Magnetoelectric topology: the rope weaving in parameter space

TL;DR

This paper reviews recent advances in the topology of magnetoelectric parameter space in multiferroics, highlighting topological behaviors during switching processes that could enable energy-efficient spintronics and quantum devices.

Contribution

It introduces the concept of magnetoelectric topology in multiferroics and summarizes recent experimental and theoretical developments in this emerging field.

Findings

Identification of topological behaviors during magnetoelectric switching

Introduction of Roman-surface and Riemann-surface magnetoelectricity

Potential applications in spintronics and quantum computing

Abstract

Topology, as a mathematical concept, has been introduced into condensed matter physics since the discovery of quantum Hall effect, which characterizes new physical scenario beyond the Landau theory. The topologically protected physical quantities, such as the dissipationless quantum transport of edge/surface states as well as magnetic/dipole quasi-particles like skyrmions/bimerons, have attracted great research enthusiasms in the past decades. In recent years, another kind of topology in condensed matter was revealed in the magnetoelectric parameter space of multiferroics, which deepens our understanding of magnetoelectric physics. This topical review summarizes recent advances in this area, involving three type-II multiferroics. With magnetism-induced ferroelectricity, topological behaviors can be manifested during the magnetoelectric switching processes driven by magnetic/electric fields, such as Roman-surface/Riemann-surface magnetoelectricity and magnetic crankshaft. These exotic topological magnetoelectric behaviors may be helpful to pursuit energy-efficient and precise-control devices for spintronics and quantum computing.