Modulated spin helicity stabilized by incommensurate orbital density   waves in a quadruple perovskite manganite
  Through a combination of neutron diffraction and Landau theory we describe the spin ordering in the ground state of the quadruple perovskite manganite CaMn7O12 - a magnetic multiferroic supporting an incommensurate orbital density wave that onsets above the magnetic ordering temperature, TN1 = 90 K. The multi-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 Mn3+ sites via trilinear magneto-orbital coupling. Our phenomenological model also shows that, above TN2 = 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 TN1 and the unusual temperature dependence of the electrical polarisation. 
R. D. Johnson, D. D. Khalyavin, P. Manuel, A. Bombardi, C. Martin, L.   C. Chapon and P. G. Radaelli
cond-mat.str-el