Magnetic hard-direction ordering in anisotropic Kondo systems

We present a generic mechanism that explains why many Kondo materials show magnetic ordering along directions are not favored by the crystal-field anisotropy. Using renormalization-group (RG) analysis of single-impurity models with single-ion anisotropy, we demonstrate strong fluctuations above temperature drive moment reorientation over wide range parameters, e.g., for different spin values $S$ and number channels $N$. In tetragonal systems, this can happen both easy-plane or easy-axis The characteristic crossing susceptibilities is an artifact weak-coupling RG treatment but be reproduced in brute-force perturbation theory. Employing numerical renormalization group (NRG), underscreened $(S=1,$ $N=1)$ also occur strong-coupling regime (below temperature). This suggests collective such moments would develop hard axis.