First-principles microscopic model of exchange-driven magnetoelectric response with application to Cr$_2$O$_3$

TL;DR

This paper develops a first-principles microscopic model for exchange-driven magnetoelectric response, applied to Cr$_2$O$_3$, revealing electronic and ionic contributions and their temperature dependence.

Contribution

The paper introduces a microscopic Hamiltonian-based approach to quantify exchange-driven magnetoelectric effects from first-principles data, including electronic and ionic contributions.

Findings

Electronic contribution to magnetoelectric susceptibility is significant and opposite to ionic contribution.

The model accurately describes the temperature dependence of $ ext{ extmu}_ ext{0} ext{ extmu}_ ext{B}$-based susceptibility in Cr$_2$O$_3$.

Non-Heisenberg interactions are insufficient to explain the sign change of $oldsymbol{ extalpha}_ extparallel$.

Abstract

The exchange-driven contribution to the magnetoelectric susceptibility $\hat\alpha$ is formulated using a microscopic model Hamiltonian coupling the spin degrees of freedom to lattice displacements and electric field, which may be constructed from first-principles data. Electronic and ionic contributions are sorted out, and the latter is resolved into a sum of contributions from different normal modes. If intrasublattice spin correlations can be neglected, the longitudinal component $\alpha_\parallel$ becomes proportional to the product of magnetic susceptibility and sublattice magnetization in accordance with Rado's phenomenological model. As an illustration, the method is applied to analyze the temperature dependence of the longitudinal magnetoelectric susceptibility of Cr$_2$O$_3$ using first-principles calculations and the quantum pair cluster approximation for magnetic thermodynamics. A substantial electronic contribution is found, which is opposite to the ionic part. The sensitivity of the results to the Hubbard $U$ parameter and the sources of error are studied. It is also found that non-Heisenberg interactions are too weak to account for the sign change of $\alpha_\parallel$ in Cr$_2$O$_3$.