Scaling theory of magnetic ordering in the Kondo lattices with anisotropicexchange interactions

The lowest-order scaling consideration of the magnetic state formation in t he Kondo lattices is performed within the s-f model with inclusion of aniso tropy for both the f-f coupling and s-f exchange interaction. The Kondo ren ormalizations of the effective transverse and longitudinal s-f coupling par ameters, spin-wave frequency, gap in the magnon spectrum, and ordered momen t are calculated in the case of both ferro- and antiferromagnets. The aniso tropy-driven change of the scaling behavior (e.g., critical value of the ba re s-f coupling parameter 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 te mperature on g weakens in the presence of anisotropy. The relative anisotro py parameters for both the s-f and f-f coupling are demonstrated to decreas e during the renormalization process. The role of next-nearest exchange int eractions for this effect in the antiferromagnet is discussed. [S0163-1829( 99)00710-9].