# Geometric vector potentials from non-adiabatic spin dynamics

## TL;DR

This paper develops a theoretical framework to understand the geometric vector potential arising from non-adiabatic spin dynamics in carriers influenced by magnetic textures, elucidating topological transitions in electron spin phases.

## Contribution

It introduces a novel theoretical approach that constrains the geometric potential and phase in non-adiabatic spin systems, aiding the analysis of topological transitions.

## Key findings

- Constraints on geometric potential and phase derived
- Characterization of topological transition in magnetic textures
- Application to ring interferometers with in-plane magnetic textures

## Abstract

We propose a theoretical framework that captures the geometric vector potential emerging from the non-adiabatic spin dynamics of itinerant carriers subject to arbitrary magnetic textures. Our approach results in a series of constraints on the geometric potential and the non-adiabatic geometric phase associated with it. These constraints play a decisive role when studying 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. [Phys. Rev. B 91, 241406(R) (2015)] in Ref. 1.