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Through first-principles density functional calculations, the magnetic ground state and electronic structure of mixed-valent manganite SrMn7O12 in the rhombohedral symmetry are investigated in detail. Our calculations show clearly that the possible magnetic ground state accommodates a particular helical spin order responsible for the insulating state in SrMn7O12. The giant ferroelectric polarization is revealed, which is almost purely from the electronic contribution rather than the ionic displacements and is closely related to the magnetism. The influence of the on-site Coulomb interaction and spin-orbit coupling on the electronic structure and multiferroicity is also discussed. The present results suggest that SrMn7O12 is a promising multiferroic candidate with desirable properties.

A magnetic skyrmion lattice is a microstructure consisting of hexagonally aligned skyrmions. While a skyrmion as a topologically protected carrier of information promises a number of applications, an easily accessible probe of the skyrmion and skyrmion lattice at mesoscopic scale is of significance. It is known that neutron scattering, Lorentz transmission electron microscopy, and spin-resolved STM as effective probes of skyrmions have been established. In this work, we propose that the spatial contour of dielectric permittivity in a skyrmion lattice with ferromagnetic interaction and in-plane (xy) Dzyaloshinskii-Moriya (DM) interaction can be used to characterize the skyrmion lattice. The phase field and Monte Carlo simulations are employed to develop the one-to-one correspondence between the magnetic skyrmion lattice and dielectric dipole lattice, both exhibiting the hexagonal symmetry. Under excitation of in-plane electric field in the microwave range, the dielectric permittivity shows the dumbbell-like pattern with the axis perpendicular to the electric field, while it is circle-like for the electric field along the z-axis. The dependences of the spatial contour of dielectric permittivity on external magnetic field along the z-axis and dielectric frequency dispersion are discussed.