Spiral ground state against ferroelectricity in the frustrated magnet BiMnFe2O6

The spiral magnetic structure and underlying spin lattice of BiMnFe${}_{2}$O${}_{6}$ are investigated by low-temperature neutron powder diffraction and density functional theory band structure calculations. In spite of the random distribution of the Mn${}^{3+}$ and Fe${}^{3+}$ cations, this centrosymmetric compound undergoes a transition into an incommensurate antiferromagnetically ordered state below ${T}_{N}\ensuremath{\simeq}220$ K. The magnetic structure is characterized by the propagation vector $\mathbf{k}=[0,\ensuremath{\beta},0]$ with $\ensuremath{\beta}\ensuremath{\simeq}0.14$ and the $P{22}_{1}{2}_{1}{1}^{\ensuremath{'}}(0\ensuremath{\beta}0)0s0s$ magnetic superspace symmetry. It comprises antiferromagnetic helixes propagating along the $b$ axis. The magnetic moments lie in the $\mathit{ac}$ plane and rotate about $\ensuremath{\pi}(1+\ensuremath{\beta})\ensuremath{\simeq}204.8$-deg angle between the adjacent magnetic atoms along $b$. The spiral magnetic structure arises from the peculiar frustrated arrangement of exchange couplings in the $\mathit{ab}$ plane. The antiferromagnetic coupling along the $c$ axis cancels the possible electric polarization and prevents ferroelectricity in BiMnFe${}_{2}$O${}_{6}$.