On the sign of the linear magnetoelectric coefficient in Cr₂O₃

We establish the sign of the linear magnetoelectric (ME) coefficient,α, in chromia, Cr₂O₃. Cr₂O₃is 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 (AFM) domains have opposite ME responses, and which AFM 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 AFM domain of Cr₂O₃to an applied in-plane electric field at zero kelvin. We find that the domain with nearest neighbor magnetic moments oriented away from (towards) each other has a negative (positive) in-plane ME coefficient,α⊥, at zero kelvin. 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 AFM domain produced by annealing in combinedEandHfields oriented along the crystallographic symmetry axis at room temperature. We find that the AFM domain with nearest-neighbor magnetic moments oriented away from (towards) each other is produced by annealing in (anti-)parallelEandHfields, corresponding to a positive (negative) axial ME coefficient,α∥, at room temperature. Sinceα⊥at zero kelvin andα∥at room temperature are known to be of opposite sign, our computational and experimental results are consistent.