On the sign of the linear magnetoelectric coefficient in Cr$_2$O$_3$

TL;DR

This paper determines the sign of the linear magnetoelectric coefficient in Cr$_2$O$_3$ using density functional theory and neutron polarimetry, clarifying the relationship between domain orientation and ME response at different temperatures.

Contribution

It provides the first consistent determination of the sign of the ME coefficient in Cr$_2$O$_3$ through combined computational and experimental analysis, resolving previous ambiguities.

Findings

The in-plane ME coefficient $eta_{ ext{perp}}$ is negative for one domain orientation at 0 K.

The antiferromagnetic domain with moments oriented away from each other produces a positive axial ME coefficient at room temperature.

Computational and experimental results are consistent, showing opposite signs of $eta_{ ext{perp}}$ and $eta_{ ext{parallel}}$ at different temperatures.

Abstract

We establish the sign of the linear magnetoelectric (ME) coefficient, $\alpha$, in chromia, Cr$_2$O$_3$. Cr$_2$O$_3$ is the prototypical linear ME material, in which an electric (magnetic) field induces a linearly proportional magnetization (polarization), and a single magnetic domain can be selected by annealing in combined magnetic (H) and electric (E) fields. Opposite antiferromagnetic domains have opposite ME responses, and which antiferromagnetic domain corresponds to which sign of response has previously been unclear. We use density functional theory (DFT) to calculate the magnetic response of a single antiferromagnetic domain of Cr$_2$O$_3$ to an applied in-plane electric field at 0 K. We find that the domain with nearest neighbor magnetic moments oriented away from (towards) each other has a negative (positive) in-plane ME coefficient, $\alpha_{\perp}$, at 0 K. We show that this sign is consistent with all other DFT calculations in the literature that specified the domain orientation, independent of the choice of DFT code or functional, the method used to apply the field, and whether the direct (magnetic field) or inverse (electric field) ME response was calculated. Next, we reanalyze our previously published spherical neutron polarimetry data to determine the antiferromagnetic domain produced by annealing in combined E and H fields oriented along the crystallographic symmetry axis at room temperature. We find that the antiferromagnetic domain with nearest-neighbor magnetic moments oriented away from (towards) each other is produced by annealing in (anti-)parallel E and H fields, corresponding to a positive (negative) axial ME coefficient, $\alpha_{\parallel}$, at room temperature. Since $\alpha_{\perp}$ at 0 K and $\alpha_{\parallel}$ at room temperature are known to be of opposite sign, our computational and experimental results are consistent.