Properties of anisotropic magnetic impurities on surfaces

Using numerical renormalization group techniques, we study static and dynamic properties of a family of single-channel Kondo impurity models with axial magnetic anisotropy $DS_z^2$ terms; such models are appropriate to describe magnetic impurity atoms adsorbed on non-magnetic surfaces, which may exhibit surface Kondo effect. We show that for positive anisotropy $D$ and for any spin $S$, the systems behave at low temperatures as regular Fermi liquids with fully compensated impurity spin. The approach to the stable fixed point depends on the value of the spin $S$ and on the ratio $D/T_K^{(0)}$, where $T_K^{(0)}$ is the Kondo temperature in the absence of the anisotropy. For S=1, the screening occurs in two stages if $D<T_K^{(0)}$; the second Kondo temperature is exponentially reduced in this case. More generally, there is an effective spin-1/2 Kondo effect for any integer $S$ if $D<T_K^{(0)}$ and for any half-integer $S$ if $D>T_K^{(0)}$. For negative anisotropy $D$, the system is a non-Fermi liquid with residual anisotropic exchange interaction. However, the presence of transverse magnetic anisotropy $E(S_x^2-S_y^2)$ restores Fermi-liquid behavior in real systems.