We develop a Green's function formalism for spin transport through heterostructures that contain metallic leads and insulating ferromagnets. While this formalism in principle allows for the inclusion of various magnonic interactions, we focus on Gilbert damping. As an application, we consider ballistic spin transport by exchange magnons in a metal-insulator-metal heterostructure with and without disorder. For the former case, we show that the interplay between disorder and Gilbert damping leads to spin current fluctuations. For the case without disorder, we obtain the dependence of the transmitted spin current on the thickness of the ferromagnet. Moreover, we show that the results of the Green's function formalism agree in the clean and continuum limit with those obtained from the linearized stochastic Landau-Lifshitz-Gilbert equation. The developed Green's function formalism is a natural starting point for numerical studies of magnon transport in heterostructures that contain normal metals and magnetic insulators.

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金属-绝缘体-金属异质结构中自旋输运的格林函数形式论

我们开发了格林函数形式主义，用于通过包含金属引线和绝缘铁磁体的异质结构的自旋输运。尽管这种形式主义原则上可以包含各种强磁相互作用，但我们将重点放在吉尔伯特阻尼上。作为一种应用，我们考虑在具有和不具有无序性的金属-绝缘体-金属异质结构中通过交换磁振子进行弹道自旋传输。对于前一种情况，我们表明无序和吉尔伯特阻尼之间的相互作用会导致自旋电流波动。对于无序的情况，我们获得了传输的自旋电流对铁磁体厚度的依赖性。此外，我们证明格林函数形式主义的结果​​与从线性随机Landau-Lifshitz-Gilbert方程获得的结果在干净和连续的范围内一致。