Lepadatu Serban
Jeremiah Horrocks Institute for Mathematics, Physics and Astronomy, University of Central Lancashire, Preston, PR1 2HE, UK.
Sci Rep. 2017 Oct 11;7(1):12937. doi: 10.1038/s41598-017-13181-x.
A three-dimensional spin current solver based on a generalised spin drift-diffusion description, including the bulk and interfacial spin Hall effects, is integrated with a magnetisation dynamics solver. The resulting model is shown to simultaneously reproduce the spin-orbit torques generated using the spin Hall effect, spin pumping torques generated by magnetisation dynamics in multilayers, as well as the spin transfer torques acting on magnetisation regions with spatial gradients, whilst field-like and spin-like torques are reproduced in a spin valve geometry. Two approaches to modelling interfaces are analysed, one based on the spin mixing conductance and the other based on continuity of spin currents where the spin dephasing length governs the absorption of transverse spin components. In both cases analytical formulas are derived for the spin-orbit torques in a heavy metal/ferromagnet bilayer geometry, showing in general both field-like and damping-like torques are generated. The limitations of the analytical approach are discussed, showing that even in a simple bilayer geometry, due to the non-uniformity of the spin currents, a full three-dimensional treatment is required. The model is further applied to the analysis of the spin Hall angle in Pt by reproducing published experimental ferromagnetic resonance data in the bilayer geometry.
一个基于广义自旋漂移 - 扩散描述的三维自旋电流求解器，包括体自旋霍尔效应和界面自旋霍尔效应，与一个磁化动力学求解器集成在一起。结果表明，所得模型能够同时再现利用自旋霍尔效应产生的自旋 - 轨道扭矩、多层结构中磁化动力学产生的自旋泵浦扭矩，以及作用于具有空间梯度的磁化区域的自旋转移扭矩，同时在自旋阀几何结构中再现类场扭矩和类自旋扭矩。分析了两种建模界面的方法，一种基于自旋混合电导，另一种基于自旋电流的连续性，其中自旋退相干长度控制横向自旋分量的吸收。在这两种情况下，都推导出了重金属/铁磁体双层几何结构中自旋 - 轨道扭矩的解析公式，表明一般会同时产生类场扭矩和类阻尼扭矩。讨论了解析方法的局限性，表明即使在简单的双层几何结构中，由于自旋电流的不均匀性，仍需要进行完整的三维处理。该模型通过再现双层几何结构中已发表的实验铁磁共振数据，进一步应用于分析铂中的自旋霍尔角。
