Short-range magnetic behavior in manganites La0.93K0.07Mn1-xCuxO3 (0.0 ⩽ x ⩽ 0.09) above the Curie temperature

Manganites La_0.93K_0.07Mn_1-xCu_xO₃ $(0.0\,\leqslant\,x\,\leqslant\,0.09),$ prepared by the solid state reaction method at high temperature, were studied structurally and magnetically. The unit cell parameters, as well as bond length ${{\text{d}}_{({\text{Mn,Cu)-O}}}}{\text{ }}\left({{{\unicode{x00C5}}}} \right)$ and the bond angle ${\theta _{({\text{Mn,Cu)-}}{{\text{O}}_{\text{1}}}{\text{-Mn}}}}$ , were determined from the Rietveld refinement of the x-ray diffraction patterns. The Fourier-transform infrared spectroscopy analysis shows that Cu²⁺ substitution induces variations in the vibration modes of the MnO₆ octahedra. Magnetization vs. temperature ${\text{M}}\left( T \right)$ at low magnetic field $H = 0.01{ }T$ were performed in the range $5 < T < 300{{\,K}}$ under field coolingand zero field cooling conditions. All the samples exhibited a second-order paramagnetic-ferromagnetic (FM) transition at Curie temperature, ${T_{\text{C}}}$ , in the range between 199 and 285 K. The inverse susceptibility, ${\chi ^{ - 1}}\left( T \right){ }$ exhibits a linear Curie-Weiss (C-W) behavior for $T --> T_{{\text{CW}}}^{\text{*}}$?> , while for ${T_{\text{C}}} < T < T_{{\text{CW}}}^{\text{*}}$ , it shows a deviation from the linear behavior predicted by the Heisenberg model. The mentioned deviation of ${\chi ^{ - 1}}\left( T \right)$ means that a short ferromagnetic state formation is present even for $T --> {T_{\text{C}}}$?> , which were characterized by the experimental effective magnetic moment, $\mu _{{\text{eff}}}^{{\text{exp}}}.$ A null spontaneous magnetization, ${{\text{m}}_{\text{S}}},$ above ${T_{\text{C}}}$ was evaluated for all samples by using the Kouvel-Fisher method. This work evaluates the short-range FM clusters by means of an extension of the C-W approach to the ${T_{\text{C}}} < T < T_{{\text{CW}}}^{\text{*}}$ region, i.e., ${ }\mu _{{\text{eff}}}^{{\text{exp}}}\left( T \right) = 2.3\sqrt {{\text{C}}\left( T \right)} { }{\mu _{\text{B}}}$ . Finally, the critical coefficient values, $\beta $ and $\gamma $ , showed that the 3D Heisenberg model fits adequately the $x = 0.0{ }$ and $x = 0.03$ samples, while the 3D Ising model fits the $x = 0.09$ sample.