Magnetic hard-direction ordering in anisotropic Kondo systems

TL;DR

This paper explains why many Kondo materials exhibit magnetic ordering along directions not favored by crystal-field anisotropy, due to fluctuation-driven moment re-orientation across a wide parameter range.

Contribution

It introduces a generic RG-based mechanism for hard-axis magnetic ordering in anisotropic Kondo systems, supported by NRG calculations.

Findings

Fluctuations induce moment re-orientation above the Kondo temperature.

Crossing of magnetic susceptibilities occurs in both weak and strong coupling regimes.

Hard-axis magnetic ordering can develop in under-screened moments.

Abstract

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