1
Mechanically induced diso de and c ys alliza ion p ocess in Ni-Mn-In ball-
milled alloys
V. Sánchez-Ala cos1,2, V. Reca e1,2, J. I. Pé ez-Landazábal1,2, S. La umbe1,2, R.
Caballe o-Flo es1,2, I. Unzue a3,4, J.A. Ga cía4,5, F. Plazaola3 and J. A. Rod íguez-
Velamazán6,7
1Depa amen o Física. Uni e sidad Pública de Na a a, Campus de A osadia, 31006 Pamplona, Spain
2Ins i u e o Ad anced Ma e ials (INAMAT), Uni e sidad Pública de Na a a, Campus de A osadía,
31006 Pamplona, Spain
3Elek i a e e a Elek onika Saila, Euskal He iko Unibe si a ea UPV/EHU, p.k. 644, 48080 Bilbao,
Spain
4BC Ma e ials (Basque Cen e o Ma e ials, Applica ions and Nanos uc u es), 48080 Leioa, Spain
5Fisika Aplika ua II Saila, Euskal He iko Unibe si a ea UPV/EHU, p.k. 644, 48080 Bilbao, Spain
6 Ins i u o de Ciencia de Ma e iales de A agón, Depa amen o de Física de la Ma e ia condensada,
CSIC–Uni e sidad de Za agoza, E-50009 Za agoza, Spain
7 Ins i u Laue Lange in, 71, A enue des Ma y s, 38042 G enoble Cedex, F ance
*Co esponding au ho : Tel.: +34 948 169582; Fax.: +34 948 169565
E-mail add ess: icen e.sanchez@una a a.es
Abs ac .
High mechanical de o ma ion has been induced in a Ni-Mn-In me amagne ic shape memo y alloy
by means o ball milling. The e olu ion o bo h he ma ensi ic ans o ma ion and he magne ic
p ope ies associa ed o he mic os uc u al a ia ions has been cha ac e ized. The as-milled
nanome ic pa icles display an amo phous s uc u e wi h a us a ed magne ic s a e compa ible
wi h a canonical spin-glass. On hea ing, an ab up c ys alliza ion p ocess occu s a ound 500K
leading o a cubic B2 s uc u e, which, in u n, does no show ma ensi ic ans o ma ion.
Modi ied A o plo s poin o compe ing long- and sho - ange magne ic couplings in he B2
s uc u e. On u he hea ing, a elaxa ion p ocess akes place abo e 700 K concu en ly wi h a
B2-L21 a omic o de ing, gi ing ise o an anomalous wo-s ep he mal expansion. The combined
e ec o bo h p ocesses makes possible he subsequen occu ence o a ma ensi ic
ans o ma ion, which akes place a he same empe a u e han in he bulk. The la ge ela i e-
cooling-powe linked o he magne ocalo ic e ec a he ma ensi ic ans o ma ion in he
annealed powde makes i in e es ing o p ac ical applica ions o magne ic e ige a ion a
nanoscale.
Keywo ds: Ni-Mn-In, ball-milling, c ys alliza ion, a omic o de , nanopa icles
This documen is he Accep ed Manusc ip e sion o a Published Wo k ha appea ed in inal o m in
Jou nal o Alloys and Compounds
689(1) : 983-991 (2016). To access he inal edi ed and published wo k see h ps://doi.o g/10.1016/j.jallcom.2016.08.068 © 2016 Else ie
unde CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
2
1. INTRODUCTION
Ni–Mn-based Heusle alloys exhibi ing bo h long- ange magne ic o de ing and he moelas ic
ma ensi ic ans o ma ion (MT) a e being in ensi ely in es iga ed o e ecen yea s, om bo h
undamen al and applied poin s o iew, due o he unique p ope ies hey show linked o he
occu ence o a i s -o de s uc u al ans o ma ion be ween magne ically o de ed phases [1-3].
The magne ism in hese alloys mainly a ises om he coupling be ween he Mn a oms, in which
he magne ic momen is chie ly con ined, so he magne ic exchange in e ac ions (which can be
ea ed in he amewo k o a Rude man-Ki el-Kasuya-Yoshida model) s ongly depend on he
Mn–Mn dis ance [4, 5]. The e o e, di e en sequences o magne os uc u al ans o ma ions can
be obse ed depending on bo h he hi d alloying elemen and he change in in e a omic dis ances
caused by he MT. In pa icula , in Ni-Mn-Z (Z=In, Sn, and Sb) alloys, he so-called
me amagne ic shape memo y alloys, he MT akes place be ween a e omagne ic aus eni e and
weak magne ic ma ensi ic phase, in such a way ha he la ge magne iza ion d op occu ing a
he MT allows he induc ion o he MT by an applied magne ic ield [6]. This phenomena gi es
ise o mul i unc ional p ope ies, namely magne ic shape memo y, gian magne o esis ance and
la ge in e se magne ocalo ic e ec (MCE), o g ea echnical in e es o p ac ical applica ions in
sensing and magne ic e ige a ion [7-14].
One o he main d awbacks o he me amagne ic shape memo y alloys, in u n, is he poo
mechanical p ope ies hey show. All hese alloys a e e y b i le and di icul o handle, and
c acks o m e y easily when he c ys al is being he mally cycled h ough he phase
ans o ma ion [15, 16]. Alloys in o m o ilms, ibbons, wi es o oams [17-20] ha e been
s udied as an al e na i e o o e come he mechanical limi a ions o he bulk ma e ial. In pa icula ,
he in eg a ion o powde alloys in o a polyme o o m composi es has been ound o be especially
in e es ing o he de elopmen o magne ically-con olled dampe s and ac ua o s. Such
composi es may show low cos , la ge mechanical ene gy abso p ion and good mechanical
p ope ies [21, 22]. In his case, a p e ious comple e cha ac e iza ion o he powde alloy is
needed in o de o p ope ly une he esponse o he composi es.
3
The magne os uc u al p ope ies o me amagne ic shape memo y alloys ha e been deeply
s udied in polyc ys alline bulk alloys. Ne e heless, up o now, much less wo k has been de o ed
o he analysis o he MT and he magne ic p ope ies a educing sizes ending o nanoscale. E en
hough he g ain size and he s a e o in e nal ensions a e known o be wo pa ame e s highly
in luencing he cha ac e is ics o he MT h ough he a ia ion o he elas ic ene gy e m [23]. In
his sense, i has been ecen ly p oposed ha below a c i ical size, shape memo y alloy
nanopa icles show non hys e e ic beha io [24]. Taking in o accoun ha he ans o ma ion
hys e esis linked o a i s o de ansi ion is an impo an d awback o magne ocalo ic
applica ions, nanopa icle alloys seem o be a p omising al e na i e p ocedu e o imp o e
simul aneously he mechanical beha io and he MCE equi ed o e ige a ion sys ems.
Ball milling echnique is one o he simples and cheapes me hods o p oduce nanos uc u ed
ma e ials. The use o ball milling as a educ ion me hod o nanoscale size has been s udied in
mul iple sys ems, and in e es ing physical and chemical phenomena ha e been ound o appea .
A conside able modi ica ion o he magne ic beha io and he syn hesis o new phases ha e been
epo ed [25-27]. Fo ins ance, he educ ion in he size o pa icles by ball milling may op imize
he MCE in di e en magne ic sys ems, ei he by inc easing he empe a u e ange [28] o by
educing he hys e e ic losses linked o a magne os uc u al i s o de ans o ma ion [29]. On he
o he hand, oge he wi h g ain size educ ion, ball milling p oduces a huge amoun o de ec s
( acancies, disloca ions, chemical diso de , s ains,…) in he ma e ial. A p ope analysis o he
milled powde may he e o e p o ide aluable in o ma ion conce ning he in luence o hose
de ec s on bo h he MT and he magne ic p ope ies. The e ec o ball milling on he
magne os uc u al p ope ies has been s udied in Ni-Mn-Ga, whe e he e ec o he mal
ea men s has been widely cha ac e ized and di e en sequences o s uc u al ansi ion (di e en
om hose in he co esponding bulk) ha e been ound in he achie ed nanopa icles [30-33].
Likewise, nanopa icles o Ni-Mn-Sn ha e been ecen ly ob ained by ball milling [34, 35]. As in
Ni-Mn-Ga, a omic diso de and la ice s ain inhibi he MT in he as-milled alloys, while pos -
mill annealing ea men s a e needed o es o e he MT. A signi ican in luence o annealing on
4
he e omagne ic exchange in e ac ion, exchange bias and MCE, has been also epo ed in hese
alloys. On he con a y, he use o ball milling in he ques o unc ional nanopa icles has been
sca cely s udied in he Ni-Mn-In alloys [36, 37]. In ac , a comple e s udy on he co ela ion
be ween mic os uc u e and magne os uc u al p ope ies in Ni-Mn-In nanopa icles is s ill
absen .
This wo k is de o ed o he s udy o he e olu ion o bo h he ma ensi ic ans o ma ion and he
magne ic p ope ies wi h mic os uc u e in ball-milled Ni-Mn-In nanome ic pa icles. I is ound
ha he as-milled sample display an amo phous s uc u e wi h a us a ed magne ic s a e
compa ible wi h a canonical spin-glass. The c ys alliza ion p ocess aking place on hea ing he
milled alloy and he magne ic p ope ies o he esul ing B2 s uc u e ha e been cha ac e ized. A
elaxa ion p ocess occu s on annealing abo e 700 K, concu en ly wi h a B2-L21 a omic o de ing,
gi ing ise o an anomalous wo-s ep he mal expansion. The combined e ec o bo h p ocesses
makes possible he subsequen occu ence o a ma ensi ic ans o ma ion, which akes place a
he same empe a u e han in he bulk. The la ge ela i e cooling powe linked o he
magne ocalo ic e ec a he ma ensi ic ans o ma ion in he annealed pa icles makes hem
in e es ing o p ac ical applica ions o magne ic e ige a ion a nanoscale.
2. EXPERIMENTAL
A Ni50Mn34In16 alloy was p epa ed om high pu i y elemen s by a c mel ing unde p o ec i e A
a mosphe e. The as-cas ingo was homogenized a 1073 K du ing 15h and hen quenched in o
iced wa e . The composi ion o he elabo a ed alloy was analyzed by EDS in a Jeol JSM-5610LV
Scanning Elec on Mic oscope (SEM). The alloy was subjec ed o a ball milling p ocess in an
a gon a mosphe e du ing an e ec i e milling ime o 40h a oom empe a u e. In o de o p e en
o e hea ing o he sample and g inding ja s, he samples we e milled du ing 5 minu es (e ec i e
milling ime) and hen s opped o 10 minu es, and so on. Ball milling was pe o med a 300 pm
using a Re sch PM4 wi h a ball:powde a io o 7:1 and 7 balls o 5 mm diame e . Bo h ja s and
balls we e o ungs en ca bide. The s uc u al ans o ma ions and he possible eco e y p ocesses
5
aking place on annealing he as-milled powde samples we e cha ac e ized by di e en ial
scanning calo ime y (Q-100 DSC, TA Ins umen s). The magne ic cha ac e iza ion
(magne iza ion and suscep ibili y measu emen s)) was pe o med by SQUID magne ome y (QD
MPMS XL-7). Pa icles size and shape we e obse ed by con en ional ansmission elec on
mic oscopy (Hi achi H600 100 kV TEM). The e olu ion o c ys al s uc u e, long- ange a omic
o de , c ys alli e size and mic os ains we e de e mined om in-si u powde neu on di ac ion
measu emen s pe o med on he high- lux D1B wo-axis di ac ome e , a he Ins i u e Laue-
Lange in (G enoble, F ance). The di ac ion pa e ns we e measu ed on hea ing om oom
empe a u e (RT) up o 1173K a 1K/min using a neu on wa eleng h o 1.28 Å. The s uc u es
we e e ined by he Rie eld me hod using he FullP o package p og ams [38].
3. RESULTS AND DISCUSSION
Figu e 1a shows he DSC he mog am pe o med on cooling/hea ing he e e ence bulk alloy
be ween 350K and 165 K. The occu ence o a i s -o de MT is e idenced by he p esence o he
exo he mic and endo he mic peaks co esponding o he o wa d and e e se MT, espec i ely.
The ans o ma ion empe a u es, aken as he empe a u e o he peak maximum, a e TM o wa d =
226 K and TMRe e se = 241 K, which means a he mal hys e esis o ∆T = 15 K o he MT. A
second-o de magne ic ansi ion aking place in he aus eni ic phase can also in e ed om he
baseline in lec ion obse ed abo e he MT, a ound 300 K. The comple e sequence o
magne os uc u al ansi ions ha e been de e mined om he low- ield (100 Oe) magne iza ion
e sus empe a u e cu e, M(T), shown in Figu e 1b. The magne iza ion inc eases on cooling
below 300 K, due o he e omagne ic o de ing o he aus eni ic phase a he Cu ie empe a u e,
TCaus , and hen i suddenly dec eases on u he cooling o he almos pa amagne ic ma ensi e.
The subsequen inc ease o magne iza ion is linked o he magne ic o de ing o he low-
empe a u e phase a TCma . As shown in he inse , he magne iza ion d op associa ed o he
ma ensi ic ans o ma ion occu s a lowe empe a u es on inc easing he applied magne ic ield,
H, acco ding o he Clausius-Clapey on equa ion
6
(1)
whe e TM is he MT empe a u e, and ∆M and ∆S he magne iza ion and en opy change a TM,
espec i ely. Since he di e en exchange in e ac ions in each s uc u al phase p omo e a
discon inui y in he magne ic en opy a he MT empe a u e, he applica ion o a magne ic ield
a empe a u es close o TM may esul in he induc ion o he ans o ma ion, and he e o e in a
magne ically induced en opy change ( ha is, in a MCE). The en opy change in iso he mal
condi ions can be calcula ed by nume ical in eg a ion o he de i a i e o he magne iza ion wi h
espec o empe a u e ollowing he exp ession
(2)
The ob ained MCE alues a e shown in Figu e 1c as a unc ion o bo h empe a u e and applied
magne ic ield. A posi i e peak (in e se MCE) is obse ed linked o he MT, which inc eases
wi h he inc easing magne ic ield up o a maximum alue o 12 J/kgK a 6 T, a alue simila o
ha ound in he li e a u e o his compound [12].
Once cha ac e ized, he e e ence bulk alloy was subjec ed o high ene gy ball-milling in o de
o p oduce nanopa icles. No ma ensi ic ans o ma ion was de ec ed om he DSC
he mog ams pe o med on he as-milled sample, sugges ing a c i ical impac o he ball-milling
on he c ys allog aphic s uc u e o he alloy. Figu e 2a shows he oom empe a u e neu on
di ac ion pa e n o he as-milled samples. The absence o well-de ined B agg e lec ions seems
o con i m he achie emen o an almos amo phous phase, as a esul o he s uc u al dis o ion
and he associa ed in oduc ion o s uc u al de ec s caused by milling. In ac , he p esence o
some small and b oad peaks would indica e some ma ginal deg ee o c ys allini y in he alloy.
As shown in he TEM image in he inse , he milled powde mainly consis s on sphe oidal
nanome ic pa icles ( ens o nm) oge he wi h some bigge clus e s. In his espec , he sligh
peaks on he di ac og am could be also hough o be due o c ys alline o de inside
nanopa icles, ha is, o size e ec s on c ys alline powde . As we will see, he clea occu ence
o a c ys alliza ion p ocess disca ds his la e hypo hesis. The magne ic p ope ies o he as-
0
M
dT M
dH S
µ
D
=-
D
( ) ( )
0
,,0
H
iso
H
M
S S T H S T dH
T
¶
æö
D=-=
ç÷
¶
èø
ò
7
milled alloy ha e been analyzed om he empe a u e dependence o magne iza ion and AC
suscep ibili y measu emen s. Figu e 2b shows he ze o- ield cooled/ ield cooling/ ield hea ing
(ZFC/FC/FH) cu es ob ained on he as-milled sample unde 100 Oe. The spli ing be ween he
ZFC and FC cu es a low empe a u e (sha p jump in ZFC), ypical o us a ed magne ic
sys ems, sugges s a spin-glass s a e, as ecen ly p oposed in simila alloys [36]. As shown in he
uppe inse , he low magne iza ion alues a 6 T and he high magne ic aniso opy ( he sys em
does no sa u a e) a e indeed in ag eemen wi h a spin-glass beha io . Fu he mo e, a equency-
dependen maximum linked o he eezing empe a u e ( empe a u e o he maximum in he ZFC
cu e, T ), appea s in he measu emen s o he eal pa o suscep ibili y. The co esponding
equency dependence o he eezing empe a u e, T ( ), pe ec ly i s o he Vogel-Fulche law
[39], again in ag eemen wi h a spin-glass s a e. Fu he measu emen s del ing in o he low
empe a u e magne ic p ope ies o he milled alloys poin o a canonical spin-glass s a e [40].
The mic os uc u al e olu ion and he eco e y p ocesses aking place on hea ing he
amo phous sample ha e been s udied by means o ‘in-si u’ powde neu on di ac ion
expe imen s. Figu e 3a shows he he modi ac og ams ob ained on hea ing om RT up o 1220
K a a 1 K/min cons an a e. I can be seen ha he amo phous s uc u e emains s able up o 500
K. A his empe a u e c ys alliza ion occu s, as e idenced by he sudden appea ance o B agg
e lec ions. The occu ence o his p ocess does indeed con i m he amo phous-like s a e o he
as-milled alloy. Speci ically, he sample c ys allizes o a diso de ed B2 cubic s uc u e wi h
nea es -neighbo s long- ange a omic o de . On hea ing a ound 700 K, he appea ance o L21
supe s uc u e e lec ions ( hose in which he h, k, l indices a e all odd, acco ding o he
co esponding uni cell s uc u e ac o ) indica es he occu ence o an o de ing p ocess om B2
o a L21 cubic s uc u e wi h nex -nea es -neighbo s long- ange a omic o de . A simila B2-L21
o de ing p ocess is obse ed on hea ing bulk Ni-Mn-In alloys p e iously quenched om high
empe a u es. In ha case, in u n, he o de ing empe a u e (which indeed depends on he deg ee
o diso de e ained by quenching) ypically lies be ween 500 K and 600 K [41, 42]. On u he
hea ing abo e 900 K, he in ensi y o he L21 e lec ions g adually dec eases un il i comple ely
8
anishes as a consequence o he L21-B2 o de -diso de ansi ion, which akes place a 1050 K,
a empe a u e again almos 100 K highe han in bulk alloys [41, 42]. The empe a u e
dependence o he in eg a ed in ensi y o he (111) e lec ion shown in Figu e 3b illus a es he
e olu ion o long- ange a omic o de o he nanome ic pa icles wi h empe a u e. The wo
consecu i e o de ing p ocesses a e clea ly iden i iable om he appea ance and subsequen
disappea ance o he supe s uc u e e lec ion.
The mic os uc u al elaxa ion can be also explo ed om he analysis o he wid h o he B agg
peaks o he di ac ion pa e ns. In his espec , he in eg al b ead h me hod has been used o
de e mine he mic os uc u al e ec s om he analysis o he di ac ion peaks’ shape. This
me hod allows us o ob ain sepa a ely he c ys alli e size and mic os ain con ibu ions o he ull-
wid h a hal maximum (FWHM) o he di ac ion peaks om i s i ing o a Thompson-Cox-
Has ing pseudo-Voig p o ile unc ion. The p o ile ins umen al esolu ion unc ion used o he
analysis o he di ac ion pa e ns has been ob ained om he RT di ac og am pe o med on a
Na2Ca3Al2F14 sample ( ypical calib a ion compound). As an example, Figu e 4 shows he
di ac og ams ob ained o he B2 s uc u e a h ee di e en empe a u es, oge he wi h he
espec i e i s by Rie eld me hod. I can be seen ha he b oadening o he e lec ions
signi ican ly dec eases (and simul aneously he in eg a ed in ensi y inc eases) on hea ing up o
1173 K, poin ing ou a elaxa ion o he mic os uc u e. I is also wo h no ing he p esence o
small addi ional peaks, especially one a a ound 2θ = 29º, p obably asc ibed o he appea ance o
a small amoun o manganese oxide. In any case, jus a e y small mass ac ion o he alleged
oxide is in e ed om he ela i e in ensi y o he peaks, so no signi ican e ec a e expec ed
nei he on he magne ic p ope ies no on he alloy composi ion. The e olu ion o bo h
mic os ain and c ys alli e size wi h empe a u e is shown in Figu e 5a. The main mic os uc u al
elaxa ion akes place be ween 700 K and 800 K, whe e he mic os ain ab up ly dec eases om
0.35% o 0.1%. This is p ecisely he empe a u e ange in which he B2-L21 o de ing p ocess
occu s (see Figu e 3b). Taking in o accoun ha a omic o de ing implies a omic di usion, as long
as i is medi a ed by acancies, i poin s o acancy elimina ion and/o acancy-assis ed
9
disloca ion annihila ion as he main eco e y p ocesses. On he o he hand, he c ys alli e size
inc eases exponen ially wi h he inc easing empe a u e, om 20 nm a RT (in ag eemen wi h
TEM obse a ions) o 150 nm a 1100 K, app oxima ely. As expec ed, he highe g ow h a e is
eached abo e 800 K, jus a e he eco e y p ocess (mic os ain d op). Likewise, i is in e es ing
o no e ha he empe a u e dependence o he la ice pa ame e s (Figu e 5b) shows a ma ked
change in slope be ween 700 K and 800 K, concu en ly wi h bo h he B2-L21 o de ing and he
elaxa ion p ocesses, hus gi ing ise o an anomalous wo-s ep he mal expansion.
The c ys alliza ion p ocess obse ed om he modi ac ion has been also analyzed om DSC
measu emen s. Figu e 6 shows he he mog am ob ained on hea ing he amo phous powde s up
o 700 K a a 1 K/min a e (same hea ing a e han in neu on di ac ion expe imen ). A na ow
exo he mic peak (P1) o e lapped o a much b oade peak (P2) is obse ed be ween 500 K and
600 K. The empe a u e ange o appea ance and he wid h o he P1 peak a e in ag eemen wi h
he sha p c ys alliza ion p ocess e ealed by di ac ion measu emen s. In u n, no signi ican
s uc u al a ia ion is de ec ed linked o he P2 peak. Ne e heless, he en halpy o he whole
double-peak (∆H ≈ 70J/g) is simila o ha ob ained o he c ys alliza ion p ocess in simila
alloys, so he same o igin could be a ibu able o bo h peaks. The kine ics o he associa ed
p ocesses has been analyzed using he well-known Kissinge ’s me hod, om which he ac i a ion
ene gy o a he mally ac i a ed p ocess can be ob ained om he a ia ion o he DSC peak
empe a u e (TP) as a unc ion o he hea ing a e (
𝜙
), h ough he exp ession
(3)
whe e kB is he Bol zmann cons an , Ea is he ac i a ion ene gy and B is a cons an . The ac i a ion
ene gies, de e mined om he linea i o
ln$
(
𝜙/𝑇!
"
) s
1/𝑇!
shown in he inse o Figu e 6, a e
Ea = 1.7 eV and Ea = 1.8 eV o he P1 and P2 peaks, espec i ely. The simila i y be ween bo h
alues, which a e also in ag eemen wi h hose ob ained o he c ys alliza ion p ocess in ball-
milled amo phous Fe2MnGe alloys [43], ein o ces he idea o a simila o igin o he p ocesses
linked o bo h exo he mic peaks.
2
ln a
PBP
EB
TkT
=-+
16
[28] P. Go ia, P. Al a ez, J. Sánchez-Ma cos, J.L. Sánchez-Llamaza es, M.J. Pé ez J.A. Blanco, C ys al
s uc u e, magne ocalo ic e ec and magne o olume anomalies in nanos uc u ed P 2Fe17, Ac a Ma e . 57
(2009) 1724.
[29] W. Dagula, O. Tegus, X.W. Li, L. Song L, E. B uck, D.T. Cam Thanh DT, F.R. de Boe , K.H.J.
Buschow, Magne ic p ope ies and magne ic-en opy change o MnFeP0.5As0.5−xSix(x=0–0.3) compounds,
J. Appl. Phys. 99 (2006) 08Q105.
[30] Y.D. Wang, Y. Ren, Z.H. Nie, D.M. Liu, P.K. Liaw, J.Q. Yan, R. McQeeney, J.W. Richa dson, A.
Huq, S uc u al ansi ion o e omagne ic Ni2MnGa nanopa icles, J. Appl. Phys. 101 (2007) 63530.
[31] B. Tian, F. Chen, Y. Liu, Y.F. Zheng, S uc u al ansi ion and a omic o de ing o
Ni49.8Mn28.5Ga21.7 e omagne ic shape memo y alloy powde s p epa ed by ball milling, Ma e . Le .
62 (2008) 2851-2854.
[32] Y.V.B. de San anna, M.A.C. de Melo, I.A. San os, A.A. Coelho, S. Gama, L.F. Có ica, S uc u al,
mic os uc u al and magne ocalo ic in es iga ions in high-ene gy ball milled NiMnGa powde s, Sol. S a e
Comm. 148 (2008) 289-292.
[33] K. Vallalpe uman, R. Chokkalingam, M. Mahend an, Annealing e ec on phase ans o ma ion in
nano s uc u ed Ni–Mn–Ga e omagne ic shape memo y alloy, Phase T ansi ions 83 (2010) 509-517.
[34] A.L. Al es, E.C. Passamani, V.P. Nascimen o, A.Y. Takeuchi, C.J. La ica, In luence o g ain
e inemen and induced c ys al de ec s on he magne ic p ope ies o Ni50Mn36Sn14 Heusle alloys, J. Phys.
D: Appl. Phys. 43 (2010) 345001.
[35] A. Gho bi Va zaneh, P. Kameli, V.R. Zahedi, F. Ka imzadeh, H. Salama i, E ec o hea ea men
on ma ensi ic ans o am ion o Ni47Mn40Sn13 e omagne ic shape memo y alloy p epa ed by
mechanical alloying, Me . Ma e . In . 4 (2015) 758-764.
[36] D.M. Liu, Z.H. Nie, Y. Ren, Y.D. Wang, J. Pea son, P.K. Liaw, D.E. B own, S uc u al ansi ions
and magne ic p ope ies o Ni50Mn36.7In13.3 pa icles wi h amo phous-like phase, Me all. Ma . T ans. A 42
(2011) 3062-3070.
[37] X. Fei, W. Li, J. Liu, F. Xu, G. Tang, W. Tan, S. Li, Phase ansi ion o ball-milled Ni50-xMn37In13Cox
(x=0.5) alloy powde s, Ma e . Sci. Fo um 809 (2015) 377-383.
[38] J. Rod íguez-Ca ajal, Recen Ad ances in Magne ic S uc u e De e mina ion by Neu on Powde
Di ac ion, J. Physica B 192 (1993) 55-69.
[39] S. Sh ikman, E.P. Wohl a h, The heo y o he Vogel-Fulche law o spin glasses, Phys. Le . A 19
(1981) 467-470.
[40] S. La umbe, I. Unzue a, V. Sánchez-Ala cos, J.I. Pé ez-Landazábal, V. Reca e, J.A. Ga cía, F.
Plazaola, Low empe a u e magne ic p ope ies o a Ni50Mn34In16 ball-milled me amagne ic shape
memo y alloy, J. Non-C ys . Solids 44 (2016) 16-20.
[41] V. Reca e, J.I. Pé ez-Landazábal, V. Sánchez-Ala cos, J.A. Rod íguez-Velamazán, Dependence o
he ma ensi ic ans o ma ion and magne ic ansi ion on he a omic o de in Ni–Mn–In me amagne ic
shape memo y alloys, Ac a Ma e . 60 (2012) 1937-1945.
[42] V. Sánchez-Ala cos, V. Reca e, J.I. Pé ez-Landazábal, C. Gómez-Polo, J.A. Rod íguez-Velamazán,
Role o magne ism on he ma ensi ic ans o ma ion in Ni–Mn-based magne ic shape memo y alloys, Ac a
Ma e . 60 (2012) 459-468.
17
[43] L. Zhang, E. B üch, O. Tegus, K.J.H. Buschow, F.R. de Boe , The c ys alliza ion o amo phous
Fe2MnGe powde p epa ed by ball milling, J. Alloys and Compd. 352 (2003) 99-102.
[44] A. A o , J.E. Noakes, App oxima e equa ion o s a e o nickel nea i s c i ical empe a u e, Phys.
Re . Le . 19 (1967) 786.
[45] H.E. S anley, In oduc ion o phase ansi ions and c i ical phenomena, London Ox o d Uni e si y
P ess, London, 1971.
[46] J. S. Kou el, M.E. Fishe , De ailed magne ic beha io o Nickel nea i s Cu ie poin , Phys. Re . 136
(1964) A1626.
[47] K.A. Gschneidne J , V.K. Pecha sky, Magne ocalo ic ma e ials. Annu. Re . Ma e . Sci. 30 (2000)
387–429.
[48] N.M. B uno, C. Yegin, I. Ka aman, J.-H Chen, J.H. Ross J ., J. Liu, J. Li, The e ec o hea ea men s
on Ni43Mn42Co4Sn11 me a-magne ic shape memo y alloys o magne ic e ige a ion, Ac a Ma e . 74
(2014) 66-84.
Figu e cap ions
FIG. 1: (a) DSC he mog am pe o med on cooling/hea ing he e e ence bulk a 10 K/min. (b)
Tempe a u e dependence o magne iza ion o he bulk alloy a 100 Oe (inse : M(T) o di e en
applied ields anging om 100 Oe up o 60 kOe). (c) Magne ically-induced en opy change in
he bulk alloys as a unc ion o empe a u e and applied magne ic ield.
18
FIG. 2: (a) Room empe a u e neu on di ac ion pa e n o he as-milled samples (inse : TEM
mic og aph). (b) ZFC/FC/FH cu es ob ained on he as-milled sample unde 100 Oe (Uppe inse :
ield dependence o magne iza ion. Lowe inse : linea i ing o he Vogel-Fulche law).
FIG. 3: (a) In-si u neu on powde he modi ac og ams on hea ing be ween 330 K and 1220 K
a 1 K/min. (b) In eg a ed in ensi y o he (111) e lec ion as a unc ion o empe a u e.
FIG. 4: Measu ed neu on di ac ion pa e n (do s), calcula ed p o ile ( ull line) and di e ence
be ween he measu ed and calcula ed p o iles (dashed line) o he milled alloy a 538 K, 630 K
and 1170 K.
FIG. 5: (a) Mic os ain and c ys alline size as a unc ion o empe a u e. (b) E olu ion o la ice
pa ame e s (in e ms o he B2 cell) wi h empe a u e.
FIG. 6: DSC he mog am on hea ing he milled sample a 1 K/min. Inse : plo o
ln$
(
𝜙/𝑇!
"
) ss
1/𝑇!
o he P1 and P2 peak empe a u es.
FIG. 7: Tempe a u e dependence o he magne iza ion (cooling cu es) a 100 Oe o milled
samples hea ed up o 538 K and 630 K (jus abo e P1 and P2 peaks, espec i ely). Inse :
co esponding M(T) cu es unde 60 kOe applied ield.
FIG. 8: Magne ic- ield dependence o magne iza ion be ween 175 K and 275 K o applied ields
up o 60 kOe o (a) sample hea ed up o 538 K and (b) sample hea ed up o 630 K.
FIG. 9: Tempe a u e dependence o spon aneous magne iza ion (MS) and in e sely ini ial
suscep ibili y (χ0-1) oge he wi h hei i ing o equa ions (4) and (5), espec i ely. (a) Sample
hea ed up o 538 K, (b) sample hea ed up o 630 K.
19
FIG. 10: Kou el-Fishe plo s o he MS(T) and χ0-1(T) da a. (a) Sample hea ed up o 538 K, (b)
sample hea ed up o 630 K.
FIG. 11: (a) Tempe a u e dependence o magne iza ion a 100 Oe o he nanome ic pa icles
hea ed up o 1170 K (inse : M(T) o di e en applied ields anging om 100 Oe up o 60 kOe).
(b) Magne ically-induced en opy change in he milled alloy hea ed up o 1170 K alloys, as a
unc ion o empe a u e and applied magne ic ield.
