Non-asymptotic Coqblin–Schrieffer interaction between local f[formula omitted]-states

Abstract

The magnetism of many cerium-based compounds has been studied considering the hybridization of its local f1 state with itinerant electrons, a mechanism that originates an anisotropic RKKY-type interaction between two neighboring local moments. The orbital degrees of freedom of the f-levels play a fundamental role in this mechanism, as shown in the well-known and broadly used Coqblin–Schrieffer formalism, which, however, is valid only for ions very far apart, yields an effective Hamiltonian that is not hermitian and does not reflect the interchange symmetry when applied for two identical ions. Therefore, the off-diagonal terms of the interaction energy do not exhibit the Friedel oscillations typical of the RKKY interactions. Through an exact evaluation of Ruderman–Kittel-like integrals, we extended such formalism to any ionic separation, corrected the non-hermiticity and the lack of ionic interchange symmetry, which recovered the Friedel oscillations. These improvements strongly impact the contribution of each angular momentum component to the ionic interaction-energy and hence whether ferro- or anti-ferromagnetic alignment is favored. As an example, we calculated the temperature dependence of the magnetic susceptibility for a simple system of Ce-Ce free dimers and show that striking differences exist when compared with the susceptibility evaluated using the original Coqblin–Schrieffer formalism.