Neutron diffraction study of successive magnetic phase transitions in ferroelectric TbMn₂O₅

Neutron diffraction measurements have been performed on a single crystal of TbMn₂O₅ to elucidate the interplay between magnetic ordering and ferroelectricity. On cooling below T_N1 = 42 K, the system enters a lock-in commensurate magnetic (CM) state with the magnetic propagation vector q = (1/2, 0, 1/4) from a two-dimensionally modulated (2D) incommensurate magnetic (ICM) one with the temperature-dependent q = (q _x,0,q_z). Unlike isomorphous YMn₂O₅ and ErMn₂O₅ where a 1D-ICM phase with q = (q _x,0,1/4) appears and separates both 2D-ICM and CM phases, the CM phase coexists with the 2D-ICM one at temperatures between T = 36.5 and 37.8 K, associated with a kink and a sharp peak in the dielectric constant along the b axis. On further cooling, the system reenters an ICM state at T = 22.4 K whose q is pinned at (20/41,0,5/16) at low temperatures. The comparison between the temperatures of dielectric anomalies and magnetic phase transitions indicates that the formation of the CM ordering is related to the appearance of ferroelectricity in TbMn₂O₅, while that of the 1D-ICM ordering is so in YMn₂O₅ and ErMn₂O ₅.