Impact of electron--spin coupling on exchange coupling parameters: a nonperturbative approach

TL;DR

This paper introduces a nonperturbative, self-consistent method to evaluate exchange coupling parameters in magnetic materials, accounting for electron--spin coupling effects, leading to more reliable spin models for predicting magnetic behavior.

Contribution

It presents a fully self-consistent, nonperturbative approach to quantify electron--spin coupling effects on exchange parameters, improving the accuracy of magnetic models.

Findings

Exchange couplings remain consistent over various spin rotation angles.

Spin models based on this method agree with experimental transition temperatures.

Electron--spin coupling significantly renormalizes exchange parameters.

Abstract

Exchange coupling parameters $J_{ij}$ in the Heisenberg model are crucial for describing magnetic behavior at the atomic level. In magnetic materials, spin fluctuations can be accompanied by a self-consistent electronic response -- including charge and magnetization redistribution and changes in orbital occupations -- reflecting electron--spin coupling in the sense of electronic feedback to finite spin rotations. However, the quantitative importance of this coupling in extracting reliable $J_{ij}$ has not been fully clarified. Here, using fully self-consistent, nonperturbative evaluations, we show that finite-angle spin rotations induce such electronic feedback and quantify how strongly it renormalizes the extracted $J_{ij}$. We examine systems of both fundamental and practical interest, including perovskite SrMnO$_3$, Nd-based permanent-magnet compounds (Nd$_2$Fe$_{14}$B and Nd$_2$Co$_{14}$B), and elemental $3d$ transition metals.The nonperturbative approach yields exchange couplings that remain consistent over a wide range of rotation angles. Moreover, spin models parameterized in this way give reasonable agreement with experimental magnetic phase-transition temperatures, underscoring the quantitative role of electron--spin coupling. Overall, our results provide a practical route to constructing quantitatively reliable spin models for predictive finite-temperature simulations and magnetic-materials design.