Ferroelectric polarization flop in a frustrated magnet MnWO4 induced by a magnetic field

Giant improper ferroelectricity in the ferroaxial magnet CaMn7O12

In rhombohedral CaMn7O12, an improper ferroelectric polarization of magnitude 2870  μC  m(-2) is induced by an incommensurate helical magnetic structure that evolves below T(N1)=90 K. The electric polarization was found to be constrained to the high symmetry threefold rotation axis of the crystal structure, perpendicular to the in-plane rotation of the magnetic moments. The multiferroicity is explained by the ferroaxial coupling mechanism, which in CaMn7O12 gives rise to the largest magnetically induced, electric polarization measured to date.

General theory for the ferroelectric polarization induced by spin-spiral order

The ferroelectric polarization of triangular-lattice antiferromagnets induced by helical spin-spiral order is not explained by any existing model of magnetic-order-driven ferroelectricity. We resolve this problem by developing a general theory for the ferroelectric polarization induced by spin-spiral order and then by evaluating the coefficients needed to specify the general theory on the basis of density functional calculations. Our theory correctly describes the ferroelectricity of triangular-lattice antiferromagnets driven by helical spin-spiral order and incorporates known models of magnetic-order-driven ferroelectricity as special cases.

Cu3Nb2O8: a multiferroic with chiral coupling to the crystal structure

By combining bulk properties, neutron diffraction, and nonresonant x-ray diffraction measurements, we demonstrate that the new multiferroic Cu(3)Nb(2)O(8) becomes polar simultaneously with the appearance of generalized helicoidal magnetic ordering. The electrical polarization is oriented perpendicularly to the common plane of rotation of the spins-an observation that cannot be reconciled with the conventional theory developed for cycloidal multiferroics. Our results are consistent with coupling between a macroscopic structural rotation, which is allowed in the paramagnetic group, and magnetically induced structural chirality.

Theory of high-temperature multiferroicity in cupric oxide

The incommensurate-commensurate phases reported in cupric oxide below 230 K are shown theoretically to realize an inverted sequence of symmetry-breaking mechanisms with respect to the usual sequence occurring in low-temperature multiferroic compounds. The sequence inversion results from a strong triggering-coupling mechanism between two antiferromagnetic order parameters inducing a first-order transition to the multiferroic phase. Such mechanism is favored by the large antiferromagnetic superexchange interactions, responsible of the high-T(N) temperature, and implies a preeminence of these interactions on the magnetocrystalline anisotropy. The magnetic structures of the equilibrium phases and the microscopic interactions giving rise to the polarization are determined.

Neutron Laue diffraction study on the magnetic phase diagram of multiferroic MnWO4 under pulsed high magnetic fields

We have combined time-of-flight neutron Laue diffraction and pulsed high magnetic fields at the Spallation Neutron Source to study the phase diagram of the multiferroic material MnWO(4). The control of the field-pulse timing enabled an exploration of magnetic Bragg scattering through the time dependence of both the neutron wavelength and the pulsed magnetic field. This allowed us to observe several magnetic Bragg peaks in different field-induced phases of MnWO(4) with a single instrument configuration. These phases were not previously amenable to neutron diffraction studies due to the large fields involved.

The splitting of the electromagnon mode in conically spiral multiferroic magnets

In this paper, we study conically spiral multiferroic magnets with coupled magnetic and ferroelectric orders. By generalizing the spin-current model, we study spin wave excitations and electromagnons. We find that the electromagnon mode will split into two branches with different dispersions in an (external or internal) magnetic field. We apply our theory to some multiferroic materials and find that the results qualitatively agree with recent experiments. We also make predictions for new experiments.

Coupled magnetic cycloids in multiferroic TbMnO3 and Eu3/4Y1/4MnO3

Based on the detailed Mn L(2,3)-edge x-ray resonant scattering results, we report a new complexity in the magnetic order of multiferroic orthomangnites, which has been considered as the simple A-type cycloid order inducing ferroelectricity. The Dzyaloshinskii-Moriya interaction involved in the orthorhombic distortion brings on F-type canting from the A type, and the ordering type becomes the off-phase synchronized bc cycloid in TbMnO(3) or the tilted antiphase ab cycloid in Eu(3/4)Y(1/4)MnO(3). The F-type canting is responsible for the magnetic field-driven multiferroicity to weak ferromagnetism transition.

Magnetic ordering and magnetodielectric phenomena in CoSeO4

CoSeO(4) has a structure consisting of edge-sharing chains of Co(2+) octahedra which are held together by SeO(4)(2-) tetrahedra via shared oxygen atoms at the edges of the octahedra. DC magnetization measurements indicate a transition to an ordered state below 30 K. Powder neutron diffraction refinements suggest an ordered state with two unique antiferromagnetic chains within the unit cell. Isothermal magnetization measurements indicate a temperature-dependent field-induced magnetic transition below the ordering temperature. From neutron diffraction, we find that this corresponds to a realignment of spins from the canted configuration towards the c-axis. The dielectric constant shows a change in slope at the magnetic ordering temperature indicating an interplay between the spin and charge degrees of freedom.

Multiferroic M-type hexaferrites with a room-temperature conical state and magnetically controllable spin helicity

Magnetic and magnetoelectric (ME) properties have been studied for single crystals of Sc-doped M-type barium hexaferrites. Magnetization (M) and neutron diffraction measurements revealed that by tuning Sc concentration a longitudinal conical state is stabilized up to above room temperatures. ME measurements have shown that a transverse magnetic field (H) can induce electric polarization (P) at lower temperatures and that the spin helicity is nonvolatile and endurable up to near the conical magnetic transition temperature. It was also revealed that the response (reversal or retention) of the P vector upon the reversal of M varies with temperature. In turn, this feature allows us to control the relation between the spin helicity and the M vectors with H and temperature.

Cross-control of magnetization and polarization by electric and magnetic fields with competing multiferroic and weak-ferromagnetic phases

From our investigation of magnetoelectric properties of a multiferroic phase in Eu0.75Y0.25MnO3 competing with a weak-ferromagnetic phase in magnetic fields, we found intriguing hysteretic behaviors of physical properties with variation of temperature and magnetic field. These hysteretic behaviors arise from the kinetic arrest (dearrest) processes of the first-order multiferroic-weak-ferromagnetic transition, resulting in frozen (melted) magnetoelectric glass states with coexisting two phases. Tipping the delicate balance of two competing phases by applying electric and magnetic fields leads to a remarkable control of magnetization and electric polarization.

Phenomenological theory of phase transitions in multiferroic MnWO₄: magnetoelectricity and modulated magnetic order

The phenomenological theory of phase transitions in multiferroic MnWO₄ is suggested. The theoretical model uses the assumption that the magnetic order is driven by the instability in the (1/4;1/2;1/2) point of the Brillouin zone, which is justified by the symmetry of the low-temperature magnetic phase. It is shown that the experimentally observed incommensurate magnetic order is due to the Lifshitz invariants allowed for the corresponding order parameters. Invariants responsible for the magnetoelectric interaction are found and a schematic phase diagram is calculated. The influence of the magnetic field on the phase transition sequence is also analyzed. It is suggested that the description of the phase transitions in MnWO₄ starting from the orthorhombic praphase significantly simplifies the approach and allows us to draw important conclusions.

Multiferroics with spiral spin orders

Cross correlation between magnetism and electricity in a solid can host magnetoelectric effects, such as magnetic (electric) induction of polarization (magnetization). A key to attain the gigantic magnetoelectric response is to find the efficient magnetism-electricity coupling mechanisms. Among those, recently the emergence of spontaneous (ferroelectric) polarization in the insulating helimagnet or spiral-spin structure was unraveled, as mediated by the spin-exchange and spin-orbit interactions. The sign of the polarization depends on the helicity (spin rotation sense), while the polarization direction itself depends on further details of the mechanism and the underlying lattice symmetry. Here, we describe some prototypical examples of the spiral-spin multiferroics, which enable some unconventional magnetoelectric control such as the magnetic-field-induced change of the polarization direction and magnitude as well as the electric-field-induced change of the spin helicity and magnetic domain.

Directional magnetoelectric effects in MnWO4: magnetic sources of the electric polarization

The ferroelectric order and magnetic field induced effects observed in the spiral phase of MnWO4 are described theoretically. It is demonstrated explicitly that the Dzyaloshinskii-Moriya antisymmetric interactions contribute to the correlation between spins and electric dipoles in the incommensurate and commensurate ferroelectric phases of magnetic multiferroics. However, other single-site symmetric interactions are shown to be involved in the magnetoelectric process, suggesting the possible existence of an electric polarization originating from purely symmetric effects.

Magnetic digital flop of ferroelectric domain with fixed spin chirality in a triangular lattice helimagnet

The ferroelectric properties in a magnetic field (H) of varying magnitude and direction have been investigated for the triangular-lattice helimagnet CuFe(1-x)Ga(x)O(2) (x = 0.035). The in-plane H was found to induce the rearrangement of six possible multiferroic domains. Upon every 60 degrees rotation of in-plane H around the c axis, a unique 120 degrees flop of electric polarization occurs as a result of the switch of the helical magnetic q vector. The chirality of the spin helix is always conserved upon the q flop. The possible origin is discussed in light of the stable structure of the multiferroic domain wall.

Novel multiferroic state of Eu1-xYxMnO3 in high magnetic fields

Magnetic and dielectric properties of Eu1-xYxMnO3 (x=0 and 0.4) are studied in pulsed magnetic fields up to 55 T. For x=0, application of magnetic fields higher than 20 T along the b axis causes magnetic transitions accompanied by generation of electric polarization (P) along the a axis. Similar first-order transitions are also observed in crystals of x=0.4, in which the ground state at zero magnetic field is already a ferroelectric P parallel a phase of different origin. Realistic model calculation indicates the presence of a novel multiferroic state induced by the spin exchange striction mechanism in high magnetic fields as an essential nature of the frustrated Mn spin system in this class of manganites.

Electric-field switching of a magnetic propagation vector in a helimagnet

We report novel magnetoelectric properties of a quantum-spin helimagnet Ba2CuGe2O7 with a noncentrosymmetric (but nonpolar) crystal structure. It was found that the spin helicity of the cycloidal spin order is always fixed to the lattice, therefore the magnetic propagation vector k determines the sign of electric polarization in Ba2CuGe2O7. Consequently, not only the magnetic-field drive of the ferroelectric domain but also the electric-field switching of magnetic k vector can be achieved.

Magnetic-field-induced polarization flop in multiferroic TmMn2O5

We discovered a reversible electric polarization flop from the a axis (P(a)) to the b axis (P(b)) in multiferroic TmMn2O5 below 5 K by applying a magnetic field of approximately 0.5 T along the c axis. This phenomenon is the first example of the rare-earth (R) compound RMn2O5. This magnetic-field-induced polarization flop corresponds to a magnetic phase transition from one incommensurate magnetic (ICM) P(a) phase to another ICM P(b) phase, which is equivalent to an ICM P(b) phase above 5 K under no magnetic field. The spin chirality in the bc plane, which was observed in the P(b) phase by polarized neutron diffraction, disappeared in the ICM P(a) phase. This indicates that the polarization in the ICM phases of TmMn2O5 was induced by an S(i) x S(j)-type interaction.

Flop of electric polarization driven by the flop of the Mn spin cycloid in multiferroic TbMnO3

Using in-field single-crystal neutron diffraction, we have determined the magnetic structure of TbMnO(3) in the high field P parallel a phase. We unambiguously establish that the ferroelectric polarization arises from a cycloidal Mn spin ordering, with spins rotating in the ab plane. Our results demonstrate directly that the flop of the ferroelectric polarization in TbMnO(3) with applied magnetic field is caused from the flop of the Mn cycloidal plane.

Magnetoelectric memory effect of the nonpolar phase with collinear spin structure in multiferroic MnWO4

The novel memory effect of a nonpolar paraelectric phase with a collinear spin structure has been observed in a magnetoelectric multiferroic material MnWO4. Since the ferroelectric polarization arises from a noncollinear spin structure, in a new class of magnetoelectric multiferroic materials with a spiral-spin structure, the information of ferroelectric domains should be lost in the collinear spin phase. However, in MnWO4, it has been found that the domain states in the ferroelectric phase are memorized even in the nonpolar phase with a collinear spin structure, when the phase transition is of the first-order type. Here we demonstrate a magnetoelectric memory effect that the ferroelectric single-domain state can be reproduced from the paraelectric phase by a magnetic field. We propose the nuclei growth model, in which the small ferroelectric embryos keep the polarization state in the nonpolar collinear spin phase.

Re-entrant spiral magnetic order and ferroelectricity in Mn1−xFexWO4 (x=0.035)

We report the observation of a re-entrant spiral (noncollinear) magnetic order and ferroelectricity below 6 K in Mn0.965Fe0.035WO4 under applied magnetic fields above 3.6 T. At zero field, this compound shows a transition into the spiral magnetic and ferroelectric phase at 12 K, and it becomes paraelectric at 10.5 K with the entrance into the commensurate magnetic phase, which is the ground state at H=0. Under magnetic field above 3.6 T, however, the spiral magnetic phases with a larger FE polarization reappears below 6 K. The re-entrant magnetic/ferroelectric phase behavior is further studied by single crystal neutron scattering and the H-T phase diagram is completely resolved from neutron, dielectric constant, polarization, and magnetic measurements.

Observation and coupling of domains in a spin-spiral multiferroic

The coexistence, coupling, and manipulation of magnetic spiral domains and magnetically induced ferroelectric domains are spatially resolved by optical second harmonic generation in multiferroic MnWO4. Eight types of magnetic domains couple to two ferroelectric domains. An electric field uniquely creates a magnetic single-domain state. A magnetic field quenches the spontaneous polarization while retaining its magnetic origin so that the ferroelectric domains are concealed instead of destroyed.

Thermally or magnetically induced polarization reversal in the Multiferroic CoCr2O4

We report the unexpected evolution, with thermal and magnetic-field (H) variations, of the interrelation between the polarization P, magnetization M, and spiral wave vector Q in CoCr2O4, which has a ferrimagnetic conical-spiral magnetic order. For example, P suddenly jumps and changes its sign at the magnetic lock-in transition (T_{L}) with thermal variation, or with isothermal variation of H (without changing its direction) at T_{L}, which surprisingly occurs without change in spiral handedness (i.e., the sign of Q). The presence of multiple spiral sublattices may be behind this unusual behavior.

Control of the magnetoelectric domain-wall stability by a magnetic field in a multiferroic MnWO4

The relation between the orientation of the magnetic field and the flopped ferroelectric polarization has been investigated for multiferroic MnWO4. The ferroelectric single-domain state is retained across the polarization flop process when the direction of the applied magnetic field slightly deviates from the b axis within the ab plane. Furthermore, the electric polarization in the high-field P parallela phase is reversed when the P parallelb-to-P parallela transition takes place while decreasing and increasing the magnetic fields oppositely canted from the b axis. These results indicate that the symmetry breaking induced by a canted magnetic field determines the direction of the polarization flop, which corresponds to the direction of the vector spin chirality. The stability of the magnetoelectric domain walls in a canted magnetic field play a key role in the directional control of the electric polarization flop phenomenon.

Cycloidal spin order in the a-axis polarized ferroelectric phase of orthorhombic perovskite manganite

The ferroelectric state in an orthorhombic perovskite RMnO3 (R=Gd0.7Tb0.3) was proved by neutron scattering studies to show the cycloidal spin state with the ab-spiral plane and the spin-helicity dependent polarization vector along the a axis, sharing the microscopic origin (inverse Dzyaloshinskii-Moriya interaction) with the more widely observed P||c state (e.g., for R=Tb and Dy) with the bc-spiral plane. The magnetic-field induced polarization flop from P||c to P||a as well known for RMnO3 is thus assigned to the orthogonal flop of the spin spiral plane from bc to ab.

Magnetic-field-induced ferroelectric state in DyFeO3

Versatile and gigantic magnetoelectric (ME) phenomena have been found for a single crystal of DyFeO3. Below the antiferromagnetic ordering temperature of Dy moments, a linear-ME tensor component as large as alphazz approximately 2.4 x 10(-2) esu is observed. It is also revealed that application of magnetic field along the c axis induces a multiferroic (weakly ferromagnetic and ferroelectric) phase with magnetization [> or =0.5 microB/formula unit (f.u.)] and electric polarization (> or =0.2 microC/cm2) both along the c axis. Exchange striction working between adjacent Fe3+ and Dy3+ layers with the respective layered antiferromagnetic components is proposed as the origin of the ferroelectric polarization in the multiferroic phase.

Correlation between spin helicity and an electric polarization vector in quantum-spin chain magnet LiCu2O2

Measurements of polarized neutron scattering were performed on a S=1/2 chain multiferroic LiCu2O2. In the ferroelectric ground state with the spontaneous polarization along the c axis, the existence of transverse spiral spin component in the bc plane was confirmed. When the direction of electric polarization is reversed, the vector spin chirality as defined by C_(ij)=S_(i)xS_(j) (i and j being the neighboring spin sites) is observed to be reversed, indicating that the spin-current model or the inverse Dzyaloshinskii-Moriya mechanism is applicable even to this e_(g)-electron quantum-spin system. Differential scattering intensity of polarized neutrons shows a large discrepancy from that expected for the classical-spin bc-cycloidal structure, implying the effect of large quantum fluctuation.

Ferroelectricity in an ising chain magnet

We report discovery of collinear-magnetism-driven ferroelectricity in the Ising chain magnet Ca3Co2-xMn(x)O6 (x approximately 0.96). Neutron diffraction shows that Co2+ and Mn4+ ions alternating along the chains exhibit an up-up-down-down ( upward arrow upward arrow downward arrow downward arrow) magnetic order. The ferroelectricity results from the inversion symmetry breaking in the upward arrow upward arrow downward arrow downward arrow spin chain with an alternating charge order. Unlike in spiral magnetoelectrics where antisymmetric exchange coupling is active, the symmetry breaking in Ca3(Co,Mn)2O6 occurs through exchange striction associated with symmetric superexchange.

Polarization reversal in multiferroic TbMnO3 with a rotating magnetic field direction

For the memory application of magnetoelectric multiferroics, not only bistability (i.e., ferroelectricity) but also the switching of the polarization direction with some noneverlasting stimulus is necessary. Here, we report a novel method for the electric polarization reversal in TbMnO3 without the application of an electric field or heat. The direction of the magnetic-field-induced polarization along the a axis (Pa) is memorized even in the zero field where Pa is absent. The polarization direction can be reversed by rotating the magnetic-field direction in the ab plane.

Multiferroicity induced by dislocated spin-density waves

We uncover a new pathway towards multiferroicity, showing how magnetism can drive ferroelectricity without relying on inversion symmetry breaking of the magnetic ordering. Our free-energy analysis demonstrates that any commensurate spin-density-wave ordering with a phase dislocation, even if it is collinear, gives rise to an electric polarization. Because of the dislocation, the electronic and magnetic inversion centers do not coincide, which turns out to be a sufficient condition for multiferroic coupling. The novel mechanism explains the formation of multiferroic phases at the magnetic commensurability transitions, such as the ones observed in YMn(2)O(5) and related compounds. We predict that in these multiferroics an oscillating electrical polarization is concomitant with the uniform polarization. On the basis of our theory, we put forward new types of magnetic materials that are potentially ferroelectric.

Electric control of spin helicity in a magnetic ferroelectric

Magnetic ferroelectrics or multiferroics, which are currently extensively explored, may provide a good arena to realize a novel magnetoelectric function. Here we demonstrate the genuine electric control of the spiral magnetic structure in one such magnetic ferroelectric, TbMnO3. A spin-polarized neutron scattering experiment clearly shows that the spin helicity, clockwise or counterclockwise, is controlled by the direction of spontaneous polarization and hence by the polarity of the small electric field applied on cooling.

Ferroelectricity in an s=1/2 chain cuprate

We report our discovery of ferroelectricity in the spiral-magnetic state in the quantum quasi-one-dimensional (1D) S=1/2 magnet of LiCu2O2. Electric polarization (P) emerges along the c direction below the spiral-magnetic order temperature, but changes from the c to a axis when magnetic fields (H) are applied along the b direction. We also found that P(c) increases with H(c), and P(a) appears with H(a). LiCu2O2 in zero field appears to be the first ferroelectric cuprate and also a prototypical example of the "1D spiral-magnetic ferroelectrics." However, the unexpected behavior in H may demonstrate the complexity of the ordered spin configuration, inherent in the 1D S=1/2 magnet of LiCu2O2.

Multiferroics: a magnetic twist for ferroelectricity

Magnetism and ferroelectricity are essential to many forms of current technology, and the quest for multiferroic materials, where these two phenomena are intimately coupled, is of great technological and fundamental importance. Ferroelectricity and magnetism tend to be mutually exclusive and interact weakly with each other when they coexist. The exciting new development is the discovery that even a weak magnetoelectric interaction can lead to spectacular cross-coupling effects when it induces electric polarization in a magnetically ordered state. Such magnetic ferroelectricity, showing an unprecedented sensitivity to ap plied magnetic fields, occurs in 'frustrated magnets' with competing interactions between spins and complex magnetic orders. We summarize key experimental findings and the current theoretical understanding of these phenomena, which have great potential for tuneable multifunctional devices.

Ferroelectricity in the magnetic E-phase of orthorhombic perovskites

We show that the symmetry of the spin zigzag chain E phase of the orthorhombic perovskite manganites and nickelates allows for the existence of a finite ferroelectric polarization. The proposed microscopic mechanism is independent of spin-orbit coupling. We predict that the polarization induced by the E-type magnetic order can potentially be enhanced by up to 2 orders of magnitude with respect to that in the spiral magnetic phases of TbMnO3 and similar multiferroic compounds.