Second-Order Phase Transition and the Magnetocaloric Effect in Nanoparticles

In this paper, we present a detailed study of the magnetocaloric effect and critical properties around the ferromagnetic-paramagnetic (FM-PM) phase transition of La_0.7Ca_0.3-xSr_xMnO₃ nanoparticles with x = 0.10, 0.11, and 0.12. The samples were synthesized by a combination of reactive milling and thermal processing. The average crystallite size of nanoparticles estimated from the linewidth of X-ray diffraction peaks by using the Williamson-Hall method is about 50 nm. Under a magnetic field change of 10 kOe, the maximum magnetic entropy change (|ΔS_max|) reaches values of 1.47, 1.42, and 1.38 J·kg^-1·K^-1 for x = 0.10, 0.11, and 0.12, respectively, at around 300 K. The refrigerant capacity is thus in between 44 and 54 J·kg^-1. Particularly, the M² versus H/M curves prove that all the samples exhibit a second-order magnetic phase transition. Based on Landau´s phase-transition theory and careful analyses of the magnetic data around the FM-PM transition region, we have determined the critical exponents β, y, δ, and T_C. Here, the β values obtained are 0.397, 0.453, and 0.456 for x = 0.10, 0.11, and 0.12, respectively, which are in between those expected on the basis of the mean-field theory (β = 0.5) and value of the 3-D Heisenberg model (β = 0.365). The result proves the coexistence of shortand long-range FM interactions in La_0.7Ca_0.3-xSr_xMnO₃ nanoparticles. The nature of this phenomenon is discussed thoroughly.