Ci a ion: Ku lyandskaya, G.V.;
Lezama, L.; Pasynko a, A.A.;
Volchko , S.O.; Lukshina, V.A.;
La añaga, A.; Dmi ie a, N.V.;
Timo ee a, A.V.; O ue, I. Amo phous
FeCoC SiB Ribbons wi h Tailo ed
Aniso opy o he De elopmen o
Magne ic Elemen s o High
F equency Applica ions. Ma e ials
2022,15, 4160. h ps://doi.o g/
10.3390/ma15124160
Academic Edi o s: Ma eo Tonezze
and Da ide Ba eca
Recei ed: 5 May 2022
Accep ed: 10 June 2022
Published: 12 June 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-
ia ions.
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/
4.0/).
ma e ials
A icle
Amo phous FeCoC SiB Ribbons wi h Tailo ed Aniso opy o
he De elopmen o Magne ic Elemen s o High
F equency Applica ions
Galina V. Ku lyandskaya 1,2,*, Luis Lezama 3,4 , Anna A. Pasynko a 2,5 , S anisla O. Volchko 2,
Ve a A. Lukshina 6, Ai o La añaga 4, Na alia V. Dmi ie a 6, Anas asia V. Timo ee a 2,5 and Iñaki O ue 4
1Depa men o Elec ici y and Elec onics, Basque Coun y Uni e si y (UPV/EHU), 48940 Leioa, Spain
2Ins 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;
[email p o ec ed] (A.A.P.); s anisla [email p o ec ed] (S.O.V.); [email p o ec ed] (A.V.T.)
3Depa men o Ino ganic Chemis y, Basque Coun y Uni e si y (UPV/EHU), 48940 Leioa, Spain;
[email p o ec ed]
4Los Se icios Gene ales de In es igación (SGIKER), Basque Coun y Uni e si y UPV/EHU,
48940 Leioa, Spain; ai o [email p o ec ed] (A.L.); [email p o ec ed] (I.O.)
5
Labo a o y o Ad anced Magne ic Ma e ials, Ins i u e o Me al Physics UD RAS, 620108 Eka e inbu g, Russia
6Mic omagne ism Labo a o y Ins i u e o Me al Physics UD RAS, 620108 Eka e inbu g, Russia;
[email p o ec ed] (V.A.L.); [email p o ec ed] (N.V.D.)
*Co espondence: ku lyandskaya.g @up .eus
Abs ac :
The e omagne ic esonance (FMR) in he equency ange o 0.5 o 12.5 GHz has been
in es iga ed as a unc ion o ex e nal magne ic ield o apidly quenched Fe
3
Co
67
C
3
Si
15
B
12
amo -
phous ibbons wi h di e en ea u es o he e ec i e magne ic aniso opy. Th ee s a es o he ibbons
we e conside ed: as-quenched wi hou any ea men ; a e elaxa ion annealing wi hou s ess a
he empe a u e o 350
◦
C du ing 1 h; and a e annealing unde speci ic s ess o 230 MPa a he
empe a u e o 350
◦
C du ing 1 h. Fo FMR measu emen s, we adap ed a echnique p e iously p o-
posed and es ed o he case o mic owi es. He e, amo phous ibbons we e s udied using he sample
holde based on a comme cial SMA connec o . On he basis o he measu emen s o he e lec ion
coe icien S
11,
he o al impedance including i s eal and imagina y componen s was de e mined
o be in he equency ange o 0.5 o 12.5 GHz. In o de o con i m he alidi y o he p oposed
echnique, FMR was also measu ed by he ce i ied ca i y pe u ba ion echnique using a comme cial
B uke spec ome e ope a ing a X-band equency o 9.39 GHz. As pa o he cha ac e iza ion
o he ibbons used o mic owa e measu emen s, compa a i e analysis was pe o med o X- ay
di ac ion, op ical mic oscopy, ansmission elec on mic oscopy, induc i e magne ic hys e esis
loops, ib a ing sample magne ome y, magne o-op ical Ke e ec (including magne ic domains)
and magne oimpedance da a o o all samples.
Keywo ds:
amo phous ibbons; magne ic aniso opy; magne iza ion p ocess; magne oimpedance;
e omagne ic esonance; magne ic ield senso s; mic owa e abso p ion
1. In oduc ion
Rapidly quenched amo phous and nanoc ys alline ibbons we e he subjec o in en-
si e esea ch in he las h ee decades [
1
–
3
]. Special in e es in his kind o ma e ial can
be explained by hei ex ensi e use in p oduc ion echniques. I is easonably s able and
applicable in a wide a ie y o composi ions, and low con amina ion can be ensu ed. In
addi ion, he ibbon’s p ope ies can be modi ied by he pos p epa a ion ea men s ac-
co ding he pa icula applica ion [
3
–
5
]. Among o he s, Co-based amo phous ibbons wi h
close- o-ze o magne os ic ion we e ex ensi ely s udied wi h he ocus on hei applica ions
o wound co e in he ield o ans o me s, wo king a equency le els o hund eds Hz
and magne ic senso s ocused on he de ec ion o small magne ic ields [6–8].
Ma e ials 2022,15, 4160. h ps://doi.o g/10.3390/ma15124160 h ps://www.mdpi.com/jou nal/ma e ials
Ma e ials 2022,15, 4160 2 o 20
One o he mos sensi i e e ec s o small magne ic ield senso applica ions is mag-
ne oimpedance (MI). The MI phenomenon consis s o he change in he o al impedance
o a e omagne ic conduc ing sample unde applica ion o an ex e nal magne ic ield (H)
and low o a high equency al e na ing cu en [
4
,
9
,
10
]. Makho kin e al. epo ed he
i s ibbon-based al e na ing cu en magne ic senso p o o ype in [
11
]. They in oduced
ibbon-based p o o ypes sui able o magne ic biosensing bo h in label- ee and magne ic
label de ec ion egimes [
12
,
13
]. In he la e , he co osion s abili y was e y impo an and
composi ions wi h ch omium o molybdenum [
14
–
16
] we e conside ed o ake accoun
o he need o low o high co osion. Fo he CoFeC SiB composi ion, he bes esul s
we e ob ained a e s ess annealing, and a sensi i i y wi h espec o he applied ield o
he o de o 200%/Oe was achie ed [
17
]. This was made possible by ho ough p e ious
s udies on he annealing condi ions: he empe a u e (T), annealing ime ( ) and speci ic
load (
σ
) we e ca e ully adjus ed [
18
]. Howe e , pas esea ch ocused on he unde s anding
o he dependence o magne ic p ope ies, e ec i e magne ic aniso opy and MI o a he
high alues o he induced magne ic aniso opy cons an (K
u
) abo e 2000 e g/cm
3
. Fo
he empe a u e o he s ess annealing o 350
◦
C, he e is only one s udy o MI wi h low
speci ic load alue unde he ollowing condi ions: = 1 h and
σ
= 210 MPa. This esul ed
in o ma ion o ans e se magne ic aniso opy wi h e y low aniso opy dis ibu ion and
high MI sensi i i y o he o de o 200%/Oe o he equency o a lowing cu en ( ) o
abou 10 MHz and samples o 10 cm in leng h [
17
]. Howe e , o he condi ions we e no
in es iga ed, and he ansi ion om he longi udinal o he ans e se aniso opy was no
eally unde s ood.
As-quenched Co-based ibbons a e cha ac e ized by he longi udinal magne ic aniso opy
wi h he in-plane magne ic aniso opy axis along he long side o he ibbon. Relaxa ion
annealing a empe a u es below he c ys alliza ion empe a u e o he pa icula alloy
esul s in he educ ion o he le el o he as-quenched s esses bu does no change he
ype o he magne ic aniso opy, which con inues o be longi udinal. S ess annealing wi h
a nega i e magne ic aniso opy cons an esul s in o ma ion o he ans e se uniaxial
magne ic aniso opy, wi h he induced aniso opy axis o ien ed along he wid h o he
ibbon and, again, he educ ion o he le el o he as-quenched s esses [
19
,
20
]. Such a
ansi ion ( om he longi udinal o ans e se e ec i e aniso opy) can be s udied in e ms
o he MI e ec . Al hough he concep o using MI as an “ins umen ” was p oposed du ing
he i s yea s o MI s udies, he numbe o sys ema ic MI wo ks o he p ecise e alua ion
o aniso opy ea u es is s ill limi ed.
The MI phenomenon has been unde s ood in he con ex o classical elec odynamics
and is well explained on he basis o he dependence o skin pene a ion dep h (
δ
) on
he dynamic magne ic pe meabili y (
µ
) o a e omagne ic conduc o . Tha is, high e-
quency impedance depends on he skin pene a ion dep h, which in u n depends on he
magne ic pe meabili y and applied magne ic ield: Z = Z(
δ
( ,
µ
(H)) [
1
–
4
]. The e ha e also
been special s udies ela ed o he connec ion be ween MI and ano he well-known high
equency phenomenon— e omagne ic esonance (FMR). FMR is he esonan abso p ion
o mic owa e adia ion in magne ic ma e ial [
21
,
22
]. Yelon e al. p oposed he poin o
iew ha calcula ions o magne oimpedance and o e omagne ic esonance esponse a e
igo ously equi alen in he case o a pla e o ibbon [
23
]. Expe imen al analysis included an
e alua ion o he changes in he a enua ion coe icien o a coaxial line, ha ing a NiFeMo
wi e as he cen al conduc o o he equency ange o 100 o 6000 MHz. Howe e , he num-
be o s udies o bo h MI and FMR emain e y limi ed. Among o he easons, b oadband
measu emen echniques we e no widely a ailable. They ha e become mo e accessible
and applied o e y di e en ypes o so magne ic ma e ials only in he las one and hal
decade [
24
–
27
]. Fo example, El Kammouni e al. s udied FMR o amo phous mic owi es
using a ne wo k analyze (Agilen E8362B) in he equency ange o up o 12GHz a a
cons an inciden powe o
−
10dBm using a comme cial SMA connec o whe e he inne
pin had been emo ed in o de o a oid adia ion e ec s [
28
]. The same echnique was
employed by Ku lyandskaya e al. o he case o CuBe/FeCoNi elec opla ed wi es in
Ma e ials 2022,15, 4160 3 o 20
he equency ange o up o 14 GHz [
29
]. In he la e , bo h FMR and MI measu emen s
we e p esen ed.
In his p esen wo k, we p oposed o design and es he b oadband measu emen
echnique based on he employmen o coaxial wa eguide, and a sample holde based on a
comme cial SMA connec o . The e lec ion coe icien S
11
measu emen s allowed accu a e
de ini ion o he o al impedance a ia ion in he equency ange o 0.5 o 12.5 GHz. Special
a en ion was paid on he selec ion and de ailed cha ac e iza ion o he model samples
p epa ed ha we e based on a single ba ch Fe
3
Co
67
C
3
Si
15
B
12
amo phous ibbon. The
amo phous s uc u e was s udied, and he s a ic and dynamic magne ic p ope ies o he
ibbons wi h di e en ea u es o e ec i e magne ic aniso opy nea he s a e o ansi ion
om longi udinal o a ans e se magne ic aniso opy we e compa a i ely analyzed using
di e en echniques p io o he mic owa e es s.
2. Ma e ials and Me hods
Amo phous ibbons wi h nominal composi ion o Fe
3
Co
67
C
3
Si
15
B
12
we e p epa ed
by apid quenching on o a Cu d um. The leng h o one ba ch was as much as se e al me e s
wi h e y close pa ame e s o he wid h and hickness o e he whole ba ch. Acco ding o
he li e a u e [
3
,
15
], he ibbons o such composi ion ha e e y small nega i e sa u a ion
magne os ic ion cons an (
λS
~10
−7
) and he e o e hey can be used o s ess annealing and
o ma ion o he ans e se magne ic aniso opy sui able o MI applica ions
[13,19,30–32]
.
Apa om he as-quenched samples in he ini ial s a e (AP), he samples ha we e consid-
e ed we e ob ained by he elaxa ion annealing (AN) a 350
◦
C du ing 1 h wi hou load and
s ess annealing (SA) du ing 1 h and speci ic load o 230 MPa.
Selec ed composi ion di e s om he widely s udied Fe
4
Co
69
Si
15
B
12
[
33
] ma e ial
by he p esence o ch omium making i e y s able in special en i onmen al condi ions
including chemically ac i e bio luids [
6
]. Fe
3
Co
67
C
3
Si
15
B
12
ibbons ha e a sa u a ion
magne iza ion M
s
= 365 G, and a Cu ie empe a u e o 160
◦
C which is qui e low in
compa ison wi h hei c ys alliza ion empe a u e o 570
◦
C. This means ha selec ed
hea ea men s a 350
◦
C we e pe o med a he empe a u e being app oxima ely 0.6 o
he c ys alliza ion empe a u e. Fo he majo i y o apidly quenched amo phous alloys,
such hea ea men s do no change he amo phous s uc u e o he ma e ial [
1
,
34
,
35
].
Fo example, Dmi ie a e al. [
33
] had s udied he Fe
5
Co
72
Si
15
B
8
alloy in he ini ial s a e,
a e elaxa ion o s ess annealing. Acco ding o magne ic measu emen s and TEM da a
analysis, all ma e ials we e amo phous bu he change o he s uc u e was obse ed a e
annealing a 430
◦
C. The Fe
5
Co
72
Si
15
B
8
alloy has a much lowe c ys alliza ion empe a u e
o 418
◦
C in compa ison wi h ha o Fe
3
Co
67
C
3
Si
15
B
12
, and a co esponding a io o 1.02
be ween he empe a u e o he hea ea men and c ys alliza ion empe a u e.
The empe a u e and ime o he annealing we e selec ed on he basis o p e ious s ud-
ies [
3
,
17
,
18
]. Howe e , he speci ic load was modi ied, namely inc eased up o
σ= 230 MPa
in compa ison wi h da a in [
18
]. The ollowing a gumen s we e used o he selec ed condi-
ions. Dmi ie a e al. had shown linea dependence o Ku(
σ
) o he speci ic load ange
400–1400 MPa. The only speci ic load in he in e al 0–400 MPa was 210 MPa epo ed by
Ku lyandskaya e al. [
17
]. Howe e , his was ollowing he linea dependence o Ku(
σ
)
wi h a somewha lowe eg ession. We he e o e decided o sligh ly inc ease he speci ic
load in he p esen s udy up o
σ
= 230 MPa in keeping wi h he join da a analysis epo ed
in [
17
,
18
]. Hea ea men s (bo h AN and SA) we e done in he sel -made e ical u nace
wi h a he mocouple empe a u e con ol using a calib a ed sys em.
The wid hs and su ace ea u es o he ibbons om bo h sides ( he ee and weal
sides) we e s udied by op ical mic oscopy (Nicon L-UEPI mic oscope, Bos on Indus ies,
Inc., MA). The geome ical pa ame e s o he samples we e de ined as ollows: wid h—d,
hickness—h and leng h—l (Figu e 1).
Ma e ials 2022,15, 4160 4 o 20
Ma e ials 2022, 15, 4160 4 o 20
(a) (b)
Figu e 1. (a) Schema ic desc ip ion o amo phous ibbon sample wi h dimensions l × d × h: H is he
ex e nal magne ic ield applied du ing magne ic and GMI measu emen s, howe e o FMR meas-
u emen s in he esonance ca i y bo h in-plane and ou -o -plane o ien a ions o he ex e nal mag-
ne ic ield we e used; EMA
1
co esponds o he easy magne iza ion axis o he sample in ini ial s a e;
EMA
2
co esponds o he easy magne iza ion axis o he sample a e elaxa ion annealing; and
EMA
3
co esponds o he easy magne iza ion axis o he sample a e TMO. (b) The scheme o he
b oadband mic owa e measu emen s using ZVA VNA o he coaxial posi ion o a sample; H is an
ex e nal magne ic ield.
The amo phous s a e o he samples in all condi ions was checked by X- ay di ac-
ion echnique. These s udies we e pe o med by ope a ing he DISCOVER D8 di ac-
ome e (B uke , Leide do p, The Ne he lands) a 40 kV and 40 mA, using Cu-Kα adia-
ion (wa eleng h o 1.5418 Å), a g aphi e monoch oma o and a scin illa ion de ec o . Rib-
bons we e cu in o pieces o abou 1 cm and placed on o ze o signal Si pla e.
In addi ion, he ibbons o all ypes we e s udied by ansmission elec on mic os-
copy using JEM 200CX elec on mic oscope (JEOL, F eising, Ge many). The samples o
TEM analysis we e p epa ed by elec opolishing wi h H
3
PO
4
+ C O
3
esh elec oly e. Bo h
he b igh ield image o e ela ion o he mic os uc u al ea u es and he mic odi ac-
ion pa e ns we e collec ed.
All magne ic and mic owa e measu emen s we e made a oom empe a u e. Mag-
ne ic measu emen s o he hys e esis loops M(H) we e ca ied ou by bo h a con en ional
induc i e sys em and a ib a ing sample magne ome e (VSM, Lake Sho e 7404, Wes e -
ille, OH, USA) in he up o ±1.8 kOe ield ange. The induc i e hys e esis loops we e
measu ed by applying a uni o m ex e nal magne ic ield in he plane o he ibbons o 45
mm leng h, i.e., he same leng h as he ones used o MI measu emen s (Figu e 1). How-
e e , as FMR s udies in bo h sys ems employed we e made o sho samples o 5 mm
leng h, apa om he induc i e hys e esis loops, VSM da a we e also collec ed and ana-
lyzed o samples o 5 mm leng h. In he VSM case, bo h in-plane and ou -o -plane (Figu e
1a) we e ca ied ou . In addi ion, magne o-op ical Ke e ec (MOKE) was employed o
magne ic measu emen s and obse a ion o magne ic domains. The hys e esis loops we e
also measu ed by Ke mic oscopy (E ico, D esden, Ge many) by plo ing he a e age
image in ensi y as a unc ion o magne ic ield.
The magne oimpedance measu emen s we e pe o med using a “mic os ip” line
wi h 50 Ohm cha ac e is ic impedance. The elec ical con ac s we e made by a conduc i e
sil e pain o p ope ins alla ion o he ibbon in o mic owa e holde . The ex e nal mag-
ne ic ield o up o H
max
± 110 Oe was c ea ed by a pai o Helmhol z coils. The o al im-
pedance (Z) was calcula ed om he e lec ion coe icien S
11
, a e p ope calib a ion and
ma hema ical sub ac ion o he mic owa e ix u e con ibu ions. S
11
(H) alues we e
measu ed by 4294A (Agilen /Keysigh Technologies, San a Rosa, CA, USA), using an ou -
pu powe o 0 dB. This means ha he ampli ude o he exci a ion cu en ac oss he sam-
ple was abou 10 mA. An ex e nal magne ic ield was applied in-plane o he ibbon along
he ibbon axis (long side o he ibbon) and in he same di ec ion as he lowing cu en .
The con igu a ion o he longi udinal MI employed was he same con igu a ion as o
FMR: he adio equency ield c ea ed by he al e na ing cu en was pe pendicula o
l
h
I
ac
H, EMA
1
,EMA
2
EMA
3
in plane
ou o plane
Figu e 1.
(
a
) Schema ic desc ip ion o amo phous ibbon sample wi h dimensions l
×
d
×
h: H is
he ex e nal magne ic ield applied du ing magne ic and GMI measu emen s, howe e o FMR
measu emen s in he esonance ca i y bo h in-plane and ou -o -plane o ien a ions o he ex e nal
magne ic ield we e used; EMA
1
co esponds o he easy magne iza ion axis o he sample in ini ial
s a e; EMA
2
co esponds o he easy magne iza ion axis o he sample a e elaxa ion annealing; and
EMA
3
co esponds o he easy magne iza ion axis o he sample a e TMO. (
b
) The scheme o he
b oadband mic owa e measu emen s using ZVA VNA o he coaxial posi ion o a sample; H is an
ex e nal magne ic ield.
The amo phous s a e o he samples in all condi ions was checked by X- ay di ac ion
echnique. These s udies we e pe o med by ope a ing he DISCOVER D8 di ac ome e
(B uke , Leide do p, The Ne he lands) a 40 kV and 40 mA, using Cu-K
α
adia ion (wa e-
leng h o 1.5418 Å), a g aphi e monoch oma o and a scin illa ion de ec o . Ribbons we e
cu in o pieces o abou 1 cm and placed on o ze o signal Si pla e.
In addi ion, he ibbons o all ypes we e s udied by ansmission elec on mic oscopy
using JEM 200CX elec on mic oscope (JEOL, F eising, Ge many). The samples o TEM
analysis we e p epa ed by elec opolishing wi h H
3
PO
4
+ C O
3
esh elec oly e. Bo h he
b igh ield image o e ela ion o he mic os uc u al ea u es and he mic odi ac ion
pa e ns we e collec ed.
All magne ic and mic owa e measu emen s we e made a oom empe a u e. Mag-
ne ic measu emen s o he hys e esis loops M(H) we e ca ied ou by bo h a con en ional
induc i e sys em and a ib a ing sample magne ome e (VSM, Lake Sho e 7404, Wes e ille,
OH, USA) in he up o
±
1.8 kOe ield ange. The induc i e hys e esis loops we e measu ed
by applying a uni o m ex e nal magne ic ield in he plane o he ibbons o 45 mm leng h,
i.e., he same leng h as he ones used o MI measu emen s (Figu e 1). Howe e , as FMR
s udies in bo h sys ems employed we e made o sho samples o 5 mm leng h, apa om
he induc i e hys e esis loops, VSM da a we e also collec ed and analyzed o samples o
5 mm leng h. In he VSM case, bo h in-plane and ou -o -plane (Figu e 1a) we e ca ied
ou . In addi ion, magne o-op ical Ke e ec (MOKE) was employed o magne ic measu e-
men s and obse a ion o magne ic domains. The hys e esis loops we e also measu ed by
Ke mic oscopy (E ico, D esden, Ge many) by plo ing he a e age image in ensi y as a
unc ion o magne ic ield.
The magne oimpedance measu emen s we e pe o med using a “mic os ip” line
wi h 50 Ohm cha ac e is ic impedance. The elec ical con ac s we e made by a conduc i e
sil e pain o p ope ins alla ion o he ibbon in o mic owa e holde . The ex e nal
magne ic ield o up o H
max ±
110 Oe was c ea ed by a pai o Helmhol z coils. The o al
impedance (Z) was calcula ed om he e lec ion coe icien S
11
, a e p ope calib a ion
and ma hema ical sub ac ion o he mic owa e ix u e con ibu ions. S
11
(H) alues we e
measu ed by 4294A (Agilen /Keysigh Technologies, San a Rosa, CA, USA), using an
ou pu powe o 0 dB. This means ha he ampli ude o he exci a ion cu en ac oss he
sample was abou 10 mA. An ex e nal magne ic ield was applied in-plane o he ibbon
along he ibbon axis (long side o he ibbon) and in he same di ec ion as he lowing
cu en . The con igu a ion o he longi udinal MI employed was he same con igu a ion as
o FMR: he adio equency ield c ea ed by he al e na ing cu en was pe pendicula
Ma e ials 2022,15, 4160 5 o 20
o he di ec ion o he applied ield. Fo he con enience o compa ison o expe imen al
esul s wi h he da a epo ed by o he esea che s, he ollowing MI a io was used:
∆Z/Z = 100% ·(Z(H) −Z(Hmax))/Z(Hmax)). (1)
In addi ion, he sensi i i y wi h espec o he cons an applied ield was de ined
as ollows:
∆(∆Z/Z)(H)= (∆Z/Z (H1) −∆Z/Z (H2))/|H1−H2|, (2)
whe e H
1
is he smalles and H
2
is he bigges alues o he applied ield o he in e al o
linea dependence o ∆Z/Z (H), i.e., he in e al o which he sensi i i y was calcula ed.
Fe omagne ic esonance measu emen s a mic owa e equency = 9.39 GHz we e
ca ied ou on an ELEXSYS 500 B uke spec ome e (B uke , Tampa, FL, USA) ope a ing by
s anda d ca i y pe u ba ion echnique p o ocol [
22
]. Bo h in-plane and ou -o -plane con-
igu a ions o he applica ion o he ex e nal magne ic ield we e used. The maximum ield
alue in ensi y was as high as 4.0 kOe (su icien o magne ic sa u a ion o he ibbons).
In p e ious wo ks [
24
,
36
], we p oposed a way o measu e he mic owa e p ope ies o
mic owi es ha a e elec opla ed and apidly quenched wi es in he coaxial line. The es
ix u es, based on he SMA-holde o 1–15 GHz ange, we e designed and es ed ( o he
cylind ical con igu a ion). All es ix u es ha e indi idual cha ac e is ics such as e minal
layou , dielec ic cons an o insula o , g ound pla e and so on. Howe e , each one can be
ma ched o he coaxial line wi h 50-Ohm cha ac e is ic impedance acco ding o he es ab-
lished calib a ion p ocess by using open, sho and load e e ence e mina ions connec ed
o he es po . Each o he e mina ions is measu ed, and he ob ained impedance alues
o hese e e ence e mina ions a e analyzed in he o m o ec o impedance coo dina es
and a Smi h cha . Compensa ion p ocedu es allow he elimina ion o e o s co esponding
o es ix u e con ibu ions and o elec ical leng h. The la e compensa ion elimina es
measu emen e o s due o phase shi in he coaxial sec ion [36].
He e we desc ibe he possibili y o adap ing a p e iously designed sys em o p ecise
measu emen s o he samples in he shape o p isms (amo phous ibbons) in a coaxial
wa eguide. The mic owa e p ope ies o he e omagne ic conduc ing ibbons we e
measu ed by he sys em based on a ZVA-67 ec o ne wo k analyze (VNA) (Rohde &
Schwa z, Munich, Ge many) using he one po me hod (Figu e 1b). The elec omagne
connec ed o he powe supply TDK-Lambda GEN100-50 was capable o c ea ing an
ex e nal magne ic ield wi h an in ensi y o up o 13 kOe. Howe e , as amo phous ibbons
a e so e omagne s, he maximum alue o he ex e nal magne ic ield (su icien o
he ibbons’ magne ic sa u a ion) was as high as 4.0 kOe. The powe ou pu o he signal
o he ZVA analyze was se a a le el o 0.1 mW, based on he maximum signal- o-noise
a io c i e ion. In addi ion, a his le el o powe , he ampli ude alues o he in ensi y o
an al e na ing magne ic ield a e signi ican ly smalle han he alue o he in ensi y o a
ield gene a ed by a pe manen magne . Since no di e ence was obse ed be ween he
posi i e and nega i e b anches o measu emen s, he g aphs discussed he e p esen he
alues ob ained in he posi i e ield in e al o 0.0–4.0 kOe only.
The measu ed samples we e placed on o a holde made o a comme cial connec o
SMA S-2454 (Mouse Elec onics, Inc., Mans ield, TX, USA) connec ed o a coaxial cable
(Pas e nack PE3C0752) ia a BN533795 adap e . The leng h o he samples o he mic owi es
was chosen based on esul s o modeling. Since a ZVA-67 ec o analyze measu es he
ampli ude and phase o he e lec ed signal as well, he alue o he pa ame e S
11
can be
compensa ed o he leng h k o he adap e wi h he holde . Full one-po calib a ion was
used o compensa e he coaxial cable [
24
,
36
]. Al hough he ange o he measu emen s using
SMA in combina ion wi h VNA is 0.1 o 15 GHz, a e ca e ul modeling o he comple e
coaxial wa eguide pa ame e s wi h speci ic geome y used by High-F equency S uc u e
Simula o so wa e, he app op ia e equency ange was conside ed o be 0.5–12.5 GHz.
The e lec ion coe icien S
11
alues we e measu ed as a unc ion o he ex e nal mag-
ne ic ield and equency. These da a can be used o es ima e such pa ame e s as mic owa e
Ma e ials 2022,15, 4160 6 o 20
abso p ion o e omagne ic samples. The nex s ep was o de e mine he impedance o
he sample Z wi h bo h eal and imagina y pa s. This equi ed he compensa ion o he
pa ame e S11 o he dis ance k:
S‘
11 =S11 ×ei2βk(3)
whe e S‘
11 is he alue o he pa ame e o he sca e ing ma ix in he plane o he sample;
S11
is he alue o he pa ame e o he sca e ing ma ix in he calib a ion plane;
β
= 2
π
/
λ
is he wa enumbe ;
λ
is he wa eleng h; and k is he elec ical dis ance o he coaxial
ansmission line. The sample impedance can he e o e be de e mined as ollows:
Z=Z0×1+S‘
11
1−S‘
11
(4)
whe e Z
0
= 50 Ohm is he impedance o he coaxial line. The change in he eac i e pa o
he impedance
∆
X( , H) = X( , H)
−
X( , 0) and loss esis ance
∆
R( , H) = R( , H)
−
R( , 0)
unde applica ion o an ex e nal cons an magne ic ield we e also aken in o accoun o
he analysis o he obse ed esonance phenomena.
3. Resul s and Discussion
Table 1summa izes he da a on he s a es and ypes o ea men s applied o he
samples, and collec s selec ed magne ic pa ame e s. In a i s s ep, he s uc u e and
geome ical pa ame e s we e de ined. Figu e 2a,b show he gene al iew o he su ace
o he ibbons om bo h sides. The su ace ea u es we e no changed du ing he hea
ea men s and he samples did no show any measu able elonga ion o he condi ions
unde conside a ion. One can see ha hey ha e qui e uni o m su ace ea u es and well-
de ined wid h which was measu ed in he op ical mic oscope a e calib a ion. The wid h
o he ibbons was 0.80 ±0.02 mm and hei hickness was 0.24 ±0.01 µm.
The XRD analysis summa y is gi en in Figu e 2b. All ypes o he ibbons p esen ed
a clea amo phous s uc u e and e y b oad di ac ion peaks, 2
θ
(
◦
) in a ange o a ound
43–46
◦
(Figu e 2c), con i ming he absence o long ange o de ing and c ys alline phases in
all cases unde conside a ion.
Such a esul was highly expec ed o he ibbons o his composi ion [
17
] as he
selec ed speci ic load alue was e y small. In addi ion, i was no ed ha mechanical
p ope ies o he samples we e no isibly changed. The absence o signi ican changes
(such as c ys alliza ion) in he amo phous s uc u e was also con i med by he analysis
o TEM da a. Figu e 3shows elec on di ac ion pa e ns and elec on mic og aphs
(
×
20,000) o di e en samples o he amo phous Fe
3
Co
67
C
3
Si
15
B
12
alloy in all s a es
unde conside a ion: AP, AN and SA.
Acco ding o elec on di ac ion da a, he samples o Fe
3
Co
67
C
3
Si
15
B
12
alloy in all
s a es a e amo phous as hey ha e no p ecipi a es o c ys alline phases. Acco ding o he
exis ing li e a u e, s uc u al inhomogenei ies can be o med in an amo phous alloy upon
annealing a high empe a u es ollowing he ule ha he highe he empe a u e, he
highe he con en o o med inhomogenei ies. The inhomogenei ies can ha e di e en
chemical composi ion, size and ea u es o a sho - ange o de . I was p e iously shown
ha he p epa ed amo phous ibbons ha e less uni o m s uc u e in compa ison wi h
ibbons a e s ess annealing a a empe a u e o abou 300
◦
C. The non-s oichiome y
in he local composi ion and he endency o a omic chemical o de ing can esul in he
o ma ion o clus e s ha a e no conside ed as he i s s age o c ys alliza ion bu a he
can inc ease he s abili y o he amo phous ma e ial [33].
Ma e ials 2022,15, 4160 7 o 20
Table 1.
Desc ip ion o he ypes and s a es o apidly quenched Fe
3
Co
67
C
3
Si
15
B
12
ibbons and
condi ions o hei he mal ea men s. Selec ed pa ame e s, ob ained o long samples o 45 mm:
K
u
—e ec i e magne ic aniso opy cons an , H
c
—coe ci i y, H
a
—magne ic aniso opy ield and
Ms—sa u a ion magne iza ion.
Sample Desc ip ion Ku, e g/cm3Hc, Oe Ha, Oe Ms, Gs
AP As-p epa ed 0 0.1 0.1 300
AN Annealed a 350 ◦C wi hou s ess du ing 1 h 0 0.1 0.1 300
SA S ess annealing a 350 ◦C wi hou s ess du ing 1 h o
speci ic s ess o 230 MPa 500 0.2 3.3 300
Ma e ials 2022, 15, 4160 7 o 20
(a)
(b)
10 20 30 40 50 60 70 80 90
AP
AN
SA
In ensi y (a b. un.)
2 (o)
0300 600 900
0.000
0.005
N
Sho
Long
(c)
(d)
Figu e 2. Gene al iew o he su ace o amo phous ibbons ob ained by op ical mic oscopy: ee
side (a) and weal side (b) o he Fe3Co67C 3Si15B12 amo phous ibbon. (c) XRD spec a o all ypes o
he samples. (d) Demagne izing ac o s calcula ed o selec ed alues o magne ic suscep ibili y χ
and wo di e en leng hs o he samples: l = 5 mm o “sho ” and l = 45 mm o “long” samples.
Acco ding o elec on di ac ion da a, he samples o Fe3Co67C 3Si15B12 alloy in all
s a es a e amo phous as hey ha e no p ecipi a es o c ys alline phases. Acco ding o he
exis ing li e a u e, s uc u al inhomogenei ies can be o med in an amo phous alloy upon
annealing a high empe a u es ollowing he ule ha he highe he empe a u e, he
highe he con en o o med inhomogenei ies. The inhomogenei ies can ha e di e en
chemical composi ion, size and ea u es o a sho - ange o de . I was p e iously shown
ha he p epa ed amo phous ibbons ha e less uni o m s uc u e in compa ison wi h ib-
bons a e s ess annealing a a empe a u e o abou 300 °C. The non-s oichiome y in he
local composi ion and he endency o a omic chemical o de ing can esul in he o -
ma ion o clus e s ha a e no conside ed as he i s s age o c ys alliza ion bu a he can
inc ease he s abili y o he amo phous ma e ial [33].
Model conside a ions we e gi en o he ole o he mic o-inhomogenei ies con ib-
u ing o he s uc u al changes unde uniaxial ensile s esses. Clus e s may become ani-
so opic in shape and a e cooling down due o di e ence in he he mal expansion coe -
icien s o he amo phous ma ix and clus e s. Mo eo e , he magne oelas ic aniso opy
a he in e ace be ween he ma ix and he clus e s may o ien he magne iza ion in he
ans e se di ec ion, i.e., along he sho side o he ibbon [35]. Howe e , he objec i es
o he p esen wo k do no include such a undamen al ques ion as he na u e o he in-
duced magne ic aniso opy in he amo phous apidly-quenched e omagne s. He e, we
use di e en s uc u al and magne ic echniques o ad anced cha ac e iza ion o he
samples, which a e p epa ed o igo ous es ing o he mic owa e abso p ion echnique
p oposed o b oadband e omagne ic esonance measu emen s.
0.5 mm 0.5 mm
Figu e 2.
Gene al iew o he su ace o amo phous ibbons ob ained by op ical mic oscopy: ee
side (
a
) and weal side (
b
) o he Fe
3
Co
67
C
3
Si
15
B
12
amo phous ibbon. (
c
) XRD spec a o all ypes
o he samples. (
d
) Demagne izing ac o s calcula ed o selec ed alues o magne ic suscep ibili y
χ
and wo di e en leng hs o he samples: l = 5 mm o “sho ” and l = 45 mm o “long” samples.
Model conside a ions we e gi en o he ole o he mic o-inhomogenei ies con ibu ing
o he s uc u al changes unde uniaxial ensile s esses. Clus e s may become aniso opic
in shape and a e cooling down due o di e ence in he he mal expansion coe icien s
o he amo phous ma ix and clus e s. Mo eo e , he magne oelas ic aniso opy a he
in e ace be ween he ma ix and he clus e s may o ien he magne iza ion in he ans e se
di ec ion, i.e., along he sho side o he ibbon [
35
]. Howe e , he objec i es o he p esen
wo k do no include such a undamen al ques ion as he na u e o he induced magne ic
aniso opy in he amo phous apidly-quenched e omagne s. He e, we use di e en
s uc u al and magne ic echniques o ad anced cha ac e iza ion o he samples, which
a e p epa ed o igo ous es ing o he mic owa e abso p ion echnique p oposed o
b oadband e omagne ic esonance measu emen s.
Ma e ials 2022,15, 4160 8 o 20
Ma e ials 2022, 15, 4160 8 o 20
Figu e 3. Mic odi ac ion pa e ns (a,c,d) and elec on mic og aphs (b,d,e) o Fe
3
Co
67
C
3
Si
15
B
12
ap-
idly-quenched ibbons in ollowing s a es: AP (a,b); AN (c,d); and SA (e, ) (see also Table 1).
We now discuss s a ic magne ic p ope ies o he samples o di e en leng hs. The
size o he unc ional elemen s o apidly-quenched ibbons can a y signi ican ly om
ens o cm o wound ans o me s o a ew mm o sensi i e elemen o he magne ic ield
senso s. The samples o 45 mm leng h (denomina ed as “long” samples) we e p epa ed
o magne oimpedance es ing. Thei s a ic magne ic hys e esis loops we e measu ed us-
ing an induc i e echnique. Bo h VSM and FMR echniques equi ed p epa a ion o he
“sho ” samples o 5 mm leng h. The leng h di e ence caused a change in he demagne -
izing ac o , a ec ing he alue o he e ec i e magne ic aniso opy on he ibbons o each
pa icula geome ic leng h.
In o de o ake in o accoun he di e ence in he geome y o he ibbons, we calcu-
la ed he demagne izing ac o s o he p isms wi h he co esponding geome ical pa am-
e e s o selec ed alues o magne ic suscep ibili y om 0 o 999. I is well known ha
demagne izing ac o s (N) o he objec s o such shapes can be calcula ed only app oxi-
ma ely [37]. Howe e , Chen e al. p oposed a use ul echnique o calcula ions o demag-
ne izing ac o s o ec angula [38] p isms, which was employed o N alue calcula ions
o he “sho ” and “long” ibbons unde conside a ion (Figu e 2d). One can see ha cal-
cula ed demagne izing ac o s a e signi ican ly highe in he case o he “sho ” ibbons
o all conside ed magne ic suscep ibili y alues.
Figu e 4a,b show he esul s o he measu emen s o induc i e hys e esis loops along
he long side o he ibbons. One can clea ly see ha AP and AN ibbons ha e longi udinal
Figu e 3.
Mic odi ac ion pa e ns (
a
,
c
,
d
) and elec on mic og aphs (
b
,
d
,
e
) o Fe
3
Co
67
C
3
Si
15
B
12
apidly-quenched ibbons in ollowing s a es: AP (a,b); AN (c,d); and SA (e, ) (see also Table 1).
We now discuss s a ic magne ic p ope ies o he samples o di e en leng hs. The
size o he unc ional elemen s o apidly-quenched ibbons can a y signi ican ly om
ens o cm o wound ans o me s o a ew mm o sensi i e elemen o he magne ic ield
senso s. The samples o 45 mm leng h (denomina ed as “long” samples) we e p epa ed o
magne oimpedance es ing. Thei s a ic magne ic hys e esis loops we e measu ed using an
induc i e echnique. Bo h VSM and FMR echniques equi ed p epa a ion o he “sho ”
samples o 5 mm leng h. The leng h di e ence caused a change in he demagne izing ac o ,
a ec ing he alue o he e ec i e magne ic aniso opy on he ibbons o each pa icula
geome ic leng h.
In o de o ake in o accoun he di e ence in he geome y o he ibbons, we cal-
cula ed he demagne izing ac o s o he p isms wi h he co esponding geome ical pa-
ame e s o selec ed alues o magne ic suscep ibili y om 0 o 999. I is well known
ha demagne izing ac o s (N) o he objec s o such shapes can be calcula ed only ap-
p oxima ely [
37
]. Howe e , Chen e al. p oposed a use ul echnique o calcula ions o
demagne izing ac o s o ec angula [
38
] p isms, which was employed o N alue calcula-
ions o he “sho ” and “long” ibbons unde conside a ion (Figu e 2d). One can see ha
calcula ed demagne izing ac o s a e signi ican ly highe in he case o he “sho ” ibbons
o all conside ed magne ic suscep ibili y alues.
Figu e 4a,b show he esul s o he measu emen s o induc i e hys e esis loops along
he long side o he ibbons. One can clea ly see ha AP and AN ibbons ha e longi udinal
Ma e ials 2022,15, 4160 9 o 20
magne ic aniso opy wi h e y simila shaped M(H) loops and e y small di e ence in he
ield ange o 0.1 o 0.3 Oe; and he sample a e elaxa ion annealing shows a sligh ly as e
app oach o magne ic sa u a ion. Bo h EMA
1
and EMA
2
a e pa allel o each o he and o
he long side o he ibbon.
Ma e ials 2022, 15, 4160 9 o 20
magne ic aniso opy wi h e y simila shaped M(H) loops and e y small di e ence in
he ield ange o 0.1 o 0.3 Oe; and he sample a e elaxa ion annealing shows a sligh ly
as e app oach o magne ic sa u a ion. Bo h EMA1 and EMA2 a e pa allel o each o he
and o he long side o he ibbon.
-5 0 5
-200
0
200
M (G)
H (Oe)
Induc i e, in plane
AP
AN
SA
-1 0 1
-200
0
200
M (G)
H (Oe)
Induc i e, in plane
AP
AN
SA
(a) (b)
-300 -200 -100 0 100 200 300
-200
0
200
M (G)
H (Oe)
In plane, VSM
AP
AN
SA
-5 0 5
-200
0
200
M (G)
H (Oe)
In plane, VSM
AP
AN
SA
(c) (d)
-15 -10 -5 0 5 10 15
-200
0
200
M (G)
H (kOe)
Ou o plane, VSM
AP
AN
SA
-4 -2 0 2 4
-200
0
200
M (G)
H (kOe)
Ou o plane, VSM
AP
AN
SA
(e) ( )
Figu e 4. Magne ic hys e esis loops o amo phous Fe3Co67C 3Si15B12 ibbons in di e en s a es, wi h
AP, AN and SA measu ed by: induc i e echnique (a,b); by VSM in he plane o he sample (c,d);
and ou -o -plane o he sample (e, ). Fo induc i e measu emen s, sample leng h was l = 45 mm and
o VSM samples, he leng h was l = 5 mm.
Figu e 4.
Magne ic hys e esis loops o amo phous Fe
3
Co
67
C
3
Si
15
B
12
ibbons in di e en s a es, wi h
AP, AN and SA measu ed by: induc i e echnique (
a
,
b
); by VSM in he plane o he sample (
c
,
d
); and
ou -o -plane o he sample (
e
,
). Fo induc i e measu emen s, sample leng h was l = 45 mm and o
VSM samples, he leng h was l = 5 mm.
Ma e ials 2022,15, 4160 16 o 20
pe u ba ion measu emen , which appea s o be e y close o he b oadband measu emen s
o co esponding he equency.
Ma e ials 2022, 15, 4160 16 o 20
Figu e 9a shows expe imen al 2(H es) dependences o all ibbon ypes and co e-
sponding i s o Equa ion (6) using expe imen al pa ame e s ob ained om magne ic
measu emen s. Bo h expe imen al cu es o all ypes and he i ed cu es show qui e
simila e olu ion, indica ing he high quali y o he p oposed me hod o e alua ion o
b oadband p ope ies.
He e we d aw a en ion o he ac ha , acco ding o HFSS simula ion, he app op i-
a e measu emen s ange was 0.5 o 12.5 GHz. Al hough Figu e 8a ep esen s he 2 ange
up o abou 14 GHz ( 2 200 GHz2), he da a abo e 12.5 GHz become less p ecise. The
dashed ec angula ame indica es his ange o de ia ions. In addi ion, he excellen
ma ch o ca i y pe u ba ion echnique da a is also shown by indica ing he posi ion o
he ca i y pe u ba ion measu emen , which appea s o be e y close o he b oadband
measu emen s o co esponding he equency.
0 1 2 3
0
50
100
150
200
Expe imen al Ki el i
AP AP
AN AN
SA SA
2 (GHz2)
H es (kOe)
- ca i y pe u ba ion
= 9.39 GHz
01000 2000 3000
0
1AP, = 9.39 GHz
Ca i y
Coaxial line
P (A b. un.)
H (Oe)
= 0o
(a)
(b)
01000 2000 3000
0
1
P (A b. un.)
H (Oe)
AN, = 9.39 GHz
Ca i y
Coaxial line
= 0o
01000 2000 3000
0
1SA, = 9.39 GHz
Ca i y
Coaxial line
P (A b.un.)
H (Oe)
= 0o
(c)
(d)
Figu e 9. Mic owa e abso p ion measu emen s using a comple e coaxial wa eguide o
Fe3Co67C 3Si15B12 amo phous ibbons in di e en s a es AP, AN and SA. Expe imen al esul s and
Ki el´s i . (a) Dashed ec angle indica es he equency ange whe e he measu emen s a e s ill
possible bu less p ecise as he app oxima ion o he 50 Ohm ma ching wa eguide cha ac e is ic
impedance (Z0) de ia es. (b–d) Di ec compa ison o he FMR esonance lines ob ained o he e-
quency = 9.39 GHz bo h by he ca i y pe u ba ion echnique and using he coaxial wa eguide o
all ibbon ypes . Red and black dashed lines indica e he wid h o he FMR esonances.
Figu e 9.
Mic owa e abso p ion measu emen s using a comple e coaxial wa eguide o
Fe
3
Co
67
C
3
Si
15
B
12
amo phous ibbons in di e en s a es AP, AN and SA. Expe imen al esul s
and Ki el
´
s i . (
a
) Dashed ec angle indica es he equency ange whe e he measu emen s a e
s ill possible bu less p ecise as he app oxima ion o he 50 Ohm ma ching wa eguide cha ac e is ic
impedance (Z
0
) de ia es. (
b
–
d
) Di ec compa ison o he FMR esonance lines ob ained o he
equency = 9.39 GHz bo h by he ca i y pe u ba ion echnique and using he coaxial wa eguide
o all ibbon ypes. Red and black dashed lines indica e he wid h o he FMR esonances.
Figu e 9b–d show expe imen al P(H) dependences o all ypes o Fe
3
Co
67
C
3
Si
15
B
12
amo phous ibbons measu ed by bo h he s anda d ca i y pe u ba ion echnique and he
coaxial wa eguide. As he o iginal measu emen s (done by he comme cial spec ome e )
we e made in dP/dH mode, in o de o pe o m such a compa ison, he ini ial signals
dP/dH we e ma hema ically in eg a ed wi h espec o he ex e nal magne ic applied ield
and he maximum o he abso p ion powe in ensi y was no malized o one uni .
Fo p ope compa ison, he e lec ion coe icien S
11
measu ed by he ZVA VNA
analyze o he calib a ion plane was ecalcula ed in acco dance wi h he me hod p oposed
in [
29
,
36
], and he changes in he eal and imagina y pa s o he impedance (
∆
R and
∆
X)
we e ob ained. Fo compa ison be ween he wo di e en mic owa e echniques, he
∆
R
Ma e ials 2022,15, 4160 17 o 20
pa was employed. Figu e 9b–d show he b oadband measu emen s da a o all ibbon
ypes. We used he no malized alue o he
∆
R a ia ion o he ield dependence o he
pu poses o di ec compa ison wi h he ca i y pe u ba ion esul s.
One can see e y good ag eemen be ween he FMR (H
es
) measu ed by he wo
mic owa e echniques. No only a e he posi ions o he maximum alues o he mic owa e
abso p ion qui e simila , bu his also applies o he wid h o he FMR lines. In igo ous
e alua ion e ms, we no e ha he wid h o he esonance line is be e de ined o he ca i y
pe u ba ion case. In he case o he coaxial wa eguide, he main p oblem is he co ec
de e mina ion o he base line. E en so, Figu e 9con incingly con i ms he esul s o he
measu emen s a = 9.39 GHz. S ic ly speaking, he compa ison o Ki el
´
s condi ions
was made o one esonance equency only and his is a disad an age. Howe e , e y
good ag eemen be ween he expe imen al esul s and i o he Equa ion (7) is ob ained,
and he p oposed measu ing echnique seems o be well adap ed o he high equency
b oadband cha ac e iza ion o he amo phous ibbons.
I isnecessa y oemphasize ha dependingon heselec edleng hso heFe
3
Co
67
C
3
Si
15
B
12
amo phous ibbons, he ob ained ma e ials can be used o high equency applica ions
in di e en equency anges. The independence o he FMR esponses o sho ibbons
on he aniso opy ea u es unde conside a ion is also e y in e es ing. I indica es he
lexibili y o he ma e ial and i s po en ial o a oiding e y s ic p o ocols o addi ional
hea ea men s, sa ing ime and ene gy in he case o some pa icula applica ions.
One o he endencies o he de elopmen o p esen -day mic ode ices and mic osys-
ems is an ex ension o he ope a ing equency ange. This ea u e equi es u he de-
elopmen o he cha ac e iza ion echniques o di e en kinds o magne ically so e -
omagne s [
5
,
31
,
36
,
48
]. He e we p oposed a simple way o measu e he b oadband FMR
cha ac e is ics o amo phous ibbons. Howe e , i can also be used o nanoc ys alline
ma e ials and oils o ec angula shape.
4. Conclusions
P oduced om one ba ch o he ma e ial, apidly quenched Fe
3
Co
67
C
3
Si
15
B
12
amo -
phous ibbons we e p epa ed and designed in o de o ob ain model ma e ials wi h di e en
ea u es o e ec i e magne ic aniso opy o mic owa e es s. The ollowing s a es we e
conside ed: (AP)—as-quenched wi hou any ea men ; (AN)—a e elaxa ion annealing
wi hou s ess a he empe a u e o 350
◦
C du ing 1 h; and (SA)—a e annealing unde
speci ic s ess o 200 MPa a he empe a u e o 350
◦
C du ing 1 h. In acco dance wi h XRD
and TEM s udies, all ma e ials we e in amo phous s a e.
Magne ic measu emen s o he long ibbons (45 mm) using induc i e echnique and
MOKE e ealed some di e ences in he e ec i e magne ic aniso opy ea u es, namely:
AP and AN samples had well de ined longi udinal e ec i e magne ic aniso opy. S ess
annealed ibbons had well-de ined ans e se e ec i e aniso opy wi h low dispe sion
o he local magne ic aniso opy axes. SA ibbons showed excellen magne oimpedance
p ope ies wi h e y high sensi i i y abo e 130%/Oe o a equency o abou 20 MHz,
which is e y con enien o senso applica ions. A he same ime, VSM measu emen s o
he sho ibbons (5 mm) showed simila i y o hei magne ic cha ac e is ics due o s ong
con ibu ion o he shape aniso opy.
Following his ho ough cha ac e iza ion, he designed ma e ials we e used o mi-
c owa e abso p ion measu emen s. Fo FMR es s o he sho (5 mm) samples, we p o-
posed, designed and es ed a b oadband measu emen echnique based on he employmen
o coaxial wa eguide and sample holde es ablished om a comme cial SMA connec o .
Measu emen s o he e lec ion coe icien S
11
allowed he accu a e de e mina ion o he
o al impedance a ia ion in he equency ange o 0.5 o 12.5 GHz. The alidi y o he
p oposed echnique was also con i med by he measu emen s using he adi ional ca i y
pe u ba ion echnique (spec ome e ope a ing a X-band equency o 9.39 GHz).
Ma e ials 2022,15, 4160 18 o 20
Au ho Con ibu ions:
Concep ualiza ion, G.V.K. and L.L.; me hodology, G.V.K., L.L., V.A.L. and
S.O.V.; so wa e, S.O.V.; alida ion, A.A.P., A.L., N.V.D. and I.O.; o mal analysis, A.L., A.V.T., N.V.D.
and A.A.P.; in es iga ion, G.V.K., L.L., I.O., V.A.L. and S.O.V.; esou ces, G.V.K.; da a cu a ion,
A.L., A.V.T. and N.V.D.; w i ing—o iginal d a p epa a ion, G.V.K. and S.O.V.; w i ing— e iew
and edi ing, G.V.K., V.A.L. and A.A.P.; isualiza ion, G.V.K., L.L., A.L., A.A.P., S.O.V. and A.V.T.;
supe ision, G.V.K. and A.A.P.; unding acquisi ion, G.V.K. All au ho s ha e ead and ag eed o he
published e sion o he manusc ip .
Funding:
The esea ch unding om he Minis y o Science and Highe Educa ion o he Russian
Fede a ion (U al Fede al Uni e si y P og am o De elopmen wi hin he P io i y-2030 P og am)
is g a e ully acknowledged. Fu he unding om Uni e si y o he Basque Coun y UPV/EHU
Resea ch G oups Funding (GMMM) is simila ly g a e ully acknowledged.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen :
Da a a e a ailable om he co esponding au ho on easonable eques .
Acknowledgmen s:
We would like o hank V.O. Vasko skiy and M. Vazquez o special suppo .
Selec ed measu emen s we e made a he SGIKER acili ies o UPV/EHU.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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