Magnetic and magnetocaloric properties in Ba-doped La_0.7Ca_0.3MnO₃ nanoparticles

La_0.7Ca_0.3−xBa_xMnO₃ nanoparticles with the crystalline size d = 38 and 39 nm for x = 0.025, and 0.05, respectively, were synthesized by utilizing the solid-state reaction and mechanical ball milling methods. We have used the Banerjee's criteria, the mean-field, and the thermodynamic theories, and isothermal magnetization, M(H), data around Curie temperature (T_C) to investigate the magnetic phase transformation and the temperature (T) and magnetic field (H) dependences of magnetic entropy change, ΔS_m(T, H), for nanoparticles. These exhibit the samples undergoing a second-order magnetic phase transition with an existence of the short-range ferromagnetic order in the samples. Under an applied magnetic field change ΔH = 30 kOe, the maximum value of ΔS_m (denoted as |ΔS_max|) are obtained about 4.4 J kg⁻¹ K⁻¹ corresponding to a relative cooling power (RCP) value about 140 J kg⁻¹. Field dependences of |ΔS_max| and RCP can be expressed by the power laws, |ΔS_max| = a × Hⁿ and RCP = b × H^N, where a and b are coefficients, n and N are the field exponents, respectively. Interestingly, all the ΔS_m(T, H) curves measured at different applied fields are collapsed onto a universal curve, ΔS_m(T, H)/ΔS_max versus θ = (T − T_C)/(T_r − T_C), where T_r is the reference temperature. - Highlights: • An existence of the short-range FM order in the La_0.7Ca_0.3−xBa_xMnO₃ nanoparticles. • High magnetic entropy change, wide operative temperature range, and high RCP value. • Field dependences of |ΔS_max| and RCP can be expressed by the power laws. • All the ΔS_m(T, H) data are followed a universal master curve