Design o Fe-con aining GdTbCoAl high-en opy-me allic-glass
composi e mic owi es wi h unable Cu ie empe a u es and enhanced
cooling e iciency
Hangboce Yin
a,b
, Jiayan Law
b
, Yongjiang Huang
a,
⇑
, Vic o ino F anco
b
, Hongxian Shen
a,
⇑
, Sida Jiang
c,
⇑
,
Ying Bao
a
, Jian ei Sun
a
a
School o Ma e ials Science and Enginee ing, Ha bin Ins i u e o Technology, Ha bin 150001, China
b
Dp o. Física de la Ma e ia Condensada, ICMS-CSIC, Uni e sidad de Se illa, Se illa 41080, Spain
c
Space En i onmen Simula ion Resea ch In as uc u e, Ha bin Ins i u e o Technology, Ha bin 150001, China
highligh s
Nanoc ys alline Fe-con aining
GdTbCoAl high-en opy-me allic-
glass we e a ained.
Cu ie empe a u e is uned by Fe-
doping in a wide empe a u e ange
o 81–108 K.
Magne ic en opy change 7.6–
8.9 J kg
1
K
1
o 5 T we e achie ed.
The dual-phase s uc u e wi h T
C
dis ibu ion enhances he cooling
e iciency.
g aphical abs ac
a icle in o
A icle his o y:
Recei ed 26 Janua y 2021
Re ised 6 May 2021
Accep ed 10 May 2021
A ailable online 12 May 2021
Keywo ds:
Fe-doping
Dual-phase mic os uc u e
Cooling e iciency
Mic owi es
Magne ocalo ic e ec
abs ac
Th ough designing he composi ion and p ocessing app oach, he non-equia omic (Gd
36
Tb
20
Co
20
Al
24
)
100-
x
Fe
x
(x = 0, 1, 2 and 3 a .%) high-en opy-me allic-glass (HE-MG) alloy mic owi es we e success ully ab-
ica ed by mel -ex ac ion echnique. The mic os uc u e and magne ocalo ic p ope ies o he mic o-
wi es we e sys ema ically in es iga ed. The mic owi es possess unable Cu ie empe a u es, i.e. 81–
108 K, abo e he ypical a e-ea h (RE) con aining HE-MG epo s. The high Cu ie empe a u es a e
a ibu ed o he designed composi ion. Magne ocalo ic esponse peak alues o Fe-con aining
GdTbCoAl alloy mic owi es ange 7.6–8.9 J kg
1
K
1
(5 T), which a e compa able o hose o many ou -
s anding RE-con aining magne ocalo ic HE-MGs. The cha ac e is ics o he mel -ex ac ion me hod, com-
bining wi h composi ional e ec s, a o he o ma ion o amo phous and nanoc ys alline phases. The
inc ease in he cooling e iciency o mic owi es wi h highe Fe con en can be a ibu ed o he b oad-
ening o he Cu ie empe a u e dis ibu ion induced by he composi ion di e ence be ween nanoc ys-
alline phase and amo phous ma ix. The designed composi ion and he mel -ex ac ion p ocessing
app oach o Fe-con aining GdTbCoAl alloys can une hei Cu ie empe a u es owa ds a empe a u e
ange o na u al gas lique ac ion and imp o e hei magne ocalo ic p ope ies. This demons a es ha
Fe-con aining GdTbCoAl HE-MG composi e mic owi es ha e g ea po en ial as high-pe o mance mag-
ne ic e ige an s.
Ó2021 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND
license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/).
h ps://doi.o g/10.1016/j.ma des.2021.109824
0264-1275/Ó2021 The Au ho (s). Published by Else ie L d.
This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/).
⇑
Co esponding au ho s.
E-mail add esses: [email p o ec ed] (Y. Huang), [email p o ec ed] (H. Shen), [email p o ec ed] (S. Jiang).
Ma e ials & Design 206 (2021) 109824
Con en s lis s a ailable a ScienceDi ec
Ma e ials & Design
jou nal homepage: www.else ie .com/loca e/ma des
1. In oduc ion
Magne ic e ige a ion based on he magne ocalo ic e ec
(MCE) o solid s a e ma e ials has been widely conside ed as a
p omising candida e o he con en ional gas comp ession-
expansion e ige a ion, due o i s excellen cooling e iciency
and en i onmen al iendliness [1]. Magne ocalo ic ma e ials
(MCMs) exploi he adiaba ic empe a u e change when subjec ed
o an applied a ying magne ic ield whe e hey can ac as solid
e ige an s. The MCE p ope y can be cha ac e ized by he mag-
ne ic en opy change (
D
S
M
).
Typically, he MCE pe o mance can be op imized by wo ways,
i.e., i) composi ional design and ii) design o p ocessing app oach.
Wi h an app op ia e composi ional design, desi ed phase selec ion
could op imize MCE pe o mance and aid he T
C
unabili y. As an
example, MCMs wi h amo phous and nanoc ys alline phases ha e
been epo ed showing enhanced cooling e iciency wi h app op i-
a ely la ge maximum magne ic en opy change (
D
S
max
M
)inan
ex ended empe a u e ange [2,3]. These cha ac e is ics ha e g ea
po en ial o E icsson cycle e ige a ion [4]. Fo he second
app oach o op imize MCE pe o mance, i has been epo ed ha
MCMs wi h educed dimensions could acili a e he design o mag-
ne ic e ige a o s, especially in hea ans e abili y [5–7]. In pa -
icula , MCMs p ocessed in o wi e o ms show g ea sui abili y
among o he educed dimensions (such as lamina o pa icles)
due o i s high su ace- o- olume a io, supe io mechanical s abil-
i y, la ge deg ee o packing, g ea empe a u e span be ween ends,
and high p essu e d op [7,8]. Using he mel -ex ac ion echnique,
high quali y me allic mic owi es (mic o-size diame e s) can be
easily ob ained. As he MCM wi e dimensions educe o mic o-
sized diame e s, i can u he os e an inc ease in he cooling
load, cooling e iciency o he sys em and p essu e d op o he
MCMs [7]. This indica es ha i is o g ea signi icance o s udy
MCM mic owi es as his o m can g ea ly acili a e he design o
magne ocalo ic e ige a o s. In addi ion, amo phous/nanoc ys-
alline dual-phase s uc u e could be de eloped in mel -ex ac ed
mic owi es wi hou addi ional pos hea ea men . This is acili-
a ed by he g ea cooling a e di e ence be ween he egion in
con ac wi h he wheel and he ee su ace o he mel du ing
he mel -ex ac ion p ocess, which has been p o en by he p e i-
ous wo k o ou g oup [9,10].
High-en opy-alloys (HEAs), as a highly ega ded new class o
ma e ials, a e designed wi h mul iple p incipal alloying elemen s
o yield high con igu a ional en opy, unlike he adi ional ma e-
ials whose designs a e based on one o wo main elemen s. Since
HEAs we e i s ly epo ed in 2004 [11,12], hey ha e e ol ed om
he i s -gene a ion quina y equimola single-phase amilies o he
second-gene a ion HEAs, ex ending composi ions o ou o mo e
p incipal componen s in non-mola concen a ions and/o wi h
mul i-phases [13]. MCE HEAs mainly ocus on a e-ea h (RE) con-
aining high-en opy-me allic-glasses (HE-MGs), which possess
ex emely low magne ic hys e esis and excellen MCE p ope ies
[14–17]. Analogous o HEAs, MCE RE-con aining HE-MGs also
epo an e olu ion end o i s ?second gene a ion composi-
ions, s a ing wi h equia omic composi ions (e.g. GdTbDyAl(Fe/
Co/Ni) [16], HoE CoAl(Gd/Dy/Tm) [17]) o non-equia omic compo-
si ions (e.g. Gd
36
Y
20
Co
20
Al
24
[15]). Howe e , bo h gene a ions end
o exhibi low ansi ion empe a u es, mainly anging <60 K
whe e hey exhibi 
D
S
max
M
alues, ypical o he MCE cha ac e is-
ics. Hence, MCE RE-con aining HE-MGs a e s ill a an eme ging
s age and i is essen ial o op imize hem wi h unable ansi ion
empe a u es, like Cu ie empe a u es (T
C
), and ex end o highe
empe a u e ange o his new class o magne ocalo ic alloys.
Xue e al. [14] designed he qua e na y equimola GdHoCoAl
and GdTbCoAl HE-MGs and ound ha T
C
can be g ea ly uned om
50 K o 73 K when subs i u ing o Tb. In addi ion, he equimola
GdTbCoAl HE-MG possesses ou s anding MCE pe o mance:

D
S
max
M
o 8.88 J kg
1
K
1
and ela i e cooling powe (RCP)o
577 J kg
1
o
l
0
D
H= 5 T. One possible way o u he op imize
MCE RE-con aining HE-MGs o highe empe a u e ange is Fe-
doping, which has been epo ed o e ec i ely inc ease T
C
and
imp o e he MCE p ope ies o Gd-based me allic glasses [18–
20]. Fu he mo e, he hea o mixing (
D
H
mix
AB
), which can a ec
he ype o phase o ma ion, is ound o be nega i e al hough small
o a om pai s be ween Fe and RE/ ansi ion elemen s: 1, 3 and
1 kJ mol
1
o Fe-Gd, Fe-Tb and Fe-Co, espec i ely [21]. La ge
nega i e
D
H
mix
AB
alues be ween he dopan and main elemen s
would a o he glass o ming abili y (GFA) [9,22,23]. The e o e,
he esul an small alues o
D
H
mix
AB
indica e ha designing compo-
si ions o GdTbCoAl wi h Fe-doping could enable he o ma ion o
dual-phase mic os uc u e consis ing o amo phous and nanoc ys-
alline phases.
Hence, he pu pose o his pape is o design and p epa e RE-
con aining HE-MG composi e mic owi es wi h widely unable T
C
abo e he ypical limi (<60 K), wi h amo phous and nanoc ys-
alline phases and enhanced MCE p ope ies. Fo ha , we selec ed
he composi ional design which is ul illed as he second-
gene a ion MCE RE-con aining HE-MG wi h mino Fe addi ions:
(Gd
36
Tb
20
Co
20
Al
24
)
100-x
Fe
x
whe e x = 0 o 3 a .%. These alloys we e
p ocessed in o mic owi es wi h s uc u e e olu ion om single
phase (amo phous phase) o wo phases (amo phous and
nanoc ys alline phases), which show unable T
C
om 81 o 100 K
wi h ela i ely la ge MCE p ope ies. The success ul MCE op imiza-
ion o hese mic owi es demons a e ha app op ia e composi-
ional design and p ocessing echnique can pa e a new pa hway
o design and ab ica e high-pe o mance MCMs as well as o
he HEA communi y.
2. Expe imen al me hods
The mas e alloys wi h nominal composi ions o (Gd
36
Tb
20
Co
20
-
Al
24
)
100-x
Fe
x
(x = 0, 1, 2 and 3 a .%) we e i s ly ab ica ed by a c-
mel ing a mix u e o cons i uen elemen s (each wi h pu i y highe
han 99.9 w %) unde a Ti-ge e ed high-pu i y A a mosphe e.
Acco ding o he Fe addi ion con en s, samples s udied in his wo k
a e deno ed he ea e as Fe0, Fe1, Fe2 and Fe3. The alloy ingo s
we e e-mel ed a leas i e imes o ensu e chemical homogenei y,
ollowed by suc ion cas ing in o a coppe mold o o m cylind ical
ods wi h 10 mm in diame e and 50 mm in leng h. Subsequen ly,
he alloy mic owi es we e p epa ed by using a mel -ex ac ion
acili y wi h a molybdenum (Mo) wheel. The line speed o Mo
wheel was 30 m s
1
. The mel -ex ac ion p ocess was unde an
A a mosphe e. Fo alloys wi h Fe con en highe han 3 a .%, e.g.
4 and 5 a .%, hei mic owi es could no be p epa ed wi hin he
limi s o he mel -ex ac ion equipmen . The de ails can be ound
in Supplemen a y In o ma ion Documen and Fig. S1.
The su ace mo phology o he mic owi es was examined by a
scanning elec on mic oscope (SEM, FEI Quan a 200FEG). Fig. 1(a)
shows he smoo h su ace o he Fe3 mic owi es. The mac oscopic
iew and he c oss-sec ional SEM image o Fe3 mic owi es a e
shown in Fig. S2. The c oss-sec ional SEM image shows ha he
diame e o Fe3 mic owi e is ~30
l
m. The he mal s abili y o
he samples was s udied by di e en ial scanning calo ime e
(DSC, Ne zsch STA449F3 Jupi e ) a a hea ing a e o 10 K min
1
.
The mic os uc u e and composi ional in o ma ion we e examined
by ansmission elec on mic oscope (TEM, FEI Talos F200X)
equipped wi h ene gy-dispe si e X- ay spec oscopy (EDS). Tem-
pe a u e dependence o magne iza ion (MT) and magne ic ield
dependence o magne iza ion (MH) we e measu ed by using a
Physical P ope y Measu emen Sys em (PPMS, Quan um Design
Dynacool-14 T). Fo a la ge signal o noise a io, a bundle o mic o-
H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824
2
wi es we e used o he magne ic measu emen s. The mic owi es
we e a anged pa allel o each o he in a non-magne ic polyme ic
ubula sample holde wi h 1 mm in inne diame e , 2.5 mm in
ou e diame e , and 3 mm in leng h.
3. Resul s and discussion
DSC cu es o Fe0, Fe1, Fe2, and Fe3 mic owi es a e p esen ed in
Fig. 1(b) and (c). These cu es show he he mophysical pa ame-
e s including he glass ansi ion empe a u es (T
g
), he onse em-
pe a u e o he i s c ys alliza ion peak (T
x
), and he liquidus
empe a u es (T
l
). I is obse ed ha wi h inc easing Fe con en ,
T
g
and T
l
inc ease whe eas T
x
dec eases. Thei de ailed in o ma ion
is summa ized in Table 1, oge he wi h he supe -cooled liquid
egion (
D
T
x
=T
x
T
g
) and
c
=T
x
/(T
g
+T
l
).
D
T
x
and
c
indica e he
he mal s abili y, i.e. esis ance o c ys alliza ion [24,25], and he
GFA [26] o he supe cooled liquid, espec i ely. As seen in Table 1,
he alues o
D
T
x
and
c
mono onically dec ease wi h inc easing Fe
con en , acili a ing he p ecipi a ion o c ys alli es on mic owi es.
I should be no ed ha he la ges dec ease o
D
T
x
and
c
akes place
be ween Fe1 and Fe2, sugges ing he possibili y o mic os uc u al
change be ween hese samples. The GFA is a ec ed by hese
pa ame e s: a omic size di e ence (d), he mixing en halpy
(
D
H
mix
) and he mixing en opy (
D
S
mix
). These a e also widely used
o p edic he phase o ma ion in HEAs, including HE-MGs [23,27–
29]. Hence, hese pa ame e s o Fe0, Fe1, Fe2 and Fe3 mic owi es
a e calcula ed and lis ed in Table 1. Fo all he s udied mic owi es,
hese pa ame e s a e in ag eemen o he c i e ia epo ed o HE-
MG (d9, 49 
D
H
mix
5.5 kJ mol
1
and 7 
D
S
mix
16 J K
1
mol
1
)[23]. The au ho s [23] u he epo ha he o ma ion o
amo phous phase is a o ed by la ge d, smalle
D
S
mix
and mo e
nega i e
D
H
mix
alues in compa ison wi h solid solu ion phases.
In ou case, d alues e ol e e y sligh ly wi h inc easing Fe con en ,
while he changes o
D
S
mix
and
D
H
mix
a e ela i ely la ge. The el-
a i ely small e ec o Fe-doping on dis o li le help o he a omic
packing densi y, which does no aid he enhancemen o GFA. The
e olu ions o
D
S
mix
and
D
H
mix
a e in ag eemen o ha o
c
. The e-
o e, he de e io a ion o he GFA should be asc ibed o he ela-
i ely la ge change o
D
H
mix
and
D
S
mix
induced by Fe-doping.
TEM obse a ions we e pe o med in o de o in es iga e he
mic os uc u es o Fe-con aining GdTbCoAl mic owi es a he
nano-scale. The homogeneous maze-like pa e ns o he high-
esolu ion TEM (HRTEM) images in Fig. 2(a) and (b) indica e he
ully amo phous s uc u e o Fe0 and Fe1 mic owi es, espec i ely
[30]. Thei ully amo phous s uc u es a e also con i med by he
a he ain and di used halo ings o he selec ed a ea elec on
di ac ion (SAED) pa e ns wi hou any dis inguishable di ac ion
spo (see inse s o Fig. 2(a) and (b)). Fig. 2(c) shows he HRTEM, he
co esponding as Fou ie ans o m (FFT)-in e se as Fou ie
ans o m (IFFT) and SAED images o Fe2 mic owi e. The FFT-IFFT
image wi h c ys alline inges, co esponding o he ed dashed
squa e ma ked by he numbe 1, indica es he exis ence o
nanoc ys alline phase wi h a g ain size o ~3nm[31]. The amo -
phous ma ix is con i med by he bo om- igh FFT-IFFT image
which shows he comple ely andom a omic a angemen and co -
esponds o he ed dashed squa e ma ked by he numbe 2. As
shown in he op- igh inse o Fig. 2(c), a ligh c ys alline- ing
SAED pa e n can be obse ed besides he s ong halo ing co e-
sponding o he amo phous ma ix, con i ming he dual-phase
mic os uc u e. The b igh - ield TEM image o he su ace a ea o
Fe3 mic owi e is shown in Fig. 2(d). A dual-phase s uc u e can
be ob iously obse ed in his image. The p esence o he nanoc ys-
als in he amo phous ma ix can be con i med by he co espond-
ing SAED esul s wi h he ligh c ys alline di ac ion spo s and
s ong halo ing (Fig. 2(e)). The c ys alline di ac ion spo s indica e
he nanoc ys alline phase is ace-cen e ed cubic (FCC) s uc u e.
The asymme ic spo s can be also obse ed in he SAED esul s.
To u he con i m he s uc u e o he nanoc ys alline phase,
HRTEM along h ee di e en zone axes we e ob ained, as shown
in he op images o Fig. 2( )–(h). The HRTEM images indica e he
nanoc ys alline phase wi h an a e age g ain size o ~27 nm. The
FFT images co esponding o he ed dashed squa es in he HRTEM
images con i m FCC s uc u e o he nanoc ys alline phase [32],as
shown in he bo om images o Fig. 2( )–(h). O e all, he single
amo phous s uc u es o he Fe0 and Fe1 mic owi es e ol e in o
a dual-phase mic os uc u e wi h inc easing Fe-doping, whe e
nanoc ys als a e obse ed ( hough a he ew) o Fe2 and Fe3. This
is in line wi h he e olu ion o
D
T
x
and
c
.
Fo he mic owi es wi hou Fe-doping, he composi ion is e y
close o he ideal glass- o ming composi ion acco ding o Lu’s
empi ical concep [33]. This composi ion no mally means he bes
glass- o ming composi ion o an alloy. Wi h he inc ease o Fe
Fig. 1. (a) SEM image o he Fe3 mic owi e, (b) and (c) DSC esul s o he Fe0, Fe1, Fe2 and Fe3 mic owi es.
Table 1
The he mophysical pa ame e s o Fe0, Fe1, Fe2 and Fe3 mic owi es.
Sample T
g
(K) T
x
(K) T
l
(K)
D
T
x
(K)
c
d
D
H
mix
(kJ mol
1
)
D
S
mix
(J K
1
mol
1
)
Fe0 586 638 1064 52 0.386 14.31 34.63 11.25
Fe1 588 637 1065 49 0.385 14.44 34.08 11.61
Fe2 590 624 1155 34 0.357 14.56 33.53 11.84
Fe3 592 622 1162 30 0.354 14.68 32.99 12.02
H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824
3
con en , he he mal s abili y and GFA o Fe-con aining GdTbCoAl
mic owi es de e io a e. Du ing he mel -ex ac ion p ocess, he
mel su ace can be di ided in o wo egions, i.e., he egion in con-
ac wi h he wheel and he ee su ace. The cooling a e o he
egion in con ac wi h he wheel eaches a high alue o o e 10
6
Ks
1
, a o ing he o ma ion o amo phous phase. Con a ily, o
he ee su ace, he cooling a e is much lowe , acili a ing he o -
ma ion o nanoc ys als i he GFA o he alloy is no high enough
[9,10]. Due o he de e io a ed GFA and ela i ely low cooling a e
a he ee su ace, nanoc ys als could be c ea ed in he case o Fe-
con aining GdTbCoAl mic owi es. Two pa ame e s can a o he
g ow h o nanoc ys al in he liquid, i.e. he ema kable long-
dis ance a omic di usion [34] and he high mobili y o a oms
[27,35]. In supe cooled liquids o Fe-con aining GdTbCoAl mic o-
wi es, he a omic di usion is kine ically e a ded by he high
deg ee o dense andom packing, which is a ibu ed o he ela-
i ely la ge absolu e alues o dand
D
H
mix
[34,36,37]. The
inc eased mel iscosi y o GdTbCoAlFe liquids, which is induced
by Fe-doping [37], kine ically es ic s he mobili y o he a oms
[35,38]. Acco dingly, he nanoc ys alline phase which exis s in
he liquid is e ained in Fe-con aining GdTbCoAl mic owi es.
Fig. 3 shows he empe a u e dependence o he ield cooling
magne iza ion (M
FC
) o Fe0, Fe1, Fe2 and Fe3 mic owi es, mea-
su ed unde a ield o 200 Oe. An ex apola ion me hod o he lin-
ea pa o he MTcu e is used o con i m he T
C,
which is he
Fig. 2. HRTEM images and co esponding SAED esul s (inse s) o (a) Fe0, (b) Fe1 and (c) Fe2 mic owi es, espec i ely. Co esponding FFT-IFFT esul s o he ed dashed
squa es ma ked by numbe s 1 and 2 a e also shown in he inse s o (c). (d) and (e) show he b igh - ield TEM image and he co esponding SAED esul s o Fe3 mic owi e,
espec i ely. ( ), (g) and (h) show HRTEM images ( op) and FFT esul s (bo om) co esponding o he ed dashed squa es in HRTEM images o Fe3 mic owi e along h ee
di e en zone axes.
Fig. 3. Tempe a u e dependence o M
FC
cu es o Fe0, Fe1, Fe2 and Fe3 mic owi es
unde an applied magne ic ield o 200 Oe.
Fig. 4. Magne ic en opy changes o Fe0, Fe1, Fe2 and Fe3 mic owi es unde
l
0
D
H
o 2 T (solid symbols) and 5 T (open symbols).
H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824
4
in e cep o he ex apola ed line and he empe a u e axis. The T
C
o he Fe-con aining GdTbCoAl mic owi es inc eases wi h inc eas-
ing Fe con en : 81, 94, 100 and 108 K o Fe0, Fe1, Fe2 and Fe3
mic owi es, espec i ely. The a e age inc ease o T
C
is 9 K pe Fe
a .%. The inc eased T
C
is due o he s ong exchange in e ac ions
o RE-Fe and Fe-Fe pai s [39,40].
The -
D
S
M
as a unc ion o he empe a u e o Fe-con aining
GdTbCoAl mic owi es unde
l
0
D
H= 2 and 5 T a e plo ed in
Fig. 4. Fo bo h ield changes, 
D
S
max
M
mono onically dec eases
whe eas hei co esponding peak empe a u es inc ease wi h
inc easing Fe con en . Fo 
D
S
max
M
, i dec eases om 8.9 o
7.6 J kg
1
K
1
unde
l
0
D
H= 5 T o Fe0 o Fe3 as shown in Fig. 5
(a). The a e age educ ion o 
D
S
max
M
is 0.43 J kg
1
K
1
pe Fe a .
%. This small educ ion in 
D
S
max
M
wi h inc easing Fe con en is
a ibu ed o he eplacemen o he RE-elemen s wi h high mag-
ne ic momen s by Fe.
TEC(10) is he empe a u e a e aged -
D
S
M
ecen ly p oposed by
G i i h e al. [41], which e e s o he maximum a e age o -
D
S
M
o e a 10 K empe a u e span. I is ega ded as an al e na i e igu e
me i o e alua ing MCE ma e ials. I can a oid a i icially la ge
alues o e ige an capaci y o MCMs in he cases o exhibi ing
shallow and wide peaks. TEC(10) can be calcula ed as ollows [41]:
TECð10Þ¼ 1
10max Z
T
mid
þ5
T
mid
5
S
M
ðTÞdT
() ð2Þ
whe e T
mid
is chosen by sweeping o e he 
D
S
M
(T) cu e o ob ain
maximum alue o TEC(10) a he empe a u e span o 10 K. In he
Fig. 5. The Fe con en dependence o (a) 
D
S
max
M
and FWHM, (b) TEC(10), TEC
(app ox.)
,RC and RCP o
l
0
D
H=5T.
Fig. 6. A o plo s o (a) Fe0, (b) Fe1, (c) Fe2 and (d) Fe3 mic owi es.
H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824
5

case ha he a ailable da a o he 
D
S
M
(T) cu es a e limi ed (e.g.
li e a u e da a), his exp ession can be app oxima ed as ollows
[42]:
TEC
ðapp ox:Þ

D
S
M
ðT
peak
5Þþ
D
S
M
ðT
peak
Þþ
D
S
M
ðT
peak
þ5Þ

3ð3Þ
The TEC(10) and app oxima e alue o TEC(10), TEC
(app ox.)
,
dec ease wi h inc easing Fe con en , as shown in Fig. 5(b). The sim-
ila i y o bo h alues shows he alidi y o he app oxima ion. They
a e in he ange o 
D
S
max
M
alues, con i ming he ela i ely b oad
peaks o 
D
S
M
(T) cu es o Fe-con aining GdTbCoAl mic owi es.
Fo alloys wi h ela i ely high 
D
S
max
M
, e ige a ion capaci y
(RC) and RCP a e usually employed o e alua e cooling e iciency,
and a e calcula ed by using he ollowing o mulas [43–45]:
RCP ¼
D
S
max
M
dT
FWHM
¼
D
S
max
M
ðT
2
T
1
Þð4Þ
RC ¼Z
T
2
T
1
D
S
M
ðTÞdTð5Þ
whe e T
1
and T
2
ep esen he endpoin s o ull-wid h a hal -
maximum (FWHM, i.e. wo king empe a u e ange) o 
D
S
M
(T)
cu es. Fig. 5(a) shows FWHM o 
D
S
M
(T) cu es. The esul s show
ha FWHM inc eases wi h inc easing Fe con en . Al hough a single
ma e ial in a e ige a o de ice will no ope a e in such b oad em-
pe a u e span, he la ge 
D
S
M
exis ing in such b oad empe a u e
ange will acili a e he ope a ion o he ma e ials in he empe a-
u e anges wi hin he FWHM. The esul s o RCP and RC o Fe-
con aining GdTbCoAl mic owi es a e shown in Fig. 5(b) o
l
0
D
H=5T.RCP and RC inc ease wi h he inc ease o Fe con en
due o he enla ged FWHM o 
D
S
M
(T) cu es. The alues o RCP
and RC inc ease o 684 J kg
1
and 520 J kg
1
, espec i ely, o Fe3
mic owi es unde
l
0
D
H=5 T. The inc ease o FWHM could be
asc ibed o he appea ance o nanoc ys als.
To de e mine he o de o magne ic phase ansi ion o he
s udied mic owi es, wo me hods we e used: 1) A o plo s (M
2
s. H/M) and 2) he quan i a i e c i e ion based on he magne ic
ield dependence o MCE [46].Fig. 6 shows he A o plo s o all
s udied mic owi es. All he cu es show posi i e angen slopes
o he whole measu emen empe a u e ange, indica ing
second-o de o phase ansi ion (SOPT) o all he s udied mic o-
wi es acco ding o Bane jee’s c i e ion [47]. Fo he nex me hod,
he exponen o he magne ic ield dependence o MCE, ep e-
sen ed as n, is calcula ed and analyzed. The ela ionship be ween

D
S
M
and
l
0
D
H ollows a powe law [48]:

D
S
M
/
l
0
D
H
n
ð6Þ
whe e nis a local exponen ha depends on bo h magne ic ield and
empe a u e. The local calcula ion o ob aining nis:
n¼dln
D
S
M
jj
dln
l
0
D
Hð7Þ
The empe a u e dependence o he calcula ed nis shown in
Fig. 7(a), which shows he ypical beha io o SOPT ma e ials in
he absence o o e shoo o nla ge han 2. This ag ees well wi h
he obse a ions o Fig. 6. Usually, mul iple phases would appea
as sepa a ed peaks in he 
D
S
M
(T) cu es unless he phase ansi-
ion empe a u es a e a he close o he ac ions o he addi ional
phase a e oo low. In such cases, he n(T) da a can be used o ana-
lyzing he exis ence o addi ional phase ansi ions [48] whe e he
exis ence o mul iple phases would show addi ional minima in n
(T). This is no he case in Fig. 7(a) whe e no addi ional minimum
is obse ed despi e Fe2 and Fe3 a e ound wi h dual-phase
mic os uc u e. Fig. 7(b) p esen s he wid hs o n(T) cu es as a
unc ion o Fe con en . The wid hs a e ob ained a n= 0.85, as
shown in he inse o Fig. 7(b). The signi ican inc ease o he wid h
is obse ed o he Fe3, in ag eemen o he wides FWHM and la -
ges nanoc ys al ac ion o Fe3 mic owi es. The absence o addi-
ional ea u es bo h in n(T) and 
D
S
M
(T) cu es could be ela ed
o p oximi y o he T
C
o wo phases o he low ac ion o
nanoc ys alline phase. The composi ional di e ences be ween
nanoc ys alline phase and amo phous ma ix (see Fig. S3 and
Fig. 7. (a) The empe a u e dependence o he exponen n. (b) Fe con en dependence o he wid h o n, wi h inse showing how he wid h o nwas ob ained. Bo h g aphs a e
unde
l
0
D
H=5T.
Fig. 8. MCE pe o mance o RE-con aining HE-MGs o
l
0
D
H=5 T. Da a o he
li e a u e a e collec ed om Re s. [14,15,49–51].
H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824
6
Table S1) lead o a b oad T
C
dis ibu ion, b oadening he FWHM.
The wide FWHM coun e ac s he small 
D
S
max
M
educ ion and
he e o e inc eases he cooling e iciency.
Fig. 8 shows he ansi ion empe a u e dependence o 
D
S
max
M
o ou s udied mic owi es in compa ison wi h hose o non-
equia omic RE-con aining HE-MGs and equia omic GdTbCoAl HE-
MG. I is obse ed ha ou HE-MG alloy mic owi es exhibi a wide
ange o ansi ion empe a u es beyond he ypical limi , <60 K.
Fu he mo e, 
D
S
max
M
is main ained in a ela i ely la ge alue ange
as compa ed wi h hose o o he epo ed non-equia omic RE-
con aining HE-MGs and equia omic GdTbCoAl HE-MG. This
demons a es ha Fe-con aining GdTbCoAl HE-MG composi e
mic owi es ha e g ea applica ion p ospec s as high-pe o mance
magne ic e ige an s.
4. Conclusion
Wi h mino Fe addi ions, (Gd
36
Tb
24
Co
20
Al
20
)
100-x
Fe
x
(x = 0, 1, 2
and 3 a .%) high-en opy-alloy mic owi es enabled unable Cu ie
empe a u es up o 108 K, which is beyond he ypical limi o
RE-con aining magne ocalo ic HEAs (<60 K). The T
C
inc eases a
an a e age a e o 9 K pe Fe a .%, asc ibed o he s ong exchange
in e ac ions o RE-Fe and Fe-Fe pai s. Fu he mo e, he Fe addi ions
acili a e he o ma ion o amo phous/nanoc ys alline dual-phase
s uc u e ha leads o inc eased cooling e iciency, keeping ela-
i ely la ge 
D
S
max
M
alues (7.6–8.9 J kg
1
K
1
o 5 T) in an
ex ended wo king empe a u e span. Compa ed o epo ed
p omising magne ocalo ic HEAs, hese mic owi es exhibi compa-
able MCE p ope ies ye a much highe wo king empe a u es.
The la ge MCE pe o mance enhanced by he app op ia e composi-
ional design and p ocessing echnique opens ano he di ec ion o
op imizing HEAs as high-pe o mance MCMs.
Decla a ion o Compe ing In e es
The au ho s decla e ha hey ha e no known compe ing inan-
cial in e es s o pe sonal ela ionships ha could ha e appea ed
o in luence he wo k epo ed in his pape .
Acknowledgmen s
The au ho s would like o acknowledge he inancial suppo
om he Na ional Na u al Science Founda ion o China unde G an
Nos. 51871076, 51671070, 51801044, and 51827801, and he 66 h
China Pos doc o al Science Founda ion unde G an No.
2019M661275. V.F. and J.L. acknowledge unding om AEI/
FEDER-UE (g an PID2019-105720RB-I00), US/JUNTA/FEDER-UE
(g an US-1260179), and Conseje ía de Economía, Conocimien o,
Emp esas y Uni e sidad de la Jun a de Andalucía (g an P18-RT-
746). H.Y. acknowledges he ellowship om China Schola ship
Council (CSC, No. 201906120183) o Visi ing PhD S uden
p og am.
Appendix A. Supplemen a y ma e ial
Supplemen a y da a o his a icle can be ound online a
h ps://doi.o g/10.1016/j.ma des.2021.109824.
Re e ences
[1] T. Go schall, K.P. Skoko , M. F ies, A. Taubel, I. Radulo , F. Scheibel, D. Benke, S.
Riegg, O. Gu leisch, Making a cool choice: he ma e ials lib a y o magne ic
e ige a ion, Ad . Ene gy Ma e . 9 (34) (2019) 1901322, h ps://doi.o g/
10.1002/aenm.201901322.
[2] C.F. Sánchez-Valdés, P.J. Iba a-Gay án, J.L.S. Llamaza es, M. Á alos-Bo ja, P.
Ál a ez-Alonso, P. Go ia, J.A. Blanco, Enhanced e ige an capaci y in wo-
phase nanoc ys alline/amo phous NdP Fe
17
mel -spun ibbons, Appl. Phys.
Le . 104 (21) (2014), h ps://doi.o g/10.1063/1.4879544 212401.
[3] H.X. Shen, D.W. Xing, J.L. Sánchez Llamaza es, C.F. Sánchez-Valdés, H.
Belli eau, H. Wang, F.X. Qin, Y.F. Liu, J.F. Sun, H. S ikan h, M.H. Phan,
Enhanced e ige an capaci y in Gd-Al-Co mic owi es wi h a biphase
nanoc ys alline/amo phous s uc u e, Appl. Phys. Le . 108(9) (2016) 092403,
h ps://doi.o g/10.1063/1.4943137.
[4] B.G. Shen, J.R. Sun, F.X. Hu, H.W. Zhang, Z.H. Cheng, Recen p og ess in
explo ing magne ocalo ic ma e ials, Ad . Ma e . 21 (45) (2009) 4545–4564,
h ps://doi.o g/10.1002/adma.200901072.
[5] H.F. Belli eau, Y.Y. Yu, Y. Luo, F.X. Qin, H. Wang, H.X. Shen, J.F. Sun, S.C. Yu, H.
S ikan h, M.H. Phan, Imp o ing mechanical and magne ocalo ic esponses o
amo phous mel -ex ac ed Gd-based mic owi es ia nanoc ys alliza ion, J.
Alloys Compd. 692 (2017) 658–664, h ps://doi.o g/10.1016/
j.jallcom.2016.08.254.
[6] V.V. Kho aylo, V.V. Rodiono a, S.N. She y alo , V. No osad, Magne ocalo ic
e ec in ‘‘ educed” dimensions: hin ilms, ibbons, and mic owi es o Heusle
alloys and ela ed compounds, Phys. S a us Solidi B 251 (10) (2014) 2104–
2113, h ps://doi.o g/10.1002/pssb.201451217.
[7] D. Vua noz, T. Kawanami, Nume ical analysis o a ecip oca ing ac i e
magne ic egene a o made o gadolinium wi es, Appl. The m. Eng. 37
(2012) 388–395, h ps://doi.o g/10.1016/j.appl he maleng.2011.11.053.
[8] M.D. Kuz’min, Fac o s limi ing he ope a ion equency o magne ic
e ige a o s, Appl. Phys. Le . 90 (25) (2007) 251916. h ps://doi.o g/10.
1063/1.2750540.
[9] S.D. Jiang, H. Wang, D. Es e ez, Y.J. Huang, L.Y. Zhang, H.X. Shen, Z.L. Ning, F.X.
Qin, J.F. Sun, Su ace mic os uc u al design o imp o e mechanical and gian
magne o-impedance p ope ies o mel -ex ac ed CoFe-based amo phous
wi es, Ma e . Des. 204 (2021), h ps://doi.o g/10.1016/j.ma des.2021.109642
109642.
[10] H. Wang, F.X. Qin, D.W. Xing, F.Y. Cao, H.X. Peng, J.F. Sun, Fab ica ion and
cha ac e iza ion o nano/amo phous dual-phase FINEMET mic owi es, Ma e .
Sci. Eng, B 178 (20) (2013) 1483–1490, h ps://doi.o g/10.1016/j.
mseb.2013.09.010.
[11] B. Can o , I.T.H. Chang, P. Knigh , A.J.B. Vincen , Mic os uc u al de elopmen
in equia omic mul icomponen alloys, Ma e . Sci. Eng. A 375–377 (2004) 213–
218, h ps://doi.o g/10.1016/j.msea.2003.10.257.
[12] J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang,
Nanos uc u ed high-en opy alloys wi h mul iple p incipal elemen s: No el
alloy design concep s and ou comes, Ad . Eng. Ma e . 6 (5) (2004) 299–303,
h ps://doi.o g/10.1002/adem.200300567.
[13] Y. Zhang, High-En opy Ma e ials, Sp inge , Singapo e, 2019. h ps://doi.o g/
10.1007/978-981-13-8526-1.
[14] L. Xue, L.L. Shao, Q. Luo, B.L. Shen, Gd
25
RE
25
Co
25
Al
25
(RE = Tb, Dy and Ho) high-
en opy glassy alloys wi h dis inc spin-glass beha io and good
magne ocalo ic e ec , J. Alloys Compd. 790 (2019) 633–639, h ps://doi.o g/
10.1016/j.jallcom.2019.03.210.
[15] L. Liang, X. Hui, Y. Wu, G.L. Chen, La ge magne ocalo ic e ec in
Gd
36
Y
20
Al
24
Co
20
bulk me allic glass, J. Alloys Compd. 457 (1–2) (2008) 541–
544, h ps://doi.o g/10.1016/j.jallcom.2007.03.101.
[16] J.T. Huo, L.S. Huo, H. Men, X.M. Wang, A. Inoue, J.Q. Wang, C.T. Chang, R.W. Li,
The magne ocalo ic e ec o Gd-Tb-Dy-Al-M (M = Fe, Co and Ni) high-en opy
bulk me allic glasses, In e me allics 58 (2015) 31–35, h ps://doi.o g/10.1016/
j.in e me .2014.11.004.
[17] J.T. Huo, L.S. Huo, J.W. Li, H. Men, X.M. Wang, A. Inoue, C.T. Chang, J.Q. Wang, R.
W. Li, High-en opy bulk me allic glasses as p omising magne ic e ige an s, J.
Appl. Phys. 117 (7) (2015), h ps://doi.o g/10.1063/1.4908286 073902.
[18] J.S. Liu, G.D. Qu, X.F. Wang, H.N. Chen, Y. Zhang, G.Y. Cao, R. Liu, S.D. Jiang, H.X.
Shen, J.F. Sun, In luence o Fe-doping amoun s on magne ocalo ic p ope ies o
Gd-based amo phous mic o ibe s, J. Alloys Compd. 845 (2020), h ps://doi.o g/
10.1016/j.jallcom.2020.156190 156190.
[19] G.L. Liu, D.Q. Zhao, H.Y. Bai, W.H. Wang, M.X. Pan, Room empe a u e able-like
magne ocalo ic e ec in amo phous Gd
50
Co
45
Fe
5
ibbon, J. Phys. D: Appl. Phys.
49 (5) (2016), h ps://doi.o g/10.1088/0022-3727/49/5/055004 055004.
[20] L. Xue, J. Li, W.M. Yang, C.C. Yuan, B.L. Shen, E ec o Fe subs i u ion on
magne ocalo ic e ec s and glass- o ming abili y in Gd-based me allic glasses,
In e me allics 93 (2018) 67–71, h ps://doi.o g/10.1016/j.
in e me .2017.11.007.
[21] A. Takeuchi, A. Inoue, Classi ica ion o bulk me allic glasses by a omic size
di e ence, hea o mixing and pe iod o cons i uen elemen s and i s
applica ion o cha ac e iza ion o he main alloying elemen , Ma e . T ans.
46 (12) (2005) 2817–2829, h ps://doi.o g/10.2320/ma e ans.46.2817.
[22] A. Inoue, S abliza ion o me allic supe cooled liquid and bulk amo phous
alloys, Ac a Ma e . 48 (1) (2000) 279–306, h ps://doi.o g/10.1016/S1359-
6454(99)00300-6.
[23] S. Guo, C.T. Liu, Phase s abili y in high en opy alloys: Fo ma ion o solid-
solu ion phase o amo phous phase, P og. Na . Sci. Ma e . In e . 21 (6) (2011)
433–446, h ps://doi.o g/10.1016/s1002-0071(12)60080-x.
[24] Y.J. Yang, B.Y. Cheng, Z.S. Jin, H.X. Gao, M.Z. Ma, X.Y. Zhang, C ys alliza ion
kine ics and mechanical p ope ies o Z
56
Cu
24
Al
9
Ni
7-x
Ti
4
Ag
x
(x = 0, 1, 3, 5, and
7) me allic glasses, J. Alloys Compd. 816 (2020), h ps://doi.o g/10.1016/
j.jallcom.2019.152589 152589.
[25] J. Xiong, S.Q. Shi, T.Y. Zhang, A machine-lea ning app oach o p edic ing and
unde s anding he p ope ies o amo phous me allic alloys, Ma e . Des. 187
(2020), h ps://doi.o g/10.1016/j.ma des.2019.108378 108378.
H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824
7
[26] Z.P. Lu, C.T. Liu, A new glass- o ming abili y c i e ion o bulk me allic glasses,
Ac a Ma e . 50 (13) (2002) 3501–3512, h ps://doi.o g/10.1016/s1359-6454
(02)00166-0.
[27] Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, P.K. Liaw, Solid-solu ion phase o ma ion
ules o mul i-componen alloys, Ad . Eng. Ma e . 10 (6) (2008) 534–538,
h ps://doi.o g/10.1002/adem.200700240.
[28] D.C. Zhao, T. Yamaguchi, D. Tusbasa, W.Q. Wang, Fab ica ion and ic ion
p ope ies o he AlFeC Co medium-en opy alloy coa ings on magnesium
alloy, Ma e . Des. 193 (2020), h ps://doi.o g/10.1016/j.ma des.2020.108872
108872.
[29] L.X. Shi, K.F. Yao, Composi ion design o Fe-based so magne ic amo phous
and nanoc ys alline alloys wi h high Fe con en , Ma e . Des. 189 (2020),
h ps://doi.o g/10.1016/j.ma des.2020.108511 108511.
[30] L. Deng, A. Gebe , L. Zhang, H.Y. Chen, D.D. Gu, U. Kühn, M. Zimme mann, K.
Kosiba, S. Pauly, Mechanical pe o mance and co osion beha iou o Z -based
bulk me allic glass p oduced by selec i e lase mel ing, Ma e . Des. 189
(2020), h ps://doi.o g/10.1016/j.ma des.2020.108532 108532.
[31] J. Zhou, Q.Q. Wang, X.D. Hui, Q.S. Zeng, Y.W. Xiong, K.B. Yin, B.A. Sun, L.T. Sun,
M. S oica, W.H. Wang, B.L. Shen, A no el FeNi-based bulk me allic glass wi h
high no ch oughness o e 70 MPa m
1/2
combined wi h excellen so
magne ic p ope ies, Ma e . Des. 191 (2020), h ps://doi.o g/10.1016/
j.ma des.2020.108597 108597.
[32] R.E. Hackenbe g, M.C. Gao, L. Kau man, G.J. Shi le , The modynamics and phase
equilib ia o he Al–Fe–Gd me allic glass- o ming sys em, Ac a Ma e . 50 (9)
(2002) 2245–2258, h ps://doi.o g/10.1016/s1359-6454(01)00435-9.
[33] Z.P. Lu, J. Shen, D.W. Xing, J.F. Sun, C.T. Liu, Bina y eu ec ic clus e s and glass
o ma ion in ideal glass- o ming liquids, Appl. Phys. Le . 89 (7) (2006),
h ps://doi.o g/10.1063/1.2336597 071910.
[34] B.C. Wei, W. Löse , L. Xia, S. Ro h, M.X. Pan, W.H. Wang, J. Ecke , Anomalous
he mal s abili y o Nd–Fe–Co–Al bulk me allic glass, Ac a Ma e . 50 (17)
(2002) 4357–4367, h ps://doi.o g/10.1016/s1359-6454(02)00272-0.
[35] C.J. Chen, K.K. Wong, R.P. K ishnan, L. Zhi Feng, D.H. Yu, Z.P. Lu, S.M. Cha ho h,
Highly collec i e a omic anspo mechanism in high-en opy glass- o ming
me allic liquids, J. Ma e . Sci. Technol. 35 (1) (2019) 44–47, h ps://doi.o g/
10.1016/j.jms .2018.09.008.
[36] A. Inoue, A. Takeuchi, T. Zhang, Fe omagne ic bulk amo phous alloys, Me all.
Ma e . T ans. A 29 (7) (1998) 1779–1793, h ps://doi.o g/10.1007/s11661-
998-0001-9.
[37] W.H. Wang, Roles o mino addi ions in o ma ion and p ope ies o bulk
me allic glasses, P og. Ma e . Sci. 52 (4) (2007) 540–596, h ps://doi.o g/
10.1016/j.pma sci.2006.07.003.
[38] Y.T. Wang, Z.Y. Pang, R.J. Wang, D.Q. Zhao, M.X. Pan, B.S. Han, W.L. Wang, W.H.
Wang, Doping-induced o ma ion o bulk nanoc ys alline alloy om me allic
glass wi h con ollable mic os uc u e and p ope ies, J. Non-C ys . Solids 352
(5) (2006) 444–449, h ps://doi.o g/10.1016/j.jnonc ysol.2006.01.015.
[39] Z.G. Zheng, X.C. Zhong, K.P. Su, H. Yu, Z.W. Liu, D.C. Zeng, Magne ic p ope ies
and la ge magne ocalo ic e ec s in amo phous Gd-Al-Fe alloys o magne ic
e ige a ion, Sci. China Phys. Mech. As on. 54 (7) (2011) 1267–1270, h ps://
doi.o g/10.1007/s11433-011-4363-4.
[40] P. Hansen, C. Clausen, G. Much, M. Rosenk anz, K. Wi e , Magne ic and
magne o-op ical p ope ies o a e-ea h ansi ion-me al alloys con aining
Gd, Tb, Fe, Co, J. Appl. Phys. 66 (2) (1989) 756–767, h ps://doi.o g/10.1063/
1.343551.
[41] L.D. G i i h, Y. Mud yk, J. Slaugh e , V.K. Pecha sky, Ma e ial-based igu e o
me i o calo ic ma e ials, J. Appl. Phys. 123 (3) (2018), h ps://doi.o g/
10.1063/1.5004173 034902.
[42] Law J.Y., F anco V., Magne ocalo ic Composi e Ma e ials, Encyclopedia o
Ma e ials: Composi es. h ps://doi.o g/10.1016/B978-0-12-819724-0.00038-0.
[43] M.F. Qian, X.X. Zhang, Z.G. Jia, X.H. Wan, L. Geng, Enhanced magne ic
e ige a ion capaci y in Ni-Mn-Ga mic o-pa icles, Ma e . Des. 148 (2018)
115–123, h ps://doi.o g/10.1016/j.ma des.2018.03.062.
[44] M.F. Qian, X.X. Zhang, X. Li, R.C. Zhang, P.G. Ma in, J.F. Sun, L. Geng, T.B. Sco ,
H.X. Peng, Magne ocalo ic e ec in bamboo-g ained Ni-Mn-Ga mic owi es
o e a wide wo king empe a u e in e al, Ma e . Des. 190 (2020), h ps://doi.
o g/10.1016/j.ma des.2020.108557 108557.
[45] S.K. Pal, C. F ommen, S. Kuma , B.C. Hauback, H. Fjell åg, G. Helgesen,
Enhancing gian magne ocalo ic e ec nea oom empe a u e by inducing
magne os uc u al coupling in Cu-doped MnCoGe, Ma e . Des. 195 (2020),
h ps://doi.o g/10.1016/j.ma des.2020.109036 109036.
[46] J.Y. Law, V. F anco, L.M. Mo eno-Rami ez, A. Conde, D.Y. Ka penko , I. Radulo ,
K.P. Skoko , O. Gu leisch, A quan i a i e c i e ion o de e mining he o de o
magne ic phase ansi ions using he magne ocalo ic e ec , Na . Commun. 9
(1) (2018) 2680, h ps://doi.o g/10.1038/s41467-018-05111-w.
[47] B.K. Bane jee, On a gene alised app oach o i s and second o de magne ic
ansi ions, Phys. Le . 12 (1) (1964) 16–17, h ps://doi.o g/10.1016/0031-
9163(64)91158-8.
[48] V. F anco, A. Conde, V.K. Pecha sky, K.A. Gschneidne J ., Field dependence o
he magne ocalo ic e ec in Gd and (E
1x
Dy
x
)Al
2
: does a uni e sal cu e
exis ?, EPL 79 (4) (2007) 47009, h ps://doi.o g/10.1209/0295-5075/79/47009.
[49] Q. Luo, B. Schwa z, N. Ma e n, J. Ecke , Gian i e e sible posi i e o la ge
e e sible nega i e magne ic en opy change e olu ion in Tb-based bulk
me allic glass, Phys. Re . B 82 (2) (2010), h ps://doi.o g/10.1103/
PhysRe B.82.024204 024204.
[50] C.M. Pang, C.C. Yuan, L. Chen, H. Xu, K. Guo, J.C. He, Y. Li, M.S. Wei, X.M. Wang,
J.T. Huo, B.L. Shen, E ec o Y ium addi ion on magne ocalo ic p ope ies o
Gd-Co-Al-Ho high en opy me allic glasses, J. Non-C ys . Solids 549 (2020),
h ps://doi.o g/10.1016/j.jnonc ysol.2020.120354 120354.
[51] Z.Q. Dong, Z.J. Wang, S.H. Yin, Magne ic p ope ies and magne o-calo ic e ec
(MCE) in Cu
22
Al
18
Ho
22
Tm
20
Gd
18
amo phous ibbons, J. Magn. Magn. Ma e .
514 (2020), h ps://doi.o g/10.1016/j.jmmm.2020.167270 167270.
H. Yin, J. Law, Y. Huang e al. Ma e ials & Design 206 (2021) 109824
8