The low-temperature ferroelectric polarization of multiferroic YMn 2 O 5 is completely reversed at a critical pressure of 10 kbar and the phase transition from the incommensurate to the commensurate magnetic phase is induced by pressures above 14 kbar. The high-pressure data correlate with thermal-expansion measurements, indicating a significant lattice strain at the low-temperature transition into the incommensurate phase. The results support the exchange striction model for the ferroelectricity in multiferroic RMn 2 O 5 compounds and they show the importance of magnetic frustration as well as the spin-lattice coupling. DOI: 10.1103/PhysRevB.77.220104 PACS number͑s͒: 77.80.Ϫe, 75.30.Ϫm, 75.50.Ee, 77.84.Bw Multiferroic magnetoelectric compounds in which ferroelectricity and magnetic order coexist and mutually interact have been in the focus of attention very recently because of a wealth of novel physical phenomena observed in these complex materials.1-4 Among the family of multiferroics, the RMn 2 O 5 ͑R ϭ rare earth, Y, Bi͒ manganites are of significant interest because of their extreme complexity with transitions between different commensurate magnetic structures ͑CM͒ and incommensurate ͑IC͒ magnetic structures ͑ICM͒, some of which exhibit ferroelectricity induced by frustrated magnetic orders.5-10 Their common phase sequence upon decreasing temperature T includes transitions from the high-T paramagnetic and paraelectric ͑PE͒ to an antiferromagnetic ͑AFM͒ but still PE phase at T N1 Ӎ 44 K, with an IC magnetic modulation along the orthorhombic a and c axes. At T C1 Ӎ 39 K, a lock-in transition takes place into a CM magnetic phase ͓q ជ = ͑0.5, 0 , 0.25͔͒, which is ferroelectric ͑FE͒. At lower temperature T C2 , all RMn 2 O 5 compounds experience another transition where q ជ unlocks again into different IC values and the FE polarization shows a sharp drop ͑but not necessarily to zero͒. Additional changes of the magnetic order that are identified as spin reorientations in the CM phase have been reported for some RMn 2 O 5 , for example DyMn 2 O 5 ͑Ref. 9͒ and HoMn 2 O 5 .11 It is remarkable that all magnetic ͑and FE͒ phase transitions are clearly resolved in anomalies of the dielectric constant, the FE polarization, and the thermal expansivities, which proves the prominent role of the spin-lattice coupling in the multiferroic properties of these compounds.11,12 The origin of the phase complexity of RMn 2 O 5 lies in the peculiarities of the lattice structure with different magnetic ions ͑Mn 4+ ,Mn 3+ , rare earth͒ and a multitude of partially competing superexchange interactions, leading to a high degree of frustration in the magnetic system. 7 In particular, the smallest loop of nearest-neighbor Mn ions with AFM exchange interactions in the a-b plane has five members, which naturally leads to geometric frustration of the Mn spins.11 Frustrated systems are susceptible to small perturbations such as magnetic fields or pressure, since many different magnetic structures are close in energy and compete for the gro...