JOURNAL OF RARE EARTHS, Vol. 33, No. 3, Mar. 2015, P. 263

* Corresponding author: Mounira Abassi (E-mail: mouniraabassi90@yahoo.com; Tel.: +216 25 012 603)

DOI: 10.1016/S1002-0721(14)60413-0

Critical parameters near the ferromagnetic-paramagnetic phase transition in La0.67–xYxBa0.23Ca0.1MnO3 compounds (x=0.10 and x=0.15)

Mounira Abassi1,*, N. Dhahri1, J. Dhahri1, K. Taibi2, E.K. Hlil3 (1. Laboratory of Condensed Matter and Nanosciences, University of Monastir, 5019, Tunisia; 2. Institut Néel, CNRS and Joseph Fourier university, B.P.166, 38042 Grenoble, France; 3. Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042, Grenoble cedex 9, France)

Received 15 May 2014; revised 26 September 2014

Abstract: The critical properties of the mixed manganite La0.67–xYxBa0.23Ca0.1MnO3 with x=0.10 and x=0.15 around the paramagnetic (PM)-ferromagnetic (FM) phase transition were investigated through various techniques. These involved modified Arrott plots, Kou-vel-Fisher method and Widom scaling relation. Magnetic data, analyzed in the critical region, using the above methods, yielded the critical exponents for (x=0.10) La0.57Y0.10Ba0.23Ca0.1MnO3 (β=0.312±0.002 and γ=1.147±0.003 at TC=299.23±0.05 K). Moreover, the estimated critical exponents of (x=0.15) La0.52Y0.15Ba0.23Ca0.1MnO3 were β=0.286±0.004 and γ=0.943±0.002 at TC=289.53±0.06 K. The critical exponents’ values were close to the theoretical values of 3D-Ising model and tricritical mean-field model. These results suggested that the present composition should be close to a tricritical point in the La0.67–xYxBa0.23Ca0.1MnO3 phase diagram. Express-ing the field dependence as ΔSM∝Hn allowed us to establish a relationship between the exponent n and the critical exponents of the material and to propose a phenomenological universal curve for the field dependence of ΔSM.

Keywords: perovskite manganites; phase transition; entropy; critical properties; rare earths

Changes in physical properties across the PM-FM phase transition are one of the vital issues related to both the physics and the functionality of perovskite mangan-ites with a generic formula RE1–xAxMnO3 (where RE= La, Pr and Nd, and A=Ca, Sr and Ba)[1–4]. To shed light on the relation between insulator-metal transition and CMR effect, two important questions about PM-FM transition should be clarified: one concerns the order of the phase transition and the other is related to the univer-sality class. A transition from a PM insulator to a FM metallic state in RE1–xAxMnO3 manganites has been qualitatively explained by Zener double exchange (DE) ferromagnetic interaction[5]. Other theories such as pola-ronic effects[6] and phase separation[7] were invoked to explain the experimental data quantitatively. Critical phenomena in the DE model have been first described within mean-field theory[8]. Therefore, to clarify field these issues, it is necessary to investigate the critical ex-ponents in the region of the PM-FM transition. Earlier studies on the critical behaviors around Curie tempera-ture have indicated that the critical exponents play im-portant roles in elucidating interaction mechanisms at near TC. Sequentially, Motome and Furulawa suggested that the critical behavior should be attributed to short-range Heisenberg model[9,10]. Critical exponents for manganites show a wide variation which covers almost all the universality classes even for the similar systems, when different experimental tools are used to determine

them. A few relevant experimental investigations on the critical phenomena also supported this viewpoint due to the obtained value of critical exponents consistent with that in the conventional ferromagnet of Heisenberg model. From neutron scattering studies on a La0.7Sr0.3MnO3 crystal, Martin et al.[11] have found a β value of 0.295 which is close to that predicted by Heisenberg model. However, a relatively high value of β=0.5 obtained in the polycrystalline La0.8Sr0.2MnO3 is in good agreement with that in mean field model[12]. Con-versely, a very low critical exponent of β=0.14 identified in the single crystal La0.7Ca0.3MnO3 suggested that the PM-FM transition in this system is of a first rather than a second order type[13]. Meanwhile, moderate critical value of β=0.25 found in the polycrystalline La0.6Ca0.4MnO3 is in excellent agreement with tricritical point values[14]. Moutis et al.[15] have reported that the calculated values of the critical exponents for La0.67Ba0.33MnO3 are be-tween those predicted for three-dimensional (3D) Heisenberg model and those predicted by mean-field theory. Therefore, in view of the varied critical exponent β from 0.1 to 0.5, four kinds of different theoretical mod-els were used to explain the critical properties in man-ganites. These models are mean field values[12,16], three- dimensional 3D-Heisenberg interaction[17], 3D-Ising values[18] and tricritical mean-field model. Due to the di-vergence in the previous reports, it is worthwhile to in-vestigate the critical behavior and the critical exponents

264 JOURNAL OF RARE EARTHS, Vol. 33, No. 3, Mar. 2015

on the analogous perovskite system from different as-pects. Nowadays, there is a need for new, advanced magnetic materials with a second-order magnetic phase transition, showing a large reversible magnetic entropy change (ΔSM) at low applied fields. For this reason, it is important to know the field dependence of (ΔSM) of a given magnetic refrigerant material[19]. In fact, the study of the field dependence of magnetic entropy change, (ΔSM), is an important implement in understanding its critical behavior. Expressing the field dependence as ΔSM∝Hn allows us to establish a relationship between the exponent n and the critical exponents of the material and to propose a phenomenological universal curve for the field dependence of ΔSM.

The aim of this work was to study the critical phe-nomena in the La0.67–xYxBa0.23Ca0.1MnO3 (x=0.10 and x=0.15) compounds by analyzing the critical exponents through various techniques.

1 Experimental

Polycrystalline samples of a nominal composition La0.67–xYxBa0.23Ca0.1MnO3 (x=0.10 and x=0.15) were prepared by conventional ceramic making technique of solid-state reaction. Details of the sample preparation and structure characterization have been described in a pre-vious work[20]. Magnetic measurements versus tempera-ture and magnetic applied field were performed using a BS1 magnetometer developed at Louis Néel Laboratory in Grenoble in a temperature range close to TC. To ex-tract the critical exponents of the samples accurately, the magnetic isotherms for both samples were measured in the range of 0–5 T, in the vicinity of the PM to FM phase transition. The isothermals are corrected by a demag-netization factor D that has been determined by a stan-dard procedure from low-field dc magnetization meas-urement at low temperatures (H=Happ–DM).

2 Scaling analysis In the vicinity of a second-order phase transition with

a Curie temperature TC, the existence of a diverging cor-

relation length C

C

T TT

ε−

= leads to universal scaling

laws for the saturation magnetization MS and susceptibil-ity χ. In standard notations, these are given by equations as follows[21–23]: Below TC, the temperature dependence of the spontane-ous magnetization

0S 0( ) lim ( )HM T Mμ →= is governed by β exponent through the relation:

S 0 C( ) ( ) , 0,M T M T Tβε ε= − < < (1)

Above TC, the initial susceptibility 1

0 ( )Tχ − =

0

00lim ( )H

H

Mμ

μ→

is given by:

1 00

0

, 0, C

hT T

Mγχ ε ε− = > =

⎛ ⎞⎜ ⎟⎝ ⎠

(2)

At TC, M and H are related by the following equation: 1/

C( ) , 0,M D H T Tδ ε= = = (3) where h0/M0 and D are the critical amplitudes (constants). The magnetic equation of state relationship between the variable M(μ0H, ε), μ0H and T is the major. Furthermore, the scaling hypothesis can be written as:

0 0( , ) ( / )M H f Hβ β γμ ε ε μ ε += ± (4) where f+ for T > TC and f– for T < TC are regular functions. Eq. (4) implies that M/|ε|β as a function of μ0H/|ε|β+γ falls into two universal curves, one for temperatures above TC and the other for temperatures below TC. In terms of the variable m=M(μ0H, ε)|ε|–β and h=μ0H|ε–(β+γ)| called the scaled or renormalized magnetization and scaled or re-normalized field, respectively. Eq. (4) is reduced to a simple form: m = f ± (h) (5)

Eq. (5) implies that for a true scaling relation with a proper selection of (β, γ) and (δ), the scaled M vs. μ0H data will fall into two universal curves; f–(h) for tem-perature below TC and f+(h) for temperature above TC. This is an important criterion for the accurate and unam-biguous values of the critical exponents.

3 Results and discussion

Fig. 1 shows a series of isotherms of magnetization M vs. μ0H, the magnetic field (the applied field corrected for demagnetization) in the immediate vicinity of Curie temperature (TC=300 K for x=0.10 and TC=289 K for x= 0.15). These curves indicate a gradual transition between ferromagnetism and paramagnetism. The curvature at low fields makes it difficult to extract accurate values for TC, the initial susceptibility χ0 (i.e., dM/μ0dH at μ0H=0) above TC, or the spontaneous magnetization MS(T) below TC. Therefore, to determine TC, as well as χ–1

0 and MS (T) we have used the Arrott method, plotting (M2 vs. μ0H/M), as indicated in inset of Fig. 1[24]. In mean field theory at near TC, M2 vs. μ0H/M at various T should form a pro-gression of parallel straight lines. The line for T=TC passes through the origin on this plot. Moreover, the in-tersections of these curves for T>TC with the μ0H/M axis give the values of 1/χ0(T) at μ0H=0. In the present case, the curves in the Arrott plot are non-linear, indicating that the mean-field theory (β=0.5, γ=1 and δ=3) charac-teristics of systems with long-range interactions is invalid for the present phase transition.

Therefore, the values of MS (T) and χ–1 0 (T) were

determined using a modified Arrott plot (also called modified Arrott plots (MAP)). In this technique, the M= f(μ0H) data are converted into series of isotherms (M1/β= f(μ0H/M)1/γ) depending on the following relationship[25]:

Mounira Abassi et al., Critical parameters near the ferromagnetic-paramagnetic phase transition in … 265

Fig. 1 Isothermal magnetization for La0.67–xYxBa0.23Ca0.1MnO3

(x=0.10 and x=0.15) (the inset shows Arrott plots of M2 vs. μ0H/M (the positive slope indicates a second-order transition))

( )1/ 1/C

0 1

1

( / ) ( / )T T

H M M MT

γ βμ−

= + (6)

The MAP is constricted using the critical exponents of 3D-Heisenberg (β=0.365, γ=1.336 and δ=4.80), 3D-Ising (β=0.325, γ=1.241 and δ=4.82) and tricritical mean field theories (β=0.250, γ=1 and δ=5). Based on these curves, all models render quasi straight lines and nearly parallel to the high field region. Thus, it is somewhat difficult to distinguish which one of them is the best for determining the critical exponents. In order to compare these results and select the best model which describes this system, we calculated their relative slopes (RS) which are de-fined as RS=S(T)/S(TC). If the modified Arrott plots show a series of absolute parallel lines, the relative slope should be kept to 1 irrespective of temperature[26]. As shown in Fig. 2, using mean-field, 3D-Heisenberg and tricritical mean-field, the RS of La0.57Y0.10Ba0.23Ca0.1MnO3 clearly deviates from RS=1, but the RS of 3D-Ising model remains close to 1. On the other hand, we noted that the RS of La0.52Y0.15Ba0.23Ca0.1MnO3 is very close to 1 when using the tricritical mean-field. Thus, the critical properties of La0.57Y0.10Ba0.23Ca0.1MnO3 and La0.52Y0.15

Ba0.23Ca0.1MnO3 samples can be described using the 3D-Ising and tricritical mean-field models, respectively.

Fig. 2 Relative slope (RS) as a function of temperature for

La0.67–xYxBa0.23Ca0.1MnO3 samples (x=0.10 and x=0.15) In Fig. 3, we present the MAP isotherms of (M)1/β vs. (μ0H/M)1/γ with 3D-Ising model for La0.57Y0.10Ba0.23Ca0.1

MnO3 sample and the tricritical mean-field model for La0.52Y0.15Ba0.23Ca0.1MnO3. As this plot results in nearly straight lines (for sufficiently high fields), a linear ex-trapolation from fields 5 T to the intercepts with the axes (M)1/β vs. (μ0H/M)1/γ gives the values of spontaneous magnetization MS (T) and inverse susceptibility χ–1

0 (T), respectively. These values as functions of temperature for the sample x=0.10 are plotted in Fig. 4. Similarly, we can also obtain MS (T) and χ–1

0 (T) for the sample with x= 0.15 (not shown here). The continuous curves in Fig. 4 denote the power law fits of MS (T) and χ–1

0 (T) according to Eqs. (1) and (2), respectively. This gives the values of β=0.312±0.002 with TC=299.23±0.005 K (Eq. 1) and γ=1.147±0.003 with TC=299.23±0.05 K (Eq. 2). Thus, new values of the critical exponents for both samples were determined and are reported in Table 1.

Similar procedures were also carried out to obtain more precise values of critical exponents. Kouvel-Fisher (KF) method was used on the following relationship[24]:

S C

S

( )

d ( ) / d

M T T T

M T T β

−= (7)

1

0 C

1

0

( )

d ( ) / d

T T T

T T

χ

χ γ

−

−

−= (8)

Under this method, using the obtained MS (T) and χ–1 0 (T)

curves, we plotted MS (T)(dMS (T)/dT)–1 and χ–1 0 (T) (dχ–1

0 (T)/

266 JOURNAL OF RARE EARTHS, Vol. 33, No. 3, Mar. 2015

Fig. 3 Modified Arrott plots: (M1/β vs. μ0H/M) for La0.57Y0.10

Ba0.23Ca0.1MnO3 and La0.52Y0.15Ba0.23Ca0.1MnO3

Fig. 4 Spontaneous magnetization MS(T,0) and the inverse ini-

tial susceptibility vs. temperature for La0.57Y0.10Ba0.23

Ca0.1MnO3 dT)–1 which should yield straight lines with slopes 1/β and 1/γ, respectively. When extrapolated to the ordinate equal to zero, these straight lines should give intercepts on their T axes equal to Curie temperature. These plots are shown in Fig. 5. The linear fitting of the plots fol-lowing the KF method (Fig. 6) gives β=0.314±0.005 with TC=299.23±0.05 K and γ=1.127±0.006 with TC=299.25± 0.03 K, respectively, for x=0.10. Similarly, the critical exponents were determined for x=0.15 and are listed in Table 1. It is noticeable that values of critical exponents as well as TC calculated using both modified Arrott plot

Table 1 Comparison of critical exponents for sample with various models (MAP: modified Arrott plot; KF: Kouvel-Fisher method; CI: critical isotherm) Material Technique TC/K β γ δ Ref.

La0.57Y0.10Ba0.23Ca0.1MnO3 MAP KF

C.I(exp) C.I(cal)

299.25±0.05 299.25±0.03

0.312±0.002

0.314±0.005 1.147±0.003 1.127±0.006

4.86±0.04 4.62

This work

La0.52Y0.15Ba0.23Ca0.1MnO3 MAP KF

C.I(exp) C.I(cal)

289.53±0.06 289.53±0.03

0.286±0.004 0.296±0.004

0.943±0.002 0.973±0.008

4.90±0.01 4.22

This work

Mean-field theroy Theory 0.5 1.0 3.0 [12] 3D Heisenberg model Theory 0.365±0.003 1.336±0.004 4.80±0.004 [12]

3D Ising model Theory 0.325±0.002 1.241±0.002 4.82±0.02 [12] Tricritical mean-field Theory 0.25 1 5 [12]

La0.6Ca0.4MnO3 MAP KF

C.I(exp) C.I(cal)

267.88 268.37

0.248 0.287

0.995 0.989

4.896 4.728

[36]

La0.8Ca0.2MnO3 MAP KF

C.I(exp) C.I(cal)

181.37 181.67

0.328 0.325

1.193 1.180

4.826 4.630

[37]

La0.75Ca0.08Sr0.17Mn0.9Ga0.1O3 MAP KF

C.I(exp) C.I(cal)

232.40±0.008 232.36±0.006

0.420±0.05 0.428±0.05

1.221±0.002 1.286±0.004

4.22±0.04 3.87

[38]

La0.67Pb0.33Mn0.92Co0.08O3 316.65 0.364 1.40 4.88 [35] LaMn0.9Ti0.1O3 145.3 0.375 1.25 4.11 [22]

La0.1Nd0.6Sr0.3MnO3 249 0.249 1.16 5.17 [39] La0.9Te0.1MnO3 239 0.201 1.27 7.14 [25]

Mounira Abassi et al., Critical parameters near the ferromagnetic-paramagnetic phase transition in … 267

Fig. 5 Kouvel-Fisher plots for the spontaneous magnetization

and the inverse initial susceptibility for La0.57Y0.10Ba0.23Ca0.1MnO3

Fig. 6 lnM vs. lnμ0H plot for La0.57Y0.10Ba0.23Ca0.1MnO3 and

La0.52Y0.15Ba0.23Ca0.1MnO3 (straight line is the linear fit to the data)

and Kouvel-Fisher plot match reasonably very well (see Table 1).

To further check the reliability of the above critical exponents we can study the relation among the three critical exponents β, γ and δ. The exponent δ has been directly obtained by plotting the critical isotherm. Fig. 6 shows this critical isotherm on a log-log scale. According to Eq. (3), this should be a straight line with slope 1/δ. From the linear fit we obtained δ=4.86±0.04 for x=0.10. From Widom scaling relation according to which critical exponents β, γ and δ are related in the following way[27]: δ=1+(γ/β). Using the above determined values of β and γ, we obtain δ values which are close to the estimates for δ from the critical isotherms at TC. Thus, the estimates of the critical exponents are consistent. The values of δ ob-tained for both compositions are reported in Table 1. Physically, β describes how the ordered moment grows below TC while γ describes the divergence of the mag-netic susceptibility at TC. β value decreases with increas-ing yttrium content, reflecting a faster growth of the or-dered moment when temperature increases. The decrease of γ yields a sharp divergence of the magnetic suscepti-bility at TC. Moreover, the increase of value suggests a

reduction in curvature and a faster saturation of the M(μ0H) curves as observed in the compound (x=0.10).

In order to check whether our data in the critical region obey the magnetic equation of state (4), M/|ε|β as a func-tion of μ0H/|ε|β+γ is plotted in Fig. 7 for x=0.10, using the values of critical exponents and TC obtained from the above analysis. The inset shows the same results on a log-log plot. It can be clearly seen that all the points fall into two branches, one for T<TC and the other for T>TC. This corroborates that the obtained values of the critical exponents and TC are reliable and in agreement with the scaling hypothesis. The reliability of the exponents and TC has been further ensured with a more rigorous method by plotting M2 vs H/M[28]. For x=0.10, Fig. 8 shows that all data collapse into two separate curves: one below TC and another above TC. This clearly indicates that the in-teractions get properly renormalized in a critical regime following scaling equation of state.

The field dependence of ΔS Peak M can be studied by

assuming a ΔSM∝Hn law, where n depends on the magnetic state of the sample. Local values of n can be extracted from the experimental data[29] by using a formula:

Fig. 7 Scaling plots indicating two universal curves below and

above TC for La0.57Y0.10Ba0.23Ca0.1MnO3 (Inset show the same plots on a log-log scale)

Fig. 8 Renormalized magnetization and field plotted in the form

of M2 vs H/M for La0.57Y0.10Ba0.23Ca0.1MnO3 (The plot shows all the data collapse into two separate branches: one below TC and another above TC)

268 JOURNAL OF RARE EARTHS, Vol. 33, No. 3, Mar. 2015

Md ln

d ln

Sn

H

Δ=

(9)

Inset of Fig. 9 shows the temperature dependence of n for different values of the maximum applied field for both samples (x=0.10 and x=0.15). Independent of the magnetic field and composition, all n(T) curves follow the universal behavior described by Franco et al.[30]. The n exponent exhibits a moderate decrease with increasing temperature, with a minimum value in the vicinity of the transition temperature. Then, it sharply increases above TC. However, for any other case, the value of the mini-mum is different from that and is related to the critical exponents of the material as predicted in[31]:

C

1 1(1( ) 1 )n T

δ β−= + (10)

Using the values of β and δ, we obtained the values of n which are calculated to be 0.72 and 0.81 for x=0.10 and x=0.15 samples, respectively. The magnetic field de-pendence of ΔSPeak

M is presented in Fig. 9. A good power law fit of the experimental ΔSPeak

M (H) data was observed. The values of n obtained from the power law fit are 0.75 and 0.83 for x=0.10 and x=0.15 samples, respectively. These are in good agreement with those obtained from the critical exponents using MAP.

Franco et al. proposed a phenomenological universal curve for the field dependence of the magnetic entropy ΔS

M[32]. Their proposition is based on the assumption that

if such a universal curve exists, all other curves measured under different applied magnetic fields should collapse onto the same point of the universal curve. Therefore, the method of construction of the universal curve is based on the selection of equivalent points of the experimental curves and for this purpose the maximum entropy change, ΔSPeak

M , is taken as a reference. This technique assumes that all points which are at the same level compared to ΔSPeak

M must be in an equivalent state. In this way, two

Fig. 9 Field dependence of the maximal ΔSPeak

M (Inset represents temperature dependence of local exponent n measured at different fields for La0.57Y0.10Ba0.23Ca0.1MnO3 and La0.52Y0.15Ba0.23Ca0.1MnO3 samples)

different reference points were found for each curve, one below TC and the other above TC. Hence all the curves are normalized with respect to their peak. The construc-tion of the universal curve requires imposing a scaling law for the temperature axis. The axis of the temperature was rescaled differently below and above TC, just requir-ing that the position of the two reference points of each curve corresponded to θ=±1.

C r1 C C

C r2 C C

( )/( ), ( )/( ),

T T T T T TT T T T T T

θ− −

− −

≤⎧= ⎨ >⎩

(11)

where Tr1 and Tr2 are the temperatures of the two refer-ence points of each curve. In fact, the collapse of the ex-perimental data of different materials in a single curve can make predictions for the response of a particular ma-terial under different experimental conditions, which is extremely useful when we need conditions that are not available (high magnetic field, very low temperature, etc.). Fig. 10 shows the universal curve for La0.57Y0.1Ba0.23Ca0.1

MnO3. We can clearly see that all the curves collapse onto a sole universal curve regardless of the magnetic field, which confirms the validity of the technique used and that the transition is of a second order. For a homogenous magnet, the universality class of the magnetic phase transition depends on the exchange interaction J(r). Fisher et al. theoretically treated this kind of long-range ferromagnetism as an attractive inter-action of spins, where a renormalization group theory analysis suggests the long-range attractive interactions decay as[33]: J(r)≈1/r(d+σ) (d is the dimension of the system and σ is the range of the interaction). When σ=2, Heisenberg model is valid for the three dimension iso-tropic ferromagnet, where J(r) decreases faster than r–5. They report that if σ is less than 3/2, the mean-field ex-ponents are valid. For an intermediate range, i.e., for J(r)≈r–(3+σ) with 3/2≤σ≤2, the exponents belong to a dif-ferent universality class which depends upon σ. In a gen-eral way, the evolution of the critical exponents tends towards the values of the mean-field theory with a long-range interaction. In Table 1, it is clearly seen that the critical exponents

Fig. 10 Master curve behavior of the curve as a function of the

rescaled temperature

Mounira Abassi et al., Critical parameters near the ferromagnetic-paramagnetic phase transition in … 269

of the x=0.15 sample match well with those derived from the tri-critical mean-field model. The critical exponents of a ferromagnetic phase transition depend on the type of ordering and the dimensionality, but, as discussed by Huang[34] at a tri-critical point, critical exponents are universal: β=0.250, γ=1 and δ=5. A similar case has also been reported on La1–xCaxMnO3 (0.25≤x≤0.5) poly- crystalline manganites, where the tri-critical point is found at x≈0.4[14]. A first-order transition in La2/3Ca1/3MnO3 and a crossover continuous phase transition on either side of phase diagram suggest that Ca-doped manganites are distinct from other manganites[35]. In the case of elec-tron-doped manganite La0.9Te0.1MnO3

[25], the critical ex-ponents are not consistent with those of hole-doped manganites and theoretical models, e.g., 3D-Heisenberg model, mean-field model, and 3D-Ising model. Therefore, the nature of the magnetic transition of La0.9Te0.1MnO3 is completely different from that of hole-doped manganites. However β value close to that predicted by tri-critical mean field theory suggests that the composition La0.9Te0.1MnO3 may be close to a tri-critical point in the La1–xTexMnO3 phase diagram[25].

4 Conclusions

In summary, we studied the effect of yttrium on the critical behavior of La0.67–xYxBa0.23Ca0.1MnO3 (x= 0.10 and x=0.15) polycrystalline sample at the PM-FM phase transition. This transition was identified to be of a second order. The reliable critical exponents δ, γ and β were es-timated from various techniques such as modified Arrott plot, Kouvel-Fisher method and critical isotherm analysis fit with 3D-Ising for x=0.10 and tricritical mean-field for x=0.15. The change in the universality class from the 3D-Ising model to the tricritical mean-field model was due to the influence of yttrium (Y) content. The field and temperature dependent magnetization followed the scal-ing theory and all data fell into two distinct branches: one for T>TC and another for T<TC, indicating that the critical exponents thus obtained in this work were accurate. The analysis of field dependence of the magnetic entropy changes revealed the power law dependence and the coupled order parameters at the transition temperature.

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