Spin–rotation coupling (SRC) is a fundamental interaction that connects electronic spins with the rotational motion of a medium. We elucidate the Einstein–de Haas (EdH) effect and its inverse with SRC as the microscopic mechanism using the dynamic spin–lattice equations derived by elasticity theory and Lagrangian formalism. By applying the coupling equations to an iron disk in a magnetic field, we exhibit the transfer of angular momentum and energy between spins and lattice, with or without damping. The timescale of the angular momentum transfer from spins to the entire lattice is estimated by our theory to be on the order of 0.01 ns, for the disk with a radius of 100 nm. Moreover, we discover a linear relationship between the magnetic field strength and the rotation frequency, which is also enhanced by a higher ratio of Young’s modulus to Poisson’s coefficient. In the presence of damping, we notice that the spin-lattice relaxation time is nearly inversely proportional to the magnetic field. Our explorations will contribute to a better understanding of the EdH effect and provide valuable insights for magneto-mechanical manufacturing.

自旋旋转耦合（SRC）是将电子自旋与介质的旋转运动连接起来的基本相互作用。我们利用弹性理论和拉格朗日形式主义导出的动态自旋晶格方程，阐明了爱因斯坦-德哈斯（EdH）效应及其以 SRC 为微观机制的逆效应。通过将耦合方程应用于磁场中的铁盘，我们展示了自旋和晶格之间的角动量和能量的传递，有或没有阻尼。对于半径为 100 nm 的圆盘，我们的理论估计角动量从自旋到整个晶格转移的时间尺度约为 0.01 ns。此外，我们发现磁场强度和旋转频率之间存在线性关系，杨氏模量与泊松系数的较高比率也增强了这种关系。在存在阻尼的情况下，我们注意到自旋晶格弛豫时间几乎与磁场成反比。我们的探索将有助于更好地理解 EdH 效应，并为磁机械制造提供宝贵的见解。