Asymmetric and Symmetric Exchange in a Generalized 2D Rashba Ferromagnet

Abstract

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.

Enhancement of perpendicular magnetic anisotropy and Dzyaloshinskii–Moriya interaction in thin ferromagnetic films by atomic-scale modulation of interfaces

“…Therefore, at highly disordered interfaces such as those studied here, the effects due to spin-orbit coupling, such as the IDMI, are expected to be enhanced. The dependence of the IDMI and the spin Hall effect on disorder strength may be probed based on the nonequilibrium Green function in the Keldysh formalism 50 . This scattering is increased when the interfacial surface becomes less smooth, especially when intermixing is present.…”

Electrically driven spin torque and dynamical Dzyaloshinskii-Moriya interaction in magnetic bilayer systems

“…We note that D 1 vanishes in the clean limit with τ → ∞. Note that D 1 does not vanish in the three-dimensional case or in the half-metallic case with J ex > ε F [40] even in the clean limit.…”

“…(Note that m × (a 2 / )δH DMI /δm leads to T 1 + T 2 ). The contribution D 1 (∝ α R ) appears even in the steady Rashba system [40,43,44]. Recent experiments indeed demonstrated voltage-induced variations of the interfacial DMI [45,46], which were ascribed to this steady Rashba contribution.…”

Light-induced Dzyaloshinskii-Moriya interactions in antiferromagnetic metals

“…In another approach, the origin of DM interactions is attributed to a Doppler shift due to an intrinsic spin current induced by SOC [20]. Several different approaches based on the Berry phase formalism and the spin-spin correlation functions have been developed recently to compute the DM interactions of realistic band structures in both FM and AFM systems in equilibrium [21][22][23][24][25]. Equilibrium DM interaction might be enhanced and even induced in magnetic thin films by breaking the inversion symmetry via, e.g., sandwiching a magnetic slab between two different layers, using proximity effects in heavy-metal (HM) and magnetic film heterostructures [26][27][28][29][30], or applying electric gate voltages and lattice strains [31][32][33].…”