Abstract
A keen interest towards technological implications of spin-orbit driven magnetization dynamics requests a proper theoretical description, especially in the context of a microscopic framework, to be developed. Indeed, magnetization dynamics is so far approached within Landau-Lifshitz-Gilbert equation which characterizes torques on magnetization on purely phenomenological grounds. Particularly, spin-orbit coupling does not respect spin conservation, leading thus to angular momentum transfer to lattice and damping as a result. This mechanism is accounted by the Gilbert damping torque which describes relaxation of the magnetization to equilibrium. In this study we work out a microscopic Kubo-Středa formula for the components of the Gilbert damping tensor and apply the elaborated formalism to a two-dimensional Rashba ferromagnet in the weak disorder limit. We show that an exact analytical expression corresponding to the Gilbert damping parameter manifests linear dependence on the scattering rate and retains the constant value up to room temperature when no vibrational degrees of freedom are present in the system. We argue that the methodology developed in this paper can be safely applied to bilayers made of non- and ferromagnetic metals, e.g., CoPt.
Highlights
A keen interest towards technological implications of spin-orbit driven magnetization dynamics requests a proper theoretical description, especially in the context of a microscopic framework, to be developed
It was clearly demonstrated that in bilayer systems made of a nonmagnetic metal (NM) and a ferromagnet material (FM) the Gilbert damping is drastically enhanced as compared to bulk FMs20–24
We provide the derivation of a Kubo-Středa formula for the components of the Gilbert damping tensor and illustrate our approach for a two-dimensional Rashba ferromagnet, that can be modeled by the interface between NM and FM layers
Summary
Consider a heterostructure made of NM with strong spin-orbit interaction covered by FM layer as shown in Fig. 1, e.g., CoPt. In general FMs belong to the class of strongly correlated systems with partially filled d or f orbitals which are responsible for the formation of localized magnetic moments The latter can be described in terms of a vector field m(r, t) referred to as magnetization, that in comparison to electronic time and length scales slowly varies and interacts with an itinerant subsystem. The first term in f describes precession around the effective magnetic field Heff created by the localized moments of FM, whereas the second term in (2) is determined by nonequilibrium spin density of conduction electrons of NM at the interface, s(r, t). Knowing the lesser Green’s function, G< (rt; rt), one can evaluate nonequilibrium spin density of conduction electrons induced by slow variation of magnetization orientation, sμ(r, t).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
