Long- and short-range magnetic interactions in nanocrystalline lightly Cr‑doped manganites

Abstract

This work investigated the effect of lightly ${\text{Cr}}^{3 + }$-doped ions on the structural, magnetic, and critical behavior of the nominal composition ${\text{La}}_{0.7} {\text{Ca}}_{0.3} {\text{Mn}}_{1 - x} {\text{Cr}}_{x} {\text{O}}_{3}$ $(0 \le x \le 0.09$). Our compounds adopted a single phase with a rhombohedral structure (space group R$\overline{3}$c). Furthermore, a comparative study of the crystallite sizes of compounds by X-ray powder diffraction, XRD, is reported. Individual contributions of the crystallite sizes and lattice microstrains were examined through the Williamson–Hall (W–H) analysis, the size-strain plot (SSP), and Halder–Wagner (H–W) methods. Greater accuracy was noted with W–H, where points were more likely to contact the fitting line than those using other methods. From magnetic data analyzed, a second-order paramagnetic–ferromagnetic phase transition appears at Curie temperatures, $T_{{\text{C}}}$, between $212$ and $261 {\text{K}}$. A deviation from the Curie Weiss law is due to the presence of local inhomogeneities in our samples for $T \ge T_{{\text{C}}}$ characteristic of a Griffiths Phase. The critical coefficient values obtained for β, γ, and δ from different methods are fairly close to the theoretical prediction of the tricritical mean-field model for $x = 0.0$ and $0.03$ and which are in accordance with those predicted by the 3D Ising model for $x = 0.06$. The values found for β, γ, and δ are close to those expected for the mean field $x = 0.09$. In our samples, we found that two types of interactions exist, long-range exchange interactions for $x = 0.0, 0.03$ and $0.06$ and short-range exchange interactions for $x = 0.09$.