Geometric vector potentials from nonadiabatic spin dynamics

We propose a theoretical framework that captures the geometric vector potential emerging from the nonadiabatic spin dynamics of itinerant carriers subject to arbitrary magnetic textures. Our approach results in a series of constraints on the geometric potential and the nonadiabatic geometric phase associated with it. These constraints play a decisive role when studying, e.g., the geometric spin phase gathered by conducting electrons in ring interferometers under the action of in-plane magnetic textures, allowing a simple characterization of the topological transition recently reported by Saarikoski et al. [H. Saarikoski, J. E. Vázquez-Lozano, J. P. Baltanás, F. Nagasawa, J. Nitta, and D. Frustaglia, Phys. Rev. B 91, 241406(R) (2015)].

Figure 1

Conducting ring with traveling spin carriers (thin arrow) subject to a hybrid magnetic-field texture: a radial effective field (originated internally by spin-orbit coupling) plus a uniform in-plane field (of external origin). The global field texture undergoes a topological transition from a rotating setup (left) to a waving one (right) as the uniform in-plane component increases.