Field-induced linear magnetoelastic coupling in multiferroic TbMnO₃

We have used in-field neutron and x-ray single-crystal diffraction to measure the incommensurability δ of the crystal and magnetic structures of multiferroic TbMnO₃. We show that the flop in the electric polarization at the critical field H_C, for field H along the a and b axes, coincides with a first-order transition to a commensurate phase with propagation vector κ=(0,1/4,0). In-field x-ray diffraction measurements show that the quadratic magnetoelastic coupling breaks down with applied field as shown by the observation of the first harmonic lattice reflections above and below H_C. This indicates that magnetic field induces a linear magnetoelastic coupling.