Radboud University, Institute for Molecules and Materials, NL-6525 AJ Nijmegen, Netherlands.
Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway.
Phys Rev Lett. 2018 Aug 24;121(8):086802. doi: 10.1103/PhysRevLett.121.086802.
Dzyaloshinskii-Moriya interaction (DMI) is investigated in a 2D ferromagnet (FM) with spin-orbit interaction of Rashba type at finite temperatures. The FM is described in the continuum limit by an effective s-d model with arbitrary dependence of spin-orbit coupling (SOC) and kinetic energy of itinerant electrons on the absolute value of momentum. In the limit of weak SOC, we derive a general expression for the DMI constant D from a microscopic analysis of the electronic grand potential. We compare D with the exchange stiffness A and show that, to the leading order in small SOC strength α_{R}, the conventional relation D=(4mα_{R}/ℏ)A, in general, does not hold beyond the Bychkov-Rashba model. Moreover, in this model, both A and D vanish at zero temperature in the metal regime (i.e., when two spin sub-bands are partly occupied). For nonparabolic bands or nonlinear Rashba coupling, these coefficients are finite and acquire a nontrivial dependence on the chemical potential that demonstrates the possibility to control the size and chirality of magnetic textures by adjusting a gate voltage.
Dzyaloshinskii-Moriya 相互作用（DMI）在具有有限温度的 Rashba 型自旋轨道相互作用的二维铁磁体（FM）中进行了研究。FM 在连续体极限中由具有任意自旋轨道耦合（SOC）和巡游电子动能对动量绝对值依赖性的有效 s-d 模型来描述。在弱 SOC 极限下，我们从电子巨势的微观分析中推导出 DMI 常数 D 的一般表达式。我们将 D 与交换弹性常数 A 进行比较，并表明，在小 SOC 强度α_{R}的主导阶次下，一般来说，在比乔科夫-拉什巴模型更广泛的范围内，传统关系 D=(4mα_{R}/ℏ)A 并不成立。此外，在该模型中，当金属区域（即当两个自旋子带部分占据时）中 A 和 D 在零温度下均为零。对于非抛物能带或非线性 Rashba 耦合，这些系数是有限的，并且对化学势具有非平凡的依赖性，这表明通过调节栅极电压可以控制磁织构的大小和手性。
