Magnetic and magnetocaloric properties of La0.55Bi0.05Sr0.4CoO3 and their implementation in critical behaviour study and spontaneous magnetization estimation

In this work, we present the results of the magnetic, critical, and magnetocaloric properties of the rhombohedral-structured La0.55Bi0.05Sr0.4CoO3 cobaltite. Based on the modified Arrott plot, Kouvel–Fisher, and critical isotherm analyses, we obtained the values of critical exponents (β, γ, and δ) as well as Curie temperature (TC) for the investigated compound. These components were consistent with their corresponding values and they were validated by the Widom scaling law and scaling theory. The obtained critical exponents were close to the theoretical prediction of the mean-field model values, revealing the characteristic of long-range ferromagnetic interactions. The magnetic entropy, heat capacity, and local exponent n(T, μ0H) of the La0.55Bi0.05Sr0.4CoO3 compound collapsed to a single universal curve, confirming its universal behaviour. The estimated spontaneous magnetization value extracted through the analysis of the magnetic entropy change was consistent with that deduced through the classical extrapolation of the Arrott curves. Thus, the magnetic entropy change is a valid and useful approach to estimate the spontaneous magnetization of La0.55Bi0.05Sr0.4CoO3.


Introduction
As a member of perovskite oxides, cobaltites are important agile and multifunctional materials that are very promising for several applications, including high-temperature oxygen separation membranes, cathodes in solid oxide fuel cells (SOFCs), magnetic storage, and magnetic refrigeration. [1][2][3] The Co-based sister compounds of manganites have been less intensively studied. [4][5][6] It is well-known that the similar Hund's rule exchange energy and crystal-eld energy both lead to an additional spin-state degree of freedom in cobaltites, which results in close competition between the multiple ground states. This, in turn, leads to phenomena such as magnetoelectronic phase separation, colossal magnetoresistance, and magnetocaloric effect. The spin state (ST) of cobalt ions is very sensitive to the application of external stimuli such as magnetic and electrical elds, temperature, pressure, or compositional doping. 7,8 This sensitivity is due to the very small energy difference between the t 2g and e g levels. Consequently, the state of Co can be presented in a low-spin (LS), intermediate-spin (IS), or high-spin (HS) state. 4,5,8 This ability of Co to exist in several STs given a principal property distinguishes the cobalt oxides from other transition metals such as manganese and makes the physical phenomena observed in the cobalt oxides very complex, due to which they have not been entirely comprehended so far. The complexity of STs provides promising opportunities for basic science as well as electronic applications, inducing a multifunctional characteristic to cobalt oxides. The latter property derives from the fact that the crystal-eld splitting of the 3d energy level of Co ions in cobalt oxides is of the same order of magnitude as the Hund's rule intraatomic exchange energy and 3d orbital bandwidth. 9 Physical effects such as magnetoresistance and magnetocaloric effects observed in manganites 10,11 and cobaltites 3, [12][13][14] have been the subject of several investigations in the last few years. Double exchange (DE), phase separation (PS), Jahn-Teller distortion (JT), and Griffiths phase (GP) have been found to explain the aforementioned effects. Moreover, these compounds are also interesting for applications since they present low costs and longer usage times. This family of materials can be easily elaborated, and grain growth can be achieved to the desired size; moreover, they possess tunable Curie temperature and high chemical stability. La-based cobaltite is one of the perovskite oxides and it shows a wide variety of physical properties with relatively high T C values. Like

Experimental details
The ceramic with a nominal composition of La 0.55 Bi 0.05 Sr 0.4 -CoO 3 was synthesized by the solid-state reaction method. The precursors of La 2 O 3 (Aldrich 99.9%; USA), Bi 2 O 3 (Aldrich 99.9%; USA), SrCO 3 (Aldrich 99.9%; USA), and Co 3 O 4 (Aldrich 99.9%; USA) were mixed in an agate mortar with the desired proportions according to the La 0.55 Bi 0.05 Sr 0.4 CoO 3 system. Then, the obtained powder was heated at 800 C for 24 h. Aer cooling to the ambient temperature, the bulk was ground and pressed into pellets and then sintered at 900, 1000, 1100, and 1200 C for 24 h with intermediate regrinding and repelling to ensure homogenization. Finally, the obtained disk-shaped samples were slowly cooled to room temperature in air. As the sample was exposed to air, it consequently became stoichiometric with respect to oxygen. 22,23 The X-ray diffraction (XRD) pattern was recorded at room temperature on a PANalytical X'PERT Pro MPD diffractometer using q/2q Bragg-Brentano geometry with diffracted beam monochromatized CuKa radiation (l ¼ 1.5406 A). The diffraction patterns were collected at steps of 0.017 over the angle range of 20-80 . Rietveld renement was performed to determine the structural parameters by using the FullProf soware. A vibrating-sample magnetometer developed at NEEL Institute was used to investigate the thermomagnetic properties of the sample. The temperature and eld dependencies of the magnetization, M(T, m 0 H), were recorded in a temperature range around the T C . To accurately extract the critical exponents of the sample, the corrected magnetic isotherms were measured in the range of 0-5 T and within a temperature interval of 2 K in the vicinity of T C .

Scaling analysis
For continuous phase transition, near T C , the critical behavior for a second-order magnetic phase transition can be investigated via a series of critical exponents (b, g, and d). According to the scaling hypothesis, these exponents are expressed as follows: 24,25 where 3 ¼ (T À T C )/T C is the reduced temperature. M 0 , h 0 , and D are the critical amplitudes; b (associated with M SP ), g (associated with magnetic susceptibility c 0 À1 ), and d (associated with the eld-dependent magnetization at T C ) are the critical parameters.
The critical exponents (b, g, and d) should obey the scaling equations. 24,25 A formulation was used in this work, which was based on the scaling equations of state. In the asymptotic critical region and according to the scaling equations, the magnetic equation can be expressed as follows: where f AE denote regular analytic functions with f À denoting the FM state for T below T C and f + denoting the PM state for T above T C . Eqn (4) shows that for true scaling relations and for the right choice of b, g, and d, M(m 0 H, 3)3 Àb vs. m 0 H3 À(b+g) yields two universal curves of temperature T above and below T C .

Results and discussions
The XRD q-2q patterns measured at room temperature show that La 0.55 Bi 0.05 Sr 0.4 CoO 3 can be rened in the perovskite structure with a rhombohedral structure with the R 3c space group. This demonstrates that the substitution of La by 5% Bi does not induce the relevant effect on the crystal structure as compared to those in the undoped La 0.5 Sr 0.4 CoO 3 compound prepared by the solid-state reaction method 26 or sol-gel technique. 14 The structural information of the prepared sample is obtained aer tting the XRD data using the Rietveld renement technique by means of the FullProf soware. 27,28 During the initial stages of renement, only the following parameters were changed: scale factor, background coefficients, unit-cell parameters, full-width parameters, sample displacement, and peak asymmetry. First, only the scale factor was rened; then, the remaining parameters were gradually included in the successive least-squares cycles. The background was t using a third-order polynomial, and the observed peak shapes were approximated by using a pseudo-Voigt prole function, limited to ten full-widths on each side of the peak maximum. Fig. 1 shows the XRD diffractogram for the investigated sample, where the open circle dots represent the measured XRD reections and the solid lines denote the Rietveld-rened results. Evidently, a marginal difference between the measured spectra and rened ones can be observed. The quality of renement is evaluated through the goodness of the t indicator c 2 , which is equal to 1.98. From Fig. 1, it is clear that a small secondary phase can be observed, which can be attributed to the presence of the CoO impurity. This impurity is identied with the X'Pert HighScore Plus soware. It is interesting to note that the most intense peak in the XRD spectra for La 0.55 Bi 0.05 Sr 0.4 CoO 3 exhibits a double peak, representing the rhombohedral phase.
The intense peak is shown in the inset of Fig. 1. The lattice parameters are found to be a ¼ b ¼ 5.415(7), c ¼ 13.326(9) A, and unit cell volume V ¼ 338.51 A 3 for La 0.55 Bi 0.05 Sr 0.4 CoO 3 . For the undoped compound prepared by using the conventional solid-state reaction method, the lattice parameters can be determined as a ¼ b ¼ 5.436(3), c ¼ 13.226(3) A, and unit cell volume V ¼ 338. 49(1) A 3 . 26 It is clear that the lattice parameter "c" and unit cell volume marginally increase with the addition of 5% Bi content, while parameter "a" slightly decreases with the addition of 5% Bi content. This almost-perfect match can be explained considering the similar ionic radii of La 3+ ions (1.16 A, 8-coordinate) and Bi 3+ ions (1.17 A, 8-coordinate). 29 In order to understand the general magnetic behavior and to estimate T C , low-eld magnetization vs. temperature (M(T)) is obtained in the eld-cooled (FC) mode for the La 0.55 Bi 0.05 Sr 0.4 -CoO 3 sample. Fig. 2 shows the M(T) curve under an applied magnetic eld of 0.05 T. This curve exhibits a sharp FM-PM phase transition, where T C , dened from the inexion point of the dM/dT vs. T curve (inset, Fig. 2), is found to be 210 K. Here, T C is suppressed by 20 K as compared to undoped La 0.5 Sr 0.4 -CoO 3 . 14 It is noteworthy that even a higher value of T C ¼ 237 K was found by T. A. Ho et al. 26 for a sample prepared under different conditions. This T C suppression correlates with the competition between the DE interaction and superexchange interactions altered by the incorporation of Bi ion in the Co-O-Co networks. The observed M(T) curve reveals a strong variation in the magnetization around T C , which indicates that there is possibly a large magnetic entropy change around the magnetic transition. 11,30 When showing the inverse of the magnetic susceptibility (1/c-1/M) curve in the PM state (insets, Fig. 2), a linear behavior with temperature is observed above T C , which can be tted with the Curie-Weiss law:  where q P is the PM T C and C is the Curie constant. The obtained q P is determined to be 230 K, which is higher than T C , where DT ¼ q P À T C ¼ 20 K. This q P value is smaller than the one observed in the undoped compound (245 K). 26 The decrease in q P with 5% Bi doping can be explained by considering the DE mechanism in cobaltites. It is known that Bi 3+ , with the 6s 2 lone pair, is a highly polarizable ion and it induces local distortions in the Co-O-Co bond angles, resulting in a decrease in the DE interaction strength. For our sample, the positive values of q P and DT reveal the existence of a FM exchange interaction between the nearest neighbors in the PM region and conrm the presence of a magnetic inhomogeneity. 31,32 Similar results are observed in several manganites 33,34 and cobaltite perovskites, such as La 0.6 Sr 0.4 CoO 3 . 14,26 However, a diminution of magnetization with increasing temperature is clearly observed. Further, it is clear that at T C , the investigated material transits from the FM state to the PM state. This transition is due to the magnetic disorder established as the temperature increases. In this case, the deection of magnetic momentum occurs, and hence, the total magnetic moment of the entire system decreases and compound magnetization gets diminished. Therefore, once the temperature reaches T C , the thermal motion of the molecules of the material affects the ordered spin at the zero eld and the PM behavior is observed instead of the FM behavior.
In order to determine the type of magnetic phase transition in the vicinity of T C , Fig. 5a shows the Arrott curves (M 2 -m 0 H/M) for the prepared La 0.55 Bi 0.05 Sr 0.4 CoO 3 compound. In these curves, it is assumed that the critical exponents follow the mean-eld theory (MFT), where b ¼ 0.5 and g ¼ 1. 38 Fig. 5a shows that in the low-eld region, the nonlinear and curvature characters in M 2 -m 0 H/M parts at T > T C and T < T C are driven toward two opposite directions. The latter phenomenon is essentially due to the misaligned magnetic domains, which reveal the FM-PM separation and indicate that the values of b ¼ 0.5 and g ¼ 1 are inaccurate.
The characteristics of the magnetic phase transition in the La 0.55 Bi 0.05 Sr 0.4 CoO 3 cobaltite can be determined by assessing the feature of the Arrott plots around T C . In our case, no inection or negative slope is observed as a signature of the metamagnetic transition above T C , indicating the nature of the second-order phase transition (SOPT). This is in agreement with those observed in earlier studies. 14,39,40 In general, for SOPT, its thermodynamic function can be expressed in the form of a power law with the aforementioned critical exponents,  to construct tentative Arrott plots and then the select the best one to be the initial Arrott plot for tting the data. The so-called normalized slope (NS) dened as NS ¼ S(T)/S(T C ) at the critical point can be used for effecting further comparisons. Since the modied Arrott plots are a series of parallel lines, the NS of the most satisfactory model should be close to 1 (unity) regardless of temperature. 42 As shown in Fig. 5b, the mean-eld model provides an NS value closest to 1 in the temperature range under investigation. The latter model is the best one to determine the critical exponents as well as to describe the material. The temperature dependencies of c 0 À1 (T) and M SP (T) are shown in Fig. 6a; eqn (1) and (2) are used for tting these data. These ts yielded the critical parameters as b ¼ 0.486 AE 0.017 with T C ¼ 211.572 AE 0.1 K and g ¼ 1.109 AE 0.065 with T C ¼ 212.024 AE 0.107 K. These results are very close to the exponents of the mean-eld model (b ¼ 0.5 and g ¼ 1). It is evident that the obtained value of T C agrees well with that obtained from the M(T) curve. Alternatively, in order to more accurately determine the b, g, and T C parameters, we can use the Kouvel-Fisher (KF) method 43,44 expressed as According to the above equations, the 1/b and 1/g slopes are obtained by linear tting and the value of T C is obtained from the intercepts on the temperature axis. The results of the best ts are shown in Fig. 6b 26 The b value of their sample was located between those expected from the mean-eld model and 3D Heisenberg model, while the g value is close to the value obtained from the 3D Ising model. Consequently, it is clear that the replacement of lanthanum by 5% Bi in the La 0.6 Sr 0.4 CoO 3 sample induced a long-range magnetic order and modied the class of universality of the sample. In general, these characteristics are related to the differences in the sintering temperatures, preparation routes, particle sizes and shapes, and local geometric structures, resulting in various inhomogeneities and magnetocrystalline anisotropies. In our case, the obvious differences in the class of universalities of La 0.55 Bi 0.05 Sr 0.4 CoO 3 and the parent compound are due to the inuence of the replacement of La 3+ ion (with zero magnetic moment) by Bi 3+ ion (with nonzero magnetic moment). Therefore, the insertion of 5% Bi may contribute toward the magnetic interactions along with Co 3+ and Co 4+ ions and causes a difference in the critical behavior in the aforementioned samples.
In addition, the scaling equation stipulates that the M(m 0 H, T) data in the critical region obeys the scaling relation expressed as 45 where f + and f À are the analytical functions for T > T C and T < T C , respectively. Eqn (8) shows that M (m 0 H, 3)3 Àb vs. m 0 H3 À(b+g) yields two distinct curves: one for T > T C and the other for T < T C .  In this work, the magnetization measurements are made under discrete magnetic elds and temperature intervals. Therefore, the magnetic entropy change can be approximately given by In this equation, M i and M i+1 are the experimental values of magnetization measured at temperatures T i and T i+1 , respectively, under the applied magnetic eld m 0 H i . Fig. 8a shows the behavior of DS m for the La 0.55 Bi 0.05 Sr 0.4 -CoO 3 sample as a function of temperature. These curves exhibit peaks around T C . Immediately below and above T C , the ÀDS m value monotonically increases with an increasing magnetic eld, which corresponds to a magnetic FM-PM transition. The dependence of the magnetic entropy changes on the value of (vM/vT) H has been clearly indicated in eqn (8). Therefore, a large magnetic entropy change usually occurs near T C , where the magnetization changes swily with a variation in temperature. Therefore, the negative sign of the magnetic entropy change conrms the FM character of our sample. 47 The large values of ÀDS m for the La 0.55 Bi 0.05 Sr 0.4 CoO 3 system are due to a secondorder magnetic transition. 48 The magnitude of DS m increases with an increasing strength of m 0 H. The maximum value of DS decreases from 2.66 J kg À1 K À1 for the La 0.6 Sr 0.4 CoO 3 sample prepared by the solid-solid reaction 49 (2.10 J kg À1 K À1 for La 0.6 Sr 0.4 CoO 3 made by the sol-gel method 14 ) to 1.45 J kg À1 K À1 under an applied magnetic eld of 5 T. This indicates that Bi substitution leads to a marginal decrease in the MCE properties with a reduced transition temperature. On the other hand, the obtained value of Bi-doped cobaltite is comparable to those obtained in other cobaltites, 3,14,50,51 indicating that our sample could be used as a refrigerant material in magnetic cooling devices.
In order to determine the magnetic refrigeration efficiency, only the magnitude of the magnetic entropy is insufficient. The relative cooling power (RCP) is another decisive parameter that can be used to select materials for practical applications. RCP can be calculated by the following expression: where dT FWHM is the full width at half maximum of DS M (T). For m 0 H ¼ 5 T, the RCP is $115.5 J kg À1 , which is of the same order of magnitude as those found in other cobaltites, such as La 0.6 -Sr 0.4 CoO 3 , La 0.5 Sr 0.5 CoO 3 , and La 2/3 Sr 1/3 CoO 3 . 49,50,52 Evidently, substituting La 3+ by Bi 3+ , DS M (T) shows a considerably broad variation with temperature around T C as compared with the parent sample. Such an effect is benecial for magnetic refrigeration. Moreover, we can use the obtained DS m curves to accurately distinguish between the order of the PM-FM phase transition according to a phenomenological universal curve of the eld dependence of magnetic entropy change. 53 Such a method has been successfully applied to FM perovskites, such as cobaltites 14,54 and manganites. [55][56][57][58] The universal curve could be plotted by means of the normalized entropy change (DS m / DS peak m ) and rescaling temperature (q) as follows: 53 where T r1 and T r2 denote the temperatures of the two reference points that were selected as those corresponding to DS peak m /2. If all the universal curves of DS m (q) at various magnetic elds collapse onto a single universal curve, the nature of the secondorder transition would be conrmed. As shown in Fig. 8b, it is evident that all the (DS m /DS peak m ) values fall onto one universal curve, which is consistent with the analysis based on the Arrott plots. The eld dependencies of T r1 and T r2 for the investigated sample are shown in the inset of Fig. 8b.
Based on the relationship between the critical exponents and the scaled equation of state 59,60 dened as where a and D are the usual critical exponents, which can be obtained by using D ¼ b + g and a + 2b + g ¼ 2. 61 The latter relation has been successfully applied to several manganite systems. 62,63 This scaling relation is used to conrm the validity of the estimated critical exponents for La 0.55 Bi 0.05 Sr 0.4 CoO 3 . Fig. 8c shows that all the DS m (T) values fall on a universal curve for several applied magnetic elds. The excellent overlap of the experimental data points conrms that the estimated critical exponents and T C for the investigated compound are in obedience with the scaling theory.
Based on the MCE data, the dependence of the magnetic entropy change on the external magnetic eld is analyzed. DS m can be expressed as a power law of the following form: where "a" depends on the temperature and exponent "n" depends, in general, on both the temperature and eld. Fig. 9a shows the temperature dependencies of the exponents a (T) and n(T), which were determined by using eqn (13) from the DS m values at several magnetic elds. From Fig. 9a, it is evident that the value of a (T) increases with the temperature, reaching the value of z0.3 at 210 K. This value is very low as compared to those observed in manganite systems. 63,64 The value of n reaches the minimum of n ¼ 0.989 at T C ¼ 210 K.
Basically, the MFT predicts that for materials with SOPT, the n(T) curve exhibits three regimes: well below T C (n ¼ 1), well above T C (n ¼ 2), and at T C (n ¼ 2/3, which is related to the critical exponents of the transition). 65 The exponent "n" depends on both temperature and eld and can be locally estimated using the following formula: 66 nðT; m 0 HÞ ¼ d lnð|DS|Þ d lnðm 0 HÞ From the curves of n(T, m 0 H) shown in Fig. 9b for the La 0.55 Bi 0.05 Sr 0.4 CoO 3 compound, it is evident that all the curves exhibit the minimum value of n at T C , which is different from the MFT value of n ¼ 2/3. In addition, we observed that the n values are unstable under varying temperature T and eld m 0 H. The minima of the curves with changes in T C with the applied magnetic eld range within 0.861-1.021. This behavior is related to the magnetic disorder and FM clusters in the vicinity of T C . 14,67,68 A similar behavior has been previously reported in other perovskites. 36,63,69,70 In order to verify the collapse or breakdown of n(T, m 0 H) curves under the inuence of different applied elds, we rst arbitrarily selected the reference temperatures (T r ) as those that have n(T r ) ¼ 1.5 (ref. 55) and constructed n(q, m 0 H) as a function of the rescaled temperature q, which is, in turn, obtained as follows: From the inset of Fig. 9b, it is evident that all the n(q, m 0 H) values collapse onto a single universal curve, revealing a universal behavior in La 0.55 Bi 0.05 Sr 0.4 CoO 3 .
Using the MCE data, we calculated the specic heat (DC P ) of La 0.55 Bi 0.05 Sr 0.4 CoO 3 by means of the rst derivative of DS m with respect to temperature: Fig. 10 shows the DC P value of the compound vs. temperature under different magnetic elds. Evidently, the DC P curves represent the alternative changes from negative to positive around T C with a negative value below T C and a positive value above T C , which can be attributed to the FM-PM transition. This behavior has also been observed in other FM systems. 56,[71][72][73] The sum of the two parts is the magnetic contribution to the total of DC P , which has an impact on the heating or cooling power of the magnetic cooling devices. 74 DC P has the advantage of delivering values necessary to select a refrigerant material, which can simplify the design of a magnetic refrigerator.
The DC P values induced by the applied magnetic elds can be plotted onto a universal curve by means of the critical exponents. The scaling method is a result of the scaling hypothesis for FM materials near their magnetic transitions. The scaling of DC P changes are plotted in terms of ÀDC P ðm 0 H; TÞ ðm 0 HÞ 1Àa=D vs: 3 ðm 0 HÞ 1=D ; as shown in the inset of Fig. 10.
The worthwhile overlap of the data points obviously suggests that the obtained exponents (b and g) and T C for the La 0.55 -Bi 0.05 Sr 0.4 CoO 3 sample are in agreement with the scaling hypothesis at various magnetic elds.
Moreover, the obtained magnetic entropy change is used to deduce the spontaneous magnetization in the La 0.55 Bi 0.05 Sr 0.4 -CoO 3 sample. According to the MFT and relationship between the magnetic entropy (S) and magnetization (M), S(s) can be expressed as follows: 75,76 SðsÞ ¼ Furthermore, it should be noted that the compound exhibits spontaneous magnetization below T C (FM state), and consequently, the s ¼ 0 state is certainly not obtained. By considering only the rst term of eqn (18), DS m may be expressed as The latter equation indicates that DS m vs. M 2 plots show a linear variation with a constant slope in the FM region. At  different temperatures, all the curves exhibit a horizontal dri from the origin corresponding to a value of M spon 2 (T). For the PM region, the DS m vs. M 2 plots start at a null M value. 77 Fig. 11 shows the M sp (T) data obtained from the DS m vs. M 2 curves by the intersection of the linearly extrapolated curve with the M 2 axis (inset, Fig. 11). The linear behavior of ÀDS m vs. M 2 conrmed the validity of the linear expansion of eqn (19). In the same gure, we show a comparison between the estimated M sp (T) values obtained from the isothermal (ÀDS m ) vs. M 2 plots and those obtained from the Arrott plots (m 0 H vs. M 2 ). The worthwhile agreement between the aforementioned methods conrms the validity of this process in order to determine the M sp value using a mean-eld analysis of DS m in the La 0.55 -Bi 0.05 Sr 0.4 CoO 3 system. The magnetic behavior of our sample is effectively described by the classical MFT.
Finally, the investigation of the scaling hypotheses of the thermomagnetic properties of the La 0.55 Bi 0.05 Sr 0.4 CoO 3 sample offer the opportunity of using the universal curve in the investigations of novel FM materials on various applied functionalities. Such methods present a simple screening procedure of the performance of FM compounds, simple way to extrapolate results to magnetic elds or temperatures not available in the laboratories, remake the impact of non-saturating conditions, reduce experimental noise, or eliminate the effects of minority magnetic phases.

Conclusion
In summary, we conducted an in-depth investigation on magnetic, critical behavior, and MCE effect on La 0.55 Bi 0.05 -Sr 0.4 CoO 3 cobaltite synthesized via the solid-state reaction. The XRD analysis shows that the sample exhibits a rhombohedral structure with the R 3c space group. The magnetic properties reveal that our sample undergoes a FM-PM second-order magnetic transition, which can be conrmed from the Arrott curves and universal curves of magnetic entropy changes. The critical behavior of the La 0.55 Bi 0.05 Sr 0.4 CoO 3 cobaltite is studied by means of various techniques and validated by using the scaling theory and Widom scaling relation. The obtained critical exponents are close to the theoretical prediction of the mean-eld model values, which implies that long-range interactions dominate the critical behavior in La 0.55 Bi 0.05 Sr 0.4 CoO 3 . Moreover, the experimental magnetic entropy changes, specic heat capacity changes, and local exponents n obtained for several magnetic elds collapse onto a universal curve, con-rming the universal behavior of the MCE properties in this oxide. The estimated spontaneous magnetization value extracted through the analysis of the magnetic entropy change (ÀDS m vs. M 2 ) is consistent with that extracted through the classical extrapolation of the Arrott plots (m 0 H/M vs. M 2 ). Consequently, the magnetic entropy change is a valid approach to determine the spontaneous magnetization of the La 0.55 Bi 0.05 Sr 0.4 CoO 3 compound.

Conflicts of interest
There are no conicts to declare.