Second-Order Phase Transition and the Magnetocaloric Effect in ${\rm La}_{{0.7}}{\rm Ca}_{0.3-{x}}{\rm Sr}_{x}{\rm MnO}_{{3}}$ 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 ${\rm La}_{0.7}{\rm Ca}_{0.3-x}{\rm Sr}_{x}{\rm MnO}_{3}$ 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 $(\vert\Delta S_{\rm max}\vert)$ reaches values of 1.47, 1.42, and 1.38 ${\rm J}\cdot{\rm kg}^{-1}\cdot{\rm K}^{-1}$ for $x=0.10$ , 0.11, and 0.12, respectively, at around 300 K. The refrigerant capacity is thus in between 44 and 54 ${\rm J}\cdot{\rm kg}^{-1}$ . Particularly, the $M^{2}$ 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 $\beta$ , $\gamma$ , $\delta$ , and $T_{C}$ . Here, the $\beta$ 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 $(\beta=0.5)$ and value of the 3-D Heisenberg model $(\beta=0.365)$ . The result proves the coexistence of short- and long-range FM interactions in ${\rm La}_{0.7}{\rm Ca}_{0.3-x}{\rm Sr}_{x}{\rm MnO}_{3}$ nanoparticles. The nature of this phenomenon is discussed thoroughly.