Thermally induced magnonic spin current, thermomagnonic torques, and domain-wall dynamics in the presence of Dzyaloshinskii-Moriya interaction

Abstract

Thermally activated domain-wall (DW) motion in magnetic insulators has been considered theoretically, with a particular focus on the role of Dzyaloshinskii-Moriya interaction (DMI) and thermomagnonic torques. The thermally assisted DW motion is a consequence of the magnonic spin current due to the applied thermal bias. In addition to the exchange magnonic spin current and the exchange adiabatic and the entropic spin transfer torques, we also consider the DMI-induced magnonic spin current, thermomagnonic DMI fieldlike torque, and the DMI entropic torque. Analytical estimations are supported by numerical calculations. We found that the DMI has a substantial influence on the size and the geometry of DWs, and that the DWs become oriented parallel to the long axis of the nanostrip. Increasing the temperature smoothes the DWs. Moreover, the thermally induced magnonic current generates a torque on the DWs, which is responsible for their motion. From our analysis it follows that for a large enough DMI the influence of DMI-induced fieldlike torque is much stronger than that of the DMI and the exchange entropic torques. By manipulating the strength of the DMI constant, one can control the speed of the DW motion, and the direction of the DW motion can be switched, as well. We also found that DMI not only contributes to the total magnonic current, but also it modifies the exchange magnonic spin current, and this modification depends on the orientation of the steady-state magnetization. The observed phenomenon can be utilized in spin caloritronics devices, for example in the DMI based thermal diodes. By switching the magnetization direction, one can rectify the total magnonic spin current.

Semirealistic tight-binding model for spin-orbit torques

“…[40]). Various techniques have been proposed including Wannier interpolation of the band structure [41][42][43][44], Korringa-Kohn-Rostoker method [45,46], or real-space Hamiltonians with tight-binding linear muffin-tin orbitals [47,48]. While the first two methods are well adapted to compute the Kubo-Streda formula, the latter is suitable for two-terminal simulations, following the Landauer-Büttiker scheme.…”

Spin caloritronics, origin and outlook

“…46 It should be noted that others have chosen to distinguish the heat currents of each spin channels. 4748 We proceed now to an identification of the physical meaning of the matrices in equation (11).…”

“…This type of torque, associated with the Dzyaloshinskii-Moriya interaction, was recently identified and its role in the dynamics of domain walls was analyzed. 11 The method of master equations was used to describe a single quantum dot with spin-dependent electron temperatures due to its connection to ferromagnetic leads. 12 The Kubo formalism of linear response theory has been applied to describe thermal spin orbit torques and the reciprocal effect, the heat current associated with magnetization dynamics.…”

Releasing latent chirality in magnetic two-dimensional materials

“…Ability of such controlled release of latent DMI is of clear fundamental value, but also bears relevance to a spectrum of potential applications in magnonics and spintronics. 31,32 To describe the magnetic interactions, we consider Heisenberg spin Hamiltonian H = 1 2 i,j S i J ij S j + i S i A ii S j , where S i = (S x i , S y i , S z i ) is the spin vector of the ith site. J ij and A ii are 3 × 3 matrices describing the total magnetic exchange interaction between the different sites and the single-ion anisotropy (SIA), respectively.…”