Magnetic Domain Walls as Hosts of Spin Superfluids and Generators of Skyrmions

A domain wall in a magnet with easy-axis anisotropy is shown to harbor spin superfluid associated with its spontaneous breaking of the U(1) spin-rotational symmetry. The spin superfluid is shown to have several topological properties, which are absent in conventional superfluids. First, the associated phase slips create and destroy Skyrmions to obey the conservation of the total Skyrmion charge, which allows us to use a domain wall as a generator and detector of Skyrmions. Second, the domain wall engenders the emergent magnetic flux for magnons along its length, which are proportional to the spin supercurrent flowing through it, and thereby provides a way to manipulate magnons. Third, the spin supercurrent can be driven by the magnon current traveling across it owing to the spin transfer between the domain wall and magnons, leading to the magnonic manipulation of the spin superfluid. The theory for superfluid spin transport within the domain wall is confirmed by numerical simulations.

Figure 1

(a) An illustration of a DW stretched along the $x$ direction, which is carrying a spin supercurrent. (b) Mapping of the spin texture in (a) onto the unit sphere, characterized by its Skyrmion charge $Q=1$. (c) An illustration for the simplified description of the DW using its vertical position $Y(x,t)$ and in-plane angle $\mathrm{\Phi }(x,t)$. (d) Mapping of the DW state in (c) onto the unit circle, characterized by its winding number $w=1$.

Figure 2

A schematic illustration of a phase slip that decreases the winding number $w$ from 1 in the initial state (a) to 0 in the final state (c) via the intermediate state (b), in which $w$ is not well defined. (c) An isolated Skyrmion with the Skyrmion charge $Q=\mathrm{\Delta }w=1$ leaves the ferromagnet through the boundary.

Figure 3

(a) An experimental setup for probing phase slips. (b) The linear relationship between the two phase-slip-induced voltages, $\mathrm{\Delta }{V}_{\mathrm{Pt}}$ in the platinum and $V_m$ in the metals. (c) The temperature dependence of $V_m/I$ induced by thermally activated phase slips with the energy barrier $E_b$.

Figure 4

(a) Magnons are deflected by the emergent magnetic field engendered by the spin supercurrent in the DW. (b) The magnon current $I^m$ flowing across the DW injects the spin supercurrent $I^s=2\hslash I^m$ into the wall via the magnonic spin-transfer torque.