Large ferroelectric polarization in the new double perovskite NaLaMnWO$_{6}$ induced by non-polar instabilities

Based on density functional theory calculations and group theoretical analysis, we have studied NaLaMnWO$_{6}$ compound which has been recently synthesized [Phys. Rev. B 79, 224428 (2009)] and belongs to the $AABB{rm O}_{6}$ family of double perovskites. At low temperature, the structure has monoclinic $P2_{1}$ symmetry, with layered ordering of the Na and La ions and rocksalt ordering of Mn and W ions. The Mn atoms show an antiferromagnetic (AFM) collinear spin ordering, and the compound has been reported as a potential multiferroic. By comparing the low symmetry structure with a parent phase of $P4/nmm$ symmetry, two distortion modes are found dominant. They correspond to MnO$_{6}$ and WO$_{6}$ octahedron textit{tilt} modes, often found in many simple perovskites. While in the latter these common tilting instabilities yield non-polar phases, in NaLaMnWO$_{6}$ the additional presence of the $A$-$A^{}$ cation ordering is sufficient to make these rigid unit modes as a source of the ferroelectricity. Through a trilinear coupling with the two unstable tilting modes, a significant polar distortion is induced, although the system has no intrinsic polar instability. The calculated electric polarization resulting from this polar distortion is as large as $sim$ 16 ${mu}{rm C/cm^{2}}$. Despite its secondary character, this polarization is coupled with the dominant tilting modes and its switching is bound to produce the switching of one of two tilts, enhancing in this way a possible interaction with the magnetic ordering. The transformation of common non-polar purely steric instabilities into sources of ferroelectricity through a controlled modification of the parent structure, as done here by the cation ordering, is a phenomenon to be further explored.