Derivation of low-energy Hamiltonians for heavy-fermion Materials

TL;DR

This paper derives effective low-energy Hamiltonians for heavy-fermion materials using a multi-orbital Anderson model combined with perturbation theory, validated by experimental data, and explains the origin of exchange anisotropy.

Contribution

It introduces a first-principles based method to derive minimal models for $4f$ materials, including anisotropy origins, improving understanding of heavy-fermion interactions.

Findings

Good agreement with experimental data for CeIn$_3$

Unveiled the microscopic origin of exchange anisotropy

Provided a framework for quantitative modeling of $4f$ materials

Abstract

By utilizing a multi-orbital periodic Anderson model with parameters obtained from \textit{ab initio} band structure calculations, combined with degenerate perturbation theory, we derive effective Kondo-Heisenberg and spin Hamiltonians that capture the interaction among the effective magnetic moments. This derivation encompasses fluctuations via both nonmagnetic $4f^0$ and magnetic $4f^2$ virtual states, and its accuracy is confirmed through comparison with experimental data obtained from CeIn$_3$. The significant agreement observed between experimental results and theoretical predictions underscores the potential of deriving minimal models from first-principles calculations for achieving a quantitative description of $4f$ materials. Moreover, our microscopic derivation unveils the underlying origin of anisotropy in the exchange interaction between Kramers doublets, shedding light on the conditions under which this anisotropy may be weak compared to the isotropic contribution.