1 Introduction

Energy consumption is increasing rapidly day by day due to the increasing human population and industrial growth. The required energy is provided from non-renewable and limited fossil fuels. In addition to these, fossil fuels directly cause an increase in CO2 emissions [1]. For the future of our world, it is imperative to make regulations in areas with high energy consumption in order to save energy and reduce its negative effects on the environment. Priority arrangements should be made in cooling technologies that consume too much energy and cause climate change and global warming [2]. Today, cooling technologies based on the gas compression principle are widely used. These systems have negative effects on the environment, and their energy consumption is quite large [3]. In addition, since the arrangements that can be made to increase the energy efficiency of these systems are limited and require high costs, it is necessary to work on the development of new systems that could be used instead of these systems.

Magnetic refrigeration (MR) systems with better energy consumption and efficiency [4] are considered the future cooling system. It is known that MR systems are also eco-friendly since a solid magnetic material is used as a cooling element in these systems [5]. The working principle of MR systems is magnetocaloric effect (MCE), which is defined as the change in the temperature of the magnetic material as a result of the change in the entropy of a magnetic material subjected to a magnetic field [6, 7]. The magnetocaloric properties of a material are defined by two fundamental quantities: magnetic entropy change (\(- \Delta S_{M}\)) and adiabatic temperature change \(\left( {\Delta T_{ad} } \right)\) [8]. The \(\Delta T_{ad}\) value is determined using direct methods, while \(- \Delta S_{M}\) is calculated indirectly from magnetization measurements depending on magnetic field [9].

Gadolinium (Gd) and Gd alloys have been used as cooling elements in many MR systems designed and developed to date [10, 11]. However, commercial use of these MR systems is not possible for some reasons [8, 11,12,13]. In the view of the applications, the most essential requirement is to provide new materials with large MCE in a low magnetic field and near room temperature. In addition, the type of magnetic phase transition and relative cooling power (RCP) are critical parameters [8].

Perovskites, which exhibit extraordinary chemical and physical properties, are one of the most intensively researched samples and have influential applications in many fields [14,15,16]. Magnetocaloric properties of La-based perovskite manganites have been studied in detail due to various properties such as high chemical stability, adjustable magnetic phase transition temperature, inexpensive raw material, and \(- \Delta S_{M}\) comparable to Gd [17,18,19,20,21]. The ratio between the number of Mn4+ and Mn3+ ions (depends on the doping level, x), the average size of the cation at the A-site \(\left( \langle{r_{A} }\rangle \right)\) [22], and the degree of disorder at the A-site [23] affect the magnetic and magnetocaloric properties of manganites. Among the studied La-based manganites, La0.57Nd0.1Sr0.33MnO3 sample shows paramagnetic (PM)-ferromagnetic (FM) phase transition above room temperature [24]. Ca-doped La-based manganites exhibit magnetic phase transition below room temperature and have acceptable \(- \Delta S_{M}\)[25]. In the literature, there are studies reporting \(- \Delta S_{M}\) values of Ca-doped LaMnO3 manganites are comparable to Gd, and Ca content induces an increment in \(- \Delta S_{M}\) values [26,27,28]. Ca ion has 2 + valence state and its ionic radius is smaller than Sr but close to La and Nd ions [29]. In the case of partial Ca addition, the Mn3+/ Mn4+ ratio remains constant, while a change occurs in the \(\langle{r_{A}}\rangle\) and the degree of disorder at the A site. This plays a critical role in the variation of magnetic and magnetocaloric properties. Moreover, it is possible to say that TC increases with increasing Sr concentration, and \(- \Delta S_{M}\) value affects positively with increment in Ca-content [30,31,32]. In this study, the structural, magnetic, and magnetocaloric properties of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) manganites have been investigated in detail. The main aim of this study is to adjust the TC towards room temperature by partial substitution of Sr with Ca in the La0.57Nd0.1Sr0.33MnO3 manganite system.

2 Experimental details

In this study, La0.57Nd0.1Sr0.33-xCaxMnO3 (x = 0.0, 0.10, 0.20, and 0.30) manganite samples were prepared by solid-state method. La2O3 (99.99%, Sigma Aldrich), Nd2O3 (99.99%, Sigma Aldrich), SrO (99.99%, Sigma Aldrich), CaO (99.995%, Sigma Aldrich), and MnO2 (99.99%, Sigma Aldrich) starting materials were used. The starting compounds were weighed in accordance with stoichiometric ratios. By using an agate mortar, the weighed raw materials were mixed and ground for a total 60 min (6 times 10 min). Afterwards, the mixture was calcined at 600 °C for 6 h. The grinding and mixing processes were repeated under the same conditions. Finally, the samples were pelleted and sintered at 1200 °C for 24 h. In forthcoming sections, the final samples were labeled as LNSM, LNSCM-1, LNSCM-2, and LNSCM-3 for undoped and 1%, 2%, and 3% Ca-added samples, respectively. To obtain information about crystal symmetry, lattice parameters and unit cell volume of the samples, X-ray diffraction (XRD) measurements were performed by a Philips PANalytical Empyrean X-ray diffraction meter. The XRD data were collected at room temperature in 0.0131 degree increments over the range of 20–80°. Scanning electron microscope (SEM) with energy dispersive X-ray spectrometry (EDS) was used to investigate the grain structure and elemental analysis of the samples. Magnetic measurements depending on temperature (M(T)) and magnetic field (M(H)) were performed by a physical property measurement system (PPMS) equipped with a vibrating sample magnetometer (VSM) module. In order to determine the magnetic phase transition temperature, described as Curie temperature (TC), a 10 mT weak field was applied to the samples in zero–field-cooled (ZFC) and field-cooled (FC) modes in the temperature range of 5–380 K. The magnetization measurements as a function of the magnetic field were made to calculate the \(- \Delta S_{M}\) of the samples and to identify the type of magnetic phase transition.

3 Results and discussion

The XRD patterns of the samples recorded at room temperature are given in Fig. 1. The observed and calculated diffraction patterns were represented by solid circles and lines, respectively. Bragg positions are marked with green vertical bars. The difference between the observed and calculated diffraction pattern was shown by the blue line. In the experimental test range, it was determined that the samples consisted of a single phase. The structural parameters of the samples were refined using Rietveld’s profile-fitting method [33] and results are given in Table 1. The lattice parameters of the samples do not show a systematic change with the increasing Ca concentration. However, the unit cell volume of the samples decreases almost linearly with the increasing Ca concentration. It is thought that this decrement may be related to the smaller ionic radius of the Ca2+ ion than Sr2+ ion [29]. The samples were crystallized in rhombohedral structure. Goldschmidt tolerance factor (tG) which is defined as the geometric measure of the size mismatch of perovskite, is given by the following formula [32]:

$$t_{G} = \frac{{\left( \langle{r_{A}\rangle + r_{O} } \right)}}{{\sqrt 2 \left( \langle{r_{B}\rangle + r_{O} } \right)}}.$$
(1)
Fig. 1
figure 1figure 1

XRD patterns of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples a LNSM, b LNSCM-1, c LNSCM-2, d LNSCM-3

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Table 1 Structural parameters of the La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples
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In the equation, the average ionic radii of A and B-site are denoted by \(\langle r_{A}\rangle\) and \( \langle r_{B}\rangle\), respectively. The ionic radius of the oxygen ion is abbreviated as \(r_{O}\). It is known that the perovskite structure is preserved within the limits of 0.75 < tG < 1.0 [32]. The crystal structure is cubic, rhombohedral, and orthorhombic for tG = 1, 0.96 < tG < 1.0, and tG < 0.96, respectively [34]. Based on Shannon’s list of effective ionic radii, \( \langle r_{A} \rangle\) and tG values of the samples were calculated for coordination number 12. According to tG value given in Table 1, it was confirmed that the samples were crystallized in rhombohedral symmetry. It was observed that the crystal symmetry of the samples did not change, although increasing Ca concentration caused a decrease in \( \langle r_{A} \rangle\) and tG values. The physical properties of the manganites also change with A-site disorder induced by the A-site ionic radius variance, (σ2), given in the following equation [35, 36]:

$$\sigma^{2} = \sum (q_{i} r_{i}^{2} -\langle r_{A} \rangle^{2} ,$$
(2)

where qi and ri show atomic concentration and ionic radius of the i-type ion, respectively. Calculated σ2 values for samples decrease linearly with increasing Ca concentration. It is inevitable that this result will cause a change in the magnetic and magnetocaloric properties of the samples.

Using the Scherrer formula, the average crystallite size (DXRD) can be calculated from the following equation [37]:

$$D_{XRD} = \frac{\kappa\lambda }{\beta\cos\theta},$$
(3)

where \(\lambda\) and κ are the X-ray wavelength (Cu–Kα = 1.5406 Å) and crystallite shape factor (0.9), respectively. β is the peak full width at half maximum at the observed peak angle. DXRD values calculated from the most intense XRD peaks of the samples are given in Table 1. For LNSM sample, this value was calculated as 67.4 nm. Although this value initially increased with the replacement of Sr with Ca, a linear decrease observed with the increase of Ca ratio.

The chemical compositions of the samples were examined by EDS analysis. Figure 2 shows the EDS spectra of the samples. All samples contain the expected chemical elements and no trace of impurity elements. The atomic percentages of the samples are given in Table 2. The obtained compositions from EDS are very close to the nominal compositions of the samples. The SEM images of the samples are given insets of Figs. 2. It can be seen that the samples consist of different polygonal-shaped grains with different sizes, and the boundaries of the grains are clear. There is no linear variation between Ca concentration and grain size. However, it was observed that the clarity of the grains boundaries increased with the increase in Ca concentration.

Fig. 2
figure 2figure 2

EDS graphs of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples a LNSM, b LNSCM-1, c LNSCM-2, d LNSCM-3. Insets show SEM images of the samples at 20 KX magnification

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Table 2 Atomic percentages of the La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples
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Figure 3 shows the M(T) curves obtained under a weak magnetic field of 10 mT at ZFC (open circle) and FC (solid circle) modes in the temperature range of 5–380 K. While the ZFC and FC curves diverge from each other by following an irreversible path in the FM region, they show a reversible trend in the PM region. This bifurcation can occur for a variety of reasons, such as magnetic inhomogeneity [38], domain pinning effect [39], and canted nature of the spins [18]. In the PM-FM transition region, ZFC and FC curves exhibit a sharp transition. It promisingly implies a high \(- \Delta S_{M}\) [39, 40]. An increase was observed in the ZFC and FC curves of the LNSCM-1 sample (see Fig. 3b), indicating the presence of a charge-ordering (CO) state [41]. The TC is mostly determined from the inflection point of dM/dT curve obtained from the M(T) curve. Figure 4a represents the dM/dT curves of the samples. These curves have a single inflection peak. This implies that samples contain a single magnetic phase. TC decreased from 356 to 224 K with increasing Ca concentration (from x = 0.0 to 0.30). When Ca2+ is substituted for Sr2+ in the samples, the Mn3+/Mn4+ ratio does not change. However, the \(\langle r_{A}\rangle\) and σ2 values of the samples decrease with increasing Ca concentration due to the difference between the ionic radii of Ca and Sr ions. As a result, the structural distortions occur, and a decrement in TC value can be observed. This may arise from the decreasing of \(\langle r_{A} \rangle\) and σ2 values [31]. The obtained results are compatible with those reported in the literature [42, 43]. Figure 4b shows the temperature dependence of the inverse magnetic susceptibility, 1/χ(T), of the curves obtained using the ZFC magnetization data. The 1/χ(T) and the fitting results by using the Curie Weiss (CW) law are presented by symbols and lines, respectively. In the paramagnetic region, for LNSM and LNSCM-1 samples, the 1/χ(T) curve shows a linear variation indicating that it obeys the CW law given by χ = C/(T−θ), where C is the Curie constant and θ is the paramagnetic Curie temperature. On the other hand, 1/χ(T) curve of LNSCM-2 and LNSCM-3 samples show a deviation from the CW law pointing out the presence of the Griffiths phase [44]. The θ value of the samples was determined from the 1/χ(T) curves. The θ values of the samples are given in Table 2. The positive value of θ implies that the interaction between the nearest spins is the FM [45]. It is seen that the θ value is slightly larger than the TC value for LNSCM-2 and LNSCM-3 samples. This difference may be due to the presence of short-range FM order related to the existence of magnetic inhomogeneity above TC [46]. The θ temperature shows a reduction with increasing Ca concentration. This verifies the weakening FM double exchange interactions [47]. The C constant is given by \(C = \frac{{N_{A} \mu_{B}^{2} }}{{3k_{B} }}\mu_{eff}^{2}\); where NA, kB, and µB represent Avogadro’s number, Boltzman’s constant, and the Bohr magneton, respectively. The µeff denotes effective magnetic moment. To calculate the experimental \(\mu_{eff} \left( {\mu_{eff}^{exp} } \right)\), C constant is derived from the linear fitting of 1/χ(T) curve of the samples. By using C constant equation, the \(\mu_{eff}^{exp}\) value was calculated experimentally as 2.89, 2.44, 2.40, and 2.61µB for LNSM, LNSCM-1, LNSCM-2, and LNSMC-3 samples, respectively. The \(\mu_{eff}^{exp}\) values show a nonlinear variation with increasing Ca concentration. This may be related to the order of magnetic inhomogeneity of the samples. The theoretical effective magnetic moment \(\left( {\mu_{eff}^{theo} } \right)\) was calculated by using the following equation [48]:

$$\mu_{eff}^{theo} = \sqrt {0.67\left[ {\mu_{eff} \left( {Mn^{3 + } } \right)} \right]^{2} + 0.33\left[ {\mu_{eff} \left( {Mn^{4 + } } \right)} \right]^{2} + 0.1\left[ {\mu_{eff} \left( {Nd^{3 + } } \right)} \right]^{2} }$$
(4)

where \(\mu_{eff} \left( {Mn^{3 + } } \right) = 4.9\), \(\mu_{eff} \left( {Mn^{4 + } } \right) = 3.87\), and \(\mu_{eff} \left( {Nd^{3 + } } \right) = 3.62\) µB [49]. The \(\mu_{eff}^{theo}\) value is larger than the \(\mu_{eff}^{exp}\) value derived from the linear fitting of 1/χ(T) curve. According to the results, it can say that large spin ordering occurs in samples. Similar results have been observed in manganites [46, 50].

Fig. 3
figure 3

The M(T) curves of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples a LNSM, b LNSCM-1, c LNSCM-2, d LNSCM-3

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Fig. 4
figure 4

a dM/dT (T) and b 1/χ(T) curves of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples

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To obtain deep information about the magnetic behavior of the samples, the M(H) measurements have been performed up to 5 T with a temperature increase of 4 K around TC. Figure 5 shows the M(H) curves of the samples. Below TC, the magnetization of the samples varies rapidly with the applied magnetic field and reaches saturation above 0.5 T. This behavior is characteristic property of FM material. Except for the LNSM sample, the M(H) curves show a linear variation with the magnetic field at temperatures above TC. The linear variation of the M(H) curves of the materials with the applied field confirms that the samples exhibit PM properties at temperatures above TC. As seen in Fig. 5a, the M(H) curve of the LNSM sample does not exhibit a linear variation, indicating that it does not show pure paramagnetic properties, which may arise from the presence of FM clusters on the TC [51, 52]. Above and below TC, the behavior of the M(H) curves confirms a magnetic phase transition from FM to PM with increasing temperature. The results obtained from M(H) measurements are in agreement with M(T). The M(H) curves of the LNSCM-3 sample (see Fig. 5d) show a S-shaped change in the temperature region of 212–252 K. This change points to the metamagnetic transition, which expresses the coexistence of FM and AFM (antiferromagnetic)-CO phases [53]. The metamagnetic transition indicates the possibility of a large \(- \Delta S_{M}\) around TC [54].

Fig. 5
figure 5

The M(H) curves of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples a LNSM, b LNSCM-1, c LNSCM-2, d LNSCM-3

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The numerical value of \(- \Delta S_{M}\) is calculated by using the following equation [55];

$$- \Delta S_{M} \left( {H,T} \right) = \sum \frac{{M_{i} - M_{i + 1} }}{{T_{i + 1} - T_{i} }}\Delta H_{i}$$
(5)

where the experimental values of magnetization under the magnetic field Hi at temperatures Ti and Ti+1 are represented by Mi and Mi+1, respectively. The \(- \Delta S_{M}\) values of the samples were calculated for different magnetic fields, and the temperature dependence of the \(- \Delta S_{M}\) values (\(- \Delta S_{M}\) (T)) was obtained. Figure 6 shows the \(- \Delta S_{M}\) (T) curves of the samples. Around TC, the \(- \Delta S_{M}\) (T) curves exhibit a maximum peak called as maximum magnetic entropy change value (\(- \Delta S_{M}^{max} )\). The value of \(- \Delta S_{M}^{max}\) increases with increasing applied magnetic field. This is related to the orientation of the magnetic moments with the magnetic field [56]. The \(- \Delta S_{M}^{max}\) value of the samples for 2 T was calculated as 2.53, 2.85, 3.17, and 5.85 Jkg−1 K−1 for LNSM, LNSCM-1, LNSCM-2, and LNSCM-3, respectively. It is observed that the \(- \Delta S_{M}^{max}\) values of the samples enhance with increasing Ca concentration in agreement with the literature [30, 57]. A comparison of the \(- \Delta S_{M}^{max}\) values of LNSCM-2 and LNSCM-3 samples with similar materials reported in the literature has given in Table 4 [24, 49, 58,59,60,61,62]. The \(- \Delta S_{M}^{max}\) value of the LNSCM-3 sample is larger than that obtained in Gd [63]. However, this sample shows a magnetic phase transition at 224 K. Therefore, this sample can be considered as a cooling sample for low-temperature MR applications. Moreover, the LNSCM-2 sample, which transitions around room temperature, may be a good candidate for room temperature MR applications as it has an acceptable value of \(- \Delta S_{M}^{max}\) under low magnetic field.

Fig. 6
figure 6

−ΔSM(T) curves of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples a LNSM, b LNSCM-1, c LNSCM-2, d LNSCM-3

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One of the critical criteria in consideration of a material as a cooling element for magnetic cooling systems is RCP. This parameter can be calculated from \(- \Delta S_{M}\) (T) curves by \({\text{RCP}} = \left| { - \Delta S_{M}^{max} } \right| \times {\updelta }T_{FWHM}\) where \({\updelta }T_{FWHM}\) is the full width at half maximum of the \(- \Delta S_{M}\) (T). The RCP value for 2 T of the samples was determined and is given in Table 3. The RCP value of the samples shows a linear increment with increasing Ca concentration. The RCP value of other magnetic compounds is listed in Table 4 for comparison purposes.

Table 3 The temperatures TC and θ and some magnetocaloric properties of the La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples
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Table 4 Comparison of \(- \Delta S_{M}^{max}\) and RCP values of LNSCM-2 and LNSCM-3 samples with some similar manganites found in the literature
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Magnetocaloric materials are classified as first- and second-order magnetic phase transition in terms of the nature of magnetic phase transition. Since first-order magnetocaloric materials show thermal and magnetic hysteresis, they are not favorable for magnetic cooling systems. Although both groups have advantages and disadvantages relative to each other, the material that can be used for magnetic cooling systems should exhibit a second-order phase transition since it does not show thermal and magnetic hysteresis [64]. The character of magnetic phase transition is generally used by the Banerjee criterion [65]. According to this criterion, Arrott curves (H/M vs. M2) are obtained by using the data obtained from the M(H) measurements. The sign of the slope of these curves plays a decisive role in determining the type of magnetic phase transition. Around TC, the positive slope of Arrott plots indicates the second-order magnetic phase transition, while the negative slope indicates first-order magnetic phase transition. Figure 7 shows the Arrott plots of the samples. It is possible to say that these samples exhibit a second-order magnetic phase transition due to the positive slope of the Arrott plots around TC. Another method for determining magnetic phase transition characteristic is universal master curve proposed by Franco et al. [66]. According to this method, the universal curve can be normalized to each isofield \(- \Delta S_{M} \left( T \right)\) curves by using \(- \Delta S_{M}^{max}\) and rescaling the temperature axis based on the following equations:

$$\theta = \left\{ {\begin{array}{*{20}c} { - \left( {T - T_{C } } \right)/\left( {T_{r1} - T_{C} } \right) T \le T_{C} } \\ { \left( {T - T_{C } } \right)/\left( {T_{r2} - T_{C} } \right) T > T_{C} } \\ \end{array} } \right.$$
(6)
Fig. 7
figure 7

Arrott plots of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples a LNSM, b LNSCM-1, c LNSCM-2, d LNSCM-3

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In Eq. 6, Tr1 and Tr2 represent the temperatures above and below TC. The universal curve of the samples is given in Fig. 8. It is observed that the curves obtained from different magnetic fields overlap. This indicates that a second-order magnetic phase transition has occurred [67]. Hence, it can be said that Banerjee criterion and Franco’s universal curve method are in good agreement with each other for the samples studied.

Fig. 8
figure 8

Rescaled universal master curves obtained under different magnetic fields of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples a LNSM, b LNSCM-1, c LNSCM-2, d LNSCM-3

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Amaral et al. [68,69,70] have proposed a succeeding model based on Landau’s theory to explain the contribution of magnetoelastic and electron interactions in manganites. From energy minimization, a magnetic equation of state based on this theory can be written as follows [69]:

$$\frac{H}{M} = A + BM^{2} + CM^{4} .$$
(7)

Magnetic entropy is obtained by differentiating the magnetic part of the free energy with respect to the temperature.

$$S_{M} \left( {T,H} \right) = - \frac{1}{2}A^{\prime}\left( T \right)M^{2} - \frac{1}{4}B^{\prime}\left( T \right)M^{4} - \frac{1}{6}C^{\prime}\left( T \right)M^{6}$$
(8)

\(A^{\prime}\left( T \right), \, B^{\prime}\left( T \right)\), and \(C^{\prime}\left( T \right)\) are the derivatives of the Landau parameters (A, B, and C) given in Eq. 7. The temperature dependence of Landau’s parameters can be determined from the linear fitting of the Arrott plots. There is an important physical meaning to these parameters [71]. Namely, parameter \(A\left( T \right)\) gives information about magnetic susceptibility and gets minimum and positive values at TC. To determine magnetic phase transition type, \(B\left( T \right)\) value at TC is checked. If its value is positive at TC, the magnetic phase transition is second order; if not, it is first order. The A\(\left( T \right)\) and B\(\left( T \right)\) parameters are presented in Fig. 9 (for clarity only LNSCM-2 sample is given). All positive values confirm that the magnetic phase transition is second order for all samples. In addition, the obtained results from Banerjee’s criterion, Franco’s universal master curve, and Landau’s theory are compatible with each other. The \(- \Delta S_{M}\) values of the samples were theoretically calculated for different magnetic fields by using Eq. 8 and the derivatives of Landau’s parameters. Figure 10 exhibits the variations of experimental and theoretical values of \(- \Delta S_{M}\) as a function of the temperature under 5 T. Solid symbols and line represent the experimental and theoretical calculation (based on the Landau theory), respectively. The experimental and theoretical \(- \Delta S_{M}\) values of the samples are in agreement with each other at TC and temperatures above TC. This implies that the magnetoelastic coupling and electron interaction influence are an important factor for magnetocaloric properties [72]. However, below TC, it is observed that there is a small-scale difference between the experimental and theoretical values. This may arise from the presence of AFM domains in the majority FM phase [73].

Fig. 9
figure 9

The temperature dependence of A and B Landau’s parameters for LNSCM-2 sample

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Fig. 10
figure 10

The experimental and theoretical \(- \Delta S_{M} \left( T \right)\) curves of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples under 5 T magnetic fields

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4 Conclusion

In this study, the structural, magnetic, and magnetocaloric properties of La0.57Nd0.1Sr0.33-xCaxMnO3 (0.0 ≤ x ≤ 0.3) samples were investigated. It was observed that there were small differences in the lattice parameter and unit cell volume of all samples crystallized in the rhombohedral symmetry. From the M(T) measurements performed to determine the dependence of magnetization on temperature and TC, it was detected that the samples showed a transition from the FM to PM phase with the increasing with temperature. The \(- \Delta S_{M}^{max}\) values of the samples \(- \Delta S_{M}\) were calculated as 2.53, 2.85, 3.17, and 5.85 J kg−1 K−1 under 2 T magnetic fields. For the same magnetic field change, the RCP values were also calculated. It is observed that the increasing of Ca content induces an increasing in the \(- \Delta S_{M}^{max}\) and RCP values and a decrement in the TC. The \(- \Delta S_{M}^{max}\) and RCP value obtained for the LNSCM-2 sample exhibiting a magnetic phase transition around room temperature is an acceptable size for MR applications in this temperature range. In addition, the \(- \Delta S_{M}^{max}\) value of LNSCM-3 sample is larger than Gd for the same magnetic field change. This sample can be considered as a working material for the low-temperature magnetic refrigeration systems. The type of magnetic phase transition was determined using Banerjee’s criterion, Franco’s universal master curve, and Landau theory. All samples show second-order magnetic phase transition. All these experimental findings and theoretical calculations show that Ca ions are suitable doping agents for La0.57Nd0.1Sr0.33MnO3 system. To increase both \(- \Delta S_{M}\) and TC (around TC), different Ca contents (especially 0.15 ≤ x ≤ 0.3) will be prepared in next studies.