标题： 二维反铁磁对称性分类及第四类磁性的出现 显示英文标题

标题： Symmetry Classification of Altermagnetism and Emergence of Type-IV Magnetism in Two Dimensions

摘要： 二维（2D）磁性，特别是二维交替磁性（AM），由于其优异的物理特性和广泛的应用潜力而引起了广泛关注。 然而，当从三维（3D）对称性强制完全补偿的共线磁性$-$过渡到二维时，AM的分类经历了一个根本性的范式转变，这一转变在很大程度上被忽视了。 在这里，通过将非常规磁性扩展到二维共线系统，我们确定了一种独特的磁相的对称性条件和电子能带特性：第四类磁性。 这个新类别超越了铁磁性、常规反铁磁性和AM的现有描述。 第四类磁性支持非相对论自旋简并和相对论自旋分裂现象的连续出现，严格不属于常规反铁磁性或标准AM。 我们进一步通过从共线自旋层群到磁层群的映射，建立了一个适用于二维第四类磁体的通用对称性分类框架。 单层MgCr$_2$O$_3$和单层BaMn$_2$Ch$_3$（Ch=Se, Te）被作为代表性材料展示，分别表现出可调控的可逆自旋结构和量子电霍尔效应。 我们的工作突显了第四类磁体丰富的功能前景，为自旋操控和异常输运提供了一条新途径，有望为高性能自旋电子器件的设计带来创新。 显示英文摘要

摘要： Two-dimensional (2D) magnetism, particularly 2D altermagnetism (AM), has attracted considerable interest due to its exceptional physical properties and broad application potential. However, the classification of AM undergoes a fundamental paradigm shift when transitioning from three-dimensional (3D) to 2D symmetry-enforced fully compensated collinear magnetism$-$a shift that has remained largely overlooked. Here, by extending unconventional magnetism to 2D collinear systems, we identify the symmetry conditions and electronic band characteristics of a distinct magnetic phase: type-IV magnetism. This new class lies beyond the established descriptions of ferromagnetism, conventional antiferromagnetism, and AM. Type-IV magnetism supports the successive emergence of both nonrelativistic spin-degenerate and relativistic spin-splitting phenomena, belonging strictly to neither conventional antiferromagnetism nor standard AM. We further establish a universal symmetry classification framework for 2D type-IV magnets via a mapping from the collinear spin layer group to the magnetic layer group. Monolayer MgCr$_2$O$_3$ and monolayer BaMn$_2$Ch$_3$ (Ch=Se, Te) are showcased as representative materials, exhibiting gate-tunable reversible spin textures and the quantum electric Hall effect, respectively. Our work underscores the rich functional prospects of type-IV magnets, offering a new route toward spin manipulation and anomalous transport that promises innovative designs for high-performance spintronic devices.