Improper magnetic ferroelectricity of nearly pure electronic nature in helicoidal spiral CaMn 7 O 12

The noncollinear cycloidal magnetic order breaks the inversion symmetry in CaMn$_{7}$O$_{12}$, generating one of the largest spin-orbit driven ferroelectric polarizations measured to date. In this Letter, the microscopic origin of the polarization, including its direction, charge density redistribution, magnetic exchange interactions, and its coupling to the spin helicity, is explored via first principles calculations. The Berry phase computed polarization exhibits almost pure electronic behavior, as the Mn displacements are negligible, $\approx$~0.7~m\textrm{\AA}. The polarization magnitude and direction are both determined by the Mn spin current, where the \emph{p}-\emph{d} orbital mixing is driven by the inequivalent exchange interactions within the \emph{B}-site Mn cycloidal spiral chains along each Cartesian direction. We employ the generalized spin-current model with Heisenberg-exchange Dzyaloshinskii-Moriya interaction energetics to provide insight into the underlying physics of this spin-driven polarization. Persistent electronic polarization induced by helical spin order in nearly inversion-symmetric ionic crystal lattices suggests opportunities for ultrafast magnetoelectric response.