Comprehensive x-ray scattering studies, including resonant scattering at Mn L-edge, Tb L- and M-edges, were performed on single crystals of TbMn2O5. X-ray intensities were observed at a forbidden Bragg position in the ferroelectric phases, in addition to the lattice and the magnetic modulation peaks. Temperature dependences of their intensities and the relation between the modulation wave vectors provide direct evidences of exchange striction induced ferroelectricity. Resonant x-ray scattering results demonstrate the presence of multiple magnetic orders by exhibiting their different temperature dependences. The commensurate-to-incommensurate phase transition around 24 K is attributed to discommensuration through phase slipping of the magnetic orders in spin frustrated geometries. We proposed that the low temperature incommensurate phase consists of the commensurate magnetic domains separated by anti-phase domain walls which reduce spontaneous polarizations abruptly at the transition.
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