The magnetoelastic coupling in multiferroic DyMn 2 O 5 is investigated by magnetostriction measurements along the three crystallographic orientations. Strong lattice anomalies as a function of the magnetic field are detected at the low temperature magnetic and ferroelectric phase transitions. The sign and magnitude of the magnetostrictive coefficient as well as the lattice anomalies at the transitions are correlated with the Dy moment order and with the sharp changes of the dielectric constant and the ferroelectric polarization. With the magnetic field applied along the c axis a high-field phase has been detected the magnetic structure of which has yet to be explored. DOI: 10.1103/PhysRevB.74.180402 PACS number͑s͒: 75.25.ϩz, 75.30.Kz, 75.80.ϩq, 77.80.Ϫe Among the multiferroic materials displaying the coexistence of magnetic and ferroelectric ͑FE͒ orders the rare earth manganites RMn 2 O 5 ͑R = rare earth, Y͒, have attracted attention because of a wealth of fundamental physical phenomena observed in these compounds. Incommensurate magnetic orders, spin frustration, lock-in transitions, and ferroelectricity have been detected with decreasing temperature and give rise to a cascade of phase transitions. 1 The physical origin of this phase complexity lies in the partially competing interactions between the Mn 4+ /Mn 3+ spins, the rare earth magnetic moments, and the lattice. 2 Geometric magnetic frustration among the Mn 3+ −Mn 4+ spins leads to a ground state degeneracy of the magnetic states that can be lifted by a distortion of the lattice ͑magnetic Jahn-Teller effect͒. This is believed to be the origin of ferroelectricity in RMn 2 O 5 compounds. [2][3][4] Strong spin-lattice coupling is needed to explain the ionic displacements in the FE state. The experimental proof of sizable lattice anomalies at the FE transitions in RMn 2 O 5 was given recently by thermal expansion experiments in zero magnetic field. 4 However, the effect of an external magnetic field on the lattice of RMn 2 O 5 has not been investigated yet. The field couples to the magnetic order resulting in fieldinduced spin reorientations and magnetic phase transitions 5 which, in turn, should affect the lattice via the spin-lattice interaction. The signature and the nature of the magnetoelastic effect provides essential information about the intrinsic magnetoelastic and magnetoelectric interactions. We have therefore investigated the magnetoelastic strain on the lattice of DyMn 2 O 5 and found large changes of the lattice parameters as a function of the magnetic field and abrupt striction effects at phase boundaries.DyMn 2 O 5 exhibits a complex magnetic phase diagram. 5,6 Large effects of an a-axis magnetic field on the dielectric constant 7 and the FE polarization 6 have been reported. Upon decreasing temperature T the sequence of phase transitions is similar for most RMn 2 O 5 . AFM order develops at T N1 = 43 K with an incommensurate ͑IC͒ magnetic modulation described by q ជ = ͑0.5+  , 0 , 0.25+ ␦͒ ͑where  , ␦ Ͻ 0 indicate the deviations from c...