Scaling theory of magnetic ordering in the Kondo lattices with anisotropic exchange interactions

The lowest-order scaling consideration of the magnetic state formation in the Kondo lattices is performed within the $s-f$ model with inclusion of anisotropy for both the $f-f$ coupling and $s-f$ exchange interaction. The Kondo renormalizations of the effective transverse and longitudinal $s-f$ coupling parameters, spin-wave frequency, gap in the magnon spectrum and ordered moment are calculated in the case of both ferro- and antiferromagnets. The anisotropy-driven change of the scaling behavior (e.g., critical value of $g$ for entering the strong-coupling region and the corresponding critical exponents) is investigated numerically for N=2 and analytically in the large-N limit. The dependence of the effective Kondo temperature on the bare $s-f$ coupling parameter $g$ weakens in the presence of anisotropy. The relative anisotropy parameters for both the $s-f$ and $f-f$ coupling are demonstrated to decrease during the renormalization process. The role of next-nearest exchange interactions for this effect in the antiferromagnet is discussed.