First-to-second-order magnetic-phase transformation in La0.7Ca0.3-xBaxMnO3 exhibiting large magnetocaloric effect

Accepted Manuscript 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

DOI:

10.1016/j.jallcom.2015.10.162

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), doi: 10.1016/j.jallcom.2015.10.162. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

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 2

Institute of Materials Science, Vietnam Academy of Science and Technology, Hoang Quoc Viet, Hanoi, Vietnam Advanced Institute for Science and Technology, Hanoi University of Science and Technology, 01 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam 6

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

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Institute of Research and Development, Duy Tan University, Da Nang, Vietnam Department of Physics, Chungbuk National University, 361-763 Cheongju, South Korea

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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

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reveal the easiness in tuning the Curie temperature (TC) from 260 to about 300 K by increasing Badoping concentration (x) from 0 to 0.1. Under an applied field H = 50 kOe, maximum magneticentropy 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 xBaxMnO3

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comparable to those of some conventional MC materials, and reveal the applicability of La0.7Ca0.3materials 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

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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: [email protected]; Phone: +82-43-261-2269; Fax: +82-43-275-6416 1

ACCEPTED MANUSCRIPT 1. Introduction Currently, hole-doped perovskite-type manganites with a generally chemical formula of R1xA’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

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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

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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

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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 R1xA’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

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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

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〈Mn-O-Mn〉, the variance σ2 of ionic radii, and the tolerance factor t = (〈 rA 〉 + rO ) / 2(〈 rB 〉 + rO ) (where 〈rA〉 and 〈rB〉 are average radii of the cations located at A and B sites in the perovskite structure ABO3,

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respectively, and rO is the radius of oxygen anion), and the effective bandwidth defined as 1 W ∝ cos ω / R〈3.5 Mn − O 〉 , with ω = 2 ( π − 〈 Mn − O − Mn〉 ) [8, 9]. Experimental studies have revealed the

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

〈 Mn-O-Mn〉 angle, reducing the bandwidth W, and consequently the ferromagnetic-paramagnetic (FMPM) phase-transition temperature (TC, the Curie temperature) [8, 10]; (ii) for Mn4+-rich manganites, a small 〈rA〉 (or t) value is required to result in colossal MR and MC effects [11]; and (iii) at any 〈rA〉 and Mn valence, an increase of σ2 tends to depress FM and AFM interactions, and to destabilize CO [12]. 2

ACCEPTED MANUSCRIPT These remarks reveal the complicated relation between the structural parameters and the magnetic and magneto-transport properties of manganites, which is an interesting theme for pure research. For La1-xA’xMnO3 compounds, the Mn3+-Mn4+ FM interaction, and colossal MR and MC effects are usually largest when the concentration ratio of Mn3+/Mn4+ is about 7/3, corresponding to an A’-

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doping content x ≈ 0.3. Below and above this value, AFM interactions of Mn3+-Mn3+ and Mn4+-Mn4+ pairs are dominant, and thus depress the FM interaction [7, 10]. Among La0.7A’0.3MnO3 compounds, La0.7Ca0.3MnO3 has attracted much more interest for both the aspects of pure research and

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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

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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

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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 CMRbased electronic devices is limited. Furthermore, large hysteretic losses of FOMT materials are

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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

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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].

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ACCEPTED MANUSCRIPT To assess the success in rounding a discontinuous FOMT, it can be based on the theory of second-order phase transitions; specifically, Arrott plot methods [26, 27], the scaling hypothesis [21], and Banerjee’s criteria [28] for assessing magnetization isotherms, and/or the universal behavior [2931] for magnetic entropy change. Such the works were performed on Sr-, Ba-, Pr-, Ga, Fe-, Co-, Cr-,

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and/or Ni-doped La0.7Ca0.3MnO3 compounds [14, 15, 21-24, 32-37]. For Ba-doped La0.7Ca0.3MnO3 compounds, though several previous works [15, 38, 39] reported on their magnetic, MC and transport behaviors, detailed analyses related to the FM-PM critical region, magnetic interactions, and

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percolation threshold of the FOMT-SOMT transformation have not been carried out yet. Moreover, it has been found that for the manganites exhibiting the crossover of the FOMT and SOMT, and magnetic

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inhomogeneity, the values of critical parameters strongly depend on field ranges chosen for analyzing the critical behavior [40, 41]. To gain more insight into these problems, we have prepared La0.7Ca0.3xBaxMnO3

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

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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.

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2. Experimental details

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

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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 4

ACCEPTED MANUSCRIPT 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

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

3. Results and discussion

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3.1. Crystal structure analysis

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

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

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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

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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

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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

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(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 5

ACCEPTED MANUSCRIPT 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

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phenomena as mentioned above.

3.2. Magnetization and susceptibility versus temperature, and the Griffiths phase

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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

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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

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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

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

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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

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ACCEPTED MANUSCRIPT changes of the structural parameters and/or Mn3+/Mn4+ content ratio, which change the bandwidth W of perovskite manganites [7-9, 54, 55]. 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

xBaxMnO3

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temperature points indicated by the arrows in Figure 3 and its inset; TG values of the samples La0.7Ca0.3are 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

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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(µBPeff)2/3kB, with

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the number of ions N = 6.023×1023 mol-1, the Bolzmann constant kB = 1.3806×10-23 J/K and the Bohr magneton µB = 9.274×10-24 J/T, we obtained the effective PM moment (Peff). The values θ and Peff 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

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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 2 2 is thus 4.6µB. This value is about 1.2-1.5 times smaller than the Peff values Peff2 = 0.3µ Mn 4+ + 0.7 µ Mn3+

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determined from fitting the χ-1(T) data to the CW law (see Table 1), suggesting the formation of FM

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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

χ −1 ∝ (T − TCrand )1−λ , where TCrand is the random transition temperature, and λ (≤ 1) is a non-universal positive exponent. Fitting the χ-1(T) data above TC to this equation determined simultaneously the values of TCrand and λ. As shown in Table 1, the TCrand values of the samples are higher than TC, proving the formation of complex FM/anti-FM states at temperatures between TC and TCrand . In the Griffith 7

ACCEPTED MANUSCRIPT phase region between TCrand 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-

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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

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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-

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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 ≤ TCrand , (iii) TCrand ≤ T ≤ TG, and (iv) T > TG. FM order is considered to be gradually decreases with increasing temperature from (i) to (iv). In

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normally inhomogeneous ferromagnets, the values of TCrand and TC are close to each other, and thus the regions (i) and (ii) are almost the same [61]. For ferromagnets with a higher inhomogeneity (like the case of our samples, and those shown in Refs. [4, 65]), all the regions (i)-(iv) would be apparent.

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3.3. Magnetic phase transition and critical behavior

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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 FMPM 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 Slike shape, and the slopes of H/M versus M2 curves at low fields are negative, Figures 4(a, b). These features disappear gradually when x in La0.7Ca0.3-xBaxMnO3 increases from 0.025 to 0.05, Figures 4(cf). 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, 8

ACCEPTED MANUSCRIPT respectively. With these features, we can precariously conclude that the samples with x = 0, 0.025 and 0.05 exhibit the FOMT characterization while those with x = 0.075 and 0.1 exhibit the SOMT characterization. In the range x = 0.05-0.075, La0.7Ca0.3-xBaxMnO3 compounds seem exhibit the crossover of the FOMT-SOMT transformation. To further clarify these preliminary judgments, it

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should be better to determine the critical exponents β, γ, and δ associated with temperature dependences of the spontaneous magnetization, Ms(T), inverse initial susceptibility, χ 0−1 (T), and critical isotherm, M(H) at TC, respectively. In method, these exponents can be determined by using the

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modified Arrott plot (MAP) method [27]. Firstly, we suppose that all the samples La0.7Ca0.3-xBaxMnO3

relations [21, 66] Ms(T) = M0(-ε)β,

χ 0−1 (T) = (h0/M0)εγ, M(H, TC) = DH1/δ,

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undergoing the SOMT. Variations of Ms(T), χ0-1(T) and M(H, TC) data around TC thus obey asymptotic

ε < 0,

(1)

ε > 0,

(2)

ε =0,

(3)

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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].

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

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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,

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ACCEPTED MANUSCRIPT 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

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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

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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

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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

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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

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method was applied for different magnetic-field intervals (with 10 kOe for each interval, see Table 2)

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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 Ms(T) and χ 0−1 (T) data are determined from the linear extrapolation in specific field ranges to the M1/β and (H/M)1/γ (= χ 0−1 )1/γ axes. The Ms(T) and χ 0−1 (T) data

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ACCEPTED MANUSCRIPT 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 Ms) and PM (associated with χ 0−1 ) 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

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6 shows the final results of Ms(T) and χ 0−1 (T) data fitted to Eqs. (1) and (2), respectively, for two typical samples with x = 0.075 and 0.1 carried out in magnetic-field ranges 10-20, 20-30, 30-40 and 4050 kOe. The values of the critical parameters obtained for all the samples in different field intervals are

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tabulated in Table 2, with β = 0.212 for x = 0 and H = 40-50 kOe, β = 0.209-0.227 and γ = 1.060-1.098

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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

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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

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M ( H , ε ) =| ε | β f ± ( H / | ε | β +γ ) , 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 < TC

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and 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 TC obtained 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. 11

ACCEPTED MANUSCRIPT In reference to the exponent δ, its value can be obtained from fitting the isotherm M(H, TC) to Eq. (3). However, we could not carry out this route because the isotherms of some samples at their accurate 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

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[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

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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

M AN U

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

TE D

= 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

EP

are close to the 3D Heisenberg exponent (γ = 1.336). These results reveal the magnetic-field-driven

AC C

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 12

ACCEPTED MANUSCRIPT 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 La0.7Ca0.3with x ≈ 0.1 [23], La2/3(Ca1-xSrx)1/3MnO3 with x ≈ 0.15 [32], La0.67(Ca1-xBax)0.33MnO3 with x

RI PT

xSrxMnO3

≈ 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

SC

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

M AN U

(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

TE D

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

EP

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

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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 13

ACCEPTED MANUSCRIPT exponent values could be very different due to the effects related to grain boundaries, crystal defects, isotropic properties and/or lattice strain; for example, the cases of La0.7Ca0.3MnO3 [16, 19, 81, 82], La0.7Ca0.2Sr0.1MnO3 [23, 40], and La0.7Sr0.3MnO3 [52, 67, 82-85]. In general, SOMT manganites exhibit short-range FM interactions with exponents in the range of the 3D Heisenberg and 3D Ising exponents,

RI PT

see Table 3. These features are completely understandable because there always coexist FM and antiFM 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

SC

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

M AN U

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

TE D

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/rd+σ, where d is the spatial dimensionality of the system and σ is

EP

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

AC C

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]

4  n+2 8(n + 2)(n − 4)  2G ( 12 d ) (7n + 20  2 γ = 1+  1 +  ∆σ ,  ∆σ + 2 2 d  n +8  d (n + 8)  (n − 4)(n + 8) 

(4)

where ∆σ = σ − 12 d , G ( 12 d ) = 3 − 14 ( 12 d ) 2 , and n is the number of spin components. For our material 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 14

ACCEPTED MANUSCRIPT 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

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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

SC

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

3.4. Magnetocaloric effect and universal magnetic-entropy curve

M AN U

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]

TE D

 ∂S m   ∂M   ∂H  =  ∂T  , H  T 

(5)

∆Sm can be calculated from the equation

 ∂M  ∆S m (T , H ) = S m (T , H ) − S m (T , 0) = ∫   dH , ∂T  H 0 

EP

H

(6)

AC C

which is approximated by

| ∆S m (T , H ) |= ∑

( M n − M n +1 ) H ∆H n , Tn +1 − Tn

(7)

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

15

ACCEPTED MANUSCRIPT ∆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 |∆Smax| ∝ Hn,

(8)

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

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∆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]

β −1 , β +γ

SC

n = 1+

(9)

M AN U

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

d ln | ∆ S m | . d ln H

(10)

TE D

n =

For a magnetic material undergoing the SOMT that interactions in it obey the MF theory, n tends to 1 and is magnetic-field independent at temperatures T << TC. At temperatures T >> TC, n tends to 2 as a

EP

result of the CW law. At T = TC, n reaches to a minimum value equal to 2/3 [29, 30]. Having compared

AC C

with calculated n(T, H) data shown in Figure 10, one can see an anomalous variation of n in the samples x = 0 and 0.025 with respect to magnetic field H. The minimum values of their n(T, H) curves (≈ 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 = 4050 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 16

ACCEPTED MANUSCRIPT 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

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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

xBaxMnO3,

SC

between the curves for H = 10 and 50 kOe gradually decreases with increasing x in La0.7Ca0.3which could be related to a gradual decrease of λ (from 0.22 for x = 0 to 0.11 for x = 0.1).

M AN U

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

TE D

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 T2

EP

assessment of the RC, which is determined by RC = − ∫ ∆S m (T )dT , where T1 and T2 are the cold and T1

AC C

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 17

ACCEPTED MANUSCRIPT 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], (Nd1xYx)0.7Sr0.3MnO3

[78], and Sm0.58Sr0.42MnO3 [96], have indicated their RCP values usually 1.2~1.4

RI PT

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

xLaxSr0.3MnO3 [101],

SC

(x = 0~0.7) [36, 48, 49], Pr0.63Sr0.37MnO3 [97], Sm1-xSrxMnO3 (x = 0.42-0.46) [96, 100], Sm0.7and (Nd1-xYx)0.7Sr0.3MnO3 [78]. At a given applied field, though -∆Smax values of

M AN U

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

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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

EP

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 mpk (i.e., ∆S ' = ∆S m (T , H ) / ∆S mpk ),

AC C

with the temperature axis above and below TC scaled as follows

θ = θ1 = (T - TC)/(Tr - TC),

(11)

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

18

ACCEPTED MANUSCRIPT −  (T − TC ) / (Tr1 − TC ),  (T − TC ) / (Tr 2 − TC ),

θ = θ2 = 

T ≤ TC T > TC

.

(12)

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

∆Sm(T, H) curves would thus be rescaled versus the temperature axis θ2, where the reference 1 2

∆S mpk (i.e., f = 0.5). It appears from

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temperatures Tr1 and Tr2 were selected corresponding to the value

Figure 11 that almost -∆Sm(T, H) data points fall into a master curve. Some low-field data points scattered from the master curve at negative θ2 values (particularly for x = 0-0.05) are probably due to a

SC

relative inaccuracy of entropy change, which is known to increase apart from the TC. For the parent sample La0.7Ca0.3MnO3 with the FOMT, a large split of universal entropy curves is usually seen at

M AN U

negative θ2 values [13, 31]. However, such the feature is invisible in Figure 11 for x = 0 and 0.025 undergoing the FOMT. This could be due to our M(H) data measured in a narrow temperature range, just in the vicinity of the FM-PM transition TC. With the features of the universal curves seen in Figure 1, it is quite difficult for us to distinguish which samples having the FOMT, SOMT, and the crossover

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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

AC C

4. Conclusion

EP

order to determine the critical exponents β, γ and δ is necessary to clarify these problems.

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

19

ACCEPTED MANUSCRIPT 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

RI PT

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,

SC

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

M AN U

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

TE D

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

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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

AC C

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 20

ACCEPTED MANUSCRIPT Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF2012R1A1A2008845 and NRF-2014R1A2A1A11051245).

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29

ACCEPTED MANUSCRIPT Figure captions Fig. 1. Room-temperature XRD patterns of La0.7Ca0.3-xBaxMnO3 compounds with x = 0, 0.025, 0.05, 0.075, and 0.1. Fig. 2. (a) M(T) data normalized to the M values at 5 K (MT = 5 K), and (b) dM/dT versus T curves for La0.7Ca0.3-xBaxMnO3 compounds in the field H = 100 Oe.

RI PT

Fig. 3. The χ-1(T) data in the PM region fitted to the CW law (the dot lines). The arrows show the onset of the departure of high-temperature χ-1 data from the CW law, known as the Griffiths temperature TG.

SC

Fig. 4. M(H) data, and inverse Arrott plots (H/M versus M2) for La0.7Ca0.3-xBaxMnO3 compounds with (a, b) x = 0, (c, d) x = 0.025, (e, f) x = 0.05, (g, h) x = 0.075, and (i, j) x = 0.1 around their FMPM phase transition. The temperature increment for each M(H) curve is kept at 2 K.

M AN U

Fig. 5. Modified Arrott plots of M1/β versus (H/M)1/γ for M(H) data of the samples La0.7Ca0.3-xBaxMnO3 corresponding to the exponents expected for (a-e) the 3D Heisenberg (β = 0.365 and γ = 1.336), (f-j) 3D Ising (β = 0.325 and γ = 1.241), and (k-o) tricritical MF (β = 0.25 and γ = 1.0) models. Fig. 6. Ms(T) and χ 0−1 (T) data are fitted to Eqs. (1) and (2), respectively, for two typical samples with

TE D

(a-d) x = 0.075, and (e-h) x = 0.1 for different magnetic-field ranges with H ≥ 10 kOe. Fig. 7. Scaling plots of M/|ε|β versus H/|ε|β+γ on a log-log scale for the M(H) data of two typical samples x = 0.075 and 0.1 at temperatures around the FM-PM transition, corresponding to the critical values determined from different field intervals: (a, b) 10-20 kOe, (c, d) 20-30 kOe, (e,

EP

f) 30-40 kOe, and (g, h) 40-50 kOe.

Fig. 8. -∆Sm(T) curves for La0.7Ca0.3-xBaxMnO3 compounds with (a) x = 0, (b) x = 0.025, (c) x = 0.05,

AC C

(d) x = 0.075, and (e) x = 0.1 in magnetic-field intervals ranging from 10 to 50 kOe. Fig. 9. Field dependences of (a) -∆Smax and (b) the RC for La0.7Ca0.3-xBaxMnO3 compounds. The solid lines are fitting curves to Eq. (8). Fig. 10. Temperature and magnetic-field dependences of n calculated from Eq. (10) for La0.7Ca0.3xBaxMnO3

compounds with (a) x = 0, (b) x = 0.025, (c) x = 0.05, (d) x = 0.075, and (e) x = 0.1.

Fig. 11. Universal curves for -∆Sm(T, H) versus θ2 of La0.7Ca0.3-xBaxMnO3 compounds with (a) x = 0, (b) x = 0.025, (c) x = 0.05, (d) x = 0.075, and (e) x = 0.1.

30

ACCEPTED MANUSCRIPT Table 1. Experimental values obtained from analyzing the XRD and M(T)H=100 Oe data for La0.7Ca0.3xBaxMnO3

samples: lattice parameters (a, b and c) and unit-cell volume (V), the average radius of the

cations located at A (〈rA〉), the tolerance factoror (t), the Curie temperature obtained from the M(T) data (TC), the CW temperature (θ), the effective-paramagnetic moment (Peff), the random temperature

TC

θ

Peff

TCrand

TG

(K)

(K)

(µB)

(K)

(K)

a

b

c

V

〈rA〉

(Å)

(Å)

(Å)

(Å3)

(Å)

0.0

5.451

5.468

7.709

229.8

1.021

0.9173

260

0.025

5.448

5.477

7.717

230.3

1.030

0.9195

260

0.05

5.452

5.479

7.725

230.8

1.039

0.9214

267

0.075

5.442

5.479

7.744

230.9

1.047

0.9235

0.10

5.433

5.495

7.740

231.1

1.056

0.9255

TE D EP 31

6.8

λ

264

275

0.22

6.7

264

320

0.18

273

6.1

277

304

0.14

268

276

6.0

287

315

0.13

300

309

5.5

314

330

0.11

SC

256

266

M AN U

t

AC C

x

RI PT

( TCrand ), the Griffiths temperature transition (TG), and a susceptibility exponent (λ).

ACCEPTED MANUSCRIPT Table 2. Critical parameters TC, β, γ and δ obtained for La0.7Ca0.3-xBaxMnO3 samples by using the MAP method. Notably, some γ (and δ) values of the samples x = 0-0.05 at lower fields could not be obtained because of the failing in the determination of χ 0−1 (T) values by the MAP method. β

γ

40-50 kOe

260.4

0.212±0.002

-

20-30 kOe

257.3

0.209±0.005

-

-

-

30-40 kOe

258.3

0.218±0.002

1.098±0.027

6.04

0.41

40-50 kOe

260.1

0.227±0.002

1.060±0.049

5.67

0.27

10-20 kOe

261.1

0.221±0.002

-

-

-

20-30 kOe

263.2

0.225±0.002

1.052±0.027

5.68

0.40

30-40 kOe

265.1

40-50 kOe

267.1

10-20 kOe

257.8

x = 0.075

20-30 kOe

258.9

30-40 kOe

261.6

40-50 kOe 10-20 kOe

-

-

0.235±0.001

1.012±0.011

5.31

0.39

0.249±0.003

1.022±0.035

5.10

0.41

0.216±0.005

0.973±-.069

5.50

0.34

0.224±0.008

0.982±0.015

5.38

0.36

0.238±0.005

1.016±0.008

5.27

0.41

0.253±0.001

0.992±0.002

4.92

0.40

292.5

0.301±0.001

1.382±0.012

5.59

0.58

292.6

0.312±0.002

1.380±0.008

5.42

0.59

30-40 kOe

293.8

0.322±0.001

1.381±0.031

5.29

0.60

40-50 kOe

294.4

0.326±0.005

1.342±0.015

5.12

0.60

AC C

x = 0.1

n

264.1

EP

20-30 kOe

SC

x = 0.05

M AN U

x = 0.025

TE D

x=0

δ

RI PT

TC (K)

La0.7Ca0.3-xBaxMnO3

32

ACCEPTED MANUSCRIPT Table 3: Critical parameters obtained from theoretical models, and perovskite-type manganites and cobaltites, which are listed for reference. Abbreviation: SC - single crystal, PC - polycrystalline TF thin film, and NPs - nanoparticles. TC (K)

β

γ

δ

Ref.

Mean-field theory

-

-

0.5

1.0

3.0

[67]

3D Heisenberg model

-

-

0.365

1.336

4.80

[67]

3D Ising model

-

-

0.325

Tricritical mean-field theory

-

-

0.25

La0.7Ca0.2Sr0.1MnO3 (SC)

Orthorhombic

289

0.26±0.01

La0.7Ca0.2Sr0.1MnO3 (PC)

Orthorhombic

284

0.394±0.008

La0.7Ca0.2Sr0.1Mn0.85Cr0.15O3 (PC)

Orthorhombic

235

0.322±0.030

La0.7Ca0.2Sr0.1Mn0.8Cr0.2O3 (PC)

Orthorhombic

225

La0.67Ca0.33Mn0.9Ga0.1O3 (PC)

Orthorhombic

La0.67Ca0.33Mn0.9Cr0.1O3 (PC)

Orthorhombic

La0.67Ca0.33Mn0.75Cr0.25O3 (PC)

Orthorhombic

La0.7Ca0.3Mn0.9Zn0.1O3 (PC)

Orthorhombic

La0.7Ca0.3Mn0.95Cu0.05O3 (PC)

Orthorhombic

La0.7Ca0.3Mn0.91Ni0.09O3 (PC)

Orthorhombic

La0.82Ca0.18MnO3 (SC) La0.8Ca0.2MnO3 (SC)

La0.8Ca0.2MnO3 (PC)*

1.0

5.0

[68, 69]

1.06±0.02

5.1±0.2

[23]

0.925±0.021

3.34±0.01

[40]

1.2±0.17

4.752

[103]

0.327± 0.020

1.26±0.01

4.89

[103]

116

0.380±0.002

1.365±0.008

4.60±0.03

[21]

233

0.555±0.006

1.17±0.04

2.71±0.01

[33]

203

0.68±0.01

1.09±0.03

2.94±0.01

[33]

207

0.474

1.152

3.430

[34]

197

0.49±0.03

1.04±0.04

3.12±0.02

[35]

199

0.171±0.006

0.976±0.012

6.7±0.1

[24]

M AN U

SC

[67]

184

0.262±0.005

0.979±0.012

4.7±0.1

[24]

Orthorhombic

170

0.320±0.009

0.990±0.082

4.09±0.17

[104]

Orthorhombic

171

0.374±0.002

1.379±0.005

4.783±0.004

[105]

Orthorhombic

179

0.373±0.002

1.382±0.004

4.779±0.004

[105]

Orthorhombic

174

0.36

1.45

5.03

[17]

186

0.349±0.013

1.231±0.030

4.524

189

0.316±0.007

1.081±0.036

4.421

190

0.281±0.009

0.992±0.036

4.534

194

0.272±0.006

0.910±0.021

4.341

195

0.259±0.004

0.918±0.036

4.552

AC C

La0.8Ca0.2MnO3 (SC)

4.82

TE D

La0.7Ca0.3Mn0.85Ni0.15O3 (PC)

1.241

Orthorhombic

EP

La0.7Ca0.3Mn0.88Ni0.12O3 (PC)

RI PT

Structure

Material

Orthorhombic

[41]

La0.7Ca0.3MnO3 (PC)

Orthorhombic

248

0.36±0.01

1.2

4.33

[82]

La0.7Ca0.3MnO3 (SC)

Orthorhombic

222

0.14±0.02

0.81±0.03

1.22±0.04

[16]

La0.67Ca0.33MnO3 (TF)

Orthorhombic

261

0.368 ±0.003

1.384±0.001

4.77±0.32

[81]

La0.67Ca0.33MnO3 (NPs)

Orthorhombic

260

0.47 ±0.01

1.06±0.03

3.10±0.13

[19]

33

ACCEPTED MANUSCRIPT Orthorhombic

265

0.25±0.03

1.03±0.05

5.0±0.8

[68]

La0.6Ca0.4MnO3 (PC)

Orthorhombic

268

0.248

0.995

4.896

[77]

249

0.249±0.002

1.008±0.021

5.043

252

0.255±0.002

0.857±0.023

4.359

255

0.262±0.002

0.833±0.017

4.180

257

0.267±0.002

0.797±0.016

3.983

260

0.263±0.006

0.776±0.012

3.954

1.146±0.006

4.83±0.01

[70]

0.948±0.008

4.90±0.02

[70]

1.432

4.928

[106]

La0.6Ca0.4MnO3 (PC)*

Orthorhombic

RI PT

La0.6Ca0.4MnO3 (PC)

[41]

Orthorhombic

226

0.311±0.003

La0.5Ca0.3Ag0.2MnO3

Orthorhombic

262

0.288±0.002

La0.18Ca0.82MnO3 (NPs)

Orthorhombic

165

0.351

Pr0.73Ca0.27MnO3 (SC)

Orthorhombic

127

0.36±0.02

1.36±0.02

4.81±0.02

[107]

Pr0.71Ca0.29MnO3 (SC)

Orthorhombic

114

0.37±0.02

1.38±0.02

6.62±0.02

[107]

Pr0.7Ca0.15Ba0.15MnO3 (PC)

Orthorhombic

Pr0.6Sr0.4MnO3 (PC)

Orthorhombic

Pr0.5Sr0.5MnO3 (PC)

Orthorhombic

Pr0.55Sr0.45MnO3 (PC)

Orthorhombic

Pr0.15Ca0.85Mn0.96Ru0.04O3 (PC)

Orthorhombic

Nd0.5Sr0.5MnO3 (SC)

M AN U

SC

La0.5Ca0.4Ag0.1MnO3

0.403±0.024

1.242±0.033

4.08±0.01

[108]

320

0.379±0.006

1.304±0.012

4.7±0.1

[109]

261

0.443±0.002

1.339±0.006

4.022±0.003

[110]

290

0.462

1.033

4.749

[111]

138

0.478±0.009

1.252±0.025

3.62±0.01

[112]

Orthorhombic

251

0.33±0.02

1.24±0.03

4.8±0.1

[113]

Orthorhombic

242

0.52±0.01

1.08±0.02

3.01±0.01

[87]

Orthorhombic

239

0.50±0.01

1.03±0.02

3.06

[86]

Orthorhombic

234

0.414

1.488

4.594

[114]

Orthorhombic

222

0.45

1.113

3.333

[114]

Orthorhombic

~270

0.51±0.02

1.01±0.03

3.13±0.02

[75]

Nd0.7Sr0.3MnO3 (SC)

Orthorhombic

203

0.57±0.01

1.16±0.03

3.13±0.02

[63]

Nd0.7Sr0.3MnO3 (PC)

Orthorhombic

238

0.271±0.006

0.922±0.016

4.4

[62]

(Nd0.93Y0.07)0.7Sr0.3MnO3 (PC)*

Orthorhombic

170

0.234±0.004

1.044±0.014

5.4

179

0.236±0.004

1.063±0.020

5.5

TE D

117

Nd0.5Sr0.5MnO3 (SC) Nd0.5Sr0.5MnO3 (SC)

Nd0.5Sr0.5Mn0.95Co0.05O3 (PC)

AC C

Nd0.6Sr0.4MnO3 (PC)

EP

Nd0.5Sr0.5Mn0.97Co0.03O3 (PC)

[62]

La0.67(Ca0.25Ba0.25)0.33MnO3 (PC)

Orthorhombic

277

0.356±0.004

1.12±0.02

4.1±0.1

[15]

La0.75Ca0.08Sr0.17MnO3 (PC)

Orthorhombic

334

0.355±0.007

1.326±0.002

4.90±0.01

[115]

La0.75Ca0.08Sr0.17Mn0.95Ga0.05O3 (PC)

Orthorhombic

281

0.389±0.006

1.251±0.003

4.12±0.02

[115]

La0.75Ca0.08Sr0.17Mn0.9Ga0.1O3 (PC)

Orthorhombic

232

0.420±0.005

1.221±0.002

4.22±0.04

[115]

34

ACCEPTED MANUSCRIPT Orthorhombic

250

0.515±0.015

1.441±0.008

3.774±0.011

[116]

La0.7Ca0.2Sr0.1MnO3 (NPs)

Orthorhombic

297

0.397±0.013

0.966±0.017

4.43

[117]

La0.7Ca0.19Sr0.11MnO3 (NPs)

Orthorhombic

301

0.453

0.956

3.11

[117]

La0.7Ca0.18Sr0.12MnO3 (NPs)

Orthorhombic

309

0.456

0.945

3.07

[117]

La0.1Nd0.6Sr0.3MnO3 (PC)

Orthorhombic

249

0.257±0.005

1.12±0.03

5.17±0.02

[79]

La0.6Ca0.2Sr0.2MnO3 (PC)

Rhombohedral

344

0.498

1.053

2.992

[77]

La0.67Pb0.33Mn0.97Co0.03O3 (PC)

Rhombohedral

345

0.233±0.002

La0.67Pb0.33Mn0.94Co0.06O3 (PC)

Rhombohedral

324

0.261±0.004

La0.9Te0.1MnO3 (PC)

Rhombohedral

240

0.201±0.003

La0.7Ca0.1Sr0.2MnO3 (SC)

Rhombohedral

326

0.36±0.01

La0.7Ca0.1Sr0.2MnO3 (PC)

Rhombohedral

336

0.472±0.016

La0.7Ca0.05Sr0.25MnO3 (SC)

Rhombohedral

344

0.42±0.02

La0.8Ba0.2Mn0.85Fe0.15O3 (PC)

Rhombohedral

La0.8Ba0.2Mn0.8Fe0.2O3 (PC)

Rhombohedral

La0.7Ba0.3MnO3 (PC)

Rhombohedral

La0.7Ba0.3MnO3 (TF)

Rhombohedral

La0.67Ba0.33MnO3 (PC)

Rhombohedral

La0.67(Ca0.5Ba0.5)0.33MnO3 (PC)

Rhombohedral

RI PT

Pr0.3Nd0.2Sr0.5MnO3 (PC)

5.52±0.04

[80]

1.05±0.02

4.98±0.03

[80]

1.27±0.04

7.14±0.04

[76]

1.22±0.01

4.4±0.2

[23]

1.061±0.024

3.125±0.013

[118]

1.14±0.05

3.7±0.2

[23] [119]

M AN U

SC

1.06±0.06

0.379±0.01

1.392±0.03

4.67±0.01

125

0.365±0.01

1.227±0.03

4.36±0.01

339

0.341±0.003

1.371±0.0196

4.882

[120]

311

0.54±0.02

1.04±0.04

3.08

[85]

338

0.464±0.003

1.29±0.02

3.78±0.01

[15]

306

0.402±0.003

1.11±0.02

3.7±0.1

[15]

TE D

158

Rhombohedral

343

0.378±0.003

1.388±0.001

4.7±0.01

Rhombohedral

190

0.398±0.002

1.251±0.005

4.5±0.01

Rhombohedral

130

0.411±0.001

1.241±0.004

4.0±0.01

Rhombohedral

321

0.396±0.016

1.349±0.002

4.477

[120]

Rhombohedral

304

0.349±0.010

1.005±0.003

3.044

[120]

Rhombohedral

360

0.367±0.008

1.22±0.02

4.29±0.03

[80]

La0.6Sr0.4MnO3 (PC)

Rhombohedral

371

0.363

1.332

4.889

[77]

La0.65Eu0.05Sr0.3Mn0.9Cr0.1O3 (PC)

Rhombohedral

310

0.489±0.04

1.17±0.13

3.372

[122]

La0.65Eu0.05Sr0.3Mn0.85Cr0.15O3 (PC)

Rhombohedral

278

0.387±0.09

1.344±0.03

4.472

[122]

La0.67Sr0.33MnO3 (PC)

Rhombohedral

369

0.41±0.01

1.13±0.01

3.8±0.1

[123]

La0.67Sr0.16Ca0.17MnO3 (PC)

Rhombohedral

333

0.324± 0.005

1.176±0.030

4.724 ± 0.03

[124]

La0.7Sr0.3MnO3 (SC)

Rhombohedral

361

0.45±0.05

-

-

[84]

La0.7Sr0.3MnO3 (SC)

Rhombohedral

354

0.37±0.04

1.22±0.03

4.25±0.2

[67]

La0.7Sr0.3MnO3 (PC)

Rhombohedral

363

0.323

1.083

4.353

[83]

La0.67Ba0.22Sr0.11MnO3 (PC) La0.67Ba0.22Sr0.11Mn0.9Fe0.1O3 (PC)

La0.6Pr0.1Ba0.3MnO3 (PC) La0.5Pr0.2Ba0.3MnO3 (PC)

AC C

La0.67Pb0.33MnO3 (PC)

EP

La0.67Ba0.22Sr0.11Mn0.8Fe0.2O3 (PC)

35

[121]

ACCEPTED MANUSCRIPT Rhombohedral

357

0.45±0.01

1.2

3.67

[82]

La0.7Sr0.3MnO3 (PC)

Rhombohedral

360

0.387±0.008

1.166±0.014

4.01

[52]

La0.7Sr0.3MnO3 (TF)

Rhombohedral

361

0.45±0.02

1.08±0.04

3.4

[85]

La0.7Sr0.3Mn0.94Co0.06O3 (PC)

Rhombohedral

311

0.478±0.013

1.165±0.027

3.44

[52]

La0.7Sr0.3Mn0.92Co0.08O3 (PC)

Rhombohedral

297

0.483±0.018

1.112±0.028

3.30

[52]

La0.7Sr0.3Mn0.9Co0.1O3 (PC)

Rhombohedral

281

0.487±0.016

1.109±0.063

3.28

[52]

La0.75Sr0.25MnO3 (SC)

Rhombohedral

346

0.40±0.02

1.27±0.06

4.12±0.33

[125]

La0.8Sr0.2MnO3 (PC)

Rhombohedral

316

0.50±0.02

1.08±0.03

3.13±0.2

[73]

La0.8Sr0.2MnO3 (SC)

Rhombohedral

305

0.45±0.05

-

-

[126]

La0.875Sr0.125MnO3 (SC)

Rhombohedral

186

0.37±0.02

1.38±0.03

4.72±0.04

[127]

La0.7Sr0.3Mn0.95Ti0.05O3 (PC)

Rhombohedral

304

0.344

1.149

4.340

[83]

La0.7Sr0.3Mn0.92Ti0.08O3 (PC)

Rhombohedral

235

0.425±0.016

1.017±0.055

3.39±0.04

[128]

La0.7Sr0.3Mn0.99Ni0.01O3 (PC)

Rhombohedral

La0.7Sr0.3Mn0.98Ni0.02O3 (PC)

Rhombohedral

La0.7Sr0.3Mn0.97Ni0.03O3 (PC)

Rhombohedral

La0.7Sr0.3Mn0.95Al0.05O3 (PC)

Rhombohedral

La0.67Sr0.33Mn0.99Mo0.01O3 (PC)

Rhombohedral

La0.67Sr0.33Mn0.98Mo0.02O3 (PC)

La0.67Sr0.33Mn0.96Mo0.04O3 (PC)

0.394±0.015

1.092±0.047

3.99±0.05

[129]

353

0.444±0.017

1.081±0.032

3.79±0.08

[129]

343

0.468±0.006

1.010±0.021

2.67±0.06

[129]

336

0.458

1.001

3.185

[83]

368

0.39±0.01

1.17±0.01

4.0±0.1

[123]

Rhombohedral

367

0.40±0.01

1.15±0.01

3.9±0.1

[123]

Rhombohedral

366

0.35±0.01

1.25±0.01

4.6±0.1

[123]

Rhombohedral

365

0.41±0.01

1.13±0.01

3.8±0.1

[123]

Rhombohedral

361

0.39±0.01

1.17±0.01

4.0±0.1

[123]

EP

La0.67Sr0.33Mn0.94Mo0.06O3 (PC)

SC

M AN U 357

TE D

La0.67Sr0.33Mn0.97Mo0.03O3 (PC)

RI PT

La0.7Sr0.3MnO3 (PC)

La0.6Sr0.4Mn0.8Fe0.1Cr0.1O3 (PC)

Rhombohedral

212

0.395±0.010,

1.402±0.010

5.208±0.007

[130]

LaMn0.95Ti0.05O3 (PC)

Rhombohedral

173

0.378±0.007

1.29±0.02

4.19±0.03

[131]

Rhombohedral

145

0.375±0.005

1.25±0.02

4.11±0.04

[131]

LaMn0.85Ti0.15O3 (PC)

Rhombohedral

122

0.376±0.003

1.24±0.01

4.16±0.03

[131]

LaMn0.8Ti0.2O3 (PC)

Rhombohedral

95

0.359±0.004

1.28±0.01

4.21±0.05

[131]

LaMn0.9Fe0.1O3 (PC)

Rhombohedral

136

0.358 ± 0.007

1.328 ± 0.003

4.71 ± 0.06

[132]

La0.79Sr0.21CoO3 (SC)

Rhombohedral

188

0.491±0.004

1.217±0.003

3.51±0.01

[71]

La0.75Sr0.25CoO3 (SC)

Rhombohedral

214

0.362±0.002

1.304±0.006

4.75±0.01

[71]

La0.5Sr0.5CoO3 (PC)

Rhombohedral

223

0.321±0.002

1.351±0.009

4.39±0.02

[66]

La0.8Sr0.2CoO3 (PC)

Rhombohedral

199

0.46

1.39

4.02

[74]

AC C

LaMn0.9Ti0.1O3 (PC)

36

ACCEPTED MANUSCRIPT Rhombohedral

222

0.46

1.39

4.02

[74]

La0.7Sr0.3CoO3 (PC)

Rhombohedral

223

0.43

1.43

4.38

[74]

La0.67Pb0.33Mn0.92Co0.08O3 (PC)

Rhombohedral

316

0.364±0.002

1.40±0.112

4.88±0.01

[80]

La0.6Nd0.1(CaSr)0.3Mn0.9V0.1O3 (PC)

Rhombohedral

298

0.385±0.001

1.481±0.003

4.672±0.002

[133]

La0.57Nd0.1Pb0.33MnO3 (PC)

Rhombohedral

350

0.371

1.380

4.270

[134]

La0.57Nd0.1Sr0.33MnO3 (PC)

Rhombohedral

352

0.356±0.009

1.152±0.016

4.235

[135]

La0.57Nd0.1Sr0.305MnO3 (PC)

Rhombohedral

350

0.320±0.005

La0.57Nd0.1Sr0.28MnO3 (PC)

Rhombohedral

349

0.312

La0.57Nd0.1Sr0.33MnO3 (PC)

Rhombohedral

341

0.326±0.007

La0.57Nd0.1Sr0.33Mn0.95Al0.05O3 (PC)

Rhombohedral

300

0.344±0.002

La0.57Nd0.1Sr0.33Mn0.9Al0.1O3 (PC)

Rhombohedral

288

0.352±0.008

La0.57Nd0.1Pb0.33Mn0.95Ti0.05O3 (PC)

Rhombohedral

321

0.391

La0.8Na0.1MnO3 (PC)

Rhombohedral

LaMnO3.14 (PC)

Rhombohedral

La0.9Pb0.1MnO3 (PC)

Pseudo-

[135]

1.173±0.004

4.760

[135]

1.329±0.001

5.07

[136]

1.332±0.004

4.87

[136]

1.342±0.002

4.81

[136]

1.276

4.466

[134]

1.083

3.18

[89]

141

0.415

1.470

4.542

[137]

162

0.498

1.456

3.92

[88]

291

0.499

1.241

3.49

[88]

TE D

M AN U

SC

4.753

0.495

346

0.502

1.063

3.12

[88]

Monoclinic

240

0.387±0.006

0.884±0.002

3.284±0.003

[138]

Monoclinic

160

0.516±0.008

0.993±0.006

3.046±0.002

[138]

Tetragonal

242

0.5217

1.209

3.162

[139]

Tetragonal

109

0.372±0.004

1.347±0.001

4.67±0.03

[140]

Pseudorhombohedral

La0.7Pb0.3MnO3 (PC)

1.201±0.002

295

rhombohedral La0.8Pb0.2MnO3 (PC)

RI PT

La0.75Sr0.25CoO3 (PC)

Pseudo-

Pr0.5Sr0.5CoO3 (PC) Pr0.5Sr0.5CoO2.83 (PC) La0.4Bi0.3Sr0.3MnO3 (PC)

AC C

Nd0.85Pb0.15MnO3 (SC)

EP

rhombohedral

Nd0.7Pb0.3MnO3 (SC)

Tetragonal

149

0.361±0.013

1.325±0.001

4.62±0.04

[140]

Nd0.6Pb0.4MnO3 (SC)

Cubic

156

0.329±0.006

1.329±0.003

4.54±0.10

[141]

Nd0.67Sr0.33MnO3 (PC)

Pseudo-cubic

227

0.23±0.02

1.05±0.03

0.513±0.04

[75]

Pr0.77Pb0.33MnO3 (SC)

Pseudo-cubic

167

0.344±0.001

1.352±0.006

4.69±0.02

[142]

Pr0.7Pb0.3MnO3 (SC)

Pseudo-cubic

197

0.404±0.001

1.357±0.006

4.37±0.09

[142]

Pr0.8Pb0.2MnO3 (PC)

Pseudo-cubic

204

0.468±0.004

1.353±0.083

3.78±0.02

[143]

Pr0.9Pb0.1MnO3 (PC)

Pseudo-cubic

151

0.443±0.027

1.337±0.042

3.99±0.07

[143]

*Note: The critical behavior with different magnetic-field ranges. 37

ACCEPTED MANUSCRIPT Table 4. Experimental values of TC (determined from the M(T)|H=100

Oe

data), and MC-related

parameters (-∆Smax, RC, and RCP) for our La0.7Ca0.3-xBaxMnO3 samples compared with those for Gd and typical manganites exhibiting the giant MC effect, with magnetic-field variations up to 50 kOe.

Gd

295

La0.7Ca0.3MnO3 (PC)

260

La0.7Ca0.275Ba0.025MnO3 (PC)

260

La0.7Ca0.25Ba0.05MnO3 (PC)

267

La0.7Ca0.225Ba0.075MnO3 (PC) La0.7Ca0.2Ba0.1MnO3 (PC)

300

La0.7Ca0.3MnO3 (PC)

264

La0.7Ca0.3MnO3 (PC)

-1

RCP

( J⋅kg ⋅K )

( J⋅kg-1 )

20

6.1

240

-

50

10.6

820

-

20

7.8

92

124

50

10.7

247

278

20

6.4

85

109

50

9.2

235

276

20

6.3

79

101

50

9.1

230

267

20

4.1

70

90

50

7.1

190

241

-1

Ref. [29] This work This work This work This work

20

3.1

79

105

This work

50

6.0

210

246

50

7.7

~187

-

[13]

20

8.0

-

-

[99]

50

9.9

-

-

50

4.9

~150

-

[13]

La0.7Ca0.3MnO3 (NPs)

260

La0.7Ca0.3MnO3 (NPs)

235-270

45

5.0-8.6

-

218-243

[25]

La0.7Ca0.3MnO3 (TFs)

TE D

242

(kOe)

RC ( J⋅kg )

-1

M AN U

268

-∆Smax

RI PT

(K)

∆H

SC

TC

Material

235

50

~2.5

200

-

[13]

275

50

10.5

-

462

[97, 98]

308

50

7.5

-

374

[97, 98]

340

50

7.0

-

369

[97, 98]

341

50

6.9

-

364

[97, 98]

284

30

4.3

116

150

[40]

100~240

20

1.3~8.0

-

100~160

[49]

50

5.4~8.2

197~259

-

[36, 48]

50

8.5

-

511

[97]

20

5.3

80

94

[62]

50

8.3

205

259

20

4.1

102

127

50

7.2

245

288

83-375

50

3.2-4.5

180-257

-

[101]

La0.7Ca0.25Sr0.05MnO3 (SC) La0.7Ca0.2Sr0.1MnO3 (SC) La0.7Ca0.1Sr0.2MnO3 (SC) La0.7Ca0.05Sr0.25MnO3 (SC)

EP

La0.7Ca0.2Sr0.1MnO3 (PC)

La0.7-xPrxCa0.3MnO3 (x = 0-0.69) (PC)

La0.7-xPrxCa0.3MnO3 (x = 0-0.45) (PC)

AC C

Pr0.63Sr0.37MnO3 (SC) Nd0.7Sr0.3MnO3 (PC)

(Nd0.93Y0.07)0.7Sr0.3MnO3 (PC)

Sm0.7-xLaxSr0.3MnO3 (x = 0-0.7) (PC) Sm1-xSrxMnO3 (x = 0.42-0.46) (PC)

305 240 175

[62]

130-134

50

4.6

178-182

-

[100]

Sm0.58Sr0.42MnO3 (PC)

135

50

9.3

302

362

[96]

Sm0.58Sr0.42MnO3 (NPs)

135

50

5.9

208

253

[96]

38

x=0 x = 0.025 x = 0.075 x = 0.1

(121)

32.2

32.4

RI PT

TE D

30

AC C

EP

20

40

2θ (degree)

Fig. 1. Phan et al.

39

Si

(321)

(103) (222)

Si

(042)

32.8

SC

(040)

32.6

M AN U

Si

(202)

(022)

(020)

Intensity (arb. units)

32.0

(200)

(220)

(200)

(121)

ACCEPTED MANUSCRIPT

x = 0.1

x = 0.075

x = 0.05

x = 0.025

x=0

50

60

ACCEPTED MANUSCRIPT

(a)

0.6

H = 100 Oe

0.4 0.2 0.0 100

150

(b)

EP

AC C

dM/dT

-0.5

200

250

TE D

0.0

SC

x=0 x = 0.025 x = 0.05 x = 0.075 x = 0.1

M AN U

M/MT = 5K

0.8

-1.0

RI PT

1.0

350

268 K

x=0 x = 0.05 x = 0.075 x = 0.1

300 K 267 K

-1.5

100

300

260 K

150

200

250

T (K) Fig. 2. Phan et al.

40

300

350

SC 320 K

500

0

2000

255

270

M AN U

-1

χ (Oe.g/emu)

275 K

1000

285

300

T (K)

315 K

TE D

−1

χ (Oe.g/emu)

x = 0.025 x = 0.05 x = 0.075 x = 0.1

x=0

1500

3000

RI PT

ACCEPTED MANUSCRIPT

304 K

EP

1000

330 K

AC C

0

260

280

300

T (K) Fig. 3. Phan et al.

41

320

340

ACCEPTED MANUSCRIPT

(a)

(b)

233 K

1200

x=0

271 K

60 233 K

271 K

30

x=0 15

30

45

(c)

60 0

2000

(d)

220 K

4000

SC

220 K

280 K

30

M (emu/g)

90

30

45

(e)

M AN U

x = 0.025 15

60

0

2500

(f)

244 K

60

5000

282 K

7500

1200 800 400 0

1200

x = 0.05 800 244 K

282 K

30

0 8000

6000

x = 0.025

280 K

60

0 0

RI PT

400

0 0 90

800

400

x = 0.05 15

(g)

45

60

0

250 K

60

2000

(h)

4000

296 K

6000

x = 0.075 250 K

0

1500 1000

296 K

500

EP

30

x = 0.075

15

30

45

AC C

0 0

30

TE D

0 0

(i)

60

0

260 K

2000

(j)

4000

314 K

6000

0

x = 0.1 1200

60

260 K

800

320 K

30

400

x = 0.1 0 0

15

30

45

60

0

H (kOe)

2000

4000

2

2

M (emu/g)

Fig. 4. Phan et al.

42

6000

0

H/M (Oe.g/emu)

90

ACCEPTED MANUSCRIPT

4

6

4

x10

x10

x10

21 (a)

235 K β = 0.365 γ = 1.336

x=0

(f)

75

235 K β = 0.325 γ = 1.241

x=0

14

0 0

50

100

150

x10

β = 0.365 γ = 1.336

220 K

300

0 0

50

100

150

β = 0.325 γ = 1.241

220 K

10

0 0

80

(h)

60

20

160

240

0 0

50

100

150

0 0

200

4

4

x10

x10 x = 0.075

12

β = 0.365 250 K γ = 1.336

x = 0.05 252 K

70

140

β = 0.325 γ = 1.241

210

280

54 (i)

x = 0.075

250 K β = 0.325 γ = 1.241

276 K

60

4

x = 0.1 280 K

β = 0.365 γ = 1.336

AC C

10 (e)

0 0

180

0 0

80

160

50

100 150 200 250

β = 0.25 γ=1

400

800

1200

6

x10

(m)

30

x = 0.05

β = 0.25 γ=1

252 K

20 10

280 K

0 0

300

600

900

1200

6

30 (n) x = 0.075

250 K

β = 0.25 γ=1

10

276 K

300

600

900

1200

x10

40 (j) 30

x = 0.1

280 K β = 0.325 γ = 1.241

20 (o) x = 0.1

280 K

15

β = 0.25 γ=1

10

10 0 0

280 K

6

20 316 K

0 0

0 320 0

240

4

x10

x10

5

120

276 K

18

EP

0 0

220 K

20

36

6

1200

x10

TE D

(d)

320

280 K

M

280 K

x = 0.025

280 K

40

5

54 (l)

M AN U

β = 0.365 γ = 1.336

x = 0.05 252 K

900

18

30

x10

15 (c)

600

36

4

x10

300

x10

90 (g) x = 0.025

200

4

0 0

SC

280 K

271 K

6

60

7

1/β

200

x10 x = 0.025

14

(emu/g)

100

4

21 (b)

1/β

0 0

200

4

15

271 K

25

RI PT

271 K

β = 0.25 γ=1

30

50 7

235 K

x=0

(k)

45

316 K

80

160

240

1/γ

320 1/γ

(H/M) (Oe.g/emu)

Fig. 5. Phan et al.

43

5

400 00

316 K

400

800

1200

1600

ACCEPTED MANUSCRIPT

55

(a)

-1

χ0

β = 0.216 ±0.005

250

γ = 0.973 ±0.069

255

260

265

TC = 292.5

TC = 292.6

TC = 257.8

γ = 1.382±0.012

β = 0.301±0.001

0

15 280

270

285

290

600 50

Ms

-1

χ0

250

0 260 265 270 275 γ = 0.982 ±0.015

255

15 280

400

χ0

-1

TE D 200

TC = 261.7

TC = 261.5

β = 0.238 ±0.005

255

60

γ = 1.016 ±0.008

30

290 295 300 305 310

30

β = 0.253 ±0.001

15 250

255

260

265

x = 0.1

300

TC = 293.8

TC = 293.9

β = 0.322±0.001

0

280

285

γ = 1.381±0.031

290

0

295 300 305 310

600

(h) 450 45

χ0

360

x = 0.1

Ms

-1

H = 40-50 kOe

TC = 264.2

450

(g)

H = 30-40 kOe

(d)

x = 0.075

45

0

150

260 265 270 275

EP

250

285

45

x = 0.075 H = 30-40 kOe

40

γ = 1.380±0.008

600

(c) 50

TC = 292.6

β = 0.312±0.002

Ms

245

150

TC = 292.7

TC = 259.1

β = 0.224 ±0.008

200 30

300

H = 20-30 kOe

M AN U

30

TC = 258.8

AC C

Ms (emu/g)

40

450

x = 0.1

400

H = 20-30 kOe

305

(f)

45

x = 0.075

300

SC

(b)

295

0

-1

35

150

150 30

40 TC = 257.8

H = 10-20 kOe

Ms

H = 10-20 kOe

45

300

x = 0.1

H = 40-50 kOe

240

300 30 120 γ = 0.992 ±0.002

270

TC = 294.4

150

TC = 264.1

15

275

TC = 294.5

β = 0.326±0.005

γ = 1.342±0.015

280 285 290 295

T (K)

300

T (K) Fig. 6. Phan et al.

44

χ0 (Oe.g/emu)

x = 0.075

RI PT

50

(e)

45

300

305

0 310

ACCEPTED MANUSCRIPT

(b)

T < TC

100

x = 0.1

T < TC

β = 0.216 γ = 0.973

200 (c)

7

6

10

(d)

x = 0.1

T < TC

T < TC

M AN U

β = 0.224 γ = 0.982

TC = 258.9

T > TC 6

10

10

200 (e)

T > TC

7

7

10

x = 0.075

TE D

T < TC

β = 0.238 γ = 1.016

100 T > TC 6

T > TC

100

6

10

8

10

300 200

100

8

10

300

x = 0.1

(h)

200

T < TC

β = 0.326 γ = 1.342

β = 0.253 γ = 0.992

TC = 264.1

T > TC

7

10

100

TC = 292.6

7

EP

T < TC

β = 0.312 γ = 1.380

10

x = 0.075

200

TC = 293.8

T > TC

10

(g)

300

β = 0.322 γ = 1.381

7

10 200

TC = 261.6

8

10

x = 0.1

(f)

T < TC

AC C

β

M/|ε| (emu/g)

7

10 10

x = 0.075

100

TC = 292.5

T > TC

SC

6

10

100

β = 0.301 γ = 1.382

TC = 257.8

T > TC

300 200

7

β+γ

H/|ε|

10

(Oe)

Fig. 7. Phan et al.

45

TC = 294.4 8

10

100

β

(a)

x = 0.075

RI PT

200

T = 276-310 K

M/|ε| (emu/g)

T = 250-274 K

ACCEPTED MANUSCRIPT

12 9

(a)

x=0

6 50 kOe

RI PT

3 10 kOe

0 240 9

250

260

270

280

(b)

x = 0.025 50 kOe

3

10 kOe

0 255

270

285

M AN U

240

x = 0.05

(c)

6

50 kOe

3

10 kOe

0 250

260

TE D

-1

-1

−∆Sm (J.kg .K )

225

6

SC

6

9

270

(d)

EP

3

260

280

50 kOe 10 kOe

270

280

290

300

x = 0.1

(e)

50 kOe

3

0 255

290

x = 0.075

AC C

0 250 6

290

10 kOe

270

285

300

T (K) Fig. 8. Phan et al.

46

315

330

ACCEPTED MANUSCRIPT

12

(a)

La0.7Ca0.3-xBaxMnO3

x=0 (n = 0.43)

RI PT

x=0.05 (n = 0.45)

-1

-1

|∆Smax| (J.kg .K )

x=0.025 (n = 0.45)

9

x=0.075 (n = 0.64)

6

x=0.1 (n = 0.73)

SC 15

30

(b)

45

60

x= 0 x = 0.025 x = 0.05 x = 0.075 x = 0.1

TE D

240

160

AC C

EP

RC (J/kg)

M AN U

0 0

80

n

|∆Smax| ~ H

3

0 0

15

30

H (kOe) Fig. 9. Phan et al.

47

45

ACCEPTED MANUSCRIPT

3 2

(a)

x=0 10 kOe 20 kOe 30 kOe 40 kOe 50 kOe

0 2

240

250

(b)

260

270

10 kOe 20 kOe 30 kOe 40 kOe 50 kOe

240

(c)

260

(d)

AC C

0 250 2

270

TE D

250

285

(e)

10 kOe 20 kOe 30 kOe 40 kOe 50 kOe

280

x = 0.075

EP

1

270

x = 0.05

1

0

255

M AN U

n(T, H)

225

SC

0

2

280

x = 0.025

1

2

RI PT

1

260

270

10 kOe 20 kOe 30 kOe 40 kOe 50 kOe

280

290

300

x = 0.1 10 kOe 20 kOe 30 kOe 40 kOe 50 kOe

1

270

285

300

T (K) Fig. 10. Phan et al.

48

315

330

ACCEPTED MANUSCRIPT

0.8

(a)

x=0

0.0 -4 0.8

-2

0

(b)

2

(c)

0.4 0.0 -4

0

2

4

x =0.05

-2

0

2

4

x = 0.075

(d)

TE D

0.8

SC

-2

M AN U

∆S'

0.8

4

x = 0.025

0.4 0.0 -4

RI PT

0.4

0.4

EP

0.0 -4

AC C

0.8

-2

0

2

4

x= 0.1

(e)

0.4 0.0 -4

-2

0

θ2

Fig. 11. Phan et al.

49

2

4

ACCEPTED MANUSCRIPT

Highlights • Threshold of first-to-second-order phase transformation in La0.7Ca0.3-xBaxMnO3 • Giant magneto-caloric effect with magnetic-entropy changes of 6~11 J⋅kg-1⋅K-1 • Detailed analyses of critical behavior in comparison with previous studies

AC C

EP

TE D

M AN U

SC

RI PT

• Magnetic phase-transition theories and universal curves of magnetic-entropy change