Ferroelectric and magnetic materials are a time-honoured subject of study and have led to some of the most important technological advances to date. Magnetism and ferroelectricity are involved with local spins and off-centre structural distortions, respectively. These two seemingly unrelated phenomena can coexist in certain unusual materials, termed multiferroics. Despite the possible coexistence of ferroelectricity and magnetism, a pronounced interplay between these properties has rarely been observed. This has prevented the realization of multiferroic devices offering such functionality. Here, we report a striking interplay between ferroelectricity and magnetism in the multiferroic TbMn2O5, demonstrated by a highly reproducible electric polarization reversal and permanent polarization imprint that are both actuated by an applied magnetic field. Our results point to new device applications such as magnetically recorded ferroelectric memory.

Unidirectional electric current flow, such as that found in a diode, is essential for modern electronics. It usually occurs at asymmetric interfaces such as p-n junctions or metal/semiconductor interfaces with Schottky barriers. We report on a diode effect associated with the direction of bulk electric polarization in BiFeO3: a ferroelectric with a small optical gap edge of approximately 2.2 electron volts. We found that bulk electric conduction in ferroelectric monodomain BiFeO3 crystals is highly nonlinear and unidirectional. This diode effect switches its direction when the electric polarization is flipped by an external voltage. A substantial visible-light photovoltaic effect is observed in BiFeO3 diode structures. These results should improve understanding of charge conduction mechanisms in leaky ferroelectrics and advance the design of switchable devices combining ferroelectric, electronic, and optical functionalities.

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The magnetic excitations of the square-lattice spin-1/2 antiferromagnet and high-Tc parent La2CuO4 are determined using high-resolution inelastic neutron scattering. Sharp spin waves with absolute intensities in agreement with theory including quantum corrections are found throughout the Brillouin zone. The observed dispersion relation shows evidence for substantial interactions beyond the nearest-neighbor Heisenberg term, which can be understood in terms of a cyclic or ring exchange due to the strong hybridization path around the Cu4O4 square plaquettes.While there is consensus about the basic phenomenology -electron pairs with non-zero angular momentum, unconventional metallic behavior in the normal state, tendencies towards inhomogeneous charge and spin density order -of the high temperature copper oxide superconductors, there is no agreement about the microscopic mechanism. After over a decade of intense activity, there is not even consensus as to the simplest "effective Hamiltonian", which is a short-hand description of the motions and interactions of the valence electrons, needed to account for cuprate superconductivity. Because much speculation is centered on magnetic mechanisms for the superconductivity, it is important to identify the interactions among the spins derived from the unfilled Cu 2+ d-shells. The present experiments show that there are significant (on the scale of the pairing energies for highTc superconductivity) interactions coupling spins at distances beyond the 3.8Å separation of nearest-neighbor Cu 2+ ions. Cyclic or ring exchange due to a strong hybridization path around the Cu 4 O 4 squares (see Fig. 1A), from which the cuprates are built, provides a natural explanation for the measured dispersion relation. CuO 2 planes are thus the second example of an important Fermi system ( 3 He is the other [1]) where significant cyclic exchange terms have been deduced.Magnetic interactions are revealed through the wavevector dependence or dispersion of the magnetic excitations. In magnetically ordered materials, the dominant excitations are spin waves which are coherent (from site to site as well as in time) precessions of the spins about their mean values. The lower frame of Fig. 1B shows the dispersion relation calculated using conventional linear spin-wave theory in the classical large-S limit, where the only magnetic interaction is a strong nearest-neighbor superexchange coupling J [2]. We identify wavevectors by their coordinates (h, k) in the twodimensional (2D) reciprocal space of the square lattice.Spin waves emerge from the wavevector (1/2,1/2) characterizing the simple antiferromagnetic (AF) unit cell doubling in La 2 CuO 4 [3], and disperse to reach a maximum energy 2J that is a constant along the AF zone boundary marked by dashed squares in Fig. 1B. Longer-range interactions manifest themselves most simply at the zone boundary. The upper frame of Fig. 1B shows the dispersion calculated with modest interactions between next nearest-neighbors. Virtually the only visible effect of the a...

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We have studied the magnetostructural phase diagram of multiferroic TbMn2O5 as a function of temperature and magnetic field by neutron diffraction. Dielectric and magnetic anomalies are found to be associated with steps in the magnetic propagation vector, including a rare example of a commensurate-incommensurate transition on cooling below 24 K, and in the structural parameters. The geometrically frustrated magnetic structure is stabilized by "canted antiferroelectric" displacements of the Mn3+ ions, an example of the magnetic Jahn-Teller effect. The Tb moments order ferromagnetically at low temperatures in an applied field, while the Mn magnetic structure is largely unchanged.

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