发表机构
Univ. Grenoble Alpes, CNRS, Institut Néel（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，尼尔研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出统一笛卡尔框架分解多极矩张量，依据磁性对称性确定多极排列，并建立多极序与性质张量的对称性关联，开发MagSymMultipoles网络应用，在多种材料中验证了方法有效性。
AI 中文摘要
晶体材料的许多结构和磁性相及其性质可归因于电多极和磁多极的有序化。实例包括铁电性、线性磁电效应和交变磁性。因此，确定晶体中对称性允许的多极对于表征其有序相和物理性质非常有用。在此，我们提出一个统一的笛卡尔框架，用于将任意阶的矩张量分解为普通、环形和极向多极，并根据晶体学和磁性对称性确定它们在晶体内的铁性、反铁性和非共线排列。我们进一步建立了多极序与相关物理性质张量允许分量之间的直接对称性关系，涵盖相对论和非相对论情形。我们将此方法实现在MagSymMultipoles（此https URL）中，这是一个用于计算和可视化对称性适配的电多极和磁多极的交互式网络应用。该应用使用有和无自旋轨道耦合的磁性对称性来推导允许的多极以及底层笛卡尔矩张量，从而便于探索给定多极序与相应物理响应张量之间的联系。我们演示了该方法在铁电BaTiO3、反铁电PbZrO3、磁电Cr2O3以及交变磁体MnF2、MnTe和Mn3IrSi上的应用。这些例子展示了我们的方法如何获得将材料的多极序直接与其物理性质联系起来的直观图像，从而有助于解释理论和实验结果。
英文摘要
Many structural and magnetic phases and properties of crystalline materials can be related to the ordering of electric and magnetic multipoles. Examples include ferroelectricity, linear magnetoelectricity, and altermagnetism. Determining the symmetry-allowed multipoles in a crystal is therefore useful for characterizing its ordered phases and physical properties. Here, we present a unified Cartesian framework for decomposing moment tensors of arbitrary rank into ordinary, toroidal, and poloidal multipoles, and for determining, from crystallographic and magnetic symmetry, their ferroic, antiferroic, and noncollinear arrangements within the crystal. We further establish the direct symmetry relationship between multipolar order and the allowed components of associated physical-property tensors in both relativistic and non-relativistic settings. We implement this methodology in MagSymMultipoles (https://mag-sym-multipoles.com), an interactive web application for calculating and visualizing symmetry-adapted electric and magnetic multipoles. The application uses magnetic symmetries both with and without spin-orbit coupling to derive the allowed multipoles as well as the underlying Cartesian moment tensors, making it easy to explore the connection between a given multipolar order and the corresponding physical response tensors. We demonstrate the approach for ferroelectric BaTiO3, antiferroelectric PbZrO3, magnetoelectric Cr2O3, and the altermagnets MnF2, MnTe, and Mn3IrSi. These examples demonstrate how our method allows us to obtain an intuitive picture linking the multipolar order of a material directly to its physical properties, thereby facilitating the interpretation of theoretical and experimental results.
