Hydrodynamic description of long-distance spin transport through noncollinear magnetization states: Role of dispersion, nonlinearity, and damping

Abstract

Nonlocal compensation of magnetic damping by spin injection has been theoretically shown to establish dynamic, noncollinear magnetization states that carry spin currents over micrometer distances. Such states can be generically referred to as dissipative exchange flows (DEFs) because spatially diffusing spin currents are established by the mutual exchange torque exerted by neighboring spins. Analytical studies to date have been limited to the weak spin injection assumption whereby the equation of motion for the magnetization is mapped to hydrodynamic equations describing spin flow and then linearized. Here, we analytically and numerically study easy-plane ferromagnetic channels subject to spin injection of arbitrary strength at one extremum under a unified hydrodynamic framework. We find that DEFs generally exhibit a nonlinear profile along the channel accompanied by a nonlinear frequency tuneability. At large injection strengths, we fully characterize a novel magnetization state we call a contact-soliton DEF (CS-DEF) composed of a stationary soliton at the injection site, which smoothly transitions into a DEF and exhibits a negative frequency tuneability. The transition between a DEF and a CS-DEF occurs at the maximum precessional frequency and coincides with the Landau criterion: a subsonic to supersonic flow transition. Leveraging the hydraulic-electrical analogy, the current-voltage characteristics of a nonlinear DEF circuit are presented. Micromagnetic simulations of nanowires that include magnetocrystalline anisotropy and non-local dipole fields are in qualitative agreement with the analytical results. The magnetization states found here along with their characteristic profile and spectral features provide quantitative guidelines to pursue an experimental demonstration of DEFs in ferromagnetic materials and establishes a unified description for long-distance spin transport.

All‐Electrical Magnon Transport Experiments in Magnetically Ordered Insulators

“…This damping compensation effect via a DC charge current may allow all-electrical experimental studies of magnon transport in the limit of spin superfluidity and magnon BoseÀEinstein condensates, [23,27,28,[190][191][192] as discussed in recent theoretical publications. [29,[193][194][195][196][197][198][199][200][201][202] For example, the study by Takei et al [197] provides analytical expressions for the evolution of the magnon transport close to the point of damping compensation. Another aspect not covered in this brief discussion is contribution from localized magnon modes, which in general exhibit lower threshold values for achieving damping compensation and may also affect the magnon transport.…”

Perspectives on spin hydrodynamics in ferromagnetic materials

“…Micromagnetic simulations have corroborated the existence of this solution both for ferromagnets [68], termed a contact-soliton DEF, and YIG [70], termed a soliton-screened spin superfluid. Detailed analytical derivations of all these modes under the DH formulation can be found in Ref.…”

“…For the case of a channel subject to spin injection on one extremum,ū 0 = 0 andū L = 0, both linear [28,69] and nonlinear [25,68] theory have been used to obtain solutions to the BVP that feature algebraic or nearalgebraic spin transport. Furthermore, these equilibrium solutions consist of a coherent, single-frequency precessional state.…”

“…Forū 0 = 0.4, the density n exhibits a nonlinear profile as shown by the numerical solution depicted by the solid blue curves. These states have been termed dissipative exchange flows (DEFs) [68]. For even stronger injection, such that the conditions at the injection site are supersonic, a so-called contact soliton centered at x = 0 is established, which then matches to a DEF solution.…”

“…Symmetry breaking due to nonlocal dipole fields has been argued to preclude the stabilization of linear DEFs or spin superfluids beyond the distance of an exchange length [73]. However, micromagnetic simulations [25,67,68,70] have demonstrated that SDWs and linear DEF solutions can be stabilized even in the presence of nonlocal dipole fields. Nonlocal dipole has also been studied in the context of the spatial modulation of SDWs [77].…”