Critical behavior near the ferromagnetic–paramagnetic phase transition in La0.5Pr0.3Ba0.2Mn1−xTixO3 (x = 0.0 and 0.1)

Abstract

The $${\text{La}}_{0.5 } { \Pr }_{0.3} {\text{Ba}}_{0.2} {\text{Mn}}_{1 - x} {\text{Ti}}_{x} {\text{O}}_{3}$$ (x = 0.0 and 0.1) compounds were elaborated by the solid-state reaction method. The X-ray diffraction characterization has indicated that these samples crystallized in the rhombohedral symmetry with $$R\bar{3}C$$ space group. The magnetic results which we obtain indicated that both samples show a paramagnetic–ferromagnetic transition with decreasing Curie temperature ($$T_{\text{C}}$$) from 170 K (x = 0.0) to 110 K (x = 0.1). The zero-field cold curve for x = 0.1 compound exhibit a clear cusp at low temperature (T = 35 K) that is generally related to a spin-glass or a cluster-glass state. Furthermore, the critical exponents’ values were founded by different techniques. Therefore, the average values of the critical exponent and the critical temperature obtained by the various methods are ($$\beta_{\text{moy}}$$ = 0.296; $$\gamma_{\text{moy}}$$ = 1.126; $$\delta_{\text{moy}}$$ = 4.875; $$T_{\text{C}}$$ = 177.63) and ($$\beta_{\text{moy}}$$ = 0.26; $$\gamma_{\text{moy}}$$ = 1.081; $$\delta_{\text{moy}}$$ = 5.155; $$T_{\text{C}}$$ = 109.99 K) for x = 0.0 and 0.1, respectively. The obtained critical exponents are in agreement with those forecasted out by the 3D-Ising model and the tricritical mean-field model for x = 0.0 and 0.1, respectively.