# Controlling topological superconductivity by magnetization dynamics

## TL;DR

This paper theoretically investigates how magnetization dynamics in a chain of magnetic impurities on a superconductor can induce and control topological superconducting phases and Majorana bound states, offering a new way to manipulate topological states.

## Contribution

It introduces a rotating wave approximation to derive an effective Hamiltonian for precessing magnetic impurity chains, revealing controllable topological phase transitions and Majorana states.

## Key findings

- Precession frequency controls topological phase transitions.
- Effective Hamiltonian exhibits non-trivial topological properties.
- Proposes experimental methods for manipulating magnetic textures.

## Abstract

We study theoretically a chain of precessing classical magnetic impurities in an $s$-wave superconductor. Utilizing a rotating wave description, we derive an effective Hamiltonian that describes the emergent Shiba band. We find that this Hamiltonian shows non-trivial topological properties, and we obtain the corresponding topological phase diagrams both numerically and analytically. We show that changing the precession frequency offers a control over topological phase transitions and the emergence of Majorana bound states. We propose driving the magnetic impurities or magnetic texture into precession by means of spin-transfer torque in a spin-Hall setup, and manipulate it using spin superfluidity in the case of planar magnetic order.