Modulated spin helicity stabilized by incommensurate orbital density waves in a quadruple perovskite manganite

Abstract

Through a combination of neutron diffraction and Landau theory we describe the spin ordering in the ground state of the quadruple perovskite manganite ${\mathrm{CaMn}}_{7}{\mathrm{O}}_{12}$---a magnetic multiferroic supporting an incommensurate orbital density wave that onsets above the magnetic ordering temperature, ${T}_{\mathrm{N}1}=90$ K. The multi-$\mathbf{k}$ magnetic structure in the ground state was found to be a nearly-constant-moment helix with modulated spin helicity, which oscillates in phase with the orbital occupancies on the ${\mathrm{Mn}}^{3+}$ sites via trilinear magneto-orbital coupling. Our phenomenological model also shows that, above ${T}_{\mathrm{N}2}=48$ K, the primary magnetic order parameter is locked into the orbital wave by an admixture of helical and collinear spin density wave structures. Furthermore, our model naturally explains the lack of a sharp dielectric anomaly at ${T}_{\mathrm{N}1}$ and the unusual temperature dependence of the electrical polarization.