The so-called Arrott plot, which consists in plotting $H/M$ against $M^2$, with $H$ the applied magnetic field and $M$ the magnetization, is used to extract valuable information in second-order magnetic phase transitions. Besides, it is widely accepted that a negative slope in the Arrott plot is indicative of a first-order magnetic transition. This is known as the Banerjee criterion. In consequence, the zero-field transition temperature $T^{*}$ is reported as the characteristic first-order transition temperature. By carefully analyzing the mean-field Landau model used for studying first-order magnetic transitions, we show in this work that $T^{*}$ corresponds in fact to a triple point where three first-order lines meet. More importantly, this analysis reveals the existence of two symmetrical second-order critical points at finite magnetic field $(T_c,\pm H_c)$. We then show that a modified Arrott plot can be used to obtain information about these second-order critical points. To support this idea we analyze experimental data on ${\mathrm{La}}_{2/3}{\mathrm{Ca}}_{1/3}{\mathrm{MnO}}_3$ and discuss an estimate for the location of the triple point and the second-order critical points.

• Received 11 March 2016
• Revised 6 June 2016

DOI:https://doi.org/10.1103/PhysRevB.93.224429