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Magnetic properties of perovskites La$_{0.7}$Sr$_{0.3}$Mn$_{0.7}^{3+}$Mn$_{0.3-x}^{4+}$Ti$_x$O$_3$:Monte Carlo simulation versus experiments

This work presents a Monte Carlo study of the phase transition in the perovskites La$_{0.7}$Sr$_{0.3}$Mn$_{0.7}^{3+}$Mn$_{0.3-x}^{4+}$Ti$_x$O$_3$ ($x$= 0.1, 0.2, and 0.25). We take into accountnearest-neighbor (NN) interactions between magnetic ions Mn$^{3+}$($S=2$) and Mn$^{4+}$($S=3/2$) using a spin model describing a strong anisotropy on the $z$ axis. We have calculated the uniform and staggered magnetizations as well as the Edwards-Anderson order parameter as functions of temperature, with and without an applied magnetic field. Fitting the experimental Curie temperature at $x=0$, we estimated values of various exchange interactions in the system. The dominant one is that between Mn$^{3+}$ and Mn$^{4+}$ which is at the origin of the ferromagnetic ordering. Effects of the very small interaction $J\_2$ between NN Mn$^{3+}$ is analyzed: we show that it can cause an antiferromagnetic phase above $T\_c$ which disappears at smaller $J\_2$ or at Mn$^{3+}$ concentrations smaller than 0.55. Our results show a good agreement with experiments on the magnetizations for substitution concentration $x=0.1$, 0.2 and 0.3. We also studied the applied-field effect on the magnetization and our obtained results are compared with experiments performed at $x=10\%$.