Energy, geometry, and topology of collective magnetic dynamics

Yaroslav Tserkovnyak, UCLA

I will review our recent work on transport phenomena engendered by large-angle magnetic dynamics, combining insights from differential geometry, topology, and overarching thermodynamic considerations. As a specific illustrative case, we study the transport of vorticity on curved dynamical two-dimensional magnetic membranes. We find that topological transport can be controlled by geometrically reducing symmetries, which enables processes that are not present in flat magnetic systems. To this end, we construct a vorticity 3-current obeying a continuity equation, which is immune to arbitrary local disturbances of the magnetic texture as well as spatiotemporal fluctuations of the membrane. We show how electric current can manipulate vortex transport in geometrically nontrivial magnetic systems. As an example, we propose a minimal setup that realizes an experimentally feasible energy storage device and discuss its thermodynamic efficiency in terms of a vorticity-transport counterpart of the thermoelectric "ZT" figure of merit.

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