Spin-orbit-induced magnetic anisotropy for impurities in metallic samples. I. Surface anisotropy

Motivated by 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 $\mathbf{n}$ which, in the case of a plane surface, is perpendicular to the surface. The anisotropy energy is $\Delta {E=K}_d(\mathbf{n}\mathbf{S}{)}^2$ for spin $\mathbf{S}$, and the anisotropy constant $K_d$ is inversionally proportional to distance $d$ measured from the surface and $K_d>0\mathrm{}$. 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 (II).