uni e sidad del País Vasco UPV-EHU, 48080 Bilbao, Spain
3Ki ensky Ins i u e o Physics FRS KSC SB RAS, 660036 K asnoya sk, Russia
4Depa amen o de Elec icidad y Elec ónica, Uni e sidad del País Vasco UPV/EHU, 48080 Bilbao, Spain
*Co espondence: [email p o ec ed]
Abs ac :
FeNi ilms o di e en hickness and FeNi/(Fe, Co)/FeNi ilaye s we e p epa ed by mag-
ne on spu e ing deposi ion on o glass subs a es. The pe malloy ilms had a columna mic os uc-
u e. The de ailed analysis o he magne ic p ope ies based on he magne ic and magne o-op ical
measu emen s showed ha a hicknesses exceeding a ce ain c i ical hickness, hys e esis loops
acqui e a speci ic shape and he coe ci e o ce o he ilms inc ease sha ply. The possibili y o he
es ima ion o he pe pendicula magne ic aniso opy cons an using he Mu ayama equa ion o he
hickness dependence o sa u a ion ield was demons a ed. The esul s o s udies o he s uc u al
and magne ic p ope ies o FeNi ilms lamina ed by Fe and Co space s wi h di e en hickness
a e p esen ed.
Keywo ds:
magne ic ield senso s; pe malloy; c ys al s uc u e; pe pendicula magne ic aniso opy;
s ipe domains; “ ansc i ical” s a e; columna mic os uc u e
1. In oduc ion
So e omagne ic ilms a e used in a ious ypes o magne oelec onic de ices [
1
].
One o he ways o inc ease he magne ic so ness o hin ilms is o c ea e he laye s wi h
helical magne ic aniso opy [
2
]. The helical a ia ion in he o ien a ion o he easy magne-
iza ion axis can be ob ained by he deposi ion o he ilms in he magne ic ield o a ing
in he plane o he subs a e [
2
,
3
]. A s able helical p o ile may occu o a ilm hickness
g ea e han he speci ic alue, de ined as 2
π
(A/K)
1/2
, whe e K is he aniso opy cons an ,
and A is he exchange s i ness cons an . Fo FeNi ilms, a speci ic hickness depends on he
deposi ion condi ions, bu i is app oxima ely equal o 1
µ
m [
3
]. Howe e , a a hickness
o se e al hund eds o nanome es, FeNi ilms can demons a e he ansi ion in o he
so-called “ ansc i ical” s a e. This s a e is cha ac e ized by an inc ease in he coe ci e o ce
H
c
, appea ance o he s ipe domains, exis ence o so-called “ o a able aniso opy” and
pa icula shape o he magne ic hys e esis loop [
4
–
11
]. An indispensable condi ion o
he possibili y o a ansi ion is he p esence o pe pendicula magne ic aniso opy in he
sample, while he quali y ac o Q = K
p
/2
π
M
s
, whe e K
p
is he pe pendicula aniso opy
cons an , M
s
is he sa u a ion magne iza ion o he sample, which should be less han
uni y. The c i ical hickness alue L
c
depends on he deposi ion condi ions (deposi ion a e,
wo king gas p essu e) and co esponds usually o he in e al o 100 o 350 nm [
5
,
6
,
12
,
13
].
The pe pendicula magne ic aniso opy is esponsible o he o ma ion o he “ ans-
c i ical” s a e in FeNi ilms p epa ed by spu e ing echnique. I migh be a s ain-caused
consequence o magne os ic ion and magne oelas ic con ibu ion and/o he colum-
na s uc u e o he ilms [
5
,
8
,
14
]. Lamina ing o he hick FeNi ilm wi h a ious non-
magne ic and weakly magne ic space s allows o a oid he ansi ion in o he “ ansc i ical”
Senso s 2022,22, 8357. h ps://doi.o g/10.3390/s22218357 h ps://www.mdpi.com/jou nal/senso s
Senso s 2022,22, 8357 2 o 10
s a e [15–18]
. The use o in e laye s o magne ically s ong ma e ials wi h a c ys al s uc u e
di e en om ha one o he Fe20Ni80 pe malloy is much less s udied [19,20].
Unde s anding he condi ions o he ansi ion in o he “ ansc i ical” s a e has e y
special impo ance o elec onics applica ions as so e omagne ic ilms wi h magne ic
pe meabili y o m pa o he induc o s, decode s, magne ic ield senso s, and many o he
kinds o he de ices [
1
,
21
]. Addi ionally, emo ing he “ ansc i ical” s a e will make i
possible o ob ain so magne ic ilms whose hickness will exceed he speci ic c i ical
hickness men ioned abo e. The e o e, he condi ion o he p epa a ion o he ilms wi h
a helical magne ic aniso opy by he deposi ion o he ilms a he o a ing magne ic ield
will be open. In addi ion, such a undamen al ques ion as he change in he alue o he
pe pendicula magne ic aniso opy cons an K
p
wi h he a ia ion in he hickness o he
FeNi ilms s ill emains open. In his wo k, he s uc u al and magne ic p ope ies o
FeNi ilms o di e en hickness and FeNi/(Fe, Co)/FeNi ilaye s we e compa a i ely
analyzed wi h he ocus on he unde s anding o he condi ions o ou -o -plane magne ic
aniso opy o ma ion.
2. Expe imen
Thin ilms and mul ilaye ed samples we e deposi ed by dc magne on spu e ing on o
Co ning glass subs a es a oom empe a u e. Me allic ci cula a ge s o Fe
20
Ni
80
, Fe o
Co we e used. The deposi ion a es we e de ined by addi ional calib a ion p ocedu e using
100 nm ilms o each composi ion. The hin ilms hicknesses o calib a ion we e e i ied
by he sha p s ep analyzed wi h Dek ak 150 S ylus P o ilome e (Veeco, Some se , NJ, USA).
The ollowing deposi ion a es we e used: 26 nm/min o FeNi laye s and 1 nm/min o Fe
and Co space ma e ials. The hickness o he FeNi ilms L a ied om 50 nm o 1000 nm
and he hickness o Fe and Co space s l
sp
was subjec o a ia ions in he in e al o 5 nm
o 100 nm. A cons an magne ic ield o 250 Oe was applied pa allel o he ilm plane du ing
deposi ion in o de o induce in-plane uniaxial magne ic aniso opy.
The phase analysis and a e age g ain size was de ined by X- ay di ac ion echnique
(XRD) using a PHILIPS X’PERT PRO au oma ic di ac ome e (Pan Analy ical, Camb idge,
UK) ope a ing a 40 kV and 40 mA wi h Cu-K
α
adia ion (wa eleng h
λ
= 1.5418 Å). The
con igu a ion used o XRD s udies has been he a- he a B agg-B en ano. The pa icula
con igu a ion was selec ed as he main objec i e has been o i adia e he maximum sample
olume o ob ain he maximum signal in ensi y. This geome y allows he co ec e alua ion
o he ull wid h a hal maximum (FWHM) o la e size es ima ions. The iden i ica ion o
he ini ial phases was pe o med using High Sco e p og am and he powde di ac ion
ile (PDF). The s uc u e o he ilms was s udied also by ansmission elec on mic oscopy
(TEM) using a Hi achi HT 7700 mic oscope (Hi achi HT, Tokyo, Japan) and scanning
elec on mic oscope (SEM) JEOL JSM-640 (JEOL, F eising, Ge many), SEM images we e
acqui ed in seconda y elec ons.
Magne ic measu emen s we e ca ied ou by means o ib a ing sample magne ome-
e 7407 VSM ib a ing-sample magne ome e (Lake Sho e C yo onics London, UK) and
magne o-op ical Ke e ec (MOKE) using he op ical mic oscope E ico (E ico, D es-
den, Ge many).
3. Resul s and Discussion
The X- ay diag ams o he FeNi ilms con i m he cc c ys alline s uc u e o all sam-
ples unde conside a ion (Figu e 1). The p esence o an (111) in ense peak is a cha ac e is ic
ea u e o he di ac og ams ob ained o all s udied ilms. An inc ease in he ilm hickness
is accompanied by an inc ease in he in ensi y o he (111) and (200) peaks.
Senso s 2022,22, 8357 3 o 10
Senso s 2022, 22, x FOR PEER REVIEW 3 o 11
3. Resul s and Discussion
The X- ay diag ams o he FeNi ilms con i m he cc c ys alline s uc u e o all sam-
ples unde conside a ion (Figu e 1). The p esence o an (111) in ense peak is a cha ac e -
is ic ea u e o he di ac og ams ob ained o all s udied ilms. An inc ease in he ilm
hickness is accompanied by an inc ease in he in ensi y o he (111) and (200) peaks.
Figu e 1. X- ay di ac ion pa e ns o FeNi ilms wi h di e en hicknesses indica ed in he legends.
Mille indexes a e shown o all b igh peaks.
Fo (220) peaks, an inc ease in he in ensi y is clea ly obse ed o he ilms o 400
and 200 nm. Howe e , he in ensi y o he (220) peak o he hinnes ilm o 50 nm is low
and i is di icul o o m a de ini e conclusion. This obse a ion con i ms he e idence o
an imp o emen in c ys allini y o he ilms. A he same ime, simila a e age g ain size
o he o de o 10–15 nm was obse ed in all cases. The size o he cohe en domain was
calcula ed using he Sche e o mula o (111) e lec ion (2θ ≈ 44.5°). A ypical cell pa am-
e e o 3.52 Å was also de ec ed o all ypes o FeNi ilms.
Figu e 2 shows he SEM mo phology o he ee su ace o he FeNi ilm and ypical
example o TEM c oss-sec ional image o FeNi ilm o 100 nm. The g ain-like SEM images
(Figu e 2a) may be due o he p esence o a columna mic os uc u e in he ilm which is
ep esen ed as ound uni s in his p ojec ion. The TEM c oss-sec ional images con i m his
assump ion (Figu e 2b). One can see ha he geome y o he c oss sec ion o he columns
on he ee su ace o he ilm is close o he ci cula shape and he diame e s o he col-
umns a e easonably close o he in e al o 4 nm o 10 nm.
Figu e 2. SEM mo phology o he ee su ace (a) and TEM c oss-sec ional image (b) o FeNi ilm o
100 nm hickness.
40 50 60 70 80
50 nm
200 nm
400 nm
(220)
(200)
In ensi y (a b. uni s)
2θ (deg)
(111) FeNi cc s uc u e
Figu e 1.
X- ay di ac ion pa e ns o FeNi ilms wi h di e en hicknesses indica ed in he legends.
Mille indexes a e shown o all b igh peaks.
Fo (220) peaks, an inc ease in he in ensi y is clea ly obse ed o he ilms o 400
and 200 nm. Howe e , he in ensi y o he (220) peak o he hinnes ilm o 50 nm is low
and i is di icul o o m a de ini e conclusion. This obse a ion con i ms he e idence
o an imp o emen in c ys allini y o he ilms. A he same ime, simila a e age g ain
size o he o de o 10–15 nm was obse ed in all cases. The size o he cohe en domain
was calcula ed using he Sche e o mula o (111) e lec ion (2
θ≈
44.5
◦
). A ypical cell
pa ame e o 3.52 Å was also de ec ed o all ypes o FeNi ilms.
Figu e 2shows he SEM mo phology o he ee su ace o he FeNi ilm and ypical
example o TEM c oss-sec ional image o FeNi ilm o 100 nm. The g ain-like SEM images
(Figu e 2a) may be due o he p esence o a columna mic os uc u e in he ilm which is
ep esen ed as ound uni s in his p ojec ion. The TEM c oss-sec ional images con i m his
assump ion (Figu e 2b). One can see ha he geome y o he c oss sec ion o he columns
on he ee su ace o he ilm is close o he ci cula shape and he diame e s o he columns
a e easonably close o he in e al o 4 nm o 10 nm.
Senso s 2022, 22, x FOR PEER REVIEW 3 o 11
3. Resul s and Discussion
The X- ay diag ams o he FeNi ilms con i m he cc c ys alline s uc u e o all sam-
ples unde conside a ion (Figu e 1). The p esence o an (111) in ense peak is a cha ac e -
is ic ea u e o he di ac og ams ob ained o all s udied ilms. An inc ease in he ilm
hickness is accompanied by an inc ease in he in ensi y o he (111) and (200) peaks.
Figu e 1. X- ay di ac ion pa e ns o FeNi ilms wi h di e en hicknesses indica ed in he legends.
Mille indexes a e shown o all b igh peaks.
Fo (220) peaks, an inc ease in he in ensi y is clea ly obse ed o he ilms o 400
and 200 nm. Howe e , he in ensi y o he (220) peak o he hinnes ilm o 50 nm is low
and i is di icul o o m a de ini e conclusion. This obse a ion con i ms he e idence o
an imp o emen in c ys allini y o he ilms. A he same ime, simila a e age g ain size
o he o de o 10–15 nm was obse ed in all cases. The size o he cohe en domain was
calcula ed using he Sche e o mula o (111) e lec ion (2θ ≈ 44.5°). A ypical cell pa am-
e e o 3.52 Å was also de ec ed o all ypes o FeNi ilms.
Figu e 2 shows he SEM mo phology o he ee su ace o he FeNi ilm and ypical
example o TEM c oss-sec ional image o FeNi ilm o 100 nm. The g ain-like SEM images
(Figu e 2a) may be due o he p esence o a columna mic os uc u e in he ilm which is
ep esen ed as ound uni s in his p ojec ion. The TEM c oss-sec ional images con i m his
assump ion (Figu e 2b). One can see ha he geome y o he c oss sec ion o he columns
on he ee su ace o he ilm is close o he ci cula shape and he diame e s o he col-
umns a e easonably close o he in e al o 4 nm o 10 nm.
Figu e 2. SEM mo phology o he ee su ace (a) and TEM c oss-sec ional image (b) o FeNi ilm o
100 nm hickness.
40 50 60 70 80
50 nm
200 nm
400 nm
(220)
(200)
In ensi y (a b. uni s)
2θ (deg)
(111) FeNi cc s uc u e
Figu e 2.
SEM mo phology o he ee su ace (
a
) and TEM c oss-sec ional image (
b
) o FeNi ilm o
100 nm hickness.
Senso s 2022,22, 8357 4 o 10
Fo Fe and Co single laye ilms, he a e age g ain size was app oxima ely equal o he
hickness alues, bu i did no exceed 15 nm. Single-laye i on ilms we e polyc ys alline
bbc s uc u es ha ing high le els o he (110) ex u ing and cell pa ame e o 2.85 Å
(Figu e 3).
Senso s 2022, 22, x FOR PEER REVIEW 4 o 11
Fo Fe and Co single laye ilms, he a e age g ain size was app oxima ely equal o
he hickness alues, bu i did no exceed 15 nm. Single-laye i on ilms we e polyc ys al-
line bbc s uc u es ha ing high le els o he (110) ex u ing and cell pa ame e o 2.85 Å
(Figu e 3).
Figu e 3. X- ay di ac ion pa e n o Fe ilms (a) and FeNi(170 nm)/Fe(lFe)/FeNi(170 nm) ilaye s
(b).
The high deg ee o ex u ing obse ed o hin Co ilms did no allows us o unam-
biguously de e mine he la ice ype, namely, cubic o hexagonal (Figu e 4a). The me als
g owing incohe en ly on he subs a es a e known o p e e he close-packed o ien a ion,
like (111) plane o he cc s uc u e [22]. I he e o e can be supposed ha in hin cobal
ilms, bo h cubic and hexagonal phases can be p esen . The appea ance o he hcp (100)
and hcp (101) peaks o hicke Co ilms es i ies he inc ease o he ela i e amoun o he
hexagonal phase wi h he inc ease o he Co ilm hickness.
Figu e 4. X- ay di ac ion pa e ns o Co ilms o di e en hicknesses (a) and FeNi(170
nm)/Co(lCo)/FeNi(170 nm) ilaye s (b). In all cases, he legends indica e he cobal laye hickness.
The c i ical hickness o FeNi ilms was close o 200 nm. Thinne ilms had uniaxial
magne ic aniso opy wi h he aniso opy axis o ien ed in he sample plane (Figu e 5a).
The easy magne iza ion axis coincided wi h he o ien a ion o he magne ic ield applied
du ing hin ilm deposi ion. The coe ci e o ce Hc o such ilms did no exceed 1 Oe, and
he aniso opy ield Hk was abou 4 Oe.
Figu e 3.
X- ay di ac ion pa e n o Fe ilms (
a
) and FeNi(170 nm)/Fe(l
Fe
)/FeNi(170 nm) ilaye s (
b
).
The high deg ee o ex u ing obse ed o hin Co ilms did no allows us o unam-
biguously de e mine he la ice ype, namely, cubic o hexagonal (Figu e 4a). The me als
g owing incohe en ly on he subs a es a e known o p e e he close-packed o ien a ion,
like (111) plane o he cc s uc u e [
22
]. I he e o e can be supposed ha in hin cobal
ilms, bo h cubic and hexagonal phases can be p esen . The appea ance o he hcp (100)
and hcp (101) peaks o hicke Co ilms es i ies he inc ease o he ela i e amoun o he
hexagonal phase wi h he inc ease o he Co ilm hickness.
Senso s 2022, 22, x FOR PEER REVIEW 4 o 11
Fo Fe and Co single laye ilms, he a e age g ain size was app oxima ely equal o
he hickness alues, bu i did no exceed 15 nm. Single-laye i on ilms we e polyc ys al-
line bbc s uc u es ha ing high le els o he (110) ex u ing and cell pa ame e o 2.85 Å
(Figu e 3).
Figu e 3. X- ay di ac ion pa e n o Fe ilms (a) and FeNi(170 nm)/Fe(lFe)/FeNi(170 nm) ilaye s
(b).
The high deg ee o ex u ing obse ed o hin Co ilms did no allows us o unam-
biguously de e mine he la ice ype, namely, cubic o hexagonal (Figu e 4a). The me als
g owing incohe en ly on he subs a es a e known o p e e he close-packed o ien a ion,
like (111) plane o he cc s uc u e [22]. I he e o e can be supposed ha in hin cobal
ilms, bo h cubic and hexagonal phases can be p esen . The appea ance o he hcp (100)
and hcp (101) peaks o hicke Co ilms es i ies he inc ease o he ela i e amoun o he
hexagonal phase wi h he inc ease o he Co ilm hickness.
Figu e 4. X- ay di ac ion pa e ns o Co ilms o di e en hicknesses (a) and FeNi(170
nm)/Co(lCo)/FeNi(170 nm) ilaye s (b). In all cases, he legends indica e he cobal laye hickness.
The c i ical hickness o FeNi ilms was close o 200 nm. Thinne ilms had uniaxial
magne ic aniso opy wi h he aniso opy axis o ien ed in he sample plane (Figu e 5a).
The easy magne iza ion axis coincided wi h he o ien a ion o he magne ic ield applied
du ing hin ilm deposi ion. The coe ci e o ce Hc o such ilms did no exceed 1 Oe, and
he aniso opy ield Hk was abou 4 Oe.
Figu e 4.
X- ay di ac ion pa e ns o Co ilms o di e en hicknesses (
a
) and FeNi(170 nm)/
Co(lCo)/FeNi(170 nm) ilaye s (b). In all cases, he legends indica e he cobal laye hickness.
The c i ical hickness o FeNi ilms was close o 200 nm. Thinne ilms had uniaxial
magne ic aniso opy wi h he aniso opy axis o ien ed in he sample plane (Figu e 5a).
The easy magne iza ion axis coincided wi h he o ien a ion o he magne ic ield applied
du ing hin ilm deposi ion. The coe ci e o ce H
c
o such ilms did no exceed 1 Oe, and
he aniso opy ield Hkwas abou 4 Oe.
Senso s 2022,22, 8357 5 o 10
Senso s 2022, 22, x FOR PEER REVIEW 5 o 11
An analysis o hys e esis loops allows us o de e mine ano he impo an magne ic
cha ac e is ic, namely, he sa u a ion ield Hs (Figu e 5b). Fo he “ ansc i ical” ilms [23–
25], he ela ionship be ween he sa u a ion ield and he ilm pa ame e s was p e iously
desc ibed by Mu ayama’s equa ion [26,27]:
1− H
H=1+
K
2πM
⁄L
L (1)
whe e Hs and Hk a e he sa u a ion and he aniso opy ields, espec i ely; Kp is pe pen-
dicula magne ic aniso opy cons an ; Lc is he c i ical hickness o he ilm. In ou case,
he hickness dependence o he magne ic sa u a ion ield Hs is well desc ibed by Mu-
ayama’s model a Ms = 810 G, Lc = 200 nm aking Kp alue as high as 5 × 104 e g/cm3
(Figu e 6). Mo eo e , his esul indica es ha he alue o he pe pendicula magne ic
aniso opy cons an emains unchanged despi e ilm hickness a ia ion in he in e al
unde conside a ion.
Figu e 5. (a) hys e esis loops o FeNi(180 nm) ilm measu ed along (1) and pe pendicula
(2) o he easy axis magne iza ion; (b) hys e esis loops o FeNi (340 nm) ilm bo h in ini ial
s a e and a e sepa a ion om he subs a e and annealing a 300 °C du ing one hou ; (c)
MOKE image o he s ipe magne ic domain s uc u e o FeNi (220 nm) ilm.
Figu e 6. Expe imen al (do s) and calcula ed on he basis o Mu ayama’s model (line) hickness de-
pendence o he sa u a ion ield Hs o FeNi ilms.
Wi hin he amewo k o he Mu ayama model, an equa ion o es ima ion he Lc was
also p oposed:
0 200 400 600 800 1000
0
30
60
90
Hs (Oe)
LFeNi (nm)
Figu e 5.
(
a
) hys e esis loops o FeNi(180 nm) ilm measu ed along (1) and pe pendicula (2) o he
easy axis magne iza ion; (
b
) hys e esis loops o FeNi (340 nm) ilm bo h in ini ial s a e and a e
sepa a ion om he subs a e and annealing a 300
◦
C du ing one hou ; (
c
) MOKE image o he s ipe
magne ic domain s uc u e o FeNi (220 nm) ilm.
An analysis o hys e esis loops allows us o de e mine ano he impo an mag-
ne ic cha ac e is ic, namely, he sa u a ion ield H
s
(Figu e 5b). Fo he “ ansc i ical”
ilms [23–25]
, he ela ionship be ween he sa u a ion ield and he ilm pa ame e s was
p e iously desc ibed by Mu ayama’s equa ion [26,27]:
1−Hs
Hk
=1+Kp
2πM2
s−1/2 Lc
L(1)
whe e H
s
and H
k
a e he sa u a ion and he aniso opy ields, espec i ely; K
p
is pe -
pendicula magne ic aniso opy cons an ; L
c
is he c i ical hickness o he ilm. In ou
case, he hickness dependence o he magne ic sa u a ion ield H
s
is well desc ibed by
Mu ayama’s model a M
s
= 810 G, L
c
= 200 nm aking K
p
alue as high as 5
×
10
4
e g/cm
3
(Figu e 6). Mo eo e , his esul indica es ha he alue o he pe pendicula magne ic
aniso opy cons an emains unchanged despi e ilm hickness a ia ion in he in e al
unde conside a ion.
Senso s 2022, 22, x FOR PEER REVIEW 5 o 11
An analysis o hys e esis loops allows us o de e mine ano he impo an magne ic
cha ac e is ic, namely, he sa u a ion ield Hs (Figu e 5b). Fo he “ ansc i ical” ilms [23–
25], he ela ionship be ween he sa u a ion ield and he ilm pa ame e s was p e iously
desc ibed by Mu ayama’s equa ion [26,27]:
1− H
H=1+
K
2πM
⁄L
L (1)
whe e Hs and Hk a e he sa u a ion and he aniso opy ields, espec i ely; Kp is pe pen-
dicula magne ic aniso opy cons an ; Lc is he c i ical hickness o he ilm. In ou case,
he hickness dependence o he magne ic sa u a ion ield Hs is well desc ibed by Mu-
ayama’s model a Ms = 810 G, Lc = 200 nm aking Kp alue as high as 5 × 104 e g/cm3
(Figu e 6). Mo eo e , his esul indica es ha he alue o he pe pendicula magne ic
aniso opy cons an emains unchanged despi e ilm hickness a ia ion in he in e al
unde conside a ion.
Figu e 5. (a) hys e esis loops o FeNi(180 nm) ilm measu ed along (1) and pe pendicula
(2) o he easy axis magne iza ion; (b) hys e esis loops o FeNi (340 nm) ilm bo h in ini ial
s a e and a e sepa a ion om he subs a e and annealing a 300 °C du ing one hou ; (c)
MOKE image o he s ipe magne ic domain s uc u e o FeNi (220 nm) ilm.
Figu e 6. Expe imen al (do s) and calcula ed on he basis o Mu ayama’s model (line) hickness de-
pendence o he sa u a ion ield Hs o FeNi ilms.
Wi hin he amewo k o he Mu ayama model, an equa ion o es ima ion he Lc was
also p oposed:
0 200 400 600 800 1000
0
30
60
90
Hs (Oe)
LFeNi (nm)
Figu e 6.
Expe imen al (do s) and calcula ed on he basis o Mu ayama’s model (line) hickness
dependence o he sa u a ion ield Hs o FeNi ilms.
Senso s 2022,22, 8357 6 o 10
Wi hin he amewo k o he Mu ayama model, an equa ion o es ima ion he L
c
was
also p oposed:
Lc= 2π(A/Kp)1/2 (2)
whe e A is he exchange s i ness cons an ; K
p
is pe pendicula magne ic aniso opy
cons an . We use he alue K
p
= 5
×
10
4
e g/cm
3
ob ained abo e. Then he expe i-
men ally obse ed L
c
alue o 200 nm can be ob ained acco ding o exp ession (2) a
A=5×10−7e g/cm
. The ob ained A alue was in good ag eemen wi h he da a epo ed
by he o he esea ch o FeNi [
28
–
30
]. Thus, he obse ed alues o L
c
and K
p
we e in a
good ag eemen wi h each o he .
In o de o de e mine he o igin o pe pendicula magne ic aniso opy in he s udied
FeNi ilms, he samples wi h low le el o he in e nal s esses we e ab ica ed as ollows.
Some ilms we e deposi ed on NaCl single c ys al subs a e, and hen hey we e sepa a ed
om he subs a e and annealed a a empe a u e o 300
◦
C du ing one hou . The shape o
he hys e esis loops o such ilms was changed e y li le, while he alues o H
c
and H
s
emained unchanged (Figu e 5b). Thus, his esul and he p esence o a columna s uc u e
(Figu e 2) allow us o conclude ha he sou ce o pe pendicula magne ic aniso opy
in he s udied FeNi ilms is he columna mic os uc u e o he ilms a he han he
magne os ic ion e ec .
Fe and Co ilms o di e en hicknesses we e used as magne ic space s in h ee-laye ed
FeNi/X/FeNi s uc u es. In he p esen s udies, he hickness o he FeNi laye s was 170 nm,
i.e., i was below he c i ical hickness o he ansi ion in o “ ansc i ical” s a e
Lc= 200 nm
.
In single-laye ed ilms o Fe and Co, uniaxial magne ic aniso opy was also o med in he
plane o he sample unde he in luence o he magne ic ield applied du ing deposi ion.
Fo hese ilms, he e we e no signs o ansi ion o he “ ansc i ical” s a e (Figu e 7). The
obse ed beha io is consis en wi h he known da a o Fe ilms, o which he epo ed
c i ical hicknesses exceed 100 nm [
31
]. Fo Co ilms, he epo ed c i ical hicknesses ange
om 10 nm o 180 nm [
31
–
33
]. Mos likely, his dis inc ion is due o he s uc u al ea u es
o he ilms p epa ed unde di e en condi ions.
Senso s 2022, 22, x FOR PEER REVIEW 6 o 11
Lc = 2π(A/Kp)1/2 (2)
whe e A is he exchange s i ness cons an ; Kp is pe pendicula magne ic aniso opy con-
s an . We use he alue Kp = 5 × 104 e g/cm3 ob ained abo e. Then he expe imen ally ob-
se ed Lc alue o 200 nm can be ob ained acco ding o exp ession (2) a A = 5 × 10−7
e g/cm. The ob ained A alue was in good ag eemen wi h he da a epo ed by he o he
esea ch o FeNi [28–30]. Thus, he obse ed alues o Lc and Kp we e in a good ag ee-
men wi h each o he .
In o de o de e mine he o igin o pe pendicula magne ic aniso opy in he s udied
FeNi ilms, he samples wi h low le el o he in e nal s esses we e ab ica ed as ollows.
Some ilms we e deposi ed on NaCl single c ys al subs a e, and hen hey we e sepa a ed
om he subs a e and annealed a a empe a u e o 300 °C du ing one hou . The shape
o he hys e esis loops o such ilms was changed e y li le, while he alues o Hc and
Hs emained unchanged (Figu e 5b). Thus, his esul and he p esence o a columna
s uc u e (Figu e 2) allow us o conclude ha he sou ce o pe pendicula magne ic ani-
so opy in he s udied FeNi ilms is he columna mic os uc u e o he ilms a he han
he magne os ic ion e ec .
Fe and Co ilms o di e en hicknesses we e used as magne ic space s in h ee-lay-
e ed FeNi/X/FeNi s uc u es. In he p esen s udies, he hickness o he FeNi laye s was
170 nm, i.e., i was below he c i ical hickness o he ansi ion in o “ ansc i ical” s a e Lc
= 200 nm. In single-laye ed ilms o Fe and Co, uniaxial magne ic aniso opy was also
o med in he plane o he sample unde he in luence o he magne ic ield applied du ing
deposi ion. Fo hese ilms, he e we e no signs o ansi ion o he “ ansc i ical” s a e
(Figu e 7). The obse ed beha io is consis en wi h he known da a o Fe ilms, o which
he epo ed c i ical hicknesses exceed 100 nm [31]. Fo Co ilms, he epo ed c i ical
hicknesses ange om 10 nm o 180 nm [31–33]. Mos likely, his dis inc ion is due o he
s uc u al ea u es o he ilms p epa ed unde di e en condi ions.
Figu e 7. Hys e esis loops measu ed along easy magne iza ion axis o Fe (100 nm) and Co (100 nm)
ilms (a). Images o he magne ic domain s uc u e o Fe ilm (b) and Co ilm (c) ob ained nea Hc
a e magne iza ion o he samples o sa u a ion along he easy magne iza ion axis (EA). The appli-
ca ion axis o he ex e nal ield is pa allel o he EA and e ical sides o he images.
The nanos uc u ing o hick FeNi ilms in o ilaye ed s uc u es ha ing magne ic
laye s wi h L < Lc by Fe space does no p e en he occu ence o he “ ansc i ical” s a e
o FeNi/Fe/FeNi ilaye s (Figu e 8a). Fo he sample wi h lFe = 5 nm, his esul can be
ela ed o he small hickness o he Fe space . Fo FeNi-based mul ilaye s, he su ace
oughness o mul ilaye s p epa ed by dc magne on spu e ing a p esen condi ions is
qui e small, only a ew Angs oms [34], and he hickness o he in e ace ( he zone o
mu ual in e laye di usion) is abou one nm [35].
Figu e 7.
Hys e esis loops measu ed along easy magne iza ion axis o Fe (100 nm) and Co (100 nm)
ilms (
a
). Images o he magne ic domain s uc u e o Fe ilm (
b
) and Co ilm (
c
) ob ained nea
H
c
a e magne iza ion o he samples o sa u a ion along he easy magne iza ion axis (EA). The
applica ion axis o he ex e nal ield is pa allel o he EA and e ical sides o he images.
The nanos uc u ing o hick FeNi ilms in o ilaye ed s uc u es ha ing magne ic
laye s wi h L < L
c
by Fe space does no p e en he occu ence o he “ ansc i ical” s a e
o FeNi/Fe/FeNi ilaye s (Figu e 8a). Fo he sample wi h l
Fe
= 5 nm, his esul can be
ela ed o he small hickness o he Fe space . Fo FeNi-based mul ilaye s, he su ace
oughness o mul ilaye s p epa ed by dc magne on spu e ing a p esen condi ions is
qui e small, only a ew Angs oms [
34
], and he hickness o he in e ace ( he zone o
mu ual in e laye di usion) is abou one nm [35].
Senso s 2022,22, 8357 7 o 10
Senso s 2022, 22, x FOR PEER REVIEW 7 o 11
I was shown ecen ly ha o a s ong/weak/s ong e omagne ic sandwich, ex-
change coupling be ween s ong e omagne ic ou e laye s can be educed when he
weakly e omagne ic ype space has a lowe Cu ie empe a u e han ha o he s ong
e omagne ic laye s [36]. Howe e , he Cu ie empe a u e o Fe and i on-en iched in e -
aces su passes he Cu ie empe a u e o he FeNi alloy. The e o e, he Fe space does no
weaken he in e laye coupling o FeNi laye s. As a esul , FeNi(170 nm)/Fe/FeNi(170 nm)
ilaye ed s uc u e was in he “ ansc i ical” s a e like a single laye ed FeNi(340 nm) ilm.
As lFe inc eases, he Fe in e laye acqui es mo e and mo e s uc u al independence, and
i s magne ic cha ac e is ics become close o hose o bulk i on.
Figu e 8. Magne ic hys e esis loops o FeNi(170 nm)/Fe/FeNi(170 nm) (a) and FeNi(170
nm)/Co/FeNi(170 nm) (b) ilaye s wi h di e en hicknesses o Fe and Co space s indica ed by he
legends.
Le us es ima e he possible alue o he pe pendicula magne ic aniso opy cons an
in he Fe ilms unde conside a ion. Acco ding o he esul s o s uc u al s udies, he Fe
ilms had he (110) ex u e. I one akes in o accoun only he i s magne oc ys alline ani-
so opy cons an and neglec s he magne oelas ic con ibu ion, hen o a cubic i on ilm
wi h (110) ex u e, he e ec i e pe pendicula aniso opy cons an can be de e mined as
Kp = 3/16 × K1 [37]. Fo i on, he magne oc ys alline aniso opy cons an K1 = 4.8 × 105
e g/cm3 [35], hen Kp = 9 × 104 e g/cm3.
Due o he s ong in e laye in e ac ion, he FeNi/Fe/FeNi h ee-laye sys em beha es
as a whole. Based on his ac , le us make an app oxima ing es ima e o he Lc alue o
he FeNi(170 nm)/Fe(100 nm)/FeNi(170 nm) sample using exp ession (2). Being awa e o
he la gely a bi a y na u e o he p ocedu e, le us a e age he alues o Kp and cons an
A using he co esponding alues o FeNi ilms (Kp = 5 × 104 e g/cm3, A = 0.5 × 10−6 e g/cm)
and Fe (Kp = 9 × 104 e g/cm3, A = 2.1 × 10−6 e g/cm) and aking in o accoun he a io o he
laye hicknesses. As a esul , o FeNi(170 nm)/Fe(100 nm)/FeNi(170 nm) we ob ain Kp =
5.9 × 104 e g/cm3, A = 0.9 × 10−6 e g/cm and Lc = 240 nm. The esul ing es ima e ag ees wi h
he expe imen ally obse ed “ ansc i ical” s a e o FeNi(170 nm)/Fe(100 nm)/FeNi(170
nm) ilm.
Lamina ing o he hick FeNi ilm wi h cobal space allows o a oid he ansi ion
in o he “ ansc i ical” s a e a lCo > 50 nm. Fo small alues o lCo, he si ua ion is appa -
en ly he same as o h ee-laye ed samples wi h small lFe. The esul s o s uc u al s udies
indica e he possibili y o he p esence o bo h cc ( ex u e (111)) and hcp (possible ex u e
(002)) cobal phases in he laye s unde conside a ion. Bo h o hese c ys allog aphic o i-
en a ions con ibu e o he appea ance o pe pendicula magne ic aniso opy in he ilm,
since he [111] axis o he cc la ice and he [002] axis o he hcp la ice a e easy magne i-
za ion axes ela ed o magne oc ys alline aniso opy. Howe e , he unce ain y in he
numbe o hcp and cc c ys alline phases in hick Co laye s makes i meaningless o y o
es ima e he alue o he e ec i e cons an o pe pendicula magne ic aniso opy in Co
Figu e 8.
Magne ic hys e esis loops o FeNi(170 nm)/Fe/FeNi(170 nm) (
a
) and FeNi(170 nm)/Co/
FeNi(170 nm) (b) ilaye s wi h di e en hicknesses o Fe and Co space s indica ed by he legends.
I was shown ecen ly ha o a s ong/weak/s ong e omagne ic sandwich, ex-
change coupling be ween s ong e omagne ic ou e laye s can be educed when he
weakly e omagne ic ype space has a lowe Cu ie empe a u e han ha o he s ong
e omagne ic laye s [
36
]. Howe e , he Cu ie empe a u e o Fe and i on-en iched in e -
aces su passes he Cu ie empe a u e o he FeNi alloy. The e o e, he Fe space does no
weaken he in e laye coupling o FeNi laye s. As a esul , FeNi(170 nm)/Fe/FeNi(170 nm)
ilaye ed s uc u e was in he “ ansc i ical” s a e like a single laye ed FeNi(340 nm) ilm.
As l
Fe
inc eases, he Fe in e laye acqui es mo e and mo e s uc u al independence, and i s
magne ic cha ac e is ics become close o hose o bulk i on.
Le us es ima e he possible alue o he pe pendicula magne ic aniso opy con-
s an in he Fe ilms unde conside a ion. Acco ding o he esul s o s uc u al s udies,
he Fe ilms had he (110) ex u e. I one akes in o accoun only he i s magne oc ys-
alline aniso opy cons an and neglec s he magne oelas ic con ibu ion, hen o a cubic
i on ilm wi h (110) ex u e, he e ec i e pe pendicula aniso opy cons an can be de-
e mined as
Kp= 3/16 ×K1[37]
. Fo i on, he magne oc ys alline aniso opy cons an
K1= 4.8 ×105e g/cm3[35], hen Kp= 9 ×104e g/cm3.
Due o he s ong in e laye in e ac ion, he FeNi/Fe/FeNi h ee-laye sys em beha es
as a whole. Based on his ac , le us make an app oxima ing es ima e o he L
c
alue o he
FeNi(170 nm)/Fe(100 nm)/FeNi(170 nm) sample using exp ession (2). Being awa e o he
la gely a bi a y na u e o he p ocedu e, le us a e age he alues o K
p
and cons an A us-
ing he co esponding alues o FeNi ilms (K
p
= 5
×
10
4
e g/cm
3
,
A = 0.5 ×10−6e g/cm
)
and Fe (K
p
= 9
×
10
4
e g/cm
3
, A = 2.1
×
10
−6
e g/cm) and aking in o accoun he a io o
he laye hicknesses. As a esul , o
FeNi(170 nm)/Fe(100 nm)/FeNi(170 nm)
we ob ain
K
p
= 5.9
×
10
4
e g/cm
3
, A = 0.9
×
10
−6
e g/cm and L
c
= 240 nm. The esul ing es ima e
ag ees wi h he expe imen ally obse ed “ ansc i ical” s a e o FeNi(170 nm)/Fe(100 nm)/
FeNi(170 nm) ilm.
Lamina ing o he hick FeNi ilm wi h cobal space allows o a oid he ansi ion in o
he “ ansc i ical” s a e a l
Co
> 50 nm. Fo small alues o l
Co
, he si ua ion is appa en ly
he same as o h ee-laye ed samples wi h small l
Fe
. The esul s o s uc u al s udies
indica e he possibili y o he p esence o bo h cc ( ex u e (111)) and hcp (possible ex u e
(002)) cobal phases in he laye s unde conside a ion. Bo h o hese c ys allog aphic
o ien a ions con ibu e o he appea ance o pe pendicula magne ic aniso opy in he
ilm, since he [111] axis o he cc la ice and he [002] axis o he hcp la ice a e easy
magne iza ion axes ela ed o magne oc ys alline aniso opy. Howe e , he unce ain y in
he numbe o hcp and cc c ys alline phases in hick Co laye s makes i meaningless o
y o es ima e he alue o he e ec i e cons an o pe pendicula magne ic aniso opy
Senso s 2022,22, 8357 8 o 10
in Co in e laye s. In addi ion, he alue and sign o his cons an can be a ec ed by a
magne oelas ic con ibu ion, he e alua ion o which is beyond he scope o he p esen
s udy, bu which can be signi ican in Co ilms [
38
]. He e, o now, we only indica e he
possibili y o a oid he ansi ion in o he “ ansc i ical” s a e by means o lamina ing
o he hick FeNi ilm wi h Co space s. Finding ou he exac eason o his equi es a
sepa a e ho ough in es iga ion. In addi ion, lamina ing o he hick FeNi ilm wi h cobal
space does no educe he coe ci e o ce o FeNi/Co/FeNi ilaye s o he le el o he
coe ci e o ce o single-laye so magne ic ilms FeNi wi h L < L
c
, as happens in he case
o non-magne ic space s [
15
–
18
]. Ne e heless, he absence o he “ ansc i ical” s a e
and, as a consequence, he absence o o a able aniso opy opens he possibili y o mo e
p ecise con ol o he ea u es o he magne ic aniso opy o such ilm sys ems. This c ea es
a pe spec i e o he p epa a ion o he ilms wi h a helical magne ic aniso opy by he
deposi ion o he ilms a he o a ing magne ic ield and possible manipula ion o he
magne iza ion o helimagne s h ough he spin- ans e o que e ec [39].
Magne ically so hin FeNi ilms and FeNi ilms based mul ilaye ed s uc u es a e
widely used in senso applica ions. In many cases, hey a e used as he main ma e ials o
sensi i e elemen o low magne ic ield measu emen s [
40
–
42
]. Howe e , o he unc ion-
ali y o he magne ic ield senso s hey mus be in eg a ed in he elec onic ci cui wi h
compa ible cha ac e is ics, o example induc o s uc u es wi h magne ic ilms, including
FeNi componen s [
43
]. In addi ion, p esen day applica ions eques mul i unc ional de-
ices in which posi ioning plays e y impo an ole. Wi h espec , so magne ic ilms may
con ibu e as addi ional posi ioning elemen o elemen s a ay up o lexible de ices [
44
–
47
].
One can also men ion he need o elec omagne ic p o ec ion o elec onic de ices including
magne ic senso s o co ec ope a ion and a oiding he unwan ed in e e ences o which
FeNi ilms wi h high magne ic pe meabili y and especially FeNi-based mul ilaye s wi h
unable dynamic magne ic p ope ies a e qui e sui able [48–50].
4. Conclusions
S uc u al and magne ic p ope ies o FeNi ilms o di e en hickness and FeNi/(Fe,
Co)/FeNi ilaye s we e compa a i ely analyzed. I was ound ha he pe malloy ilms had
a columna mic os uc u e. I is shown ha pe pendicula magne ic aniso opy cons an
does no depend on he FeNi ilm hickness in he ange o he hicknesses o 50 o 1000 nm.
Based on he esul s o s uc u al and magne ic measu emen s, i can be concluded ha
he main o igin o he pe pendicula magne ic aniso opy in FeNi ilms is he columna
mic os uc u e. I was demons a ed ha o FeNi(170 nm)/Fe/FeNi(170 nm) ilaye s he
“ asc i ical” s a e exis s a any Fe space hickness up o 100 nm. A he same ime, o
FeNi(170 nm)/Co/FeNi(170 nm) ilaye s he “ ansc i ical” s a e disappea s a l
Co
> 50 nm.
I is possible o a oid he ansi ion in o he “ ansc i ical” s a e by means o lamina ing o
he hick FeNi ilm wi h Co space s.
Au ho Con ibu ions:
Concep ualiza ion, A.V.S. and G.V.K.; me hodology, A.V.S. and A.N.G.;
so wa e, A.V.S.; alida ion, A.V.S. and G.V.K.; o mal analysis, G.V.K.; in es iga ion, A.V.S., A.N.G.,
A.L. and M.N.V.; da a cu a ion, G.V.K.; w i ing—o iginal d a p epa a ion, A.V.S. and G.V.K.;
w i ing— e iew and edi ing, A.V.S. and G.V.K.; isualiza ion, A.N.G., A.L. and M.N.V.; supe ision,
A.V.S. All au ho s discussed he esul s and implica ions and commen ed on he manusc ip a all
s ages. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding:
This esea ch was unded by he Russian Science Founda ion (RSF), p ojec no. 22-29-00980,
h ps:// sc . u/en/p ojec /22-29-00980/ and in pa by he Resea ch G oups o he UPV-EHU.
Ins i u ional Re iew Boa d S a emen :
This wo k did no in ol e humans o animals and he e o e
i did no equi e he Ins i u ional Re iew Boa d S a emen and app o al.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen :
Da a a ailable om he co esponding au ho upon easonable eques .
Senso s 2022,22, 8357 9 o 10
Acknowledgmen s:
M.N.V. is g a e ul o K asnoya sk Regional Cen e o Resea ch Equipmen o
Fede al Resea ch Cen e «K asnoya sk Science Cen e SB RAS» o he TEM s udies suppo . Selec ed
measu emen s (XRD and magne ic measu emen s) we e made a SGIKER Se ices o UPV-EHU.
We hank I. O ue o special suppo . The au ho s wish o hank he anonymous e e ees o hei
commen s and sugges ions.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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