Institute for Molecules and Materials, Radboud University Nijmegen, Heijendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands.
J Phys Condens Matter. 2010 May 5;22(17):176001. doi: 10.1088/0953-8984/22/17/176001. Epub 2010 Apr 7.
We propose new semi-implicit numerical methods for the integration of the stochastic Landau-Lifshitz equation with built-in angular momentum conservation. The performance of the proposed integrators is tested on the 1D Heisenberg chain. For this system, our schemes show better stability properties and allow us to use considerably larger time steps than standard explicit methods. At the same time, these semi-implicit schemes are also of comparable accuracy to and computationally much cheaper than the standard midpoint implicit method. The results are of key importance for atomistic spin dynamics simulations and the study of spin dynamics beyond the macro spin approximation.
我们提出了新的半隐式数值方法，用于积分带有内置角动量守恒的随机朗道-利夫希茨方程。在所提出的积分器的性能在一维海森堡链上进行了测试。对于这个系统，我们的方案显示出更好的稳定性，并允许我们使用比标准显式方法大得多的时间步长。同时，这些半隐式方案也与标准中点隐式方法具有相当的准确性和计算效率，并且比标准中点隐式方法便宜得多。这些结果对于原子自旋动力学模拟和超越宏观自旋近似的自旋动力学研究具有重要意义。
