First to second order magnetic phase transformation in la0 7ca0 3 xbaxmno3 exhibiting large magnetocaloric effect

Yu4 1 Department of Physics and Oxide Research Center, Hankuk University of Foreign Studies, Yongin 449-791, South Korea 5Advanced Institute for Science and Technology, Hanoi University

First-to-second-order magnetic-phase transformation in La0.7Ca0.3-xBaxMnO3

exhibiting large magnetocaloric effect

The-Long Phan, N.T Dang, T.A Ho, T.V Manh, T.D Thanh, C.U Jung, B.W Lee,

A.T Le, Anh D Phan, S.C Yu

PII: S0925-8388(15)31418-3

Reference: JALCOM 35717

To appear in: Journal of Alloys and Compounds

Received Date: 9 January 2015

Revised Date: 12 October 2015

Accepted Date: 19 October 2015

Please cite this article as: T.-L Phan, N.T Dang, T.A Ho, T.V Manh, T.D Thanh, C.U Jung,

B.W Lee, A.T Le, A.D Phan, S.C Yu, First-to-second-order magnetic-phase transformation in

La0.7Ca0.3-xBaxMnO3 exhibiting large magnetocaloric effect, Journal of Alloys and Compounds (2015),

First-to-second-order magnetic-phase transformation in La0.7Ca0.3-xBaxMnO3

exhibiting large magnetocaloric effect

The-Long Phan1,*, N T Dang2, T A Ho3, T V Manh3, T D Thanh4, C U Jung1, B W Lee1, A T Le5,

Anh D Phan6, and S C Yu4

1

Department of Physics and Oxide Research Center, Hankuk University of Foreign Studies,

Yongin 449-791, South Korea

5Advanced Institute for Science and Technology, Hanoi University of Science and Technology,

01 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam

6

Department of Physics, University of Illinois at Urbana-Champaign, Urbana 61801, USA

Abstract

We have prepared polycrystalline samples La0.7Ca0.3-xBaxMnO3 (x = 0, 0.025, 0.05, 0.075 and 0.1) by

solid-state reaction, and then studied their magnetic properties and magnetocaloric (MC) effect based

on magnetization versus temperature and magnetic-field (M-H-T) measurements Experimental results reveal the easiness in tuning the Curie temperature (TC) from 260 to about 300 K by increasing Ba-

doping concentration (x) from 0 to 0.1 Under an applied field H = 50 kOe, maximum entropy changes around TC of the samples can be tuned in the range between 6 and 11 J⋅kg-1⋅K-1, corresponding to refrigerant-capacity values ranging from 190 to 250 J⋅kg-1 These values are comparable to those of some conventional MC materials, and reveal the applicability of La0.7Ca0.3-

magnetic-xBaxMnO3 materials in magnetic refrigeration Analyses of the critical behavior based on the Banerjee

criteria, Arrott plots and scaling hypothesis for M-H-T data prove a magnetic-phase separation when Ba-doping concentration changes In the doping region x = 0.05-0.075, the samples exhibits the

crossover of first- and second-order phase transitions with the values of critical exponents β and γ

close to those expected for the tricritical mean-field theory The samples with x < 0.05 and x > 0.075

exhibit first- and second-order transitions, respectively More detailed analyses related to the Griffiths singularity, the critical behavior for different magnetic-field intervals started from 10 kOe, and the

magnetic-ordering parameter n = dLn|∆Sm|/dLnH (where ∆Sm is the magnetic-entropy change) demonstrate magnetic inhomogeneities and multicritical phenomena existing in the samples

Keywords: Perovskite manganites, Magnetic properties, Critical behavior

*Electronic mail: ptlong2512@yahoo.com;

Phone: +82-43-261-2269; Fax: +82-43-275-6416

Currently, hole-doped perovskite-type manganites with a generally chemical formula of R

1-xA’xMnO3 (R = La, Pr, Nd; and A’ = Ca, Sr, Ba, Pb) are still attracting intensive interest of the

solid-state physics community because they exhibit many intriguing physical phenomena (typically, colossal magnetoresistance (MR) and magnetocaloric (MC) effects) taking place around magnetic-phase transitions To explain these physical phenomena, theoretical models of exchange interactions [1], polarons (causing Jahn-Teller lattice distortions) [2, 3], and phase separation combined with the percolation and Griffiths singularity have been proposed [4-6] It has been agreed with opinions that colossal MR and MC effects in manganites are directly related to ferromagnetic (FM) or antiferromagnetic (AFM) ordering, charge ordering (CO), and orbital ordering (OO), meaning the

interplay of spin, orbital and lattice/phonon degrees of freedom [7] These properties found in R

1-xA’xMnO3 compounds are dependent on concentration of Mn3+ and Mn4+ ions, which can be easily

controlled by changing A’-doping content (x) A coexistence of Mn3+ and Mn4+ ions leads to interaction types known as the FM double-exchange interaction associated with a Mn3+-Mn4+ pair, and the AFM super-exchange interaction associated to Mn3+-Mn3+ and Mn4+-Mn4+ pairs The strength of these

interactions is dependent on the structural parameters, such as the bond distance R〈Mn-O〉, the bond angle

〈Mn-O-Mn〉, the variance σ2

of ionic radii, and the tolerance factor t=(〈 〉r A +r O) / 2 (〈 〉r B +r O) (where

〈r A 〉 and 〈r B 〉 are average radii of the cations located at A and B sites in the perovskite structure ABO3,

respectively, and rO is the radius of oxygen anion), and the effective bandwidth defined as

ω= −〈 − − 〉 [8, 9] Experimental studies have revealed the

following phenomena: (i) for Mn3+-rich FM manganites, a decrease of 〈r A 〉 (or t) tends to diminish the

〈Mn-O-Mn〉 angle, reducing the bandwidth W, and consequently the ferromagnetic-paramagnetic

(FM-PM) phase-transition temperature (TC, the Curie temperature) [8, 10]; (ii) for Mn4+-rich manganites, a

small 〈r A 〉 (or t) value is required to result in colossal MR and MC effects [11]; and (iii) at any 〈r A〉 and

Mn valence, an increase of σ2

tends to depress FM and AFM interactions, and to destabilize CO [12]

La0.7Ca0.3MnO3 has attracted much more interest for both the aspects of pure research and technological applications because colossal MR and MC effects together with intriguing physical properties occur near room temperature These properties can be controlled by doping suitable elements into the sites of La/Ca and/or Mn to change the structural parameters and the Mn3+/Mn4+ ratio Interestingly, the FM-PM phase transition of La0.7Ca0.3MnO3 polycrystalline and single-crystal bulks is followed up with structural changes is discontinuous, which is known as a first-order magnetic phase transition (FOMT) [13-17] For La0.7Ca0.3MnO3 nanoparticles, there is a critical particle size (dc) The

nanoparticles with average particle sizes larger than dc exhibit the FOMT [18, 19] Because the width

of FM-PM transition region in FOMT materials is narrow, the operating temperature range of based electronic devices is limited Furthermore, large hysteretic losses of FOMT materials are detrimental to the refrigerant capacity (RC, an important parameter used in evaluating a MC material besides the magnetic-entropy change) in refrigeration applications To improve these restrictions, it is necessary to widen the FM-PM transition region upon modifying the FOMT of La0.7Ca0.3MnO3 to a second-order phase transition (SOMT) This process is known as the rounding, where a discontinuous FOMT is rounded to a continuous SOMT by quenched disorder [20, 21] In practice, it can be doped suitable elements into the Mn and/or La/Ca sites [14, 15, 21-24] Another effective route has also been suggested to be the fabrication of low-dimensional La0.7Ca0.3MnO3 materials (thin films and nanoparticles) [13, 18, 19, 25]

xBaxMnO3 compounds, and then investigated in detail their magnetic and MC behaviors The results obtained from analyzing magnetization versus temperature and magnetic-field data reveal all the

compounds giving a large MC effect While the samples x = 0.05-0.075 exhibit the crossover of the FOMT and SOMT, those with x < 0.05 and x > 0.075 exhibit the FOMT and SOMT, respectively

These results are discussed and compared carefully with previous studies on the same topic

2 Experimental details

Five perovskite-type manganite samples La0.7Ca0.3-xBaxMnO3 (with x = 0, 0.025, 0.05, 0.075, and

0.1) were prepared from high-purity (99.9 %) precursors La2O3, CaCO3, BaCO3 and MnCO3 in powder (they were purchased from Aldrich, and used as received from commercial sources, without further purification and/or treatment) by using conventional solid-state reaction These precursors combined with stoichiometric masses were well ground and mixed, and then calcinated in air at 1200 oC for 24 hrs After calcinating, the obtained mixtures were re-ground and pressed into pellets under a pressure of about 5000 psi by using a hydraulic press These pellets were finally sintered at 1400 oC for 24 hrs The crystal structure at room temperature of obtained products after sintering was checked by an X-ray

diffractometer (Bruker AXS, D8 Discover) equipped with a Cu-Kα radiation source with wavelength λ

=1.5406 Å To minimize errors related to the position calibration of X-ray incident angles, a small amount of standard Si powders was mixed with the samples before recording their X-ray diffraction (XRD) patterns Magnetization measurements versus temperature and magnetic field were performed

on a superconducting quantum interference device (SQUID) according to the increasing direction of

temperature, with increments of 2 K for M(H) and 5 K for M(T)

3 Results and discussion

3.1 Crystal structure analysis

Figure 1 shows room-temperature Miller-indexed XRD patterns of La0.7Ca0.3-xBaxMnO3 samples

with x = 0-0.1 Detailed analyses of the crystal structure based on the card PDF#49-0416 in MDI Jade 5.0 reveal that all the samples crystallized in the orthorhombic structure (space group: Pnma) Though

Ba doping with x = 0.025-0.1 does not change the structure type (i.e., no indication of crystal-structure separation), the shift of the XRD peaks towards smaller angles (particularly for the sample x = 0.1, see the inset of Fig 1) demonstrates the change of the lattice parameters (a, b and c) in the doped samples

compared with the parent compound La0.7Ca0.3MnO3 Based on the XRD data, we calculated the

volume of unit cell (V) from a, b and c As shown in Table 1, V increases from 229.8 to 231.1 Å3 with

increasing Ba-doping content (x) in La0.7Ca0.3-xBaxMnO3 from 0 to 0.1, respectively This is due to the substitution of Ba2+ with a larger ionic radius (1.35 Å) for Ca2+ (or La3+) with a smaller radius of 1.18 Å (or 1.03 Å) [42] The Ba2+ replacement does not change the Mn3+/Mn4+ content ratio (= 7/3) in the

samples, but enhances slightly the values of 〈rA〉 and t from 1.021 Å and 0.871 for x = 0 to 1.056 Å and

0.884 for x = 0.1, respectively, see Table 1 Increasing Ba-doping content also enhances t towards the value t = 1 of the cubic perovskite (such as SrTiO3), indicating an increase of 〈Mn-O-Mn〉 towards values closer to 180o [15] Furthermore, with the difference in the electronic structure, the Ba2+substitution for Ca2+ also causes the difference in the relative intensity of diffraction peaks when Ba concentration increases, see the inset of Fig 1 as an example The results obtained from the structural

analyses are different from those reported by Ulyanov et al on La0.7Ca0.3-xBaxMnO3 [39], where they

found the orthorhombic-rhombohedral transformation taking place at a threshold concentration xc = 0.09 Having studied La0.67(Ca1-yBay)0.33MnO3 compounds, Moutis et al found this transformation at y

= 0.5 (corresponding to xc ≈ 0.17) [15] Different sample-fabrication conditions could lead to the phenomena as mentioned above

3.2 Magnetization and susceptibility versus temperature, and the Griffiths phase

The structural changes influence directly the magnetic and MC properties of the samples Learning about these problems, we have investigated temperature and magnetic-field dependences of

magnetization, M(T, H) Figure 2(a) shows field-cooled M(T) data normalized to the M values at 5 K

for La0.7Ca0.3-xBaxMnO3 samples in the field H = 100 Oe The results reveal that M values at temperatures below 250 K for x = 0-0.075 and 280 K for x = 0.1 are quite stable Increasing temperature above these values leads to a rapid decrease of M because of the FM-PM transition, where

FM coupling of magnetic moments is collapsed by thermal energy By plotting the dM/dT versus T curves, their minima indicate the FM-PM transition temperature (TC, the Curie temperature) of the

samples As shown in Figure 2(b) and Table 1, the TC values are about 260 K for x = 0 and 0.025, and

267, 268 and 300 K for x = 0.05, 0.075 and 0.1, respectively The increase of TC with increasing doping content in La0.7Ca0.3-xBaxMnO3 is in good agreement with the previous reports [15, 38, 39], and

Ba-related to the increase of 〈rA〉 and t, as mentioned in the introduction part Carefully reviewing previous

studies on doped La0.7Ca0.3MnO3 compounds, it can be found that the replacement of Ca2+/La3+ by Ba2+,

Sr2+ or Pb2+ usually increases TC [14, 15, 23, 43, 44] A similar situation is also found in

La0.7Ca0.3MnO3 compounds doped with Ag+, Na+ or K+ [45-47] In contrast, the replacements of

Ca2+/La3+ by Pr3+ and Cd2+ [36, 48-50], and of Mn by a transition metal (Co, Fe, Ni, Ti, Cr, Cu, Ga or

Al) [21, 22, 24, 33, 35, 37, 51-53] decrease Tc remarkably These results are tightly related to the

From the M(T) data, performing χ-1

(T) = H/M(T) curves (see Figure 3) reveals their linear variation at temperatures above the so-called Griffiths temperature (TG) [6], corresponding to

temperature points indicated by the arrows in Figure 3 and its inset; TG values of the samples La0.7Ca

0.3-xBaxMnO3 are also listed in Table 1 In this temperature range (T > TG), the samples exhibit the

Curie-Weiss (CW) PM behavior; i.e., the magnetic susceptibility (χ

-) versus temperature obeys a function

χ(T) = C/(T-θ), where C and θ are the Curie constant and CW temperature, respectively Fitting the linear χ-1

(T) data to the CW law introduces C and θ values Using the relation C = N(µB P eff)2/3k B, with

the number of ions N = 6.023×1023 mol-1, the Bolzmann constant k B = 1.3806×10-23 J/K and the Bohr magneton µB = 9.274×10-24 J/T, we obtained the effective PM moment (P eff) The values θ and P eff of the samples are shown Table 1 It is known that for La0.7Ca0.3-xBaxMnO3 compounds in the PM region, there is the contribution of free magnetic moments of Mn3+ (Peff = 4.9µB) and Mn4+ (Peff = 3.9µB) ions

to the PM susceptibility, Peff = 0 for La3+ [56] Because the Mn3+/Mn4+ content ratio (= 7/3) in the samples is unchanged by the Ba doping, the effective moment calculated from the equation

P = µ + + µ + is thus 4.6µB This value is about 1.2-1.5 times smaller than the Peff values

determined from fitting the χ-1

(T) data to the CW law (see Table 1), suggesting the formation of FM

clusters of Mn3+-Mn4+ double-exchange pairs in the PM region [57]

Particularly, below TG there is a downturn in the χ-1

(T) curves before TC is reached This is an indication of the Griffiths transition [4, 6], characterized by a susceptibility exponent

T and TG, there is a random distribution of FM clusters within the globally

PM phase [6] For the parent compound La0.7Ca0.3MnO3 exhibiting simultaneously the FOMT and Griffiths singularity [4, 6], its CW temperature θ = 256 K is a little bit smaller than TC = 260 K However, a similar circumstance did not happen for the Ba-doped samples because their magnetic-phase feature was changed, as being further confirmed below For the exponent λ, its value gradually

decreases from 0.22 to 0.11 when x in La0.7Ca0.3-xBaxMnO3 increases from 0 to 0.1, respectively, see Table 1, proving the suppression of the Griffiths phase At high applied fields, it has been observed the suppression of the Griffiths phase [5, 58, 59] In fact, the Griffiths phase was found popularly in some manganites and cobaltites; for examples, La1-x(Ca, Ba, Sr, Pb)xMnO3 [4, 6, 60, 61], (Nd1-xYx)0.7-

Sr0.3MnO3 [62, 63], Sm1-x(Ca, Sr)xMnO3 [5, 58, 64], and La0.6Sr0.4Mn1–xCoxO3 [65] For compounds with the presence the Griffiths phase, their magnetic properties versus temperature can be divided into

the following characteristic regions: (i) T ≤ TC, (ii) TC≤ T ≤ rand

3.3 Magnetic phase transition and critical behavior

To get more insight into the phase-transition type, magnetic interactions and MC effect of the samples La0.7Ca0.3-xBaxMnO3, we have recorded M(H) data at different temperatures around the FM-

PM transition These M(H) data are then performed as H/M versus M2, and graphed in Figure 4, which

are defined as the inverse Arrott plots [26] For x = 0, in the vicinity of TC, its M(H) curves have the like shape, and the slopes of H/M versus M2 curves at low fields are negative, Figures 4(a, b) These

S-features disappear gradually when x in La0.7Ca0.3-xBaxMnO3 increases from 0.025 to 0.05, Figures

4(c-f) For higher x values (= 0.075 and 0.1), positive slopes and no S shape are observed, Figures 4(g-j)

According to Banerjee’s criteria [28], a positive or negative slope indicates the FOMT or SOMT,

dependences of the spontaneous magnetization, Ms(T), inverse initial susceptibility, χ0−1

(T), and critical isotherm, M(H) at TC, respectively In method, these exponents can be determined by using the modified Arrott plot (MAP) method [27] Firstly, we suppose that all the samples La0.7Ca0.3-xBaxMnO3

undergoing the SOMT Variations of Ms(T), χ0-1(T) and M(H, TC) data around TC thus obey asymptotic relations [21, 66]

1 0

χ−

(T) = (h0/M0)εγ

M(H, TC) = DH1/δ, ε =0, (3)

where M0, h0 and D are critical amplitudes, and ε = (T-TC)/TC is the reduced temperature According to

the MAP method, the values of critical parameters TC, β andγ are determined from the Arrott-Noakes

equation of state (H/M)1/γ = aε + bM1/β, where a and b are temperature-dependent parameters [21]

This equation implies that with correct β and γ values the performance of M1/β versus (H/M)1/γ curves in

the vicinity of TC introduces parallel straight lines, and one of these lines passes through the coordinate

origin at TC According to the mean-field (MF) theory proposed for ferromagnets exhibiting long-range magnetic interactions, β and γ values are 0.5 and 1.0, respectively [67] The plot of M1/β versus (H/M)1/γ

curves with β = 0.5 and γ = 1.0 (corresponding to normal Arrott plots of M2 versus H/M) [26] does not

introduce parallel straight lines as mentioned, see Figure 4 This demonstrates that the MF exponents are unsuitable to describe magnetic interactions in the samples La0.7Ca0.3-xBaxMnO3 In other words,

the samples exhibit short-range magnetic interactions rather than long-range ones Finding other values

of β andγ is thus necessary

To estimate the values of β and γ, we firstly plot the M1/β versus (H/M)1/γ curves for the M(H)

data with the exponents expected for the 3D Heisenberg (β = 0.365 and γ = 1.336), 3D Ising (β = 0.325 and γ = 1.241), and tricritical MF (β = 0.25 and γ = 1) models [67-69] One can see that among the

plots shown in Figure 5, only the M1/β versus (H/M)1/γ curves in Figures 5(e, j) for x = 0.1, and 5(k-n) for x = 0-0.075 at high fields are most suitable to the descriptions of the Arrott-Noakes equation because the curvature of M1/β versus (H/M)1/γ curves are smallest if comparing with the other cases Alternatively, it is possible to assess which model describes better magnetic interactions taking place in

materials upon the relative slope (RS) defined by RS = S(T)/S(TC), where S(T) and S(TC) are slopes at

temperatures T and TC, respectively [70] The RS of the most satisfactory model would be close to unity With the observed features, we believe that β and γ values responsible for x = 0-0.075 are close

to the tricritical MF-theory exponents, while those responsible for x = 0.1 are located in between the 3D

Heisenberg and 3D Ising exponents The sets of β = 0.23 and γ = 1.2 (close to tricritical MF exponents)

for x = 0-0.075, and β = 0.33 and γ = 1.3 (located in between the 3D Heisenberg and 3D Ising

exponents) for x = 0.1 were thus selected as the trial values for the MAP process In our work, the MAP

method was applied for different magnetic-field intervals (with 10 kOe for each interval, see Table 2) because it is well known that the FOMT could be driven towards SOMT by the field, and/or magnetic inhomogeneities usually exist in the samples According to our experience, for a homogeneous ferromagnet undergoing the SOMT, exponents obtained from the MAP method for different field intervals are almost the same If obtained exponents are dependent on field intervals, the ferromagnet is inhomogeneous and/or exhibits the FOMT or the mixture of FOMT and SOMT

With the trial exponents as selected, the M s (T) and 1

0

χ− (T) data are determined from the linear

extrapolation in specific field ranges to the M1/β and (H/M)1/γ (= 1

are then fitted to Eqs (1) and (2), respectively, to achieve better β and γ values After fitting, the TC

values corresponding to the extrapolations from FM (associated with M s) and PM (associated with 1

0

χ−

) regions would also be determined The values of β, γ and TC are then used for the next MAP These processes are repeated several times until the critical parameters converge to their stable values Figure

6 shows the final results of M s (T) and 1

for x = 0.025 and H = 20-50 kOe, β = 0.221-0.249 and γ = 1.022-1.052 for x = 0.05 and H = 10-50

kOe, β = 0.216-0.253 and γ = 0.973-1.116 for x = 0.075 and H = 10-50 kOe, and β = 0.301-0.326 and γ

= 1.342-1.382 for x = 0.1 and H = 10-50 kOe Performing the MAP at magnetic fields lower than the

values shown in Table 2 is not successful, due to the domination of the FOMT, the rearrangement of magnetic domains and/or the effect related to the uncertainty in the calculation of demagnetization factor [71] The reliability of the critical values could be checked by using the scaling hypothesis [21],

which predicts that M(ε, H) in the FM-PM transition region is a universally exponent function

)

|

|/(

M , where f+ for T > TC and f- for T < TC are regular functions This means

that plotting M/|ε|β versus H/|ε|β+γ with correct values of β, γ and TC makes all data points with T < TCand T > TC falling on two universal branches f- and f+, respectively With the critical values obtained

from different field intervals, we have performed M/|ε|β versus H/|ε|β+γ curves for the samples, and

found the M(H, T) data falling completely on two universal branches (the first one for T < TC, and the

other for T > TC), as can be seen clearly in Figure 7 (the scaling plots on the log-log scale) for two

typical samples with x = 0.07 and 0.1 These results prove that the critical parameters β, γ and TCobtained from the MAP method are believable Here, the TC values determined from the M(T) and

M(H) data could be different because of the effect of field-driven FM-PM phase transition

TC value were not recorded, and TC values of some samples are strongly dependent on the magnitude of

applied magnetic field Alternatively, it can be based on the Widom relation δ = 1 + γ/β to calculate δ

[72] Using this route, δ values calculated are shown in Table 2 As proved by previous works [21, 40,

73, 74], the δ values obtained from Eq (3) and the Widom relation are close to each other

Comparing the exponents determined from our work (as summarized in Table 2) with those expected for the MF, 3D Heisenberg, 3D Ising, and tricritical MF theories (their exponents are shown

in Table 3), one can see that the exponents (β = 0.209-0.227 and γ = 1.060-1.098) of the samples x = 0

and 0.025 in the interested field ranges are not suitable to any theories A similar circumstance is also

observed for x = 0.05 and 0.075 at magnetic fields H < 40 kOe At higher fields H = 40-50 kOe,

however, the values β≈ 0.25 and γ ≈ 1 of x = 0.05 and 0.075 are very close to tricritical MF-theory exponents For x = 0.1 in the FM region, its β exponent (= 0.301-0.322) obtained for magnetic fields H

= 10-40 kOe are located in between those expected for the tricritical MF (β = 0.25) and 3D Ising (β =

0.325) theories, and at higher fields H = 40-50 kOe its β exponent (= 0.326) is close to the 3D Ising exponent (β = 0.325) Meanwhile, the values γ = 1.342-1.382 associated with the PM region of x = 0.1

are close to the 3D Heisenberg exponent (γ = 1.336) These results reveal the magnetic-field-driven phase separation in La0.7Ca0.3-xBaxMnO3 as follows The samples x = 0 and 0.025 exhibit the FOMT in the whole field range H = 0-50 kOe The samples x = 0.05 and 0.075 exhibit the crossover of the FOMT-SOMT transformation at fields H = 40-50 kO, while they have the FOMT nature in the field intervals H = 0-40 kOe For x = 0.1 at all magnetic fields, it is assigned to be a SOMT compound

Besides the magnetic phase separation, the samples also exhibit inhomogeneities due to the formation

of FM, leading to short-range magnetic order This is in good agreement with the discussion related to

the above M(T) analyses If carefully considering the feature of the XRD data (Fig 1), one can see a remarkable shift of the diffraction peaks of the sample x = 0.1 towards smaller angles Also, its t value

is larger than the t values of the samples x < 0.05, as shown in Table 1 Clearly, the FOMT-SOMT

transformation in our orthorhombic La0.7Ca0.3-xBaxMnO3 samples depends not only on the applied field magnitude, but also on the structural parameters

In fact, the FOMT-SOMT transformation was also found in some manganites, such as La0.7Ca

0.3-xSrxMnO3 with x ≈ 0.1 [23], La2/3(Ca1-xSrx)1/3MnO3 with x ≈ 0.15 [32], La0.67(Ca1-xBax)0.33MnO3 with x

≈ 0.25 [15], La0.7Ca0.3Mn1-xNixO3 with x = 0.12 [24], La0.7Ca0.3Mn1-xFexO3 with x = 0.05~0.07 [22],

Nd1-xSrxMnO3 with x = 0.33 [75], and La0.7-xPrxCa0.3MnO3 with x = 0.3~0.4 [49] This transformation

is related to structural changes and/or the variation of Mn3+/Mn4+ content ratio, which modify the strength of FM interactions between Mn ions Additionally, the suppression of the Griffiths phase (related to the decrease of λ with increasing x in La0.7Ca0.3-xBaxMnO3, see Table 1) could also plays an important role for the magnetic phase transformation Having reviewed previously critical-behavior studies on perovskite manganites and cobaltites (their exponents are summarized in Table 3), we find that orthorhombic manganites give more interesting magnetic properties For example, (i) the FOMT with β < 0.25 found in La0.7Ca0.3MnO3 [16], La0.7Ca0.3Mn0.88Ni0.12O3 [24] and La0.9Te0.1MnO3 [76]; (ii) the crossover of the FOMT-SOMT transformation with β ≈ 0.25 found in La1-xCaxMnO3 (x = 0.2 and

0.4) [41, 68, 77], La0.7Ca0.3Mn0.88Ni0.12O3 [24], (Nd1-xYx)0.7Sr0.3MnO3 (x = 0 and 0.07) [78] and

La0.1Nd0.6Sr0.3MnO3 [79]; and (iii) the SOMT with exponents close to those expected for the MF, 3D Heisenberg and/or 3D Ising models (see Table 3 for orthorhombic manganites) These features are also found in the current work, see Table 2 For manganites (as well as cobaltites) crystallized in other crystal structures, there are two typical candidates showing the crossover property, which are

La0.67Pb0.33Mn1-xCoxO3 (x = 0.03 and 0.06) [80] and Nd0.7Sr0.3MnO3 [75] These structures usually lead

to the SOMT in manganites and cobaltites, where their exponents are close to the MF, 3D Heisenberg and/or 3D Ising exponents (see Table 3 for rhombohedral/pseudo-rhombohedral, tetragonal, monoclinic, and cubic/pseudo-cubic structures) For a specific manganite/cobaltite compound crystallized in

different forms (i.e., single-crystal and polycrystalline bulks, nanoparticles, and thin films), its

FM interactions associated with Mn3+-Mn4+, and Mn3+-Mn3+ and Mn4+-Mn4+ pairs, respectively A similar circumstance also happens for cobalties, where FM and anti-FM interactions are associated with

Co3+-Co4+, and Co3+-Co3+ and Co4+-Co4+ pairs, respectively [55, 66, 71, 74] However, long-range FM interactions can be still established in some manganites, where their exponents are very close the exponents β = 0.5 and γ = 1 of the MF theory; for example, Nd1-xSrxMnO3 (x = 0.4 and 0.5) [75, 86, 87],

La0.8Sr0.2MnO3 [73], La0.7Pb0.3MnO3 [88], La0.8Na0.1MnO3 [89], and La0.7Ca0.3Mn0.95Cu0.05O3 [35] Recently, Skomski has used the MF theory, and showed that long-range FM interactions could be easily established in complex spin structures of feromagnet, antiferomagnets and noncollinear magnets with two or more sub-lattices [90] According to the renormalization group analysis performed by

Fisher et al [91] for an exchange-interaction system, the values of the exponents depends on the exchange-interaction range J(r) = 1/r d+σ, where d is the spatial dimensionality of the system and σ is the range of interaction The MF exponents are valid for 0<σ < ½ while the 3D Heisenberg ones are valid for σ≥ 2 In the range ½ < σ < 2, the exponents belong to other universality classes (which could

be the tricritical MF and 3D Ising models) Based on the obtained γ values, it can be calculated σ

values from the following relation [91]

system of La0.7Ca0.3-xBaxMnO3 with the γ values shown in Table 2, calculated σ values for x = 0-0.075 are located in the range 1.4~1.6, and for x = 0.1 are 1.9~2.1 whenever d = 3 and n > 1 Clearly, these

values almost fall within the range ½ < σ < 2 of the universality classes no-belonging to the MF and

3D Heisenberg models Particularly, several σ values of the sample x = 0.1 are greater than 2 This is

ascribed to the coexistence of the 3D Heisenberg and 3D Ising ferromagnetism, which is in good

agreement with the exponents obtained by the MAP method for x = 0.1, as shown in Table 2 It should

be noticed that the above results indicate the complication of critical-behavior-related problems of perovskite-type magnanites/cobaltites There is no standard token to affirm exactly whether which theoretical model (MF, 3D Heisenberg, or 3D Ising model) is suitable to describe magnetic interactions

in a perovskite sample unless one analyzes carefully its M-T-H data

3.4 Magnetocaloric effect and universal magnetic-entropy curve

Together with studying the magnetic properties of the samples La0.7Ca0.3-xBaxMnO3, we have assessed their MC effect through magnetic-entropy change (∆Sm), an important thermodynamic

parameter characteristic of the disorder of magnetic moments Based on the M(H, T) data and the

Maxwell relation [92]

m

H T

−

−

where Mn and Mn+1 are magnetization values measured in a magnetic field H at temperatures T n and

T n+1, respectively In Figure 8, it shows -∆Sm(T) curves of La0.7Ca0.3-xBaxMnO3 for different field variations At a specific temperature, -∆Sm increases with increasing H from 10 to 50 kOe Maximum -

∆Sm values (denoted as -∆Smax) are found around the FM-PM transition temperature (TC) due to the

strong disorder of magnetic moments H dependences of -∆Smax can be described by a power function

where H changes from 0 to 50 kOe and n is an exponent related to magnetic order [29, 30] Fitting the

-∆Smax(H) data to Eq (8) gave n values of about 0.43 0.45, 0.46, 0.64 and 0.73 for x = 0, 0.025, 0.05,

0.075 and 0.1, respectively, as also attached in Figure 9(a) These values are much different from those

calculated from the exponent relation at TC (corresponding to the peak entropy change) [29, 30]

11

particularly for the samples x = 0-0.075 exhibiting the FOMT and/or the crossover property, see Table

2 Such the difference is due to the instability of the -∆Smax position versus magnetic field, which is

shifted towards higher temperatures when magnetic field increases It has been found that n is a

function of temperature and magnetic field as follows

(≈ 0.3) achieved at temperatures below TC, see Figs 10(a, b), are quite different from the n values

obtained from Eqs (8, and 9), and smaller than those of manganites studied previously [93, 94] This is

due to x = 0 and 0.025 undergoing the FOMT completely The same situation is also observed for x = 0.05 and 0.075 at fields below 40 kOe, where they have the first-order nature At higher fields (H = 40-

50 kOe), these samples exhibit the crossover of the FOMT-SOMT transformation The minimum n values at TC of x = 0.05 and 0.075 are about 0.36 and 0.49, respectively Different from the mentioned

samples, there is a small deviation between the n(T, H) curves of x = 0.1 The n minimum at TC varies

in the range from 0.62 (for H = 50 kOe) to 0.74 (for H = 10 kOe), see Figure 10(e) These values are

quite close to those determined from Eqs (8 and 9), see Figure 9(a) and Table 2, proving that the analyses of the -∆Sm(T, H) data based on Eqs (8-10) are more suitable for ferromagnets having the SOMT It should be noticed that the n values determined at TC of all the samples are magnetic-field

dependent, and not equal to the MF-theory value n = 2/3 (≈ 0.67) Furthermore, if more attention is

given to the n(T, H) curves at T > TC (associated with the PM region) shown in Figure 10, the deviation

between the curves for H = 10 and 50 kOe gradually decreases with increasing x in La0.7Ca

0.3-xBaxMnO3, which could be related to a gradual decrease of λ (from 0.22 for x = 0 to 0.11 for x = 0.1) These features are ascribed to the existence of FM disorder (i.e., short-range FM order) and magnetic

inhomogeneities, which tends to decrease with increasing Ba-doping content In previous studies on single-crystal [95], and poly- and nano-crystalline manganites [93, 94], around the FM-PM transition,

one also indicated a strong dependence of n on microstructures In general, nano-crystalline manganites usually have n values slightly larger than those of single-crystal and poly-crystalline ones This could

be due to the effects related to of grain boundaries, lattice defects, and magnetic anisotropy

In addition to the MC-effect assessment based on the ∆Sm, it can also be paid attention to the

assessment of the RC, which is determined by

2

1( )

T m T

RC= − ∆∫ S T dT , where T1 and T2 are the cold and

hot ends of an ideal thermodynamic cycle [92] Figure 9(b) plots magnetic-field dependences of the RC for the samples La0.7Ca0.3-xBaxMnO3 An increase of H enhances the RC Under a field variation H = 50

kOe, though -∆Smax values (are about 10.7, 9.2, 9.1, 7.1 and 6.0 J⋅kg-1⋅K-1 for x = 0, 0.025, 0.05, 0.075 and 0.1, respectively) decrease with increasing x (due to the decrease of TC and FM coupling), RC values are quite stable in the range between 210 and 250 J/kg, see Figure 9(b) and Table 4 This is due

to the fact that the FOMT-SOMT transition enhances the width of the FM-PM transition region though

-∆Sm is reduced, and thus improves the RC With the same meaning of the RC, it can be assessed the

MC effect upon the relative cooling power (RCP) calculated by RCP = -∆Smax×δTFWHM, where δTFWHM

is the full-width-at-half maximum of the -∆Sm(T) curve [92] Our careful studies on manganite

compounds, such as La0.7Ca0.3-xBaxMnO3 (in this work), La0.7Ca0.2Sr0.1MnO3 [40], (Nd

1-xYx)0.7Sr0.3MnO3 [78], and Sm0.58Sr0.42MnO3 [96], have indicated their RCP values usually 1.2~1.4

times higher than RC ones, see Table 4 Considering typical manganites offering the giant MC effect,

as listed in Table 4, the -∆Smax and RC (or RCP) values of our La0.7Ca0.3-xBaxMnO3 samples are comparable to those obtained from La0.7Ca0.3-xSrxMnO3 (x = 0-0.1) [13, 40, 97-99], La0.7-xPrxCa0.3MnO3

(x = 0~0.7) [36, 48, 49], Pr0.63Sr0.37MnO3 [97], Sm1-xSrxMnO3 (x = 0.42-0.46) [96, 100], Sm

0.7-xLaxSr0.3MnO3 [101], and (Nd1-xYx)0.7Sr0.3MnO3 [78] At a given applied field, though -∆Smax values of these samples are comparable with Gd (a prototype magnetic-refrigerant material), their RC (or RCP) values are much smaller than those of Gd However, with a simple and cheap fabrication technology found in perovskite manganites, and with tunable/reversible MC effect [102], these materials are thus considered as an alternative option for refrigeration applications because the expensiveness of Gd is limited its applicability in commercial cooling devices

Recently, Franco et al [29, 30] have proposed a phenomenological method to construct a

universal entropy curve They have suggested that if single-phase magnetic materials are measured at

different applied fields, their -∆Sm(T, H) curves could be rescaled into a universal curve This is carried out by normalizing -∆Sm(T, H) curves to their respective peak ∆S m pk (i.e., ∆ = ∆S' S T H m( , ) /∆S m pk),

with the temperature axis above and below TC scaled as follows

where Tr is the reference temperature corresponding to a certain fraction f = ∆Sm(Tr)/∆Smax The choice

of f does not affect the construction of the universal curve For multiphase materials, it is necessary to use two reference temperatures Tr1 and Tr2 to contract the universal curve The temperature axis is accordingly scaled as

Because our samples La0.7Ca0.3-xBaxMnO3 are inhomogeneous and not singlephase magnetic phase,

-∆Sm(T, H) curves would thus be rescaled versus the temperature axis θ2, where the reference

temperatures Tr1 and Tr2 were selected corresponding to the value 1

2

pk m

1, it is quite difficult for us to distinguish which samples having the FOMT, SOMT, and the crossover

of the FOMT-SOMT transformation Detailed investigations into these issues warrant further study Clearly, if solely using the universal entropy curve and Banerjee criteria, we could not assess which samples exhibiting the crossover behavior An additional assessment based on the MAP method in order to determine the critical exponents β, γ and δ is necessary to clarify these problems

4 Conclusion

We studied the magnetic and MC properties of orthorhombic La0.7Ca0.3-xBaxMnO3 (x = 0-0.1)

samples prepared by solid-state reaction Careful analyses related to the CW law and Griffiths phase for

the M(T) data revealed the presence of FM clusters and magnetic inhomogeneities in the PM region, particularly at temperatures TC < T < TG FM clusters and magnetic inhomogeneities tend to decrease

with increasing x in La0.7Ca0.3-xBaxMnO3 Using the MAP method, scaling hypothesis, and

renormalization group analysis in order to determine and assess the exponents from the M(H, T) data at

various magnetic-field ranges, we found the magnetic-phase separation in La0.7Ca0.3-xBaxMnO3 as

follows: the samples with x = 0 and 0.025 in the whole field range H = 0-50 kOe, and x = 0.05 and 0.075 at fields H = 0-40 kOe exhibit the FOMT, corresponding to critical exponent values of β = 0.209~0.238 and γ≈ 1 At higher fields of H = 40-50 kOe, the samples x = 0.05 and 0.075 exhibit the

crossover of the FOMT-SOMT transformation, with β ≈ 0.25 and γ ≈1 For the sample x = 0.1, it

exhibits the SOMT nature Its values (β = 0.301-0.322) at magnetic fields H = 10-40 kOe are located in between those expected for the tricritical MF and 3D Ising models, and at higher fields, H = 40-50 kOe,

its β exponent (= 0.326) is close to the 3D Ising exponent Meanwhile, its values γ = 1.342-1.382

associated with the PM region of x = 0.1 are close to the 3D Heisenberg exponent Investigations into

the MC effect indicated the samples offering large -∆Smax and RC values around room temperature

With H = 50 kOe, -∆Smax values are about 10.7, 9.2, 9.1, 7.1 and 6.0 J⋅kg-1⋅K-1 for x = 0, 0.025, 0.05,

0.075 and 0.1, respectively, corresponding to RC values in the range between 210 and 250 J/kg These values are comparable to those of typical manganite materials exhibiting the giant MC effect, making them become an alternative option for refrigeration applications The physical phenomena related to the magnetism, critical behavior and MC effect observed in the samples La0.7Ca0.3-xBaxMnO3 were discussed in detail, in comparison with previous reports on manganites and cobaltites Concerning the issues of the critical behavior, the simultaneous combination of the Banerjee criteria and MAP method

as analyzing the M(T, H) data is an effective approach to assess the magnetic phase transition, the

crossover behavior, and interactions existing in ferromagnets We also constructed the universal entropy curve, and found the overtone of almost data points on it However, it seems to be that the use

of the universal curve is not a powerful criterion to distinguish the FOMT, SOMT, and the crossover of the FOMT-SOMT transformation in our La0.7Ca0.3-xBaxMnO3 samples

Acknowledgement

T L Phan was supported by Hankuk University of Foreign Studies Research Fund of 2015 This research was supported by the Basic Science Research Program through the National Research

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