发表机构
School of Science, University of Emergency Management; Institute of Theoretical Physics and Department of Physics, University of Science and Technology Beijing（应急管理大学理学院; 北京科技大学理论物理研究所与物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过数值计算揭示方格海森堡 $J_1$-$J_2$-$J_2^\prime$ 模型中 $J_2\neq J_2^\prime$ 导致有限温度弱铁磁性，且各向异性 $D$ 支持二维磁有序，为实验探测提供新机制。
AI 中文摘要
受近期利用光晶格中的超冷原子实现海森堡模型和二维交变磁性的实验启发，我们系统研究了在易轴单离子各向异性 $D$ 存在下，方格海森堡 $J_1$-$J_2$-$J_2^\prime$ 模型的磁性质。这里，$J_1 (>0)$ 是最近邻反铁磁交换参数，而 $J_2$ 和 $J_2^\prime$ 是两种在晶格上交替分布的不同次近邻超交换参数。我们对亚晶格磁化强度、净磁化强度和临界温度进行了数值计算。有趣的是，净磁化强度在有限温度下并不恒为零；其绝对值随温度升高先增大后减小，揭示了随温度变化的弱铁磁性。我们发现 $J_2\not=J_2^\prime$ 是有限温度下弱铁磁性的主要因素，而 $D$ 为二维长程磁有序提供了必要的背景。此外，对于固定的 $J_2+J_2^\prime$，我们观察到更大的 $|J_2-J_2^\prime|$ 导致更大的最大净磁化强度和临界温度，以及更宽的弱铁磁性温度范围。$J_2$ 和 $J_2^\prime$ 之间的差异源于磁性原子之间不同的超交换路径，这些路径由两种不同类型的非磁性原子介导。这一机制不同于传统的机制（如 Dzyaloshinskii-Moriya 相互作用），可能在真实材料中被探测到。
英文摘要
Motivated by recent experimental realizations of the Heisenberg model and two-dimensional altermagnetism using ultracold atoms in optical lattices, we systematically investigate the magnetic properties of the square-lattice Heisenberg $J_1$-$J_2$-$J_2^\prime$ model in the presence of easy-axis single-ion anisotropy $D$. Here, $J_1 (>0)$ is the nearest-neighbor antiferromagnetic exchange parameter, while $J_2$ and $J_2^\prime$ are two distinct next-nearest-neighbor superexchange parameters that alternate on the lattice. We perform numerical calculations of the sublattice magnetization, net magnetization, and critical temperature. Interestingly, the net magnetization is not identically zero at finite temperatures; its absolute value first increases and then decreases with increasing temperature, revealing a temperature-dependent weak ferromagnetism. We find that $J_2\not=J_2^\prime$ is the primary factor responsible for weak ferromagnetism at finite temperatures, while $D$ provides the necessary background for two-dimensional long-range magnetic ordering. Moreover, for a fixed $J_2+J_2^\prime$, we observe that a larger $|J_2-J_2^\prime|$ leads to a greater maximum net magnetization and critical temperature, as well as a broader temperature range for weak ferromagnetism. The difference between $J_2$ and $J_2^\prime$ originates from the distinct superexchange pathways between magnetic atoms, with these pathways mediated by two different types of nonmagnetic atoms. This mechanism, which differs from conventional ones such as the Dzyaloshinskii-Moriya interaction, may be detectable in real materials.
