Non-linear magnetotropic susceptibility in FePS₃

Magnetotropic susceptibility is the thermodynamic coefficient that maps the curvature of free energy with respect to an applied magnetic field orientation, providing a means to quantify the magnetic anisotropy of a crystal. In this context, non-linear magnetic torque behavior has been reported in FePS₃, motivating the investigation of similar non-linear characteristics in its magnetotropic susceptibility. In this work, we derive the non-linear magnetotropic susceptibility expressions for FePS₃in both<i>ac*</i>-and<i>bc*</i>-planes using complementary approaches: by taking the first derivative of torque and through the formal calculation of the magnetotropic susceptibility. Higher-order terms in the magnetization are included, and the final equations are obtained by applying symmetry constraints imposed by the<i>C</i>_2hpoint group of the material. We analyze the behavior of the resulting non-linear expressions and identify the contributions of each parameter. Our theoretical results show good agreement with preliminary, unpublished experimental data, offering meaningful guidance for ongoing and future experimental work.