AI 中文总结
该研究探讨二维交替磁有序的稳定性，通过玻戈留波夫不等式分析最小d波交替磁自旋模型，发现纯交换相互作用无法在二维稳定长程交替磁有序，三维系统则不受默明-瓦格纳论证排除。
AI 中文摘要
交替磁体（AMs）是共线补偿磁体，无需净磁化即可呈现动量依赖的自旋分裂。由于局域磁矩和交换驱动的有序性不依赖相对论效应，交替磁性可自然地在非相对论自旋群框架下表述，这引发了一个基本问题：在无自旋轨道诱导各向异性的情况下，二维交替磁有序能否仅通过纯交换相互作用稳定？我们通过将玻戈留波夫不等式应用于最小d波交替磁自旋模型来解决该问题。研究表明，负责交替磁性的各向异性交换模式仅对玻戈留波夫分母贡献二次长波项，因此当连续自旋旋转对称性保持时，短程交换相互作用本身无法在二维中稳定长程交替磁有序。相比之下，对应的三维系统具有有限的小动量贡献，未被默明-瓦格纳论证排除。
英文摘要
Altermagnets (AMs) are collinear compensated magnets that exhibit momentum-dependent spin splitting without requiring a net magnetization. Since local magnetic moments and exchange-driven order do not rely on relativistic effects, altermagnetism can be naturally formulated in a nonrelativistic spin-group framework. This raises a basic question: can two-dimensional altermagnetic order be stabilized by purely exchange interactions in the absence of spin-orbit-induced anisotropy? We address this question by applying Bogoliubov's inequality to a minimal $d$-wave altermagnetic spin model. We show that the anisotropic exchange pattern responsible for altermagnetism still contributes only a quadratic long-wavelength term to the Bogoliubov denominator. Consequently, short-ranged exchange interactions alone cannot stabilize long-range altermagnetic order in two dimensions when continuous spin-rotation symmetry is preserved. In contrast, the corresponding three-dimensional system has a finite small-momentum contribution and is not ruled out by the Mermin-Wagner argument.
