Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric $\mathrm{Gd}\mathrm{Mn}{\mathrm{O}}_3$ and $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_3$ compounds

Single-crystal synchrotron x-ray diffraction measurements in strong magnetic fields have been performed for magnetoelectric compounds $\mathrm{Gd}\mathrm{Mn}{\mathrm{O}}_3$ and $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_3$. It has been found that the $\mathit{P}\Vert a$ ferroelectric phase induced by the application of a magnetic field at low temperatures is characterized by commensurate lattice modulation along the orthorhombic $b$ axis with $q=1∕2$ and $q=1∕4$. The lattice modulation is ascribed to antiferromagnetic spin alignment with a modulation vector of $(01∕41)$. The change of the spin structure is directly correlated with the magnetic-field-induced electric phase transition, because any commensurate spin modulation with $(01∕41)$ should break glide planes normal to the $a$ axis of the distorted perovskite with the $Pbnm$ space group.