Title: Dynamics of magnetic moments coupled to electrons and lattice oscillations Show Chinese title

Title: 与电子和晶格振动耦合的磁矩的动力学

Abstract: Inspired by the models of A. Rebei and G. J. Parker and A. Rebei et. al., we study a physical model which describes the behaviour of magnetic moments in a ferromagnet. The magnetic moments are associated to 3d electrons which interact with conduction band electrons and with phonons. We study each interaction separately and then collect the results assuming that the electron-phonon interaction can be neglected. For the case of the spin-phonon interaction, we study the derivation of the equations of motion for the classical spin vector and find that the correct behaviour, as given by the Brown equation for the spin vector and the Bloch equation, using the results obtained by D. A. Garanin for the average over fluctuations of the spin vector, can be obtained in the high temperature limit. At finite temperatures we show that the Markovian approximation for the fluctuations is not correct for time scales below some thermal correlation time $\tau_{Th}$. For the case of electrons we workout a perturbative expansion of the Feynman-Vernon functional. We find the expression for the random field correlation function. The composite model (as well as the individual models) is shown to satisfy a fluctuation-dissipation theorem for all temperature regimes if the behaviour of the coupling constants of the phonon-spin interaction remains unchanged with the temperature. The equations of motion are derived. Show Chinese abstract

Abstract: 受A. Rebei和G. J. Parker以及A. Rebei等人的模型启发，我们研究了一个物理模型，该模型描述了铁磁体中磁矩的行为。磁矩与3d电子相关联，这些电子与导带电子以及声子相互作用。我们分别研究每种相互作用，然后收集结果，假设可以忽略电子-声子相互作用。对于自旋-声子相互作用的情况，我们研究了经典自旋矢量运动方程的推导，并发现使用D. A. Garanin对自旋矢量涨落平均得到的结果，在高温极限下可以获得由Brown自旋矢量方程和Bloch方程给出的正确行为。在有限温度下，我们表明对于低于某些热关联时间$\tau_{Th}$的时间尺度，涨落的Markov近似是不正确的。对于电子的情况，我们计算了Feynman-Vernon泛函的微扰展开式。我们得到了随机场相关函数的表达式。如果声子-自旋相互作用的耦合常数随温度的变化保持不变，则证明复合模型（以及各个模型）在所有温度范围内都满足涨落耗散定理。运动方程被推导出来。