Abstract The magnetization response including dipole–dipole interactions of a pair of macrospins following the sudden alteration of a dc magnetic field is calculated from the stochastic Gilbert-Landau-Lifshitz equation by reducing the overall task to an infinite hierarchy of differential-recurrence relations in the time domain for the statistical moments (averaged products of spherical harmonics in this case), which is exactly solved in the frequency domain by matrix continued fractions. The greatest relaxation time and dynamic susceptibility are then compared with the corresponding results for two exchange-coupled spins using the same exact method. For a given interaction parameter dipole–dipole coupling in the circularly symmetric configuration considered has a much more pronounced effect on the magnetization dynamics than exchange coupling principally manifested by a greater increase in the relaxation time.

中文翻译：

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偶极-偶极和交换相互作用对两个宏自旋磁化弛豫的影响：比较

摘要 直流磁场突然变化后，包括一对宏自旋的偶极-偶极相互作用的磁化响应是根据随机 Gilbert-Landau-Lifshitz 方程计算出来的，方法是将整个任务简化为无限层次的微分递归关系。统计矩的时域（在这种情况下是球谐函数的平均乘积），它在频域中通过矩阵连分数精确求解。然后使用相同的精确方法将最大弛豫时间和动态磁化率与两个交换耦合自旋的相应结果进行比较。