DSpace at VNU: Critical behavior of La0.7Ca0.3Mn1-xNixO3 manganites exhibiting the crossover of first- and second-order phase transitions

In the FM region, experimental results for the critical exponent β ¼0.171 and 0.262 for x¼0.09 and 0.12, respectively reveal twoﬁrst samples exhibiting tricriticality associated with the

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Critical behavior of La 0.7 Ca 0.3 Mn 1 x Ni x O 3 manganites exhibiting the

The-Long Phana,b,1, Q.T Tranb,e, P.Q Thanhb,c, P.D.H Yenb,d, T.D Thanhb,e, S.C Yua,b

Q1

a

Department

Q2 of Physics, Chungbuk National University, Cheongju 361-763, South Korea

b Center for Science

Q3 and Technology Communication, Ministry of Science and Technology, 113 Tran Duy Hung, Hanoi, Vietnam

c

Faculty of Physics, Hanoi University of Science, Vietnam National University, Hanoi, Vietnam

d

Faculty of Engineering Physics and Nanotechnology, VNU – University of Engineering and Technology, Xuan Thuy, Cau Giay, Hanoi, Vietnam

e

Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

a r t i c l e i n f o

Article history:

Received 29 October 2013

Received in revised form

28 December 2013

Accepted 29 December 2013

by F Peeters

Keywords:

A Perovskite manganites

D Critical behavior

D Magnetic entropy change

a b s t r a c t

We used Banerjee0s criteria, modified Arrott plots, and the scaling hypothesis to analyze magnetic-field dependences of magnetization near the ferromagnetic–paramagnetic (FM–PM) phase-transition tem-perature (TC) of perovskite-type manganites La0.7Ca0.3Mn1xNixO3(x¼0.09, 0.12 and 0.15) In the FM region, experimental results for the critical exponent β (¼0.171 and 0.262 for x¼0.09 and 0.12, respectively) reveal twofirst samples exhibiting tricriticality associated with the crossover of first- and second-order phase transitions Increasing Ni-doping content leads to the shift of theβvalue (¼0.320 for

x¼0.15) towards that expected for the 3D Ising model (β¼0.325) This is due to the fact that the substitution of Ni ions into the Mn site changes structural parameters and dilutes the FM phase, which act asfluctuations and influence the FM-interaction strength of double-exchange Mn3þ–Mn4þpairs, and the phase-transition type For the critical exponent γ (¼0.976–0.990), the stability in its value demonstrates the PM behavior above TCof the samples Particularly, around TCof La0.7Ca0.3Mn1xNixO3 compounds, magnetic-field dependences of the maximum magnetic-entropy change can be described by

a power law of |ΔSmax|pHn, where values n¼0.55–0.77 are quite far from those (n¼0.33–0.48) calculated from the theoretical relation n¼1þ(β1)/(βþγ) This difference is related to the use of the mean-ﬁeld theory for the samples exhibiting the magnetic inhomogeneity

& 2014 Published by Elsevier Ltd

1 Introduction

It is known that hole-doped lanthanum manganites of

La1x(Ca, Sr, Ba)xMnO3 with x¼0.3 (corresponding to Mn3 þ/

Mn4þ¼7/3) usually exhibit colossal magnetoresistance (MR) and

magnetocaloric (MC) effects around their the ferromagnetic–

paramagnetic (FM–PM) phase-transition temperature (the Curie

temperature, TC)[1] With this doping content, double-exchange

(DE) FM interactions between Mn3 þ and Mn4 þ are dominant as

comparing with super-exchange anti-FM interactions of Mn3 þ–

Mn3þ and Mn4þ–Mn4 þ pairs The strength of magnetic

interac-tions thus depends on the average bond length〈Mn–O〉, and bond

angle 〈Mn–O–Mn〉 of the perosvkite structure Different

com-pounds have different bond parameters, which are related to

Jahn–Teller lattice distortions due to strong electron–phonon

coupling[2] In reference to the symmetry of MnO6octahedra, it

has been noted that cooperative Jahn–Teller distortions are

present in an orthorhombic structure rather than in the rhombo-hedral one[3]

Among hole-doped manganites, orthorhombic La0.7Ca0.3MnO3

is known as a typical material exhibiting MR and MC effects much greater than those obtained from the other compounds Particu-larly, depending on bulk or nanostructured sample types, its TCin the range of 222–265 K [3–9] can be tuned towards room temperature by doping Sr, Ba or Pb [10–14] Meanwhile, the transition-metal doping (such as Co, Fe, Ni and so forth) lowers

TC[15–17] Additionally, its discontinuous FM–PM transition at TC

is followed up with structural changes, and is known as a first-order magnetic phase transition (FOMT)[8,9,12] This discontin-uous phase transition can be rounded to a contindiscontin-uous one of a second-order magnetic phase transition (SOMT) upon the doping, and reduced dimensionality (i.e.,finite-size effects), and external fields[5,7,11,12,16,18,19] The assessment of a continuous SOMT can base on the success in determining the critical exponentsβ,γ, and δ associated with temperature dependences of the sponta-neous magnetization, Ms(T), inverse initial susceptibility, χ0 –1(T), and critical isotherm at TC, respectively[20,21] Distinguishing the FOMT from the SOMT can be based on the criteria proposed by

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Contents lists available atScienceDirect

journal homepage:www.elsevier.com/locate/ssc

Solid State Communications

0038-1098/$ - see front matter & 2014 Published by Elsevier Ltd.

http://dx.doi.org/10.1016/j.ssc.2013.12.032

E-mail address: ptlong2512@yahoo.com (T.-L Phan).

1 Tel.: þ82 43 261 2269.

Please cite this article as: T.-L Phan, et al., Solid State Commun (2014),http://dx.doi.org/10.1016/j.ssc.2013.12.032i

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theﬁeld, and M is the magnetization) in the vicinity of TC, and then

suggested that their positive or negative slopes are indication of a

second- or ﬁrst-order phase transition, respectively Reviewing

-MnO3-based materials showing the FOMT and/or SOMT However,

the crossover region from ﬁrst-order to second-order phase

transitions, and some related physical properties, such as the

magnetic entropy change versus T and H, ΔSm(T, H), have not

been widely studied Furthermore, there is no much attention

given to the assessment of a magnetic ordering parameter (n)

determined from the relations n¼1þ(β1)/(βþγ)[23], and from

a power law|ΔSmax(H)|pHn[24](where|ΔSmax| is the maximum

magnetic entropy change around TC) To get more insight into the

above problems, we prepared La0.7Ca0.3Mn1 xNixO3compounds,

and have studied their critical behaviors upon Banerjee0s criteria

[22], modiﬁed Arrott plots and the scaling hypothesis[20,21] The

determined critical values are then discussed together with the

magnetic ordering parameter n

2 Experimental details

Three polycrystalline perovskite-type manganites La0.7Ca0.3

Mn1xNixO3with x¼0.09, 0.12 and 0.15 were prepared by

solid-state reaction as using purity commercial powders La2O3, CaO,

NiO, and MnCO3(99.9%) as precursors These powders combined

with stoichiometrical quantities were well mixed and ground, and

then pre-annealed at 9001C for 24 h After pre-annealing, three

mixtures were re-ground and pressed into pellets, and annealed at

13001C for 72 h in air For reference, the parent compound

La0.7Ca0.3MnO3 was also prepared with the same conditions as

described X-ray diffraction (XRD) patterns of theﬁnal products

checked by an X-ray diffractometer (Bruker AXS, D8 Discover)

revealed the single phase in an orthorhombic structure (the space

group Pbnm) of La0.7Ca0.3Mn1xNixO3samples, seeFig 1(a) Basing

on the XRD data, we calculated the lattice parameters (a, b, and c)

and unit cell (V), as shown in Table 1 The variation of these

parameters indicates the substitution of Ni ions (could be

Ni2þ, Ni3þ, and/or Ni4þ) for Mn in the perovskite structure

Magnetic measurements were performed on a superconducting

quantum interference device magnetometer (SQUID) The TC

values obtained from the ﬂexion points in temperature

depen-dences of magnetization, M(T), with the appliedﬁeld H¼100 Oe,

Fig 1(b) are about 200, 185 and 170 K for x¼0.09, 0.12 and 0.15,

respectively, which are lower than the value TCE260 K of the

parent compound

3 Results and discussion

Fig 2shows M–H data and inverse Arrott plots (H/M versus M2)

at different temperatures around the FM–PM phase transition of

La0.7Ca0.3Mn1xNixO3 It appears from the M–H data that there is

no saturation magnetization value in spite of the H variation up to

40 kOe This is assigned to the existence of the magnetic

inhomo-geneity or short-range FM order At a given temperature, higher

Ni-doping content reduces the magnetization With increasing

temperature, nonlinear M–H curves in the FM region become

linear because the samples enter the PM state Different from the

parent compound[5,7–9,12], there is no S-like shape in the M–H

curves, and negative slopes in the H/M versus M2curves, seeFig 2

These tokens demonstrate our Ni-doped samples undergoing the

FOMT[22,25]

According to the mean-ﬁeld theory (MFT) proposed for a ferro-magnet exhibiting the SOMT and long-range FM interactions[26], the free energy GLis expanded in even powers of M: GL¼aM2þ

bM4þ⋯ – HM, where a and b are temperature-dependent para-meters Minimizing GLas∂GL/∂M¼0 results in the relation H/M¼ 2aþ4bM2 It means that if magnetic interactions of the FM system exactly obey the MFT, M2versus H/M curves in the vicinity of TC

are parallel straight lines At TC, the M2 and H/M line passes through the origin [27,28] However, these features are absent from the Arrott performance shown inFig 2(b, d, and e) It means that magnetic interactions in the samples could not be the long-range type The critical exponentsβ¼0.5 andγ¼1.0 (in the normal Arrott plots[20,27]) based on the MFT are thus not suitable to describe magnetic interactions taking place in our samples Within the framework of the MFT, we need to find other sets of the critical-exponent values reflecting more frankly the magnetic properties of the samples This work is based on the modified Arrott plot (MAP) method [20], which is generalized by the scaling equation of state, (H/M)1/ γ¼c1εþc2M1/ β, where c

1and c2

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0 50 100 150 200 250 300 0.0

0.3 0.6 0.9 1.2

x = 0.15

x = 0.12

x = 0.09

x = 0

T (K)

x = 0 x = 0.09

x = 0.12 x = 0.15

H = 100 Oe

Fig 1 (Color online) (a) Room-temperature XRD patterns, and (b) normalized M(T) curves with the applied ﬁeld of H¼100 Oe for La 0.7 Ca 0.3 Mn 1x Ni x O 3 (x ¼0, 0.09, 0.12, and 0.15).

Table 1 Values of the lattice parameters and unit cell calculated from XRD analyses of

La 0.7 Ca 0.3 Mn 1x Ni x O 3 with x¼0.09, 0.12 and 0.15.

)

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are temperature-dependent parameters, andε¼(TTC)/TCis the

reduced temperature βand γ values can be obtained from the

asymptotic relations[18,20]

where M0, h0, and D are the critical amplitudes Additionally,

according to the static-scaling hypothesis[21], M is a function ofε

and H, MðH;εÞ ¼ jεjβf7ðH=jεjβþγÞ This equation reﬂects that, with

determinedβandγvalues, plotting M/εβversus H/εβ þ γmakes all

data points falling on the fand fþbranches for ToTCand T4TC,

respectively Here, determining the critical parameters is based on

the MAP method, and started from the scaling equation of state

Correctβandγ values make M–H data points falling on a set of

parallel straight lines in the performance of M1/ βversus (H/M)1/ γ.

Moreover, the M1/ βversus (H/M)1/ γline passes through the origin

at TC Similar to the MFT case, our analyses indicated that the

exponent values β¼0.365 and γ¼1.336 expected for the 3D

Heisenberg model [21] do not match with the descriptions of

the MAP method Only β¼0.25 and γ¼1.0 expected for the

tricritical MFT model (T-MFT), andβ¼0.325 andγ¼1.241 expected

for the 3D Ising model[12,29]can be used as initially trial values

toﬁnd optimal exponent values for the samples with x¼0.09 and 0.12, and for x¼0.15, respectively With these trial values, Ms(T) andχ0(T) data would be obtained from the linear extrapolation in the high-ﬁeld region for the isotherms to the co-ordinate axes of

M1/ βand (1/χ0)1/ γ¼(H/M)1/ γ, respectively The M

s(T) andχ0(T) data obtained from the linear extrapolation are thenﬁtted to Eqs.(1) and (2), respectively, to achieve betterβ,γand TCvalues, as can be seen fromFig 3 These new values ofβ,γ, and TCare continuously used for next MAP processes until their optimal values are achieved Notably, the TC values of the samples obtained from

M–T measurements were also used as reference in the ﬁtting With such the careful comparison, only the sets of critical parameters with TCE199.4 K, β¼0.17170.006 and γ¼0.97670.012 for x¼ 0.09; TCE184.4 K, β¼0.26270.005 and γ¼0.97970.012 for

x¼0.12; and TCE170 K, β¼0.32070.009 and γ¼0.99070.082 for x¼0.15 are in good agreement with the MAP descriptions, see

Fig 4 With the obtained critical exponents, the scaling perfor-mance of M/|ε|βversus H/εβ þ γcurves, seeFig 5and their inset, reveals the M–H data points at high-magnetic ﬁelds falling into two f and fþ universal branches for ToTCand T4TC, respec-tively These results prove the reliability in value of the critical values obtained from our work It should be noticed that the MAP method only works well for theﬁelds (HL) higher than 28, 24 and

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0 20 40 60 80

2 4 6 8

0 20 40 60

2 4 6 8

0 20 40 60 80

2 4 6 8

206 K

168 K

206 K

168 K

220 K

182 K

220 K

182 K

2, Oe.g/emu)

190 K

152 K

H (kOe)

190 K

152 K

Fig 2 (Color online) M–H data and inverse Arrott plots for La 0.7 Ca 0.3 Mn 1x Ni x O 3 with (a, b) x¼0.09, (c, d) x¼0.12, and (e, f) x¼0.15.

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12 kOe for x¼0.09, 0.12 and 0.15, respectively At the ﬁelds lower

than HL, there may be rearrangement of magnetic domains, the

effect due to the uncertainty in the calculation of demagnetization

factor, and/or the persistence of the FOMT (particularly for the

samples with x¼0.09 and 0.12) [12,30] Unexpected errors for

critical values can thus be occurred, leading to the scattering of the

M–H data points (at the ﬁelds lower than HL) from the universal

curves[5,12], as can be seen inFig 5 For the exponentδ, its value

can be obtained from ﬁtting the isotherms at T¼TC to Eq (3)

Basically, theδvalues determined from Eq.(3)would be equal to

those calculated from the Widom relation δ¼1þγ/β [21] In

our work, δ values are about 6.7, 4.7, and 4.1 for x¼0.09, 0.12

and 0.15, respectively Clearly, with increasing Ni concentration in

La0.7Ca0.3Mn1 xNixO3, there is a shifting tendency of the exponent values (β,γandδ) towards those of the MFT (withβ¼0.5,γ¼1 and

δ¼3) This is tightly related to the FOMT–SOMT transformation The better applicability of the MAP method has been found for the samples with high-enough Ni concentrations as x40.12 We believe that the substitution of Ni ions into the Mn site not only changes structural parameters of 〈Mn–O〉 and 〈Mn–O–Mn〉, but also leads to the additional presence of anti-FM interactions related to Ni ions (for example, super-exchange pairs of Ni2 þ

–Ni2 þ, Ni3 þ–Ni3 þ, Ni4 þ–Ni4 þ, and/or Ni2þ ,3 þ ,4 þ–Mn3 þ ,4 þ) beside pre-existing anti-FM interaction pairs of Mn3 þ–Mn3þ and

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0 2 4

170 175 180 185 30

40 50 60

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2 4

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40 50

175 180 1850

1 2 3

T (K)

Ms

χ0

2, Oe.g/emu)

β = 0.171 ± 0.006

γ = 0.976 ± 0.012

β = 0.262 ± 0.005

γ = 0.979 ± 0.012

β = 0.320 ± 0.009

γ = 0.990 ± 0.082

Fig 3 (Color online) M s (T) and χ 1

0 ðTÞ data ﬁtted to Eqs (1 ) and ( 2 ) for La 0.7 Ca 0.3 Mn 1x Ni x O 3 with (a) x¼0.09, (b) x¼0.12, and (c) x¼0.15.

0 10 20 30

0.0 0.2 0.4 0.6

0 4 8

214 K

186 K

β (x10

6, emu/g)

200 K

174 K

180 K

152 K

x104

x = 0.09

x = 0.15

β = 0.320

γ = 0.990

β = 0.262

γ = 0.978

β = 0.171

γ = 0.976

Fig 4 (Color online) MAPs of M 1/β versus (H/M) 1/γ with the critical exponents obtained for La 0.7 Ca 0.3 Mn 1x Ni x O 3 with (a) x¼0.09, (b) x¼0.12 and (c) x¼0.15.

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Mn4þ–Mn4 þ These factors act asﬂuctuations, reduce the strength

of Mn3þ–Mn4 þ FM interactions (which thus reduce the

magne-tization and TCvalues), and inﬂuence the phase transition as well

Comparing with the theoretical models [21,29], one can see

that the values ofγ(¼0.976–0.990) are quite stable,

demonstrat-ing the complete PM state in the samples at temperatures above

TC For the FM region, however,β¼0.262 for x¼0.12 is close to that

expected for the T-MFT (β¼0.25) This sample thus exhibits

tricriticality associated with the crossover ofﬁrst- and

second-order phase transitions Similar results were also found in some

manganites [9,12,29] A smaller value of β¼0.171 for x¼0.09

reveals this sample lying in the region close to the crossover,

where the FOMT is still persistent It is also known that the

MAP application for the materials with the presence of the FOMT

makes of their exponent values different from those expected for

the theoretical models, such as the cases of La0.7Ca0.3MnO3 and

La0.9Te0.1MnO3[5,31] With a higher Ni-doping content of x¼0.15,

one can see that itsβvalue (¼0.320) is close to that expected for

the 3D Ising model (β¼0.325), indicating the existence of

short-range FM order associated with the magnetic inhomogeneity, and

FM/anti-FM mixed phase It comes to our attention that the β

value tends to shift towards the values of the Heisenberg model

and MFT if Ni content (x) in La0.7Ca0.3Mn1xNixO3is higher than

0.15 For inhomogeneous ferromagnets, the critical values usually

depend on the magneticﬁeld ranges employed for MAP analyses

because of a signiﬁcant ﬁeld-induced change in the nature and

range of the FM interaction[9,32] Performing a renormalization

group analysis of exchange-interaction systems, Fisher et al found

the exponent values depending on the range of exchange

interac-tion characterized by J(r)¼1/rd þ s(where d, andsare the

dimen-sion of the system, and the interaction range, respectively)[33]

The MFT exponents are valid for so1/2 while the Heisenberg

ones are valid fors42 The exponents belong to other

univers-ality classes (such as the T-MFT and 3D Ising models) if 1/2oso2,

which can be the case taking place in our samples

Together with assessing the critical behaviors of La0.7Ca0.3Mn1x

-NixO3 samples, we have also considered the magnetic-entropy

change (ΔSm) and its ﬁeld dependence, as shown in Fig 6 At a

given temperature for each sample,ΔSmincreases with increasing

H Around TC, ΔSm(T) curves reach the maxima, |ΔSmax| The

|ΔSmax| values determined for x¼0.09, 0.12, and 0.15 in the ﬁeld

H¼40 kOe are about 7.1, 5.2, and 3.4 J kg1K1, respectively, which are smaller than those obtained from the parent compound [7] Though the Ni doping reduces the|ΔSmax| value, the linewidth of the

ΔSm(T) curves become broadened due to the FOMT–SOMT trans-formation, enhancing the refrigerant capacity (RC) Particularly, at TC the H dependences of|ΔSmax| can be well described by a power law

of|ΔSmax|pHn[24], where values n¼0.55, 0.68, and 0.77 for x¼0.09, 0.12, and 0.15, respectively These values are different from those (n¼0.33, 0.41, and 0.48 for x¼0.09, 0.12, and 0.15, respectively) calculated from the relation n¼1þ(β1)/(βþγ)[23] As shown in Ref.[34], n is known as a function of T, H and|ΔSm|, which can also be obtained from the relation n¼d ln|ΔSm|/d ln H Depending on the variation of these parameters, n would be different It reaches the minimum at temperatures in the vicinity of TC[23] We believe that a large deviation of the n values obtained from two routes is because the exponent valuesβandγdetermined from the MAP method are much different from those expected for the MFT In other words,

La0.7Ca0.3Mn1xNixO3 samples are not conventional ferromagnets There are the magnetic inhomogeneity, and the existence of FOMT and/or SOMT properties (particularly for two samples with x¼0.09 and 0.12 lying in the crossover region) For conventional ferro-magnets obeyed the MFT, n is equal to 2/3 However, experimental results based on the framework of the SOMT (MFT) theory for inhomogeneous ferromagnets, like the present cases, introduce the values n different from 2/3[23,24]

4 Conclusions

We studied the critical behavior and related physical properties

of manganites La0.7Ca0.3Mn1xNixO3 (x¼0.09, 0.12 and 0.15) around their TCvalues Detailed analyses of the M–H–T data based

on the MAP method revealed the stability in value of γE1, demonstrating the real PM behavior above TC in the samples However, in the FM region, experimental results revealed the

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β (emu/g)

Fig 5 (Color online) Scaling performance of M/|ε| β versus H/|ε| β þ γ in the log scale at temperatures ToT C and T4T C for La 0.7 Ca 0.3 Mn 1x Ni x O 3 with (a) x¼0.09, (b) x¼0.12 and (c) x¼0.15 The insets plot the same data in the linear scale.

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sample x¼0.15 undergoing the SOMT Its βexponent is close to

that expected for the 3D Ising model For the samples with lower

Ni-doping contents, their exponents β (¼0.171 and 0.262 for

x¼0.09 and 0.12, respectively) indicate the samples exhibiting

tricriticality associated with the FOMT–SOMT transformation; in

which, the FOMT is dominant at theﬁelds lower than HL

Short-range FM interactions are thus found in all the samples

Interest-ingly, around TC,ﬁeld dependences of |ΔSmax| can be described by

a power law |ΔSmax|pHn The n values (¼0.55–0.77) obtained

from the power-lawﬁtting are higher than those (n¼0.33–0.48)

calculated from the relation n¼1þ(β1)/(βþγ) We believe that

the deviation of the n values obtained from two ways is related to

the using of the approximate MFT (the MAP method) for

uncon-ventional ferromagnets (with the existence of the magnetic

inhomogeneity, and FOMT and/or SOMT properties), where the

exponent values β and γ determined are much different from

those expected for the MFT

Acknowledgment

This research was supported by the Converging Research

Center Program through the Ministry of Science, ICT and Future

Planning, Korea (2013K000405)

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0 2 4 6 8

0 2 4 6

1 2 3 4

0 2 4 6 8

0 2 4 6

0 1 2 3

40 kOe

30 kOe

20 kOe

10 kOe

40 kOe

30 kOe

20 kOe

Sm

-1.K

-1)

10 kOe

40 kOe

30 kOe

20 kOe

10 kOe

T (K)

|ΔSmax| α Hn

(with n = 0.77) (with n = 0.68) (with n = 0.55)

Smax

-1K

-1)

H (kO e) Fig 6 (Color online) ΔS m (T) curves with the fields H¼10, 20, 30 and 40 kOe, and field dependences of |ΔS max | at T C fitted to a power law |ΔS max |pH n

for

La 0.7 Ca 0.3 Mn1xNi x O 3 with (a, b) x ¼0.09, (c, d) x¼0.12 and (e, f) x¼0.15.

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