Field-induced linear magnetoelastic coupling in multiferroicTbMnO3

We have used in-field neutron and x-ray single-crystal diffraction to measure the incommensurability $\delta$ of the crystal and magnetic structures of multiferroic ${\mathrm{TbMnO}}_3$. 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 $\kappa =(0,\frac{1}{4},0)$. 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.