Freimuth Frank, Blügel Stefan, Mokrousov Yuriy
Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany.
J Phys Condens Matter. 2016 Aug 10;28(31):316001. doi: 10.1088/0953-8984/28/31/316001. Epub 2016 Jun 15.
Using the Kubo linear-response formalism we derive expressions to calculate the electronic contribution to the heat current generated by magnetization dynamics in ferromagnetic metals with broken inversion symmetry and spin-orbit interaction (SOI). The effect of producing heat currents by magnetization dynamics constitutes the Onsager reciprocal of the thermal spin-orbit torque (TSOT), i.e. the generation of torques on the magnetization due to temperature gradients. We find that the energy current driven by magnetization dynamics contains a contribution from the Dzyaloshinskii-Moriya interaction (DMI), which needs to be subtracted from the Kubo linear response of the energy current in order to extract the heat current. We show that the expressions of the DMI coefficient can be derived elegantly from the DMI energy current. Guided by formal analogies between the Berry phase theory of DMI on the one hand and the modern theory of orbital magnetization on the other hand we are led to an interpretation of the latter in terms of energy currents as well. Based on ab initio calculations we investigate the electronic contribution to the heat current driven by magnetization dynamics in Mn/W(0 0 1) magnetic bilayers. We predict that fast domain walls drive strong heat currents.
利用久保线性响应形式，我们推导了表达式，用于计算具有破缺反演对称性和自旋轨道相互作用（SOI）的铁磁金属中，磁化动力学产生的热电流的电子贡献。磁化动力学产生热电流的效应构成了热自旋轨道扭矩（TSOT）的昂萨格互易关系，即由于温度梯度而在磁化上产生扭矩。我们发现，由磁化动力学驱动的能量电流包含来自Dzyaloshinskii-Moriya相互作用（DMI）的贡献，为了提取热电流，需要从能量电流的久保线性响应中减去这一贡献。我们表明，DMI系数的表达式可以从DMI能量电流中优雅地推导出来。基于DMI的贝里相位理论与现代轨道磁化理论之间的形式类比，我们进而也对后者进行了能量电流方面的解释。基于第一性原理计算，我们研究了Mn/W(0 0 1)磁性双层中磁化动力学驱动的热电流的电子贡献。我们预测，快速畴壁驱动强热电流。
