On the sign of the linear magnetoelectric coefficient in Cr₂O₃

We establish the sign of the linear magnetoelectric (ME) coefficient, α, in chromia, Cr₂O₃. Cr₂O₃ 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 Cr₂O₃ 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, α⊥, 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, α∥, at room temperature. Since α⊥ at 0 K and α∥ at room temperature are known to be of opposite sign, our computational and experimental results are consistent. This dataset contains the input data to reproduce the calculation of the magnetoelectric effect as plotted in Fig. 3 of the manuscript, for Elk, Vasp, and Quantum Espresso.

本研究确立了铬氧化物（Cr₂O₃）中线性磁电系数（α）的符号。Cr₂O₃ 作为典型的线性磁电材料，其特征在于电场（磁场）可诱导产生线性相关的磁化（极化）效应，且通过在联合磁场（H）和电场（E）中的退火处理，可选取单一的磁畴。具有相反反铁磁畴的磁电响应相反，然而以往关于哪种反铁磁畴对应于何种响应符号尚不明确。本研究采用密度泛函理论（DFT）计算了 Cr₂O₃ 单一反铁磁畴在 0 K 下对施加的平面内电场的磁响应。我们发现，相邻磁矩相互远离（靠近）的畴在 0 K 时具有负（正）的平面磁电系数 α⊥。我们证实，这一符号与文献中所有其他指定了畴取向的 DFT 计算结果一致，无论所选择的 DFT 代码或泛函，以及应用场的方法，抑或直接（磁场）或逆向（电场）磁电响应的计算。接着，我们对先前发表的球形中子极化率数据进行重新分析，以确定在室温下沿晶体对称轴方向施加的联合电场（E）和磁场（H）退火产生的反铁磁畴。我们发现，相邻磁矩相互远离（靠近）的反铁磁畴是由退火在（反）平行 E 和 H 场中产生的，对应室温下正（负）的轴向磁电系数 α∥。鉴于 0 K 时的 α⊥ 和室温时的 α∥ 被知具有相反的符号，我们的计算和实验结果一致。本数据集包含了用于再现手稿中图 3 所示磁电效应计算的输入数据，适用于 Elk、Vasp 和 Quantum Espresso。