Hybrid improper dipolar density wave in NaLaCoWO6

The Hybrid Improper Ferroelectricity (HIF) mechanism allows the generation of an electrical polarization thanks to the combination of two non polar octahedral distortions in the AA'BB'O6 double perovskite materials. Nevertheless, for selected combination of the A and A' cations a non-polar incommensurate phase is observed with average symmetry C2/m. Thanks to a detailed crystallographic description of the incommensurate phase, based on electron, neutron and xray diffraction data, we show that the incommensurate modulation is related to an abrupt sign change of the out-of-phase tilting along the a and c axis. By using group theory and symmetry analysis we show that we observe an incommensurate analog of the HIF mechanism which induces a hybrid improper dipolar density wave in NaLaCoWO6.