Friedel oscillations induced surface magnetic anisotropy

TL;DR

This paper investigates how Friedel oscillations influence surface magnetic anisotropy in metallic hosts, revealing that host-induced anisotropy is much weaker than local impurity effects, with implications for understanding size-dependent Kondo resistance.

Contribution

It provides a detailed numerical analysis of magnetic anisotropy energy near surfaces, incorporating realistic Green's function techniques and spin-orbit coupling effects.

Findings

Magnetic anisotropy energy oscillates with impurity-surface distance

Host-induced anisotropy decays as 1/d^2 with distance

Local spin-orbit coupling dominates the anisotropy effects

Abstract

We present detailed numerical studies of the magnetic anisotropy energy of a magnetic impurity near the surface of metallic hosts (Au and Cu), that we describe in terms of a realistic tight-binding surface Green's function technique. We study the case when spin-orbit coupling originates from the d-band of the host material and we also investigate the case of a strong local spin-orbit coupling on the impurity itself. The splitting of the impurity's spin-states is calculated to leading order in the exchange interaction between the impurity and the host atoms using a diagrammatic Green's function technique. The magnetic anisotropy constant is an oscillating function of the separation d from the surface: it asymptotically decays as 1/d2 and its oscillation period is determined by the extremal vectors of the host's Fermi Surface. Our results clearly show that the host-induced magnetic anisotropy energy is by several orders of magnitude smaller than the anisotropy induced by the local mechanism, which provides sufficiently large anisotropy values to explain the size dependence of the Kondo resistance observed experimentally.