AI 中文总结
研究巡游电子产生的轨道磁相，利用标准和修正Haldane模型在蜂窝晶格中证明其可能性，通过实空间公式分解轨道磁化确定轨道序，改变参数发现不同区域，由低能理论依谷机制解释。
AI 中文摘要
由于固体中电子轨道角动量本质上是非局域的，其对磁性的贡献通常用净轨道磁化来描述。本文表明巡游电子可产生具有铁磁、反铁磁或亚铁磁序的轨道磁相。在蜂窝晶格中利用标准和修正的Haldane模型证明了这种可能性。采用实空间公式将巡游轨道磁化分解为子晶格贡献\(M_A\)和\(M_B\)，通过它们的净组合\((M_z = M_A + M_B)\)和交错组合\((M_z^s = M_A - M_B)\)来确定轨道序。通过改变子晶格势和费米能，发现了不同的区域，包括修正Haldane模型中的(PT)对称轨道反铁磁体、标准Haldane模型中的轨道铁磁体、净和交错轨道磁化共存的亚铁磁金属态以及铁磁和反铁磁轨道特征可共存的绝缘区域。这些发现由低能理论根据两种不同的谷机制来解释：标准Haldane模型中依赖谷的狄拉克质量和修正版本中依赖谷的能量偏移。
英文摘要
Because electronic orbital angular momentum in solids is inherently non-local, its contribution to magnetism is usually cast in terms of a net orbital magnetization. Here, we show that itinerant electrons can generate orbital magnetic phases with ferromagnetic, antiferromagnetic, or ferrimagnetic orders. We demonstrate this possibility in a honeycomb lattice, using both the standard and a modified Haldane model. Employing real-space formulations, we decompose the itinerant orbital magnetization into sublattice contributions, $M_A$ and $M_B$. Their net ($M_z=M_A+M_B$) and staggered ($M_z^s=M_A-M_B$) combinations are then used to identify the orbital order. By varying the sublattice potential and the Fermi energy, we find distinct regimes: a (PT)-symmetric orbital antiferromagnet in the modified Haldane model, an orbital ferromagnet in the standard Haldane model, ferrimagnetic metallic states where net and staggered orbital magnetizations coexist, and insulating regimes in which the ferro- and antiferromagnetic orbital characters can be interchanged. These findings are explained by a low-energy theory in terms of two distinct valley mechanisms: valley-dependent Dirac masses in the standard Haldane model and valley-dependent energy shifts in its modified version.
