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We report synchrotron radiation diffraction and muon spin rotation (muSR)measurements on the frustrated pyrochlore magnet Tb2Ti2O7. The powderdiffraction study of a crushed crystal fragment does not reveal any structuralchange down to 4 K. The muSR measurements performed at 20 mK on a mosaic ofsingle crystals with an external magnetic field applied along a three-fold axisare consistent with published a.c. magnetic-susceptibility measurements at 16mK. While an inflection point could be present around an internal fieldintensity slightly above 0.3 T, the data barely support the presence of amagnetization plateau.

Low temperature crystal structure and local magnetometry for the geometrically frustrated pyrochlore Tb2Ti2O7