Third-order magnetic susceptibility as a new method for studying quadrupolar interactions in rare-earth compounds

Abstract

We present a new method based on the detailed analysis of the magnetization curve in the paramagnetic range for studying the quadrupolar interactions in cubic rare-earth intermetallic compounds; the third-order magnetic susceptibility characterizes the anisotropic curvature of the magnetization curve. It corresponds to the $H^3$ coefficient in the odd field development of the magnetization. This high-order coefficient receives a contribution from the induced quadrupolar moment which varies as $H^2$. Thus studied in the nonordered (cubic and paramagnetic) range with magnetic fields applied along the [001] and [111] directions, the third-order magnetic susceptibility provides information on the quadrupolar interactions associated with the two tetragonal and trigonal symmetry-lowering modes. Using perturbation theory and mean-field approximation, we give analytical expressions for the third-order magnetic susceptibility in the presence of a crystalline electric field, bilinear exchange, and quadrupolar (exchange and magnetoelastic) interactions. Application to ${\mathrm{Tm}}^{3+}$ cubic intermetallic compounds, for which large quadrupolar interactions have been shown to exist, is then given, illustrating the reliability of the method.