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Topological defects in ordered states with spontaneously broken symmetryoften have unusual physical properties, such as fractional electric charge or aquantised magnetic field-flux, originating from their non-trivial topology.Coupled topological defects in systems with several coexisting orders give riseto unconventional functionalities, such as the electric-field control ofmagnetisation in multiferroics resulting from the coupling between theferroelectric and ferromagnetic domain walls. Hexagonal manganites provide anextra degree of freedom: In these materials, both ferroelectricity andmagnetism are coupled to an additional, non-ferroelectric structural orderparameter. Here we present a theoretical study of topological defects inhexagonal manganites based on Landau theory with parameters determined fromfirst-principles calculations. We explain the observed flip of electricpolarisation at the boundaries of structural domains, the origin of theobserved discrete vortices, and the clamping between ferroelectric andantiferromagnetic domain walls. We show that structural vortices inducemagnetic ones and that, consistent with a recent experimental report,ferroelectric domain walls can carry a magnetic moment.

Landau theory of topological defects in multiferroic hexagonal manganites