Topological transport of vorticity in Heisenberg magnets

Abstract

We study a robust topological transport carried by vortices in a thin film of an easy-plane magnetic insulator between two metal contacts. A vortex, which is a nonlocal topological spin texture in twodimensional magnets, exhibits some beneficial features as compared to skyrmions, which are local topological defects. In particular, the total topological charge carried by vorticity is robust against local fluctuations of the spin order-parameter magnitude. We show that an electric current in one of the magnetized metal contacts can pump vortices into the insulating bulk. Diffusion and two-dimensional nonlocal Coulomb-like interaction between these vortices will establish a steadystate vortex flow. Vortices leaving the bulk produce an electromotive force at another contact, which is related to the current-induced vorticity pumping by the Onsager reciprocity. The voltage signal decays algebraically with the separation between two contacts, similarly to a superfluid spin transport. Finally, the vorticity and closely related skyrmion type topological hydrodynamics are generalized to arbitrary dimensions, in terms of nonsingular order-parameter vector fields.

Transport signature of the magnetic Berezinskii-Kosterlitz-Thouless transition

“…First, a meron represents the vortex spin-field configuration -an example being shown in Fig. 1 (a) -and hence carries the quantized spin current vorticity [34,[43][44][45]. By using the formal analogy (see Appendix A) between the charge current carried by the Cooper pair condensate J = qK∇φ/ħ h (with K the phase stiffness and φ the Cooper-pair wavefunction phase) and the spin current carried by the easy-plane order-parameter texture J sp z = −K∇ϕ (with K the spin stiffness and ϕ the azimuthal angle of the magnetic order parameter) and by considering that the vorticity is defined in terms of the gradient of the dimensionless phase/angle variables (∇φ and ∇ϕ), we substitute on the right-hand side of Eq.…”

Spin superfluidity in noncollinear antiferromagnets

“…In particular, we estimate that iron jarosites can be promising for realizing spin superfluidity in nAFMs. nAFMs hold promise for realizing spin flows with low dissipation and the theoretical framework presented here can be useful for exploring the interplay between transport phenomena [55,56] and topological defects, i.e., domain walls [33,34], or skyrmions [57].…”

Quantum hydrodynamics of vorticity

“…If µL = µR = µ (which could be accomplished by attaching the same magnet symmetrically to both sides), an equilibrium state with the vortex chemical potential µ is established in the steady state, which has a vanishing vortex flux. If µL = µR, a dc vortex flux (driven by thermal and/or quantum fluctuations) is expected towards the lower chemical-potential side [10].…”

“…The longitudinal conductivity σ xx reflects the intrinsic vorticity transport across the bosonic lattice. In the particle-superfluid limit, when the vorticity is carried by the plasma of solitonic defects with quantized topological charge ±1 and mobility M , the corresponding conductivity is simply σ xx = 2ρM , where ρ is the density of the unbound vortex-antivortex pairs (well above the Kosterlitz-Thouless transition) [10]. The associated diffusion coefficient is given by D = k B T M , according to the Einstein-Smoluchowski relation.…”