  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.
