Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic Insulators
Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic Insulators
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DOI：
10.1103/physrevx.14.011041
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发表时间：
2023-07
影响因子：
12.5
通讯作者：
Shang Ren;J. Bonini;M. Stengel;C. Dreyer;D. Vanderbilt
中科院分区：
文献类型：
--
作者：
Shang Ren;J. Bonini;M. Stengel;C. Dreyer;D. Vanderbilt
在传统的\textit{从头算}方法中，声子是通过求解涉及静态原子间力常数和原子质量的运动方程来计算的。波恩-奥本海默近似，其中所有的电子自由度被假定为绝热跟随核动力学，也被采用。这种方法不能完全解释磁序系统中时间反转对称性破缺的影响。最近的纠正尝试包括在运动方程中包含原子间力的速度依赖性，这解释了时间反转对称性破缺，并且可以导致即使在区域中心也具有非零角动量的手性声子模式。然而，由于声子和磁振子的能量范围通常是重叠的，自旋不能被视为遵循晶格自由度的绝热。相反，声子和自旋必须在类似的基础上处理。聚焦于区中心模式，我们提出了一种涉及Hessian矩阵和Berry曲率张量的声子和自旋自由度的方法，并描述了计算这些的第一性原理方法。然后，我们求解拉格朗日运动方程，以确定混合激发的能量和特征，使我们能够量化，例如，在某些情况下，手性声子对之间的能量分裂，以及在其他情况下，红外和拉曼模式之间的磁诱导混合程度。该方法具有通用性，可用于确定任何慢变量混合集的绝热动力学。
In conventional \textit{ab initio} methodologies, phonons are calculated by solving equations of motion involving static interatomic force constants and atomic masses. The Born-Oppenheimer approximation, where all electronic degrees of freedom are assumed to adiabatically follow the nuclear dynamics, is also adopted. This approach does not fully account for the effects of broken time-reversal symmetry in systems with magnetic order. Recent attempts to rectify this involve the inclusion of the velocity dependence of the interatomic forces in the equations of motion, which accounts for time-reversal symmetry breaking, and can result in chiral phonon modes with non-zero angular momentum even at the zone center. However, since the energy ranges of phonons and magnons typically overlap, the spins cannot be treated as adiabatically following the lattice degrees of freedom. Instead, phonon and spins must be treated on a similar footing. Focusing on zone-center modes, we propose a method involving Hessian matrices and Berry curvature tensors in terms of both phonon and spin degrees of freedom, and describe a first-principles methodology for calculating these. We then solve Lagrange's equations of motion to determine the energies and characters of the mixed excitations, allowing us to quantify, for example, the energy splittings between chiral pairs of phonons in some cases, and the degree of magnetically induced mixing between infrared and Raman modes in others. The approach is general, and can be applied to determine the adiabatic dynamics of any mixed set of slow variables.