### On-line SPICE-SPIN+X Seminars

### On-line Seminar: 03.11.2021 - 15:00 German Time

**Analytic and ab initio theory of magnetization dynamics**

### Peter Oppeneer, Uppsala University

The Landau-Lifshitz-Gilbert (LLG) equation forms a cornerstone of contemporary magnetism research, yet it was originally proposed on the basis of phenomenological considerations. To put the equation on a fundamental footing, we start from the relativistic Dirac-Kohn-Sham equation, consider the motion of spin angular momentum in an external electromagnetic field and show that it leads to the LLG equation with anisotropic damping, as well as to additional terms, such as the field-derivative torque, the optical spin-orbit torque, spin-transfer torque, and inertial term [1,2]. Besides providing a foundational basis for the LLG equation, our analytic theory predicts new effects that could be observed in experiments.

Electric field or current induced spin-orbit torques (SOTs) arising from the spin Hall effect or Rashba-Edelstein effect (REE) have recently emerged as promising tools to achieve efficient magnetization dynamics [3]. To explore the origin of SOTs on a materials’ specific level, we employ density functional and linear-response theory to calculated ab initio the electric field induced magnetic polarizations. For the noncentrosymmetric antiferromagnets CuMnAs and Mn2Au we compute the induced polarizations and find that there exists dominantly an orbital Rashba-Edelstein effect that is much larger than the spin REE and does not require spin-orbit coupling to exist [4]. The staggered, field-induced orbital polarization moreover exhibits Rashba-type symmetry in contrast to the induced spin polarization.

Considering typical bilayer systems consisting of Pt and 2 monolayers of a 3d element (Co, Ni, Cu) we compute in a layer-resolved manner the spin and orbital conductivities and spin and orbital moment accumulations. We identify the contributions that lead to the fieldlike SOT and the dampinglike SOT, which are mainly the spin REE and magnetic spin Hall effect, respectively. The current-induced orbital accumulation transverse to the electric field is always much larger than the corresponding spin accumulation and exist without spin-orbit interaction [5]. This exemplifies that the induced orbital polarization is the primary response to the electric field and suggests the possibility of utilizing large orbital effects in light-metal devices.

[2] R. Mondal, M. Berritta, and P.M. Oppeneer, Phys. Rev. B 94, 144419 (2016); Phys. Rev. B 98, 214429 (2018).

[3] A. Manchon, J. Železný, I.M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello, and P. Gambardella, Rev. Mod. Phys. 91, 035004 (2019).

[4] L. Salemi, M. Berritta, A.K. Nandy and P.M. Oppeneer, Nature Commun. 10, 5381 (2019).

[5] L. Salemi, M. Berritta, and P.M. Oppeneer, Phys. Rev. Mater. 5, 074407 (2021).

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