The e ec o dis ibu ed exchange pa ame e s on magne ocalo ic e ige a ion capaci y
in amo phous and nanocomposi e ma e ials
N. J. Jones, H. Uca , J. J. Ipus, M. E. McHen y, and D. E. Laughlin
Ci a ion: Jou nal o Applied Physics 111, 07A334 (2012); doi: 10.1063/1.3679456
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The e ec o dis ibu ed exchange pa ame e s on magne ocalo ic
e ige a ion capaci y in amo phous and nanocomposi e ma e ials
N. J. Jones,
a)
H. Uca , J. J. Ipus, M. E. McHen y, and D. E. Laughlin
Ma e ials Science and Enginee ing, Ca negie Mellon Uni e si y, Pi sbu gh, Pennsyl ania 15213, USA
(P esen ed 31 Oc obe 2011; ecei ed 24 Sep embe 2011; accep ed 13 Decembe 2011; published
online 17 Feb ua y 2012)
The empe a u e dependen magne iza ion o nanocomposi e alloys has been i wi h a modi ied
Hand ich-Kobe equa ion wi h an asymme ic exchange luc ua ion pa ame e combined wi h he
A o -Noakes equa ion. The wo equa ions o s a e a e combined o calcula e he en opy change in
he magne ocalo ic e ec associa ed wi h he e omagne ic o pa amagne ic phase ans o ma ion.
The comple e i o he M(T) o (Fe
70
Ni
30
)
88
Z
7
B
4
Cu nanocomposi e powde is accomplished by
combining he wo heo ies. We in es iga e he b oadening o he second-o de ansi ion a ising
om asymme ic exchange pa ame e s and esul ing om he luc ua ions o in e a omic spacing
ound in an amo phous ma ix and he asymme ic dependence o exchange ene gy on in e a omic
spacing. The magne ic en opy cu e e ealed ex a b oadening wi h a e ige a ion capaci y (RC)
alue o 135 J/kg a 5 T, which is compa able o (Fe
76
C
8-x
Mo
x
Cu
1
B
15
) ibbons, which ha e a RC
alue o 180 J/kg o he same applied ield. B oadening o he magne ic en opy can lead o la ge
RC alues and a wide wo king empe a u e ange, making nanocomposi e alloys p omising o
magne ocalo ic applica ions. V
C2012 Ame ican Ins i u e o Physics. [doi:10.1063/1.3679456]
I. INTRODUCTION
So nanocomposi e alloys ha e he po en ial o be good
candida es o magne ocalo ic applica ions. No only do hey
possess unique amo phous alloy p ope ies such as ha ing
low hys e esis losses, low elec ical esis i i y, and uneable
Cu ie empe a u es, T
C
, wi h mino composi ional changes,
hey a e also easy o suspend in solu ions hus p o iding e -
sa ili y in applica ions.
The pe o mance o he alloys is assessed by a pa ame e
called e ige a ion capaci y. Acco ding o Wood and Po -
e ’s de ini ion o e ige a ion capaci y,
1
peak magni ude
and wid h a e equally impo an hus making i a sui able
me ic o compa ing di e en alloys. The magne ocalo ic
esponse o so amo phous alloys has been i using he
A o -Noakes equa ion by F anco e al. a ound he ansi ion
empe a u e.
2
Howe e , his equa ion does no adequa ely
app oxima e he magne ic esponse o he alloy a empe a-
u es well below T
C
.
Well below T
C
, he empe a u e dependence o magne -
iza ion can be app oxima ed using he Hand ich-Kobe equa-
ion wi h a modi ied B illouin unc ion.
3
Addi ionally, his
equa ion o s a e helps us unde s and he ex a b oadening in
DS
M
esul ing om he amo phous phase o he nanocompo-
si es. Acco ding o he Be he-Sla e cu e,
4,5
luc ua ions in
a omic spacing, as well as o he diso de a de ec s and in e -
aces can lead o an asymme ic dependence o he exchange
in e ac ions. These change he magne iza ion beha io , which
ul ima ely in oduces ex a b oadening in he magne ic en-
opy esponse o he alloy. In his pape , we combine he wo
a o emen ioned equa ions o s a es o ha e a be e desc ip ion
o M(T) o so nanocomposi e alloys. This will lead o a be -
e desc ip ion o magne ic en opy change, DS
M
(T), and
mo e accu a e p edic ions o e ige a ion capaci y.
II. EXPERIMENTAL PROCEDURE
Amo phous ibbons o (Fe
70
Ni
30
)
88
Z
7
B
4
Cu
1
( ypically
2–3 mm wide and 20 lm hick) we e ob ained by he mel -
spinning echnique in an A a mosphe e, s a ing om a c-
mel ed p ecu so s. The amo phous cha ac e o he as-cas
alloy was e i ied by X- ay di ac ion (XRD). Ribbons wi h
a leng h o app oxima ely 30 mm we e cu and sealed in
ha dened s eel ials adding ha dened s eel balls in a a io o
10:1. This p ocedu e was done unde A a mosphe e in a glo-
ebox. Ball milling o ibbon pieces was pe o med using a
Spex 8000 D mill o 4 h. In o de o ob ain a single cc
phase, he powde ed sample was sealed in a qua z c ucible
in an A a mosphe e, annealed in he cc egion o he phase
diag am, 700 C, and quenched in wa e o s abilize he me -
as able cc c-FeNi phase.
The ield dependence o magne iza ion was measu ed in
a physical p ope ies measu emen sys em (PPMS) wi h a
ib a ing sample magne ome e (VSM) head in a liquid
helium-cooled Dewa . Magne iza ion e sus empe a u e
was measu ed wi h applied ields o 5500 Oe and 500 Oe
om 400 K o app oxima ely 100 K, along wi h hys e esis
loops measu ed e e y 2 K, wi h ields up o 90 kOe.
III. FITTING MODELS
Two equa ions ha e been s udied o desc ibe he mag-
ne iza ion phenomenon o so magne ic alloys. Howe e ,
nei he one o hem was su icien o app oxima e he mag-
ne iza ion esponse a all empe a u e egimes. Gallaghe
e al.
3
modi ied he Hand ich-Kobe equa ion by in oducing
a)
Au ho o whom co espondence should be add essed. Elec onic mail:
[email protected].
0021-8979/2012/111(7)/07A334/3/$30.00 V
C2012 Ame ican Ins i u e o Physics111, 07A334-1
JOURNAL OF APPLIED PHYSICS 111, 07A334 (2012)
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wo asymme ic exchange luc ua ion pa ame e s, d
þ
and d
-
,
yielding Eq. (1)
ðTÞ¼1
2 Bs½ð1þdþÞxþBs½ð1dÞxg:(1)
He e, he diso de o he alloy has been aken in o conside a-
ion by assuming non-symme ic exchange in e ac ions p es-
en in he amo phous ma ix o he nanocomposi e alloy. This
equa ion desc ibes he M(T) esponse well o low empe a-
u es. Howe e , i is insu icien o he egime whe e he an-
si ion om e omagne ic o pa amagne ic phases occu s.
Mo e ecen ly F anco e al.
6
used he A o -Noakes
equa ion (Eq. (2)) o i hei magne iza ion e sus empe a-
u e cu es a ound he Cu ie empe a u e, and p edic he
DS
M
esponse o so amo phous alloys.
H1=c¼aðTTCÞM1=cþbM1=bþ1=c:(2)
In Eq. (2),band ca e c i ical exponen s desc ibing he em-
pe a u e dependence o magne iza ion and in e se suscep i-
bili y, espec i ely. This equa ion was accu a e in desc ibing
and p edic ing he M(T) nea he ansi ion empe a u e, bu
i was no as accu a e a lowe empe a u es.
Combining he wo equa ions b ings bo h he low em-
pe a u e accu acy and diso de wi hin he con ex o a modi-
ied B illouin unc ion and he Cu ie ail oge he in o one
cu e. Because he wo equa ions a e implici ly de ined o
no exac ly sol able, he equa ions need o be e alua ed sep-
a a ely and combined using wo possible me hods. In his
wo k, Ma hema ica
7
was used o abula e da a a e sol ing
he equa ions, and hen he da a was in e pola ed o c ea e a
unc ion ha was di e en iable.
The A o -Noakes equa ion was bo h i ed using he
hys e esis loops o es ima e band c, and by adjus ing he
cons an s by hand o ge a good i ; he i ing p ocedu e as
de ailed by F anco e al.
6
was no di ec ly applicable o he
nanocomposi e powde s analyzed in his pape , and, as men-
ioned by F anco e al., a ull compu e i o he equa ion o
he cu e is un easonable. Bo h cu es had adjus able pa am-
e e s o sa u a ion magne iza ion, Cu ie empe a u e, and all
o he cons an s. In joining he cu es, bo h ma ching he
slopes and inding he angen poin s whe e he cu es o e -
lap was used. The minimum change in slope be ween he
cu es o minimum dis ance be ween hem was calcula ed in
he ansi ion egion and used o c ea e a piecewise di e en-
iable unc ion u ilizing bo h equa ions. Bo h joining me h-
ods p o ided i ually he same joining empe a u e. Nei he
cu e had he same end in slope, howe e , so he inal
en opic e alua ion, which elies on he de i a i e o he
M T cu e, had a jump in i , due o he inaccu acy. This a i-
ac a ound 165 K is due o he union o he wo heo ies and
is no p esen in he da a. The ag eemen be ween he wo
heo ies a ound he ansi ion poin is con inually being
in es iga ed and will be imp o ed wi h u u e esea ch.
IV. RESULTS AND DISCUSSION
Figu e 1shows expe imen al da a om he PPMS
along wi h he da a i s using bo h he A o -Noakes and
modi ied-B illouin i o Gallaghe . As can be seen, he
B illouin- i is necessa y a lowe empe a u es, howe e , he
Cu ie ail is no accoun ed o ; despi e he below- oom-
empe a u e Cu ie empe a u e, he magne iza ion s ill ails
o well un il a ound 400 K. This la ge ail is e en ue in he
lowe ield da a. To i he da a, he A o -Noakes i had he
ollowing pa ame e s: a ¼0.79, b ¼0.00893, b¼0.428,
c¼1.38, T
C
¼216 K. The B illouin i needed modi ying pa-
ame e s as well o i he cu a u e o he expe imen al da a:
d
þ
¼0.75, d

¼0.26, T
C
¼208 K, M
s
¼60.1 emu/g. The
a iable Cu ie empe a u e is due o he wo di e en i s and
how hey unde s and Cu ie empe a u e and is wi hin de ini-
ional limi s.
8
The ansi ion egion was ound o be 163 K
o he de i a i e me hod, wi h he p oximi y me hod yield-
ing 166 K; he de i a i e me hod is used o Fig. 2, below.
The magne ic en opy change due o he applica ion o a
magne ic ield, H, was e alua ed by p ocessing he empe a-
u e and ield dependen magne iza ion cu es using a nu-
me ical app oach using Eq. (3):
DSM¼ðHmax
0
@M
@T

H
dH;(3)
whe e DS
M
is he magne ic en opy change, M is he magne -
iza ion, and T is he empe a u e. Re ige an capaci y, RC,
is calcula ed using Wood and Po e ’s me hod,
1
whe e
RC ¼DS
M
DT, and DT¼T
h
–T
c
is he di e ence be ween he
ho and cold ese oi s. The calcula ed en opy cu e is
shown in Fig. 2 o he combined i and he A o -Noakes
i o a maximum ield o 5 T. The en opy cu e calcula ed
om he ac ual da a is also shown in Fig. 2. The expe imen-
al da a was smoo hed by aking he a e age o 25 poin s on
each side o a da a poin (co esponding o an a e age o e
4.5 C); his smoo hing was necessa y o educe he noise
p esen in expe imen al da a as magni ied by aking he de-
i a i e o he da a. The combined i gi es a ue measu e
o he ac ual beha io o he ma e ial and does no pla eau a
low empe a u es gi ing a alse e ige an capaci y. The dis-
c epancy be ween he i and he expe imen al da a is due o
he quali y o he i (especially he ma ching o he expe i-
men al slope), as well as he a e aging o he da a.
By using ull wid h a hal maximum (FWHM) as an indi-
ca ion o ou RC ec angle, we can calcula e he magne ocalo ic
FIG. 1. (Colo online) A i o expe imen al da a (dashed line) using bo h an
exchange-pa ame e -modi ied B illouin equa ion (lowe solid line) and he
A o -Noakes (uppe solid line) equa ion, wi h a ansi ion in i ing me hod
a ound 160 K (da a aken wi h an applied ield o 5500 Oe).
07A334-2 Jones e al. J. Appl. Phys. 111, 07A334 (2012)
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p ope ies o ou powde , as compa ed wi h common alues
om he li e a u e, and compa ing he esul wi h he possible
alue wi hou he combined i . F om Fig. 2, he nanocomposi e
powde has a e ige an capaci y o 135 J/kg using he ull
combined i ; when using jus he A o -Noakes equa ion, ou
alue would ha e been much highe and a ound 186 J/kg. Wi h-
ou he a ied exchange pa ame e s, ou B illouin slope would
no ha e been co ec and would also ha e been oo s eep,
educing he e ige an capaci y om ha calcula ed abo e.
The RC alue o an ini ial nanocomposi e sample
shows p omise o use in magne ocalo ic applica ions, since
i is on pa wi h hose ound in he li e a u e, speci ically
when compa ed wi h amo phous (Fe
76
C
8-x
Mo
x
Cu
1
B
15
) ib-
bons,
2
which ha e a RC alue o 180 J/kg.
V. CONCLUSIONS
We ha e shown he e icacy and he necessi y o includ-
ing he ull magne iza ion cu e in magne ocalo ic calcula-
ions o e ige an capaci y. While he A o -Noakes
equa ion p o ides a good i o he ansi ion empe a u e, a
ull i o he magne iza ion e sus empe a u e cu e is
necessa y o a uly accu a e calcula ion o RC. When
calcula ing he alues o he nanocomposi e powde p e-
pa ed abo e, we ound ha i has s ong capabili ies as a ma-
e ial o magne ocalo ic applica ions. When conside ing
nanocomposi e ma e ials, howe e , a a ied exchange pa-
ame e is necessa y o he B illouin i , as shown by
Gallaghe and is needed no only o i he da a well bu also
o ge he co ec RC alue.
ACKNOWLEDGMENTS
N.J.J. g a e ully acknowledges suppo om a DOD
SMART schola ship. N.J.J., M.E.M., and D.E.L. acknowl-
edge suppo o he NSF h ough G an No. DMR #0804020
and he Da a S o age Sys ems Cen e .
1
M. E. Wood and W. H. Po e , C yogenics 25, 667 (1985).
2
V. F anco e al., Appl. Phys. Le . 90, 052509 (2007).
3
K. A. Gallaghe e al., J. Appl. Phys. 85, 5130 (1999).
4
H. A. Be he and A. Somme eld, Handbuch de Physik, Vol. 24 (Sp inge ,
Be lin, 1933).
5
J. C. Sla e , Phys. Re . 36, 57 (1930).
6
V. F anco e al., J. Appl. Phys. 104, 033903 (2008).
7
Wol am Resea ch, Inc., Ma hema ica, Ve sion 8.0, Champaign, IL, 2010.
8
B. D. Culli y and C. D. G aham, In oduc ion o Magne ic Ma e ials, 2nd
ed. (John Wiley & Sons, Hoboken, NJ, 2009), p. 126.
FIG. 2. (Colo online) Change in en opy in e-
g a ed om Fig. 1wi h H
max
a 5 T using jus
he A o -Noakes equa ion (dashed), he com-
bined i (da k line), and a e aged expe imen al
da a (ligh g ay line).
07A334-3 Jones e al. J. Appl. Phys. 111, 07A334 (2012)
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