Mechanism of the Ferroelectric Phase Transformation in Rare-Earth Molybdates

Neutron scattering experiments on ${\mathrm{Tb}}_2$ ${\left(\mathrm{M}\mathrm{o}{\mathrm{O}}_4\right)}_3$ show the ferroelectric orthorhombic phase to result from a phonon instability at the (½, ½, 0) Brillouin zone corner of the parent tetragonal phase. Anharmonic coupling to these antiferroelectric displacements produces a spontaneous strain which in turn causes a spontaneous polarization through normal piezoelectric coupling. The rare-earth molybdates thus represent a new class of displacive ferroelectric materials without a soft polar mode.