AI 中文总结
本文对比三种方法推导声子有效磁场，证明其在低频极限下等效，确定声子对磁化的两类贡献，为声子磁效应建立统一理论提供关键基础。
AI 中文摘要
声子角动量会诱导出有效磁场，这一现象被称为声子磁效应，已测得其大小存在显著差异。本文利用电子-声子耦合与轨道磁性，对比了三种推导声子有效磁场的方法：绝热方法假设离子运动缓慢，使电子保持在基态；微扰方法将电子-声子相互作用视为对电子基态的微扰；弗洛凯方法则基于离子圆周运动的时间周期性。我们证明，在低频极限下，这三种方法均能得到相同的有效哈密顿量，这使我们更接近建立声子磁效应的统一理论。此外，我们确定了样品磁化强度的两种声子贡献：自发贡献与感应贡献，从而阐明了有效磁场在声子诱导磁化强度中的作用。最后，我们给出了SrTiO₃中有效磁场的数值估计。
英文摘要
Phonon angular momentum induces an effective magnetic field, a phenomenon called phono-magnetic effect, which has been measured to vary significantly in size. Here, we compare three approaches for deriving the effective magnetic field of a phonon, using electron-phonon coupling and orbital magnetism. The adiabatic approach assumes a slow ionic motion, keeping electrons in the ground state. The perturbative approach treats the electron-phonon interaction as a perturbation to the electronic ground state, and the Floquet approach is based on the time-periodicity of the circular ionic motion. We show that all three approaches lead to the same effective Hamiltonian in the low-frequency limit, which moves us closer towards a unified theory of the phono-magnetic effect. Furthermore, we identify two phononic contributions to the sample magnetization, spontaneous and induced. Thus, we clarify the role of the effective magnetic field in the phonon-induced magnetization. We conclude by providing a numerical estimate for the effective magnetic field in SrTiO$_3$.
Comments10 pages, 2 figures
