Magnetic anisotropy is one of the important factors in determining magnetic structures. The type of magnetic anisotropy is closely related to the symmetry of crystals. We theoretically investigate magnetic anisotropy and its related magnetic instability arising from an electric axial moment, which appears under the breaking of the mirror symmetry parallel to the moment but does not require the breakings of both spatial inversion and time-reversal symmetries. By performing perturbation and mean-field calculations in a complementary way, we show the appearance of the in-plane magnetic anisotropy when the electric axial moment occurs, which tends to tilt in-plane spin moments from the crystal axes in collaboration with relativistic spin-orbit coupling. We demonstrate such a tendency for single-sublattice and four-site cluster models. In the four-site cluster model, we show that a spin configuration consisting of magnetic monopole and magnetic toroidal dipole tends to be realized in the region where a spin vortex is stabilized by the exchange interactions.

中文翻译：

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铁轴力矩下的磁不稳定性

磁各向异性是决定磁结构的重要因素之一。磁各向异性的类型与晶体的对称性密切相关。我们从理论上研究了由电轴力矩引起的磁各向异性及其相关的磁不稳定性，它出现在平行于力矩的镜面对称性破缺的情况下，但不需要空间反演对称性和时间反演对称性的破缺。通过以互补的方式进行扰动和平均场计算，我们展示了当电轴力矩发生时面内磁各向异性的出现，这往往与相对论自旋相结合，使面内自旋力矩从晶轴倾斜。轨道耦合。我们证明了单子晶格和四位点簇模型的这种趋势。在四位点簇模型中，我们表明，由磁单极子和磁环形偶极子组成的自旋构型往往在通过交换相互作用稳定自旋涡旋的区域中实现。