We use symmetry analysis and density-functional theory to determine and characterize surface terminations that have a finite equilibrium magnetization density in antiferromagnetic materials. A nonzero magnetic dipole moment per unit area or “surface magnetization” can arise on particular surfaces of many antiferromagnets due to the bulk magnetic symmetries. Such surface magnetization underlies intriguing physical phenomena like interfacial magnetic coupling and can be used as a readout method of antiferromagnetic domains. However, a universal description of antiferromagnetic surface magnetization is lacking. We first introduce a classification system based on whether the surface magnetization is either sensitive or robust to roughness and on whether the magnetic dipoles at surface of interest are compensated or uncompensated when the bulk magnetic order is retained at the surface. We show that roughness-sensitive categories can be identified by a simple extension of a previously established group-theory formalism for identifying roughness-robust surface magnetization. We then map the group-theory method of identifying surface magnetization to a novel description in terms of bulk magnetic multipoles, which are already established as symmetry indicators for bulk magnetoelectric responses at both linear and higher orders. We use density-functional calculations to illustrate that nominally compensated surfaces in magnetoelectric ${\mathrm{Cr}}_2{\mathrm{O}}_3$ and centrosymmetric altermagnetic ${\mathrm{FeF}}_2$ develop a finite magnetization density at the surface, in agreement with our predictions based on both group theory and the ordering of the bulk multipoles. Our analysis provides a comprehensive basis for understanding the surface magnetic properties and their intimate correspondence to bulk magnetoelectric effects in antiferromagnets and has important implications for technologically relevant phenomena such as exchange-bias coupling.

中文翻译：

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反铁磁体的表面磁化：分类、示例材料以及与磁电响应的关系


我们使用对称分析和密度泛函理论来确定和表征反铁磁材料中具有有限平衡磁化密度的表面终端。由于体磁对称性，许多反铁磁体的特定表面上可能会出现每单位面积的非零磁偶极矩或“表面磁化强度”。这种表面磁化是界面磁耦合等有趣物理现象的基础，可用作反铁磁畴的读出方法。然而，缺乏反铁磁表面磁化的通用描述。我们首先引入一个分类系统，该系统基于表面磁化强度对粗糙度是否敏感或鲁棒，以及当体磁序保留在表面时，感兴趣表面的磁偶极子是否得到补偿或未补偿。我们表明，可以通过先前建立的用于识别粗糙度鲁棒表面磁化的群论形式主义的简单扩展来识别粗糙度敏感类别。然后，我们将识别表面磁化强度的群论方法映射到体磁多极子方面的新颖描述，这些多极子已经被确立为线性和高阶体磁电响应的对称指标。我们使用密度泛函计算来说明磁电 ${\mathrm{Cr}}_2{\mathrm{O}}_3$ 和中心对称交变磁 ${\mathrm{FeF}}_2$ 中的名义补偿表面在表面形成有限的磁化密度，这与我们基于两个群论的预测一致以及批量多极的排序。 我们的分析为理解表面磁特性及其与反铁磁体中体磁电效应的密切对应关系提供了全面的基础，并对交换偏置耦合等技术相关现象具有重要意义。