[Paper Review] Coupled electricity and magnetism in solids: multiferroics and beyond

D. I. Khomskiǐ|arXiv (Cornell University)|Oct 17, 2015

Multiferroics and related materials61 references3 citations

TL;DR

This paper provides a comprehensive theoretical overview of coupled electricity and magnetism in solids, focusing on multiferroics and related phenomena such as magnetoelectric effects, magnetic domain walls, and spin textures like skyrmions. It explains how spin-driven ferroelectricity and linear magnetoelectric coupling arise from symmetry and microscopic mechanisms, with key results showing that spin waves and topological spin textures can carry electric polarization, enabling electric control of magnetism and new functionalities in spintronic devices.

ABSTRACT

The interplay of electricity and magnetism, one of the cornerstones of modern physics, takes a special form in solids in such phenomena as magnetoelectricity and the possibility of multiferroic behaviour. In this paper I give a short survey of the main notions of this field, paying special attention to microscopic aspects. Some related phenomena, such as electric activity of magnetic domain walls, etc., are also shortly discussed.

Motivation & Objective

• To provide a foundational understanding of the microscopic origins of magnetoelectric coupling and multiferroic behavior in solids.
• To explore how magnetic ordering and spin textures—such as domain walls, vortices, and skyrmions—can induce or respond to electric polarization.
• To highlight the potential for electric-field control of magnetic states, enabling low-power spintronic devices.
• To connect theoretical concepts with experimental observations, including the magnetoelectric effect in Cr2O3 and skyrmions.
• To establish the relevance of multiferroics beyond their own class, influencing broader fields like topological spintronics and quantum materials.

Proposed method

• Analyzes symmetry constraints and group theory to determine allowed magnetoelectric coupling tensors (e.g., symmetric αij for radial vortices, antisymmetric for transverse effects).
• Applies Landau-Ginzburg-Devonshire theory to describe coupled ferroelectric and magnetic order parameters in multiferroics.
• Uses a classical analogy between magnetic currents and electric fields to explain the electric dipole moment induced by propagating spin waves (magnons).
• Examines spin configurations such as cycloids, vortices, and skyrmions to determine their magnetoelectric response based on spin topology.
• Reviews experimental realizations, including the linear magnetoelectric effect in Cr2O3 and electric activity in skyrmions observed in [70].
• Draws parallels between Maxwell’s equations and the duality between electric and magnetic phenomena to explain emergent electric fields in dynamic spin textures.

Experimental results

Research questions

• RQ1 How can a magnetic ordering induce a spontaneous electric polarization in certain insulating materials?
• RQ2 What microscopic mechanisms underlie the linear magnetoelectric effect in multiferroics, and how do they depend on crystal symmetry?
• RQ3 Can topological spin textures such as skyrmions or magnetic vortices exhibit a magnetoelectric response, and if so, what is its nature?
• RQ4 How do spin waves (magnons) in magnetic insulators generate an electric dipole moment, and what is the physical origin of this effect?
• RQ5 What are the implications of electrically induced magnetization or polarization for future low-power electronic and memory devices?

Key findings

• The linear magnetoelectric effect was theoretically predicted by Dzyaloshinskii in 1960 and experimentally confirmed in Cr2O3, establishing the first known magnetoelectric material.
• Multiferroics such as Ni–I boracite and rare-earth manganites exhibit coexisting ferroelectric and magnetic order, enabling electric-field control of magnetism.
• Spin-driven ferroelectricity arises from spin cycloids in type-II multiferroics, where the spin spiral breaks inversion symmetry and induces a net polarization.
• Magnetic skyrmions can exhibit both transverse and longitudinal magnetoelectric responses depending on their topology, with experimental evidence reported in [70].
• Spin waves in ferromagnets carry both magnetization and an induced electric dipole perpendicular to both the wavevector and magnetization, due to effective magnetic currents.
• The electric activity of magnons can be understood via classical duality: a precessing magnetic dipole (equivalent to a current loop) generates an electric field, analogous to Faraday’s law.