Spin wave excitations in the antiferromagnetic Heisenberg-Kondo model for heavy fermions

TL;DR

This paper models spin wave excitations in heavy fermion antiferromagnets using a microscopic Heisenberg-Kondo model, providing insights into experimental neutron scattering data and the interplay of RKKY and Kondo interactions.

Contribution

It introduces a perturbative derivation of an effective Hamiltonian for magnons in heavy fermion systems, linking microscopic interactions to observable spin wave spectra.

Findings

Good agreement with neutron scattering data in CeIn₃

Shows how model parameters affect magnon renormalization

Provides a framework for analyzing heavy fermion antiferromagnets

Abstract

Recent inelastic neutron scattering experiments in CeIn$_{3}$ and CePd$_{2}$Si$_{2}$ single crystals measured spin wave excitations at low temperatures. These two heavy fermion compounds exhibit antiferromagnetic long-range order, but a strong competition between the Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction and Kondo effect is evidenced by their nearly equal N\'eel and Kondo temperatures. Our aim is to show how magnons such as measured in the antiferromagnetic phase of these Ce compounds, can be described with a microscopic Heisenberg-Kondo model introduced by J.R.Iglesias, C.Lacroix and B.Coqblin, used before for studies of the non-magnetic phase. The model includes the correlated Ce-$4 f$ electrons hybridized with the conduction band, where we also allow for correlations, and we consider competing RKKY (Heisenberg-like $J_{H} $) and Kondo ($J_{K}$) antiferromagnetic couplings. Carrying on a series of unitary transformations, we perturbatively derive a second-order effective Hamiltonian which, projected onto the antiferromagnetic electron ground state, describes the spin wave excitations, renormalized by their interaction with correlated itinerant electrons. We numerically study how the different parameters of the model influence the renormalization of the magnons, yielding useful information for the analysis of inelastic neutron scattering experiments in antiferromagnetic heavy fermion compounds. We also compare our results with the available experimental data, finding good agreement with the spin wave measurements in cubic CeIn$_3$.