Numerical Renormalization Group calculations of the magnetization of isotropic and anisotropic Kondo impurities

TL;DR

This paper uses Numerical Renormalization Group calculations to analyze how uniaxial anisotropy and magnetic fields influence the magnetization of Kondo impurities, revealing non-universal behaviors and field-induced effects.

Contribution

It provides a detailed NRG-based analysis of impurity magnetization in anisotropic Kondo models, including effects of g-factor variations and anisotropy types, with implications for magnetic molecules on surfaces.

Findings

Zero-temperature magnetization M(B) is non-universal for isotropic impurities.

Easy axis anisotropy leads to magnetization described by a shifted Brillouin function.

Hard axis anisotropy can produce steps in magnetization due to pseudo-spin-1/2 Kondo effects.

Abstract

We study a Kondo impurity model with additional uniaxial anisotropy D in a non-zero magnetic field B using the Numerical Renormalization Group (NRG). The ratio g_e/g_S of electron and impurity g-factor is regarded as a free parameter and, in particular, the special cases of a "local" (g_e=0) and "bulk" (g_e=g_S) field are considered. For a bulk field, the relationship between the impurity magnetization M and the impurity contribution to the magnetization M_imp is investigated. Furthermore, we study how the value of g_e affects the impurity magnetization curves. In case of an isotropic impurity with g_e=g_S, it is demonstrated that at zero temperature M(B), unlike M_imp(B), does not display universal behavior. With additional "easy axis" anisotropy, the impurity magnetization is well described by a shifted and rescaled Brillouin function on energy scales that are small compared to |D|. In case of "hard axis" anisotropy, the magnetization curves can feature steps which are due to field-induced pseudo-spin-1/2 Kondo effects. For large anisotropy and a local field, these screening effects are described by an anisotropic spin-1/2 Kondo model with an additional scattering term that is spin-dependent (in contrast to ordinary potential scattering). Our study is motivated by the question how the magnetic properties of a deposited magnetic molecule are modified by the interaction with a non-magnetic metallic surface.