# Polarizability of electrically induced magnetic vortex plasma

## TL;DR

This paper investigates how electric fields can create and manipulate magnetic vortices in magnetoelectric materials, revealing a new form of topological defect plasma with temperature-dependent polarizability.

## Contribution

It introduces the concept of electric field-induced magnetic vortex plasma and analytically and numerically studies its density distribution and polarizability.

## Key findings

- Electric fields can create localized magnetic vortex structures.
- The polarizability depends on temperature as lpha  1/T^{1-ta}.
- The results align with Euclidean random matrix theory predictions.

## Abstract

Electric field control of magnetic structures, particularly topological defects in magnetoelectric materials, draws a great attention in recent years, which has led to experimental success in creation and manipulation by electric field of single magnetic defects, such as domain walls and skyrmions. In this work we explore a scenario of electric field creation of another type of topological defects -- magnetic vortices and antivortices, which are characteristic for materials with easy plane (XY) symmetry. Each magnetic (anti)vortex in magnetoelectric materials (such as type-II multiferroics) possesses a quantized magnetic and an electric charge, where the former is responsible for interaction between vortices and the latter couples the vortices to electric field. This property of magnetic vortices opens a peculiar possibility of creation of magnetic vortex plasma by non-uniform electric fields. We show that the electric field, created by a cantilever tip, produces a "magnetic atom" with a localized spatially ordered spot of vortices ("nucleus" of the atom) surrounded by antivortices ("electronic shells"). We analytically find the vortex density distribution profile and temperature dependence of polarizability of this structure and confirm it numerically. We show that electric polarizability of the "magnetic atom" depends on temperature as $\alpha \sim 1/T^{1-\eta}$ ($\eta>0$), which is consistent with Euclidean random matrix theory prediction.