Investigation of Low Temperature Non-Linear Magnetization Behavior in Al and Ga$-$ Substituted La$_{\mathrm{0.4}}$Bi$_{\mathrm{0.6}}$Mno$_{\mathrm{3}}$ Manganites.

Low temperature magnetization measurements have been carried out for the samples containing Al and Ga at B-site in La$_{\mathrm{0.4}}$Bi$_{\mathrm{0.6}}$MnO$_{\mathrm{3}}$ manganites. The magnetization (M) vs. T(K) data shows strong ferromagnetic behavior with highest magnetization of 6.45 emu/g for La$_{\mathrm{0.4}}$Bi$_{\mathrm{0.6}}$Mn$_{\mathrm{0.95}}$Al$_{\mathrm{0.05}}$O$_{\mathrm{3}}$ and 5.40 emu/g for La$_{\mathrm{0.4}}$Bi$_{\mathrm{0.6}}$Mn$_{\mathrm{0.90}}$Al$_{\mathrm{0.1}}$O$_{\mathrm{3}}$ samples respectively for an applied magnetic field of H$=$100 Oe at T$=$20 K. Similarly at T$=$20 K for La$_{\mathrm{0.4}}$Bi$_{\mathrm{0.6}}$Mn$_{\mathrm{0.95}}$Ga$_{\mathrm{0.05}}$O$_{\mathrm{3}}$ the highest magnetization (M$_{\mathrm{S}})$ was found to be 5.44 emu/g and for La$_{\mathrm{0.4}}$Bi$_{\mathrm{0.6}}$Mn$_{\mathrm{0.90}}$Ga$_{\mathrm{0.1}}$O$_{\mathrm{3}}$ the M$_{\mathrm{S}}$ is 5.05 emu/g. The decrease in magnetization with both Al and Ga substitution produces magnetic dilution with increasing concentrations. Both Al and Ga substituted samples exhibit non-linear behavior in their magnetization (M$_{\mathrm{NL}})$ curves around 40$-$120 K due to the frustrations arising from mismatch in their magnetic spin arrangements. The quantity non linear susceptibility, $\chi _{\mathrm{NL}}= \quad -$M$_{\mathrm{NL}}$/H, diverges as the temperature approaches the frustrated region T$_{\mathrm{f}}$ from above (i.e.T$_{\mathrm{C}})$. Further from d$\chi_{\mathrm{NL}}$/dT vs. T(K) plots and critical analysis with unusual critical exponent's $\gamma $ and $\beta $ gives an experimental evidence for the observed non linearity and magnetic frustration.