Spin-Orbit-Induced Magnetic Anisotropy for Impurities in Metallic Samples of Reduced Dimensions: Finite Size Dependence in the Kondo Effect

We show that the conduction electron mediated interaction between a magnetic impurity and a nonmagnetic, semi-infinite host can lead to an impurity magnetic anisotropy with an easy plane parallel to the surface. Similarly, that anisotropy occurs in any mesoscopic sample. The effect is due to spin-orbit coupling and can lead to the freezing out of an $S=5\mathrm{}/2$ or $S=2\mathrm{}$ spin into an $S_z=1\mathrm{}/2$ or $S_z=0\mathrm{}$ state at low temperatures. We argue that this phenomenon provides a natural explanation for the anomalous behavior of the Kondo resistivity in a number of experiments involving thin films.