Perspective: (Beyond) spin transport in insulators
Insulating materials with dynamical spin degrees of freedom have recently emerged as viable conduits for spin flows. Transport phenomena harbored therein are, however, turning out to be much richer than initially envisioned. In particular, the topological properties of the collective order-parameter textures can give rise to conservation laws that are not based on any specific symmetries. The emergent continuity relations are thus robust against structural imperfections and anisotropies, which would be detrimental to the conventional spin currents (that rely on approximate spin-rotational symmetries). The underlying fluxes thus supersede the notion of spin flow in insulators, setting the stage for nonequilibrium phenomena termed topological hydrodynamics. Here, we outline our current understanding of the essential ingredients, based on the energetics of the electrically-controlled injection of topological flows through interfaces, along with a reciprocal signal generation by the outflow of the conserved quantity. We will focus on two examples for the latter: winding dynamics in one-dimensional systems, which supplants spin superfluidity of axially-symmetric easy-plane magnets, and skyrmion dynamics in two-dimensional Heisenberg-type magnets. These examples will illustrate the essential common aspects of topological flows and hint on generic strategies for their generation and detection in spintronic systems. Generalizations to other dimensions and types of order-parameter spaces will also be briefly discussed.