Spin-Orbit-Induced Magnetic Anisotropy for Impurities in Metallic Samples I. Surface Anisotropy

TL;DR

This paper investigates how surface-induced spin-orbit interactions create magnetic anisotropy in impurities within metallic samples, affecting their magnetic behavior and potentially explaining the suppression of Kondo resistivity in thin films.

Contribution

It introduces a model for surface anisotropy caused by spin-orbit interactions near metallic surfaces, detailing how anisotropy energy depends on impurity distance from the surface.

Findings

Anisotropy energy $ ext{ΔE} = K_d (nS)^2$ with $K_d$ inversely proportional to distance $d$.

Surface anisotropy aligns impurity spins perpendicular to the surface at low temperatures.

Impurity spins are frozen in low-energy states due to surface anisotropy.

Abstract

Motivated by the recent measurements of Kondo resistivity in thin films and wires, where the Kondo amplitude is suppressed for thinner samples, the surface anisotropy for magnetic impurities is studied. That anisotropy is developed in those cases where in addition to the exchange interaction with the impurity there is strong spin-orbit interaction for conduction electrons around the impurity in the ballistic region. The asymmetry in the neighborhood of the magnetic impurity exhibits the anisotropy axis $n$ which, in the case of a plane surface, is perpendicular to the surface. The anisotropy energy is $\Delta E=K_d (nS)^2$ for spin $S$, and the anisotropy constant $K_d$ is inversionally proportional to distance $d$ measured from the surface and $K_d>0$. Thus at low temperature the spin is frozen in a singlet or doublet of lowest energy. The influence of that anisotropy on the electrical resistivity is the subject of the following paper (part II).