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 DSz² terms; such models are appropriate to describe magnetic impurity atoms adsorbed on nonmagnetic 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/TK⁽⁰⁾, where TK⁽⁰⁾ is the Kondo temperature in the absence of the anisotropy. For $S=1$, the screening occurs in two stages if D<TK⁽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<TK⁽⁰⁾ and for any half-integer S if D>TK⁽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(Sₓ²-Sy²) restores Fermi-liquid behavior in real systems.