Analogy between the magnetic dipole moment at the surface of a magnetoelectric and the electric charge at the surface of a ferroelectric

Abstract

In honor of Igor Dzyaloshinskii on his 90th birthday, we revisit his pioneering work on the linear magnetoelectric effect in light of the modern theory of ferroelectric polarization. We show that the surface magnetic dipole moment associated with magnetoelectric materials is analogous to the bound surface charge in ferroelectrics, in that it can be conveniently described in terms of a bulk magnetoelectric multipolization that is analogous to the ferroelectric polarization. We define the intrinsic surface magnetization to be this surface magnetic dipole moment per unit area, and provide a convenient recipe for extracting it for any surface plane, from knowledge of the bulk magnetic order. We demonstrate the procedure for the prototypical magnetoelectric material, Cr${}_2$O${}_3$, in which Dzyaloshinskii first identified the linear magnetoelectric effect, and compare the value of the intrinsic surface magnetization to recent experimental measurements. Finally, we argue that non-magnetoelectric antiferromagnets whose multipolization lattices do not contain zero should have an intrinsic surface magnetization, in the same way that non-polar insulators whose polarization lattices do not contain zero have an intrinsic surface charge.

12 pages, 9 figures

References in corpus (5)

• First-principles study of spontaneous polarization in multiferroic BiFeO${}_3$
• Ferroelectricity in ultra-thin perovskite films
• Towards a microscopic theory of toroidal moments in bulk periodic crystals
• Equilibrium magnetization at the boundary of a magnetoelectric antiferromagnet
• Vector Potential and Surface Magnetic Field in Magnetoelectric Antiferromagnetic Materials

Cited by in corpus (6)

• Surface Magnetization in Antiferromagnets: Classification, example materials, and relation to magnetoelectric responses
• Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products
• Spin-phonon interactions and magnetoelectric coupling in Co${}_4$$B_2$O${}_9$ ($B$ = Nb, Ta)
• Characterizing and Overcoming Surface Paramagnetism in Magnetoelectric Antiferromagnets
• Post deposition interfacial Néel temperature tuning in magnetoelectric B:Cr2O3
• Anti-symmetric Compton scattering in LiNiPO${}_4$: Towards a direct probe of the magneto-electric multipole moment