1
C i ical beha io s udy o magne ic ansi ions in Dy3Co single c ys als
A. He e o a, A.Oleaga a, *, A Salaza a, A. F. Gubkin b, c, N. V. Ba ano b, c
a Depa amen o de Física Aplicada I, Escuela de Ingenie ía de Bilbao, Uni e sidad del
País Vasco UPV/EHU, Plaza To es Que edo 1, 48013 Bilbao, Spain
bM.N. Mihee Ins i u e o Me al Physics, U al B anch o he Russian Academy o
Sciences, 620108 Eka e inbu g, Russia
cIns i u e o Na u al Sciences and Ma hema ics, U al Fede al Uni e si y, 620083
Eka e inbu g, Russia
*Co esponding au ho : Depa amen o de Física Aplicada I, Escuela de Ingenie ía de
Bilbao, Uni e sidad del País Vasco UPV/EHU, Plaza To es Que edo 1, 48013 Bilbao,
Spain. Phone +34946014008. E-mail: a[email p o ec ed]
Abs ac
An ac pho opy oelec ic calo ime e has been used o s udy he c i ical beha iou o he
magne ic ansi ions in Dy3Co measu ing he mal di usi i y, speci ic hea and he mal
conduc i i y, a low empe a u e. The e a e wo phase ansi ions, bo h o which p esen
singula i ies in he h ee a iables. The an i e omagne ic o pa amagne ic phase
ansi ion a ≈ 42 K complies wi h he sho ange, iso opic uni e sali y class, 3D-
Heisenbe g (
α
exp = -0.133 o speci ic hea , bexp = -0.145 o he mal di usi i y,
α
heo =
b heo = -0.13). In he case o he lowe ansi ion whe e he e is a ea angemen o he
an i e omagne ic spin o de ing a ≈ 32 K he c i ical beha io shows a de ia ion om
iso opy. These esul s a e linked o magne ic measu emen s al eady ound in li e a u e.
Keywo ds: C i ical beha io ; R3Co; uni e sali y class; Pho opy oelec ic calo ime e ;
spin-o de ing
1. In oduc ion
The in e me allic amily R3T (R=Gd, Tb, Dy, Ho, E ; T=Co, Ni) is specially
in e es ing because o i s p omising echnological applica ions: in he i s place hey a e
po en ial c yocoole s due o he p esence o an impo an magne ocalo ic e ec ; besides,
hey also p esen gian magne o esis ance as well as ela i ely high spin-o de ing
empe a u es o he a e ea hs [1]. In o de o explo e he possible capabili ies and
This is he accep ed manusc ip o he ollowing a icle: A. He e o, A. Oleaga, A. Salaza , A.F. Gubkin, N.V. Ba ano , C i ical beha io o
magne ic ansi ions in Dy3Co single c ys al, Jou nal o Alloys and Compounds 741 : 1163-1168 (2018), which has been
published in inal o m a h ps://doi.o g/10.1016/j.jallcom.2018.01.261. © 2018 Else ie unde CC BY-NC-ND license (h p://
c ea i ecommons.o g/licenses/by-nc-nd/4.0/)
2
applica ions, a knowledge as deep as possible o he physical p ope ies o he sys em is
necessa y, including he de ails o he phase ansi ions, such as he o de ing o he spins,
he ex en o he in e ac ion (sho o long ange o de ), e c.
The spin o de ing in a e ea hs has adi ionally been explained by means o he
RKKY (Rude man–Ki el–Kasuya–Yosida) in e ac ion, which consis s o an indi ec
exchange in e ac ion be ween 4 -4 elec on spins by means o conduc ion elec on spins.
Bu his desc ip ion has been ound no o be adequa e o a e ea h in me als, whe e i
p esen s signi ican sho comings [2]. Along he las 30 yea s a mo e comple e pic u e
has been de eloped o accoun o he magne ic in e ac ions in a e ea h in me als and,
in pa icula , in R3Co.
Though i could be expec ed, a i s , o ha e wo spin-o de ing ansi ions in R3Co
(one co esponding o he 3d elec on spins o he ansi ion me al Co and ano he one
o he 4 spins o he a e ea h R), he e is no o de ing o he Co spins. Se e al exchange
in e ac ions ake pa in he magne ic o de ing in a e ea h (R)–3d ansi ion me al (T)
compounds [2-5]. The i s p ocess in ol ed is he pola iza ion o 5d spin momen s
pa allel o he 4 momen s, which akes place in R ions wi h a non- illed 4 elec on shell,
due o a 4 -5d in a-a omic exchange. This kind o pola iza ion has al eady been
expe imen ally obse ed in R-T compounds [6]. Fu he mo e, as i is well known, he
inc ease o he a e ea h a omic numbe con ac s he 4 shell educing he o e lap
be ween his and he 5d shell. This ac implies a dec ease on he 4 -5d exchange ene gy
o inc easing a omic numbe s o R.
A second ype o mechanism is caused by he hyb idiza ion e ec s be ween 5d
and 3d elec ons and hei sho - ange exchange and, as a consequence, 4 and 3d spins
align hemsel es in an ipa allel o ien a ion, which is known as he -d exchange
in e ac ion.
A e p esen ing hese mechanisms, we can go on desc ibing he mos accep ed
model o he indi ec 4 -4 coupling in pu e a e ea hs, wi h he aim o unde s anding
he RnTm compounds. In he model in oduced by Campbell [2] (which is alid o pu e R
compounds), he 4 -4 coupling consis s o wo s eps: an in a-a omic 4 -5d exchange
ollowed by an in e -a omic 5d-5d spin in e ac ion be ween neighbou ing R a oms,
leading o a 4 -5d-5d-4 in e ac ion. This mechanism also a ises in RnTm compounds, bu
when hese bina y elemen s ha e a high a e ea h con en , he p e ious mechanism comes
oge he wi h a 4 –5d–3d–5d–4 p ocess. The e o e, RnTm compounds show di e en
beha iou , ega ding hei magne ic o de ing, depending on he n:m a io. I his a io is
3
small, he ansi ion me al ions can ha e a ne momen i espec i e o he magne ic s a e
o he a e ea h subla ice. As he n:m a io inc eases he e is a dec ease in he magne ic
momen o he ansi ion me als ions due o he illing o he 3d band on T a oms by ou e -
shell elec ons o R a oms [7-9]. In pa icula , wi hin he R-Co se ies, i has been ound
ha , i he R a omic concen a ion is highe han 1/3, he magne ic momen o Co is los .
Di e en s udies ha e been unde aken o s udy he pa icula s o he magne ic
o de ing o he a e ea h spins in R3Co wi h R = Gd [10-15], Tb [16-18], Dy [19-22], Ho
[23], and E [24-25]. A sha ed ea u e among all o hem is ha he e is an
an i e omagne ic o de ing om he pa amagne ic phase, wi h TN lowe ing as he a omic
numbe inc eases. All o hem ha e an o ho hombic c ys al s uc u e o he Fe3C ype
(space g oup Pnma) whe e he a e ea h occupies wo non-equi alen posi ions: 4c (si e
symme y m) and 8d (si e symme y I). The low symme y o ho hombic c ys alline
s uc u e in which R a oms occupy hese wo nonequi alen si es leads o an inc ease in
c ys al ield e ec s. Acco ding o neu on di ac ion s udies [26], he magne ic s uc u e
o Tb3Ni is non-coplana owing o he compe i ion be ween he in luence o he low
symme y c ys al elec ic ield and he RKKY-exchange in e ac ion desc ibed abo e.
This complica ed a angemen has been con i med o Gd3Co [11], Tb3Co [18], Dy3Co
[19], E 3Co [25], and Ho3Co [23] wi h pa icula i ies depending on he a e ea h a om.
In he pa icula case o Dy3Co, a e he an i e omagne ic phase ansi ion a abou 42
K, he e is a eo ien a ion o he an i e omagne ic s uc u e a abou 32 K whose pe iod
has been sugges ed o be doubled along he a- and c- axes [19]. Ano he in e es ing ea u e
in Dy3Co is ha i is sugges ed ha he e migh exis a su i al o sho - ange magne ic
co ela ions in he pa amagne ic s a e [20], as well as i happens in some o he R3(Co;Ni)
compounds [27].
The aim o his pape is o s udy in de ail he c i ical beha io o he wo magne ic
ansi ions in Dy3Co associa ed wi h changes in spin o de ings. C i ical beha io heo y
assesses ha a ce ain numbe o physical a iables p esen anomalies in he nea icini y
o he c i ical empe a u e TC o a con inuous phase ansi ion, go e ned by a se ies o
c i ical exponen s, whose alues a e g ouped in uni e sali y classes [28]. Fo example,
he anomalies in speci ic hea and spon aneous magne iza ion can be w i en in ha
egion, as a unc ion o he educed empe a u e = (T
−
TC)/TC, as:
cp (T) ~ A± | |-
α (
A- o T < TC, A+ o T > TC) (1)
MS (T) ~ | |
β
(T < TC), (2)
4
whe e
α
,
β
, A+, A- a e he c i ical exponen s and coe icien s, whose alues ha e been
heo ized by eno maliza ion g oup heo y o each uni e sali y class, on he basis o a
pa icula Hamil onian used as a s a ing poin , which akes in o accoun pa icula
mechanisms and in e ac ions o desc ibe he phase ansi ion. The exponen s a e uni e sal
in he sense ha magne ic phase ansi ions in ma e ials which a e e y di e en will be
desc ibed by he same se o c i ical exponen s, hus belonging o he same uni e sali y
class. Table 1 shows he alues o hese exponen s and coe icien s o he mos common
magne ic uni e sali y classes [29-33]. This kind o s udy gi es a clea insigh in he
unde lying physics o a phase ansi ion.
We will ocus his wo k on he s udy o he c i ical beha io o he magne ic
ansi ions in Dy3Co using he mal a iables: speci ic hea , he mal di usi i y and
he mal conduc i i y. The main ad an age o he he mal a iables is ha he c i ical
exponen s o he di e en uni e sali y classes a e much mo e di e en among hem (wi h
e en changes in sign) han wha happens in he case o he magne ic exponen s, whe e
he di e ences a e smalle (see Table 1).
2. Samples and expe imen al echniques
Dy3Co polyc ys alline samples we e p epa ed by a c mel ing in a helium
a mosphe e using Dy and Co o 99.9% and 99.99% pu i y, espec i ely. The single c ys al
sample wi h dimensions o app oxima ely 4 × 4 × 5 mm3 was g own by emel ing he
ingo s a empe a u es jus abo e he pe i ec icpoin in a esis ance u nace wi h a high
empe a u e g adien , ollowed by annealing a 900 K o 3 days. The quali y o he as-
g own single c ys al sample was cha ac e ized by he back e lec ion Laue me hod
measu ing x- ay di ac ion pa e ns om di e en su aces o he sample. No ex a
e lec ions om o he g ains we e de ec ed. Then he single c ys al sample was cu in o
he plane-pa allel slabs ha a e pa allel o he (010) c ys allog aphic plane. Those
su aces had been well polished and addi ionally checked by he back Laue me hod. The
hicknesses o he slabs was abou 600 µm.
A high- esolu ion ac pho opy oelec ic calo ime y in he back de ec ion
con igu a ion has been used in his wo k o ex ac he mal di usi i y D, speci ic hea cp
and he mal conduc i i y K. This echnique is pa icula ly i ed o s udy phase ansi ions
5
in de ail as a small empe a u e g adien in he sample gi es ise o a high signal- o-noise
a io in he de ec o , ob aining he p ecise shape o he ansi ions in he close icini y o
he c i ical empe a u e wi h g ea esolu ion and a small unce ain y [34]. This echnique
has been ex ensi ely used o his end bo h wi h solid ma e ials ( o s udy magne ic as well
as e oelec ic ansi ions) [35-41] and liquid c ys als [42, 43].
The de ails o he expe imen al se up, measu emen p ocedu e, and he heo y
which explains how o e ie e he mal di usi i y, speci ic hea and he mal conduc i i y
om he pho opy oelec ic signal can be ound elsewhe e [34, 40]. The slowes cooling
and hea ing a es used o he high- esolu ion uns close o he ansi ion empe a u es
ha e been abou 20 mK/min.
3. Expe imen al Resul s
Fig. 1a p esen s he he mal di usi i y as a unc ion o empe a u e in he egion
o in e es . I is wo h men ioning ha a oom empe a u e, he he mal di usi i y is 2.65
mm2/s and i dec eases wi h empe a u e ill i eaches he alue o 1.16 mm2/s a 100 K,
a beha iou qui e ypical o in e me allic ma e ials due o he added con ibu ion o he
elec onic and phononic pa o he he mal di usi i y; below 100 K he phonon
con ibu ion s a s o domina e, making he he mal di usi i y inc ease ill 1.21 mm2/s a
50K. F om hen on, he he mal di usi i y backg ound quickly inc eases as he phonon
mean ee pa h is se e ely educed and he magne ic ansi ions a e supe imposed on his
backg ound as wo dips, as i has been ound in many o he ma e ials [35-37, 40-41]. In
his pa icula case, he dips a e loca ed a 32.07 K and 41.57 K.
Fig. 1b shows he speci ic hea in he same empe a u e ange as Fig. 1a while
Fig. 1c shows he he mal conduc i i y. Speci ic hea and he mal conduc i i y a e always
noisie han he mal di usi i y using his echnique, as he la e is ob ained only using
he phase o he pho opy oelec ic signal while o he o me wo bo h ampli ude and
phase a e needed. The posi ion o he speci ic hea peaks (32.26 K and 41.82 K.) a e
simila o hose ound in li e a u e [19], whe e i is i mly es ablished ha he ansi ion
a highe empe a u e co esponds o an an i e omagne ic o de ing o he a e ea h spins
6
om a pa amagne ic s a e while he one a lowe empe a u e is due o a eo de ing o
hose spins in o ano he an i e omagne ic dis ibu ion. The he mal conduc i i y also
p esen s singula i ies a bo h ansi ions; his magni ude has no been measu ed be o e in
his in e me allic amily. I is no usual o ind anomalies in he o m o peaks a magne ic
ansi ions bu i has been ound o se e al magne ic ansi ions in ma e ials such as Gd
[35], FeF2 [36], RbMnF3 [37], and KMnF3 [44]. The dec easing backg ound in he mal
conduc i i y wi h dec easing empe a u e is also ano he ea u e common o many
in e me allic amilies [45-47].
4. Fi ing p ocedu e and discussion
The equa ion used o i he expe imen al speci ic hea cu es is:
( )
5.0
1 E AC Bc
p±
−
±
+++=
α
, (3)
whe e
( )
NN
TTT /−=
is he educed empe a u e, TN he c i ical empe a u e, and α, A±,
B, C and E± a e adjus able pa ame e s. Supe sc ip s + and - s and o T > TN and T < TN
espec i ely. The linea e m ep esen s he backg ound con ibu ion o he speci ic hea ,
while he las e m is he anomalous con ibu ion o he speci ic hea . The ac o unde
pa en hesis is he co ec ion o scaling ha ep esen s a singula con ibu ion o he
leading powe as known om expe imen s and heo y [48, 49]. A simul aneous i o bo h
b anches (T > TN and T < TN) has been unde aken using a non-linea leas squa e ou ine
using a Le enbe g-Ma qua d me hod. The de ails o he i ing p ocedu e can be ound
elsewhe e [40].
Conce ning he mal di usi i y, a simila equa ion o Eq. (3), used o speci ic
hea , wi h i s own c i ical pa ame e s, is w i en as
( )
5.0
1 F UW VD b±
−
±+++=
(4)
and an equi alen p ocedu e o he one ca ied ou wi h cp has been ollowed.
7
The ela ions be ween he c i ical pa ame e s o speci ic hea and he mal
di usi i y a e al eady s udied o he mos common magne ic uni e sali y classes: 3D-
Heisenbe g (iso opic dis ibu ion o spins), 3D-XY (easy plane aniso opy) and 3D-Ising
(uniaxial aniso opy) [36, 37, 44, 50, 51]. In pa icula , in he Heisenbe g case, he
ollowing ela ions can be w i en among he c i ical pa ame e s [51]
b ≈
α
, (5a)
U+/U- ≈ A+/A- (5b)
In he case o he mal conduc i i y, he i ing is pe o med using i s in e se, because all
he he mal esis ances associa ed o he a ious hea conduc ion mechanisms in he
sample a e in se ies:
()
5
.
0
1
/
1
/
1
/
1
H
NM
L
K
K
K
g
mag
nonmag ±
−
±
+
+
+
=
+
=
(6)
so ha he singula e m in Eq. (6) can be ela ed o he magne ic con ibu ion o he hea
conduc ion p ocesses. Knonmag has o do wi h phonon-phonon sca e ing, umklapp,
sca e ing wi h impu i ies, e c., while Kmag e e s o he spin-phonon sca e ing
mechanisms. The magne ic esis i e e m o igina es om he spin-la ice in e ac ion and,
close o TN, om an addi ional e m ha accoun s o phonon sca e ing by c i ical
luc ua ions o he o de pa ame e .
Fig. 2 shows he i ings o he h ee magni udes: he mal di usi i y, speci ic
hea and he in e se o he he mal conduc i i y, o he pa amagne ic o
an i e omagne ic phase ansi ion in he nea icini y o he Néel empe a u e as a
unc ion o he educed empe a u e =(T-TN)/TN, whe e he do s co espond o he
expe imen al and he con inuous lines o he bes i ing o Eqs. (3), (4) and (6). The
igu e also con ains he de ia ion plo s o each i ing wi h espec o he expe imen al
cu es, assessing he quali y o he i ings . Table 2 con ains he alues o he c i ical
pa ame e s oge he wi h he oo mean squa e alue (R2 = 1 means a pe ec i ing). I
a en ion is ocused on he esul s o speci ic hea , he c i ical pa ame e s ag ee qui e well
wi h he iso opic 3D-Heisenbe g model (αexp = -0.133±0.014, A+/A-exp = 1.64, α heo = -
0.134 [31], A+/A-exp = 1.52 [33]). We would like o poin ou ha he heo e ical alue o
he c i ical pa ame e
α
in he 3D-Heisenbe g uni e sali y class mainly used in li e a u e
8
is -0.115 bu he mos ecen calcula ions pe o med by Campos ini e al. [31] ha e
inc eased his alue o -0.134, which is p ecisely he alue we ha e ob ained in his
ansi ion.
The sligh de ia ion be ween he expe imen al and he heo e ical alue o he
c i ical a io A+/A- migh be a ibu ed o a lack o comple e iso opy, as mani es ed in he
ac suscep ibili y measu emen s along he h ee axes [19], which shows some di e ences.
Ou esul s con i m ha bo h he c i ical exponen and he a io o he c i ical
coe icien s o he he mal di usi i y nea ly ma ch hose o speci ic hea , whe e b = -
0.145±0.020, U+/U- = 1.41. Bo h pa ame e s can be conside ed o ul ill he app oxima e
Eqs. (5a) and (5b), con i ming he adsc ip ion o he Heisenbe g class. Finally, he in e se
o he he mal conduc i i y also gi es a close alue o i s c i ical exponen g o he
Heisenbe g model (-0.101) while he a io o he c i ical coe icien s N+/N- ge s away
om he heo e ical alue (0.94). This beha io o he in e se o he mal conduc i i y is
e y simila o he one ound o o he iso opic magne s such as RbMnF3 (g = -0.08,
N+/N- =1.1) [37] and KMnF3 (g = -0.10, N+/N- =1.15) [44], al hough u he s udies a e
necessa y in o de o ully unde s and i s meaning.
Ano he in e es ing conclusion is ha , indeed, ou esul s decla e ha sho ange
o de in e ac ions a e esponsible o his magne ic ansi ion and no long ange ones ( o
which he p ope uni e sali y class would ha e been he mean ield model). This is in
ag eemen wi h he s udies which ha e poin ed ou ha e en in he pa amagne ic phase
he e is a su i al o sho ange o de in e ac ions [20], as i also happens in some o he
R3(Co,Ni) [27].
Now we will u n ou a en ion o he lowe empe a u e ansi ion, whe e he
o de ing changes om one an i e omagne ic s uc u e o ano he one. Fig. 3 shows he
equi alen o Fig. 2 o his ansi ion and Table 3 displays he equi alen in o ma ion o
Table 2. The c i ical exponen o speci ic hea does no eally comply wi h any
uni e sali y class (αexp = -0.168±0.009, A+/A-exp = 1.18); he e is a s onge de ia ion om
he 3D-Heisenbe g class bu wi hou eaching nei he he 3D-XY (α heo = -0.014, A+/A-
exp =1.06) no he 3D-Ising (α heo = 0.11, A+/A-exp = 0.53). Ou in e p e a ion is ha he
iso opy is being smoo hed somehow, in ag eemen wi h Ba ano e al [21] who showed
ha he e is a smalle p ojec ion o he magne ic momen along he b-axis han along he
a- and c- axes (4.5 µB, 6.0 µB and 6.3 µB, espec i ely) [19,21], gi ing ise o wha is
labeled as “a highly aniso opic non-collinea magne ic s uc u e” [21] bu wi hou he
9
p esence o an easy plane o an easy axis. Magne ic suscep ibili y measu emen s ha e
also assessed an impo an di e ence in he spin o de ing in he wo ansi ions: In he
highe empe a u e one he e is an anomaly in χ when applying magne ic ield along he
h ee axes a, b and c while in he lowe empe a u e one he anomaly is only isible when
applying he ield along he b-axis [19, 22].
This de ia ion om an iso opic magne is u he con i med wi h he i ings o
he mal di usi i y (b = -0.139±0.020, U+/U- = 0.85) and he in e se o he he mal
conduc i i y (g = -0.096, N+/N- = 0.98). The de ia ions in he ul illmen o Eqs. (5a) and
(5b) a e now s ong, suppo ing ha he Heisenbe g class is no longe o applica ion.
5. Conclusions
The c i ical beha iou o he wo magne ic ansi ions ha Dy3Co p esen s a low
empe a u e has been s udied on he singula i ies ha he mal di usi i y, speci ic hea
and he mal conduc i i y show. The an i e omagne ic o pa amagne ic phase ansi ion
a abou 42 K is go e ned by sho ange in e ac ions and belongs o he 3D-Heisenbe g
uni e sali y class, p o ed no only by he c i ical exponen s o speci ic hea (
α
= -0.133)
and he mal di usi i y (b = -0.145) bu also by he ela ions be ween he pa ame e s
ob ained in he i ings. In he case o he lowe ansi ion a abou 32 K (change o
an i e omagne ic o de ing) he e is a clea de ia ion om his iso opic class.
Acknowledgmen s
This wo k has been suppo ed by Uni e sidad del País Vasco/Euskal He iko
Unibe si a ea (UPV/EHU-GIU16/93) and also pa ially suppo ed by FASO o Russia
( hemes No 01201463328 and 01201463334). The Laue x- ay di ac ion measu emen s
ha e been pe o med in he Cen e o Collabo a i e Access o IMP UB o RAS.
16
Fig. 1
17
Fig. 2
Fig. 3
