Orbital gravitomagnetoelectric response and orbital magnetic quadrupole moment correction
Orbital gravitomagnetoelectric response and orbital magnetic quadrupole moment correction
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DOI：
10.1103/physrevb.107.214109
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发表时间：
2023-02
影响因子：
3.7
通讯作者：
Koki Shinada;R. Peters
中科院分区：
文献类型：
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作者：
Koki Shinada;R. Peters
自从在反铁磁材料中首次观察到磁电效应以来，人们一直在积极地研究多铁性材料中的磁电效应。这种效应出现在没有空间反演对称性和时间反演对称性的系统中，并且对检测磁四极矩很敏感。它通常被讨论为诱导自旋磁化;然而，金属中的轨道磁电效应最近引起了人们的广泛关注，因为它在$\mathrm{MoS_2}$和扭曲双层石墨烯中被观察到。在这项工作中，我们提出了温度梯度诱导轨道磁电效应（轨道重力ME效应）的完整量子形式。效果由两部分组成，即，外在部分和内在部分。我们证明，除了通常的久保公式，内在的部分需要从轨道磁四极矩的校正，以避免在零温度下的非物理发散，并满足莫特关系。此外，我们显示的分类表与磁点群的内在和外在的影响。最后，我们分析了本征部分的$\mathcal{PT}$-对称模型表现出轨道磁化顺序，即，一个回路电流的顺序，并证明了狄拉克点附近的增强。我们相信，这些结果将有助于探测和利用轨道磁矩以外的自旋矩。
The magnetoelectric effect has been actively studied in multiferroics since the first observation in an antiferromagnetic, $\mathrm{Cr_2O_3}$. This effect appears in systems without spatial inversion symmetry and time-reversal symmetry and is sensitive to detecting magnetic quadrupole moments. It is often discussed as inducing spin magnetizations; however, the orbital magnetoelectric effect in metals has recently attracted much attention since its observation in $\mathrm{MoS_2}$ and twisted bilayer graphene. In this work, we propose the full quantum formalism for the temperature gradient induced-orbital magnetoelectric effect (orbital gravito-ME effect). The effect consists of two parts, i.e., an extrinsic part and an intrinsic part. We demonstrate that the intrinsic part needs a correction from the orbital magnetic quadrupole moment besides the usual Kubo formula to avoid an unphysical divergence at zero temperature and to satisfy the Mott relation. Furthermore, we show the classification table with the magnetic point group for the intrinsic and extrinsic effects. Finally, we analyze the intrinsic part in a $\mathcal{PT}$-symmetric model exhibiting an orbital magnetization order, i.e., a loop current order, and demonstrate the enhancement near Dirac points. We believe that these results will contribute to the detection and usage of orbital magnetic moments beyond spin moments.