Ci a ion: Salaheldeen, M.; Zhuko a,
V.; Lopez An on, R.; Zhuko , A.
Dependence o Magne ic P ope ies o
As-P epa ed Nanoc ys alline
Ni2MnGa Glass-Coa ed Mic owi es
on he Geome ical Aspec Ra io.
Senso s 2024,24, 3692. h ps://
doi.o g/10.3390/s24113692
Academic Edi o s: Seung-bok Choi
and E angelos H is o o ou
Recei ed: 26 Ap il 2024
Re ised: 21 May 2024
Accep ed: 4 June 2024
Published: 6 June 2024
Copy igh : © 2024 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
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/).
senso s
A icle
Dependence o Magne ic P ope ies o As-P epa ed
Nanoc ys alline Ni2MnGa Glass-Coa ed Mic owi es on he
Geome ical Aspec Ra io
Mohamed Salaheldeen 1,2,3,4,* , Valen ina Zhuko a 1,2,4 , Rica do Lopez An on 5and A cady Zhuko 1,2,4,6,*
1Depa men o Polyme s and Ad anced Ma e ials, Facul y o Chemis y, Uni e si y o he Basque Coun y,
UPV/EHU, 20018 San Sebas ian, Spain; [email p o ec ed]
2Depa men o Applied Physics I, EIG, Uni e si y o he Basque Coun y, UPV/EHU,
20018 San Sebas ian, Spain
3Physics Depa men , Facul y o Science, Sohag Uni e si y, Sohag 82524, Egyp
4EHU Quan um Cen e , Uni e si y o he Basque Coun y, UPV/EHU, 20018 San Sebas ian, Spain
5Depa men o Applied Physics, Regional Ins i u e o Applied Scien i ic Resea ch (IRICA),
Uni e si y o Cas illa-La Mancha, 13071 Ciudad Real, Spain; [email p o ec ed]
6IKERBASQUE, Basque Founda ion o Science, 48011 Bilbao, Spain
*Co espondence: [email p o ec ed] (M.S.); [email p o ec ed] (A.Z.)
Abs ac : We ha e p epa ed NiMnGa glass-coa ed mic owi es wi h di e en geome ical aspec
a ios,
ρ
=d
me al
/D
o al
(d
me al
—diame e o me allic nucleus, and D
o al
— o al diame e ). The s uc u e
and magne ic p ope ies a e in es iga ed in a wide ange o empe a u es and magne ic ields. The
XRD analysis illus a es s able mic os uc u e in he ange o
ρ
om 0.25 o 0.60. The es ima ions o
a e age g ain size and c ys alline phase con en e idence a ema kable a ia ion as he
ρ
- a io sweeps
om 0.25 o 0.60. Thus, he mic owi es wi h he lowes aspec a io, i.e.,
ρ
= 0.25, show he smalles
a e age g ain size and he highes c ys alline phase con en . This change in he mic os uc u al
p ope ies co ela es wi h d ama ic changes in he magne ic p ope ies. Hence, he sample wi h
he lowes
ρ
- a io exhibi s an ex emely high alue o he coe ci i y, H
c
, compa ed o he alue o
he sample wi h he la ges
ρ
- a io (2989 Oe and 10 Oe, espec i ely, i.e., almos 300 imes highe ).
In addi ion, a simila end is obse ed o he spon aneous exchange bias phenomena, wi h an
exchange bias ield, H
ex
, o 120 Oe o he sample wi h
ρ
= 0.25 compa ed o a H
ex
= 12.5 Oe o he
sample wi h
ρ= 0.60
. Howe e , he he momagne ic cu es ( ield-cooled—FC and ield-hea ing—FH)
show simila magne ic beha io o all he samples. Meanwhile, FC and FH cu es measu ed a low
magne ic ields show nega i e alues o
ρ
= 0.25, whe eas posi i e alues a e ound o he o he
samples. The ob ained esul s illus a e he subs an ial e ec o he in e nal s esses on mic os uc u e
and magne ic p ope ies, which leads o magne ic ha dening o samples wi h low aspec a io.
Keywo ds: NiMnGa alloys; glass-coa ed mic owi es; magne ic ield; Taylo –Uli o sky echnique;
coe ci i y; mic os uc u al p ope ies
1. In oduc ion
S udies o alloys exhibi ing he moelas ic ma ensi ic phase ans o ma ions (TMPTs)
ep esen a p omising di ec ion o a ious s uc u al and unc ional applica ions due o
hei ema kable p ope ies, including shape memo y (SM), gian supe elas ici y (GS), mag-
ne ic ield-induced s ain (MFIS), and elas ocalo ic and magne ocalo ic (EMC)
e ec s [1–20]
.
These p ope ies may be used o he de elopmen o ac ua o s, senso s, ene gy ha es ing
de ices, biomedical d ug deli e y pumps, and sola cells, among o he s [1–22].
S udies o Ni
2
MnGa alloys ha e ecen ly gained signi ican a en ion due o hei
unique magne ic shape-memo y e ec (MSE). This e ec p o ides bo h la ge ield-induced
s ains and supe elas ici y exceeding adi ional shape-memo y alloys (SMAs), which a e
Senso s 2024,24, 3692. h ps://doi.o g/10.3390/s24113692 h ps://www.mdpi.com/jou nal/senso s
Senso s 2024,24, 3692 2 o 13
ela ed o he moelas ic ma ensi e ans o ma ion [
13
–
22
]. Con en ional SMAs unde go e-
e sible shape changes be ween aus eni e and ma ensi e phases igge ed by empe a u e
o s ess a ia ions, enabling hei use in ac ua o s, senso s, and ene gy ansduce s equi -
ing high- equency esponses and e e sible s ains. Minia u iza ion o SMA-based de ices
has inc eased he demand o small-scaled samples like pa icles, wi es, ibbons, ilms,
and mic os uc u es [
23
–
26
]. Howe e , NiMnGa alloys, ypically in e me allic compounds,
exhibi b i leness ha hinde s ab ica ion using adi ional me hods like cold d awing
o o ging [
15
]. While single c ys als o e imp o ed duc ili y, hei p oduc ion is ime-
consuming and p one o chemical seg ega ion, comp omising hei
pe o mance [13–17]
.
The Taylo –Uli o sky echnique [
27
] o e s a iable solu ion, enabling he p oduc ion o
glass-coa ed mic owi es wi h leng hs eaching kilome e s and diame e s anging om
0.1 o 100
µ
m [
28
,
29
]. This me hod p o ided high cooling a es, allowing he p epa a ion
o amo phous, nanoc ys alline, mic oc ys alline, o g anula s uc u es in high-en opy
s a es [
28
–
30
]. The unique combina ion o unable magne ic p ope ies oge he wi h im-
p o ed mechanical and co osion p ope ies (linked o he exis ence o insula ing and
lexible glass-coa ing), low dimensionali y, and educed eddy cu en losses make such
glass-coa ed mic owi es a ac i e o a ious magne ic senso applica ions [28–31].
P e ious s udies success ully u ilized apid quenching me hods o ab ica e Heusle -
ype magne ic wi es [
30
–
39
]. No ably hicke (226-
µ
m diame e ) glass-coa ed NiMnGa
wi es exhibi ed e e sible supe elas ici y up o 4% ensile s ain [
40
]. Howe e , gi en
he limi a ions o he p epa a ion me hod, only a he sho and ai ly hick wi es we e
ob ained. Mo eo e , qui e hick glass coa ings a e epo ed o a ec mechanical p ope -
ies and de e io a e he hea exchange a e [
32
,
41
,
42
]. While sui able o Heusle alloys
wi h mode a e Magne ocalo ic E ec (MCE) and nea -ambien Cu ie empe a u es, he
glass-coa ed echnique o en ailed o exhibi ma ensi ic ans o ma ion (MT) in Heusle
mic owi es [
30
–
39
]. High in e nal s esses (100–1000 MPa), small g ain size, and s uc u al
diso de associa ed wi h mel quenching a e likely esponsible [
30
,
38
]. Only ecen ly, MT
has been obse ed in p ope ly annealed Ni-Mn-Ga glass-coa ed mic owi es [
31
,
38
]. The e-
o e, iden i ying app op ia e ab ica ion condi ions emains c ucial o achie ing MT and
unlocking e sa ile p ope ies in Heusle - ype mic owi es.
Based on ou p e ious esea ch on he magne ic and s uc u al p ope ies o NiMnGa-
based glass-coa ed mic owi es [
30
,
31
,
35
,
37
–
39
,
41
], his wo k aims o elucida e he in luence
o he aspec a io on he magne o-s uc u al beha io o as-p epa ed NiMnGa alloys wi h-
ou any u he addi ional he mal p ocess. We ha e obse ed how he main key magne ic
pa ame e s o sensing applica ions (coe ci i y, exchange bias, hys e e ic beha io
. . .
) can
be uned jus by con olling he mic os uc u al p ope ies by changing he geome ic
aspec a io.
2. Ma e ials and Me hods
Fo Ni
2
MnGa alloy ab ica ion, we used p ecise a c mel ing, consis ing o he ol-
lowing s eps: (i) Ni, Mn, and Ga powde s (99.99% pu i y) we e weighed and placed in
a g aphi e c ucible. (ii) Mel ing occu ed unde acuum/a gon in an elec ic a c u nace
wi h empe a u e con ol o comple e mel ing and mixing. (iii) The c ucible cooled a -
e comple e mel ing, solidi ying in o an ingo . This p ocess was epea ed i e imes o
achie e op imal homogenei y and mic os uc u e. The ingo was hen used o he p epa-
a ion o mic owi es coa ed wi h hin glass coa ings below a ew
µ
m) p ese ing c i ical
elec ical/magne ic p ope ies using he Taylo –Uli o sky me hod.
The well-es ablished Taylo –Uli o sky p ocess is desc ibed elsewhe e [
28
,
30
,
36
,
41
].
The diame e o he me allic nucleus and he hickness o he glass coa ing can be con olled
by adjus ing se e al key pa ame e s du ing he wi e ab ica ion p ocess, such as he speed
a which he wi e is d awn, he eed a e o he glass ube, o he ingo empe a u e [
28
,
30
].
In his s udy, we ab ica ed ou dis inc ypes o Ni
2
MnGa glass-coa ed mic owi es wi h
a ying geome ical cha ac e is ics, speci ically he diame e s o he me allic nucleus and
he o e all wi e diame e . We achie ed his a ia ion by manipula ing he a o emen ioned
Senso s 2024,24, 3692 3 o 13
pa ame e s, such as he d awing speed, he pick-up bobbin o a ion speed, o he ingo
empe a u e (see Table 1).
Table 1. Chemical composi ions and geome ical pa ame e s o Ni
2
MnGa glass-coa ed mic owi e
o ms wi h di e en aspec a ios.
Sample Chemical Composi ion D o al (µm) dme al (µm) Aspec Ra io (ρ)
A Ni49Mn24Ga27 26.58 6.77 0.25
B Ni50.5Mn23Ga26.5 69.10 31.6 0.47
C Ni50Mn24.5Ga25.5 24.33 13.4 0.55
D Ni50Mn24Ga26 21.07 12.20 0.60
Ene gy Dispe si e X- ay Spec oscopy (EDX) analysis con i med he chemical com-
posi ion o he me allic nucleus as Ni
59.2
Mn
12.2
Ga
28.6
(a omic pe cen ). Scanning Elec on
Mic oscopy (SEM) e ealed a cylind ical c oss-sec ion wi h a no ably homogeneous dis i-
bu ion o elemen s wi hin he me allic nucleus. No ably, an in e ace laye was obse ed
be ween he me allic nucleus and he su ounding glass coa ing. Fu he mo e, a BRUKER
X- ay di ac ome e (D8 Ad ance, B uke AXS GmbH, Ka ls uhe, Ge many) was u ilized o
execu e Cu K
α
(
λ
= 1.54 Å) adia ion o hei s uc u al in es iga ion. All he magne ic mea-
su emen s we e pe o med using a PPMS (Physical P ope y Magne ic Sys em, Quan um
Design Inc., San Diego, CA, USA) ib a ing-sample magne ome e . The mo-magne iza ion
measu emen s we e pe o med in he empe a u e, T, ange om
5 o 400 K
wi h a magne ic
ield anging om 10 kOe o 20 kOe (applied along he sample’s axis), whe eas he hys e e-
sis loops we e ob ained using a ze o- ield-cooled (ZFC) p o ocol a di e en empe a u es
in he p e ious ange and wi h a maximum applied ield o 30 kOe. All he magne ic esul s
a e p esen ed in e ms o no malized magne iza ion (
M/Mmax ield o M/M5K
) o accoun
o he ela i e na u e o he measu emen s, whe e M
5K (max. ield)
e e s o he magne ic
momen measu ed a 5 K o unde maximum ield, espec i ely. The Cu ie empe a u e, Tc,
has been de e mined as he minimum o he i s de i a i e o he magne ic momen .
3. Resul s
3.1. Mo phological P ope ies o Ni2MnGa Samples
To explo e he in luence o aspec a io,
ρ
, on magne ic and mic os uc u al p ope ies
o as-p epa ed Ni
2
MnGa glass-coa ed mic owi es p oduced using he Taylo –Uli o sky p o-
cess, ou samples wi h di e en diame e
ρ
- a ios (
ρ
=d
me al
/D
o al
, being d
me al
—diame e
o he me allic nucleus, and D
o al
— o al mic owi e diame e ) we e chosen. The i s
sample (A) has an a e age me allic nucleus diame e (d
me al
) o ~6.77
µ
m and a o al
diame e (D
o al
) o ~26.58
µ
m, i.e., aspec a io
ρ
= 0.25. The second sample (B) has
an a e age me al nucleus diame e (d
me al
) o ~31.60
µ
m and a o al diame e (D
o al
)
o ~69.10
µ
m (
ρ
= 0.47). The o he wo samples ha e highe geome ical aspec a ios:
ρ= 0.55 and 0.60
, espec i ely (see Table 1). Ene gy-dispe si e X- ay spec oscopy (EDX)
combined wi h scanning elec on mic oscopy (SEM) was used o de e mine he ac ual
chemical composi ion o he Ni
2
MnGa- based glass-coa ed mic owi es wi h di e en aspec
a ios (see Figu e 1and Table 1
). Analysis o six di e en loca ions e ealed a e age chemi-
cal composi ions as ollows: Ni
49
Mn
24
Ga
27
(A), Ni
50.5
Mn
23
Ga
26.5
(B),
Ni50Mn24.5Ga25.5 (C)
,
and Ni
50
Mn
24
Ga
26
(D), espec i ely. These composi ions a e close o he in ended s oi-
chiome ic a io o 2:1:1 (Ni
50
Mn
25
Ga
25
) and con i m he consis ency wi h he expec ed
alues (Table 1). The EDX elemen s mapping o all samples shows a homogeneous elemen
dis ibu ion o Ni, Mn, and Ga. The e o e, we only show hose composi ional maps o he
Ni2MnGa-MWs wi h he lowes aspec a io as an example (see Figu e 1c– ).
Senso s 2024,24, 3692 4 o 13
Figu e 1. (a) C oss-sec ions o selec ed Ni
2
MnGa mic owi es wi h an aspec a io o 0.25.
(b,c) SEM
image o single Ni
2
MnGa mic owi e a di e en magni ica ions. (d– ) show he chemical composi ion
mapping ob ained using EDX analysis in one o mic owi es.
3.2. XRD Analysis o Ni2MnGa-Based Glass-Coa ed Mic owi e Samples
X- ay di ac ion (XRD) analysis was pe o med a oom empe a u e on as-p epa ed
Ni
2
MnGa glass-coa ed mic owi es wi h a ying
ρ
- a ios. While he XRD pa e ns show
qui e simila di ac og ams o all c ys alline phases, sub le s uc u al di e ences (peak
in ensi y and posi ion) a e obse ed be ween mic owi es wi h di e en
ρ
- a ios. These
a ia ions a e mos p onounced in he analysis o he i s peak, iden i ied as (110) using
he In e na ional Cen e o Di ac ion Da a (ICDD) da abase (h ps://www.icdd.com/,
accessed on 23 Feb ua y 2024). Gaussian i ing o he c ys alline peak allows o he
calcula ion o i s a ea, p opo ional o he co esponding c ys alline phase con en .
The a e age c ys alline g ain size (D
g
) can be de e mined om he i s peak’s posi ion
and wid h using he es ablished Debye–Sche e equa ion (Equa ion (1)):
Dg= Kλ/(B cos(θ)) (1)
whe e Dg ep esen s he a e age c ys alli e size, K is he shape ac o (
assumed o be 0.9
),
λ
is he X- ay wa eleng h (0.154 nm o Cu K
α
1 adia ion), B is he ull wid h a hal
maximum (FWHM) o he co esponding di ac ion peak in adians, and
θ
ep esen s he
B agg angle.
As can be seen in Figu e 2, all he samples show wo main peaks wi h Mille indices
(110) and (200) a 2
θ
= 45
◦
and 60
◦
, espec i ely. These ob ained by XRD da a a e pe ec ly
ma ched wi h hose epo ed elsewhe e [
42
]. The main peak is a 2
θ
= 45
◦
wi h (110). These
Senso s 2024,24, 3692 5 o 13
di e ences a e s ongly ela ed o he a ia ion in he geome ical pa ame e s (
ρ
- a io).
Figu e 3illus a es
he dependence o he a e age g ain size o wo phases, es ima ed
using (1)
, o wo peaks wi h mille pa ame e s (110) and (200), espec i ely, on he geome -
ical aspec a io,
ρ
. As we inc ease he geome ical aspec a io, a no able inc ease in D
g
is
obse ed, inc easing om 13.6 nm (ρ= 0.25) up o 27.2 nm (ρ= 0.65).
Figu e 2. (a) X- ay di ac ion (XRD) pa e ns ob ained a oom empe a u e o Ni
2
MnGa glass-
coa ed mic owi es wi h a ying aspec a ios. (b) De ail o X he B agg Peak a 2
θ
= 45
◦
is shown as
yellow a ea.
Figu e 3. The a e age g ain size, D
g
, o he wo c ys alline phases Ga
4
Ni
3
-BCC and Ni
2
MnGa-FCC
o as-p epa ed Ni
2
MnGa-based glass-coa ed mic owi es wi h di e en aspec a ios. The ed lines
indica e he e o ba s.
Following he same p ocedu es epo ed in ou p e ious wo k (see [
31
,
38
]), we ha e
analyzed he XRD peaks and de e mined he di e en phase s uc u es. Two main phases,
Ga
4
Ni
3
(BCC) and Ni
2
MnGa (FCC), a e iden i ied om he XRD spec a, ag eeing well wi h
he esul s om e e ences [
31
,
38
]. The e is also a wide halo ( om 15
◦
o 22
◦
;
in Figu e 2
)
due o he amo phous glass. Table 2summa izes he a ia ions o di e en s uc u e phases
and la ice pa ame e s wi h he a ia ion o he geome ical aspec a ios. As can be seen,
he e is a clea a ia ion in he Ga
4
Ni
3
and Ni
2
MnGa con en due o changes in he geome -
ical aspec a io. The sample wi h he smalles
ρ
- a io shows he highes
Ni2MnGa-FCC
con en (abou 78%) and he lowes pe cen age o Ga
4
Ni
3
-BCC (22%). Meanwhile, he
Senso s 2024,24, 3692 6 o 13
samples wi h high
ρ
- a ios (0.55 and 0.60) show he highes Ga
4
Ni
3
-BCC (83% and 81%)
and lowes Ni
2
MnGa-FCC (17% and 19%), espec i ely. The changes in hese mic os uc-
u e pa ame e s a ec he magne ic beha io o he samples a di e en empe a u es and
di e en ex e nal magne ic ields, as will be discussed in he nex sec ion.
Table 2. The calcula ions o he c ys alline phase con en , la ice pa ame e s, and ela ed g ain size
o Ni2MnGa glass-coa ed mic owi es wi h di e en aspec a ios.
Aspec Ra io (ρ)Ga4Ni3-BCC Ni2MnGa-FCC
Dg(nm) % La ice Pa ame e (a) Dg(nm) % La ice Pa ame e (a)
0.25 9.7 22 0.235 nm 16.1 78 0.309 nm
0.47 26.9 68 0.286 nm 27 32 0.244 nm
0.55 25.5 83 0.204 nm 24 17 0.242 nm
0.60 27.8 81 0.221 nm 26.9 19 0.241 nm
3.3. Magne ic P ope ies o Ni2MnGa Samples
Figu e 4p esen s he magne iza ion (M)- e sus-magne ic ield (H) loops o samples
wi h di e en
ρ
- a ios, measu ed a bo h T= 5 K (Figu e 4a) and T= 300 K (Figu e 4b).
In e es ingly, he sample wi h he smalles
ρ
- a io exhibi s unexpec ed magne ically ha d
beha io , cha ac e ized by high coe ci i y and emanence. In con as , he emaining
mic owi es display so e omagne ic beha io , as e idenced by he M-H loops measu ed a
T= 5 K and he p onounced pa amagne ic beha io obse ed in he M-H loops measu ed a
T= 300 K. These la e loops appea nea ly linea wi h negligible emanence and coe ci i y.
The obse ed M-H beha io sugges s a link be ween he geome ical aspec a io and he
magne ic p ope ies o he me allic nucleus in hese glass-coa ed mic owi es. This link is
u he suppo ed by he appa en changes in Cu ie empe a u e (Tc). Ou esul s indica e
ha he Tc o he sample wi h
ρ
= 0.25 lies abo e oom empe a u e (RT), whe eas he Tc o
he o he samples alls below RT. I is no ewo hy ha he Cu ie empe a u e o he NiMnGa
alloy is a he sensi i e o ac o s such as chemical composi ion, p epa a ion me hod,
s uc u e, physical o m, and hea ea men [
30
,
38
]. Gene ally, he Cu ie empe a u e o
his alloy can ange be ween 160 K and 360 K.
Figu e 4. (a) Hys e esis loops, measu ed in magne ic ield applied pa allel o he axis o mic owi es
o as-p epa ed Ni
2
MnGa glass-coa ed mic owi es wi h di e en
ρ
- a ios (a) measu ed a 5 K and
(b) measu ed a 300 K.
Senso s 2024,24, 3692 7 o 13
In ou expe imen , e en hough all NiMnGa-based glass-coa ed mic owi es we e
p epa ed using he same p ocess and exhibi e y simila chemical composi ions (as shown
in Table 1), a clea shi in Tc is obse ed be ween he samples. This sugges s ha he
mic os uc u e o he sample plays a signi ican ole in de e mining he Tc alue and, as
will be discussed la e , he o e all magne ic beha io .
The H
c
(T) dependencies o all he samples a e summa ized in Figu e 5. The sample
wi h
ρ
= 0.25 shows he highes H
c
- alues o all measu ed empe a u es, whe e he highes
H
c
- alue (H
c
= 2989 Oe) is obse ed a T= 200 K and he lowes H
c≈
480 Oe is obse ed a
T=5K
(see Figu e 5a). The H
c
- alue o he sample wi h
ρ
= 0.25 is 300 imes highe han he
H
c
o
ρ
= 0.47 and
ρ
= 0.55 and 75 imes highe han o he sample wi h
ρ= 0.60 measu ed
a he same empe a u e (T= 200 K). In addi ion, he H
c
(T) dependence is subs an ially
a ec ed by
ρ
- a io. Hence, a coe ci i y maximum is obse ed a T
= 200 K o he sample
wi h
ρ
= 0.25 while, in con as , a dec ease in H
c
is gene ally obse ed as
Tdec eases
o he
o he h ee mic owi es. In pa icula , a mono onic dec ease in H
c
- alue while dec easing
he T om 265 K o 5 K is ob ained o he sample wi h
ρ= 0.60 (see Figu e 5d)
, whe eas
o he samples wi h
ρ
= 0.47 and
ρ
= 0.55, a local maximum a
≈
100 K and an inc ease in
Hc- alue a T≤20 K a e obse ed, espec i ely.
Figu e 5. (a–d) The a ia ion o coe ci i y wi h empe a u e o Ni
2
MnGa-based glass-coa ed mi-
c owi es wi h di e en aspec a ios a ied om 0.25 o 0.60. Red lines indica e he e o ba s.
Figu e 6shows he dependence o he spon aneous exchange bias ield, H
EB
, s. em-
pe a u e o all he samples. The obse a ion o H
EB
is qui e common in NiMnGa alloys and
is a ibu ed o he coexis ence o an i e omagne ic and e omagne ic phases in di e en
ange empe a u es [
28
,
31
]. In ou case, i is no ewo hy ha we obse e spon aneous
exchange bias (i.e., we obse e hese phenomena e en hough he measu emen s we e
pe o med ollowing a ZFC p o ocol) and wi h alues qui e simila o hose ound in
o he cases o mic owi es o NiMnGa alloys bu ollowing an FC p o ocol [
31
]. As seen
in Figu e 6
, he sample wi h
ρ
= 0.25 shows he highes spon aneous exchange bias alue,
H
EB
, compa ed o he es o he mic owi es. In addi ion, he H
EB
depends on he em-
pe a u es and shows a clea maximum o a ound 100 K. The H
EB
- alue o (
ρ
= 0.25) is
≥12 imes
highe han he H
EB
- alue obse ed in he o he samples. The empe a u e de-
pendencies o H
EB
o samples wi h
ρ
=0.47 and 0.55 show a simila endency, al hough wi h
a maximum ai ly less ma ked and a qui e low empe a u es (a abou 10 K). Meanwhile,
Senso s 2024,24, 3692 8 o 13
wo di e en slopes in he H
EB
(T) dependence a e obse ed o he sample wi h
ρ= 0.60
,
whe e H
EB
dec eases apidly as he empe a u e dec eases om 265 o 150 K compa ed
o a less p onounced H
EB
dec ease o empe a u es anging om 150 o 5 K. Gi en hese
ema kable esul s o he spon aneous exchange bias, we in end o pe o m addi ional
s udies ocusing on he con en ional exchange bias o hese samples in he nea u u e.
Figu e 6. Tempe a u e dependence o he spon aneous exchange bias o Ni
2
MnGa glass-coa ed
mic owi es wi h di e en aspec a ios (lines o eye guide).
These changes in he H
c
and H
EB
beha io wi h empe a u e con i m, again, he
subs an ial e ec o he geome ical aspec a ios on he magne iza ion e e sal p ocess
h ough he changes in he in e nal s ess alue induced by he glass-coa ing.
To gain a deepe unde s anding o he magne ic beha io o he samples, he mo-
magne iza ionmeasu emen swe epe o medunde wodi e en p o ocols:
ield cooling (FC)
and ield hea ing (FH). In FC, he samples we e cooled om 400 K o he lowes empe a u e
(5 K) unde di e en applied ields (H) o 10 kOe and 20 kOe. The FH p o ocol in ol ed
he e e se p ocess a he same H alues. The FC and FH cu es o all he samples a e
p esen ed in Figu e 7. Fo samples wi h
ρ
= 0.25, 0.55, and 0.60, he M/M
5K
(T) depen-
dencies exhibi a non-mono onic dec ease wi h
empe a u e (see Figu e 7a,c,d)
wi h a knee
obse ed a T
≈
136 K o bo h applied ields. Simila beha io was p e iously obse ed
in as-p epa ed NiMnGa-based glass-coa ed mic owi es and hin ilms [
31
,
33
,
35
,
39
,
43
–
47
].
Such M/M
5K
(T) dependencies and lack o sa u a ion in M-H loops (see Figu e 4) ha e
been discussed in e ms o a nonuni o m magne ic cha ac e , he a omic diso de , and he
magne ic clus e ing o he as-p epa ed mic owi es [
32
,
39
]. Meanwhile, o he sample wi h
ρ
= 0.47, he empe a u e dependence o he magne ic momen ,
M/M5K (T) (see Figu e 7b)
,
shows a small and na ow hys e e ic anomaly be ween ield cooling (FC) and ield hea -
ing (FH) cu es. A sub le change (hys e e ic anomaly) is obse ed in he M/M
5K
(T)
dependencies o s udied mic owi es a a speci ic empe a u e ange (85–120 K) ega dless
o he applied magne ic ield (H). This anomaly sugges s he p esence o a ma ensi ic
ans o ma ion in he mic owi es. Howe e , he di e ence in magne iza ions be ween
he ma ensi ic and aus eni ic phases is small, which does no lead o a no iceable shi in
he ans o ma ion empe a u e unde changes in magne ic ields. The empe a u e o
ma ensi ic ansi ion, T
M
, is below 120 K o samples wi h small
ρ
- a ios, i.e., 0.25 and 0.47,
while o samples wi h highe aspec a ios, i.e., 0.55 and 0.60, T
M
is abo e 120 K (see g een
highligh s in Figu e 7). The M/M
5K
(T) dependencies (Figu e 7) and M-Hloops (Figu e 4)
e lec a nonuni o m magne ic cha ac e o he as-p epa ed Ni
2
MnGa-based glass-coa ed
mic owi es wi h di e en
ρ
- a ios p oduced by he a omic diso de and magne ic clus e ing.
Despi e he smea ed shape o M/M
5K
(T) dependencies, o he sample wi h
ρ
= 0.25, i can
be es ima ed ha Tc is abo e oom empe a u e (Tc
≈
363 K). Meanwhile, o he es o
Senso s 2024,24, 3692 9 o 13
he NiMnGa mic owi es, T
C
a ies be ween 250 and 265 K. Howe e , abo e 130 K all he
samples p esen weak e omagne ic beha io .
Figu e 7. (a–d) Field cooling (FC) o Ni
2
MnGa glass-coa ed mic owi es a empe a u e ange
400 K o 5 K
wi h di e en applied magne ic ield H = 10 kOe o 20 kOe. The g een a ea poin s
ou he egion whe e he TMis expec ed o be obse ed.
4. Discussion
The Taylo –Uli o sky me hod, used o ab ica e glass-coa ed mic owi es, is challeng-
ing due o he a he di e en he mal expansion coe icien s o he in ol ed ma e ials
(me allic alloy and glass-coa ing). The employed echnique in ol es apid solidi ica ion
o a mol en me al nucleus su ounded by a glass coa ing. The signi ican di e ence in
he mal expansion coe icien s be ween he me allic alloy and glass leads o he onse o
in e nal s esses dis ibu ed in a complex manne wi hin he me allic nucleus. Theo e ical
calcula ions and indi ec expe imen s sugges hese s esses can each peak alues be ween
100 and 1000 MPa [
31
,
36
], being conside ably highe han he s esses exe ed by ex e nal
magne ic ields (1–7 MPa). These subs an ial in e nal s esses, caused by he he mal ex-
pansion misma ch, hinde c ucial p ope ies like ma ensi ic ans o ma ion cha ac e ized
by hys e esis beha io and magne ic esponse o empe a u e and magne ic ields. The e is
a s ong co ela ion be ween glass coa ing hickness and in e nal s ess magni ude, wi h
hicke coa ings leading o highe in e nal s ess le els, as epo ed o mic owi es wi h
lowe
ρ
- a ios [
36
,
48
–
50
]. Fu he mo e, he impac o in e nal s ess on he c ys alliza ion
p ocess can be unde s ood h ough he lens o non-equilib ium he modynamics: s ess
in luences a omic di usion, he eby a ec ing c ys al nuclea ion and g ow h [
51
]. Recen
s udies on Heusle -alloy glass-coa ed mic owi es p o ide expe imen al e idence o his e -
ec , as he ec ys alliza ion p ocess di e s signi ican ly be ween glass-coa ed and uncoa ed
samples [
52
–
54
]. Addi ionally, he p esence o an insula ing glass coa ing can a ec he
hea exchange a e and, hence, he quenching a e du ing he p epa a ion o mic owi es
by he Taylo –Uli o sky me hod [
28
–
30
]. The quenching a e can a ec he a e age g ain
size. Howe e , we canno obse e a di ec co ela ion be ween he D
g
- alues and glass
coa ing hickness (see Table 2). The e o e, we mus assume ha he main ac o in luencing
he magne ic and mic os uc u al p ope ies o s udied mic owi es is he in e nal s esses’
magni ude and dis ibu ion. In he cu en s udy, he modi ica ion in he in e nal s ess
