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Based on density functional theory calculations and group theoreticalanalysis, we have studied NaLaMnWO$_{6}$ compound which has been recentlysynthesized [Phys. Rev. B 79, 224428 (2009)] and belongs to the $AA'BB'{\rmO}_{6}$ family of double perovskites. At low temperature, the structure hasmonoclinic $P2_{1}$ symmetry, with layered ordering of the Na and La ions androcksalt ordering of Mn and W ions. The Mn atoms show an antiferromagnetic(AFM) collinear spin ordering, and the compound has been reported as apotential multiferroic. By comparing the low symmetry structure with a parentphase of $P4/nmm$ symmetry, two distortion modes are found dominant. Theycorrespond to MnO$_{6}$ and WO$_{6}$ octahedron \textit{tilt} modes, oftenfound in many simple perovskites. While in the latter these common tiltinginstabilities yield non-polar phases, in NaLaMnWO$_{6}$ the additional presenceof the $A$-$A^{'}$ cation ordering is sufficient to make these rigid unit modesas a source of the ferroelectricity. Through a trilinear coupling with the twounstable tilting modes, a significant polar distortion is induced, although thesystem has no intrinsic polar instability. The calculated electric polarizationresulting from this polar distortion is as large as $\sim$ 16 ${\mu}{\rmC/cm^{2}}$. Despite its secondary character, this polarization is coupled withthe dominant tilting modes and its switching is bound to produce the switchingof one of two tilts, enhancing in this way a possible interaction with themagnetic ordering. The transformation of common non-polar purely stericinstabilities into sources of ferroelectricity through a controlledmodification of the parent structure, as done here by the cation ordering, is aphenomenon to be further explored.

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