Bonding anisotropy in multiferroic TbMnO3 probed by polarization dependent x-ray absorption spectroscopy

O K- and Mn L-2,L-3-edges x-ray absorption spectra of orthorhombic TbMnO3 single crystals show strong polarization dependence, in contrast with results of previous experiments on orthorhombic LaMnO3 and DyMnO3 thin films that show nearly isotropic spectral structure. First-principles calculations reveal that TbMnO3 exhibits a zigzag e(g) orbital ordering ground state. The highly distorted MnO6 octahedron and orbital ordering in TbMnO3 produce highly anisotropic Mn-O bonding within the ab plane, a frustration of the magnetic ordering, and the formation of complicated incommensurate magnetic structures.