Ferroelectricity in an s=1/2 chain cuprate

Direct Evidence for an Intermediate Multiferroic Phase in LiCuFe2(VO4)3

Magnetic susceptibility, specific heat, dielectric, and electric polarization of LiCuFe₂(VO₄)₃ have been investigated. Two sequential antiferromagnetic transitions at T_N1 ∼ 9.95 K and T_N2 ∼ 8.17 K are observed under zero magnetic field. Although a dielectric peak at T_N1 is clearly identified, the measured pyroelectric current also exhibits a sharp peak at T_N1, implying the magnetically relevant ferroelectricity. Interestingly, another pyroelectric peak around T_N2 with an opposite signal is observed, resulting in the disappearance of electric polarization below T_N2. Besides, the electric polarization is significantly suppressed in response to external magnetic field, evidencing a remarkable magnetoelectric effect. These results suggest the essential relevance of the magnetic structure with the ferroelectricity in LiCuFe₂(VO₄)₃, deserving further investigation of the underlying mechanism.

Magnetically Induced Polarization in Centrosymmetric Bonds

We reveal the microscopic origin of electric polarization P[over →] induced by noncollinear magnetic order. We show that in Mott insulators, such P[over →] is given by all possible combinations of position operators r[over →][over ^]_{ij}=(r[over →]_{ij}^{0},r[over →]_{ij}) and transfer integrals t[over ^]_{ij}=(t_{ij}^{0},t_{ij}) in the bonds, where r[over →]_{ij}^{0} and t_{ij}^{0} are spin-independent contributions in the basis of Kramers doublet states, while r[over →]_{ij} and t_{ij} stem solely from the spin-orbit interaction. Among them, the combination t_{ij}^{0}r[over →]_{ij}, which couples to the spin current, remains finite in the centrosymmetric bonds, thus yielding finite P[over →] in the case of noncollinear arrangement of spins. The form of the magnetoelectric coupling, which is controlled by r[over →]_{ij}, appears to be rich and is not limited to the phenomenological law P[over →]∼ε_{ij}×[e_{i}×e_{j}] with ε_{ij} being the bond vector connecting the spins e_{i} and e_{j}. Using density-functional theory, we illustrate how the proposed mechanism works in the spiral magnets CuCl_{2}, CuBr_{2}, CuO, and α-Li_{2}IrO_{3}, providing a consistent explanation for the available experimental data.

Quantum phases and thermodynamics of a frustrated spin-1/2 ladder with alternate Ising-Heisenberg rung interactions

We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either isotropicS-type or discrete anisotropicσ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, bothSandσ-type of spins are anti-ferromagnetically aligned with each other, two nearestSspins along the rung form an anisotropic singlet bond whereas two nearestσspins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like specific heatC_v(T), magnetic susceptibilityχ(T) and thermal entropyS(T) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed fromχ(T) andC_v(T) curves.

Stripe structures in phase separated magnetic oxides

We investigate the phase separated inhomogeneous charge and spin states in magnetic oxides. In particular, we study one dimensional harmonic waves and stripe structures. We show that harmonic spin charge waves are unstable and inevitably transform into two or three dimensional structures, while the stripe structures can be stable for certain parameters. Such stripe structures may allow the control of magnetic state with electric field in a magnetic oxide thin film.

Quest for Compounds at the Verge of Charge Transfer Instabilities: The Case of Silver(II) Chloride †

Electron-transfer processes constitute one important limiting factor governing stability of solids. One classical case is that of CuI2, which has never been prepared at ambient pressure conditions due to feasibility of charge transfer between metal and nonmetal (CuI2 → CuI + ½ I2). Sometimes, redox instabilities involve two metal centers, e.g., AgO is not an oxide of divalent silver but rather silver(I) dioxoargentate(III), Ag(I)[Ag(III)O2]. Here, we look at the particularly interesting case of a hypothetical AgCl2 where both types of redox instabilities operate simultaneously. Since standard redox potential of the Ag(II)/Ag(I) redox pair reaches some 2 V versus Normal Hydrogen Electrode (NHE), it might be expected that Ag(II) would oxidize Cl− anion with great ease (standard redox potential of the ½ Cl2/Cl− pair is + 1.36 V versus Normal Hydrogen Electrode). However, ionic Ag(II)Cl2 benefits from long-distance electrostatic stabilization to a much larger degree than Ag(I)Cl + ½ Cl2, which affects relative stability. Moreover, Ag(II) may disproportionate in its chloride, just like it does in an oxide; this is what AuCl2 does, its formula corresponding in fact to Au(I)[Au(III)Cl4]. Formation of polychloride substructure, as for organic derivatives of Cl3− anion, is yet another possibility. All that creates a very complicated potential energy surface with a few chemically distinct minima i.e., diverse polymorphic forms present. Here, results of our theoretical study for AgCl2 will be presented including outcome of evolutionary algorithm structure prediction method, and the chemical identity of the most stable form will be uncovered together with its presumed magnetic properties. Contrary to previous rough estimates suggesting substantial instability of AgCl2, we find that AgCl2 is only slightly metastable (by 52 meV per formula unit) with respect to the known AgCl and ½ Cl2, stable with respect to elements, and simultaneously dynamically (i.e., phonon) stable. Thus, our results point out to conceivable existence of AgCl2 which should be targeted via non-equilibrium approaches.

Spin-reorientation-induced magnetodielectric coupling effects in two layered perovskite magnets

Spin-reorientation-induced magnetodielectric coupling effects were discovered in two layered perovskite magnets, [C6H5CH2CH2NH3]2[MCl4] (M = Mn2+ and Cu2+), via isothermal magnetodielectric measurements on single-crystal samples. Specifically, peak-like dielectric anomalies and spin-flop transitions appeared simultaneously at around ±34 kOe for the canted antiferromagnet (M = Mn2+) at below 44.3 K, while a low-field (1 kOe) controlled magnetodielectric effect was observed in the "soft" ferromagnet (M = Cu2+) at below 9.5 K. These isothermal magnetodielectric effects are highly reproducible and synchronous with the field-induced magnetization at different temperatures, well confirming the essential role of spin reorientation on inducing magnetodielectric coupling effects. These findings strongly imply that the layered perovskite magnets are new promising organic-inorganic hybrid systems to host magnetodielectric coupling effects.

Dielectric properties of complex magnetic field induced states in PbCuSO4(OH)2

Spin spirals, which coexist with collinear spin order in linarite PbCuSO₄(OH)₂, indicate electrical polarisation textures of spin-multipolar phases. We derive experimental evidence by a detailed investigation of the magnetic-field dependent dielectric and electric polarization properties at low temperatures. Linarite exhibits a quasi-one-dimensional frustrated S = ½ spin chain, which forms 3D spin-spiral order in zero magnetic field for T < 2.85 K. Recently, due to the monoclinic lattice of linarite with CuO₂ ribbon chains, complex magnetic field induced states were found. These spin-multipolar phases, which compete with spin-density waves at low magnetic fields, exist in close vicinity to the transition from the spin spiral into field induced spin polarized state. Via antisymmetric Dzyaloshinskii-Moriya interaction spin-driven ferroelectricity develops in the spin-spirals state. Via electric polarization measurements this allows to prove the transitions into complex magnetic field induced phases. Thorough analyses of the temperature and magnetic field dependent dielectric properties of a naturally grown single crystalline sample provide a detailed (T,H) phase diagrams for the three different crystallographic directions.

Electronic Phase Separation and Dramatic Inverse Band Renormalization in the Mixed-Valence Cuprate LiCu_{2}O_{2}

We measured, by angle-resolved photoemission spectroscopy, the electronic structure of LiCu_{2}O_{2}, a mixed-valence cuprate where planes of Cu(I) (3d^{10}) ions are sandwiched between layers containing one-dimensional edge-sharing Cu(II) (3d^{9}) chains. We find that the Cu(I)- and Cu(II)-derived electronic states form separate electronic subsystems, in spite of being coupled by bridging O ions. The valence band, of the Cu(I) character, disperses within the charge-transfer gap of the strongly correlated Cu(II) states, displaying an unprecedented 250% broadening of the bandwidth with respect to the predictions of density functional theory. Our observation is at odds with the widely accepted tenet of many-body theory that correlation effects generally yield narrower bands and larger electron masses and suggests that present-day electronic structure techniques provide an intrinsically inappropriate description of ligand-to-d hybridizations in late transition metal oxides.

Superadiabatic quantum heat engine with a multiferroic working medium

A quantum thermodynamic cycle with a chiral multiferroic working substance such as LiCu_{2}O_{2} is presented. Shortcuts to adiabaticity are employed to achieve an efficient, finite-time quantum thermodynamic cycle, which is found to depend on the spin ordering. The emergent electric polarization associated with the chiral spin order, i.e., the magnetoelectric coupling, renders possible steering of the spin order by an external electric field and hence renders possible an electric-field control of the cycle. Due to the intrinsic coupling between the spin and the electric polarization, the cycle performs an electromagnetic work. We determine this work's mean-square fluctuations, the irreversible work, and the output power of the cycle. We observe that the work mean-square fluctuations are increased with the duration of the adiabatic strokes, while the irreversible work and the output power of the cycle show a nonmonotonic behavior. In particular, the irreversible work vanishes at the end of the quantum adiabatic strokes. This fact confirms that the cycle is reversible. Our theoretical findings evidence the existence of a system inherent maximal output power. By implementing a Lindblad master equation we quantify the role of thermal relaxations on the cycle efficiency. We also discuss the role of entanglement encoded in the noncollinear spin order as a resource to affect the quantum thermodynamic cycle.

Rigorous determination of the ground-state phases and thermodynamics in an Ising-type multiferroic chain

To understand the ferroelectricity driven by collinear magnetism in a multiferroic spin-chain system, we have adopted an elastic diatomic Ising spin-chain model with axial next-nearest-neighbor interaction to describe its magnetoelectric properties. By employing magneto-phonon decoupling and the transfer-matrix method, the possible ground-state configurations and thermodynamic behaviors of the system have been determined exactly. The parameter relation for the appearance of electric polarization has been discussed from the perspective of the ground-state configuration. In the case of nearest-neighbor antiferromagnetic coupling, a novel series of zero-temperature transitions induced by magnetic field have been observed, from the ↑↑↓↓ spin configuration associated with ferroelectric order to the ↑↓↑ state with a peculiar 1/3 magnetization plateau, then to the ↑↑↑↓ state, and finally saturation in the ↑↑↑↑ state.

Observation of S = 1/2 quasi-1D magnetic and magneto-dielectric behavior in a cubic SrCuTe2O6

We investigate the magnetic, thermal, and dielectric properties of SrCuTe2O6, which is isostructural to PbCuTe2O6, a recently found, Cu-based 3D frustrated magnet with a corner-sharing triangular spin network having dominant first and second nearest neighbor (nn) couplings (Koteswararao et al 2014 Phys. Rev. B 90 035141). Although SrCuTe2O6 has a structurally similar spin network, the magnetic data exhibit the characteristic features of a typical quasi-1D magnet, which mainly resulted from the magnetically dominant third nn coupling, uniform chains. The magnetic properties of this system are studied via magnetization (M), heat capacity (C p ), dielectric constant ([Formula: see text]), and measurements along with ab initio band structure calculations. The magnetic susceptibility [Formula: see text] data show a broad maximum at 32 K and the system orders at low temperatures [Formula: see text] K and [Formula: see text] K, respectively. The analysis of the [Formula: see text] data gives an intra-chain coupling, [Formula: see text], to be about  ≈  -  42 K with non-negligible frustrated inter-chain couplings ([Formula: see text] and [Formula: see text]). The hopping parameters obtained from the LDA band structure calculations also suggest the presence of coupled uniform chains. The observation of simultaneous anomalies in [Formula: see text] at [Formula: see text] and [Formula: see text] suggests the presence of a magneto-dielectric effect in SrCuTe2O6. A magnetic phase diagram is also built based on the M, C p , and [Formula: see text] results.

Thermally mediated mechanism to enhance magnetoelectric coupling in multiferroics

The main roadblock on the way to practical realization of magnetoelectric devices is the lack of multiferroics with strong magnetoelectric coupling. We propose an unusual route to dramatically enhance this coupling through a thermally mediated mechanism. Such a thermally mediated magnetoelectric effect is quantified by an isentropic rather than isothermal magnetoelectric response and is computed here from first principles. A robust enhancement of the magnetoelectric coupling is predicted for both naturally occurring and heterostructured materials.

Spin and orbital orderings behind multiferroicity in delafossite and related compounds

Coupling between noncollinear magnetic ordering and ferroelectricicty in magnetoelectric multiferroics has been extensively studied in the last decade. Delafossite family compounds with triangular lattice structure provide a great opportunity to study the coupling between spin and electric dipole in multiferroics due to the variety of magnetic phases with different symmetry. This review introduces the magnetic and ferroelectric phase transitions in delafossite ferrites, CuFe(1-x)X(x)O(2) (X = Al, Ga), AgFeO(2) and the related compound α-NaFeO(2). In CuFeO(2), the ferroelectric phase appears under a magnetic field or chemical substitution. The proper screw magnetic ordering with the magnetic point group 21', which has been determined by detailed analysis in neutron diffraction experiments, induces the ferroelectric polarization along the monoclinic b axis in CuFeO2. The cycloidal magnetic orderings are realized in AgFeO(2) and α-NaFeO(2), which are of the point group m1' allowing polarization in the ac plane. The emergence of ferroelectric polarization can be explained by both the extended inverse Dzyaloshinsky-Moriya effect and the d − p hybridization mechanism. These mechanisms are supported by experimental evidence in CuFe(1-x)Ga(x)O2. The polarized neutron diffraction experiment demonstrated one-to-one correspondence between ferroelectric polarization and spin helicity, S(i) × S(j). The incommensurate orbital ordering with 2 Q wave vector, observed by the soft x-ray resonant diffraction experiment, proved that the spin-orbit interaction ties spin and orbital orders to each other, playing a crucial role for the emergence of ferroelectricity in CuFe(1-x)Ga(x)O2.

Electric field control of ferroelectric domain structures in MnWO4

Competing interactions make the magnetic structure of MnWO4 highly frustrated, and only the AF2 phase of the three magnetically ordered phases (AF1, AF2, AF3) is ferroelectric. The high frustration may thus allow a possibility to tune the magnetic structure by means of an electric field via magnetoelectric coupling. By using the pyroelectric current method, we measure the remnant ferroelectric polarization in MnWO4 upon application of a poling electric field via two different roadmaps. It is demonstrated that an electric field as low as 10 kV cm(-1) is sufficient to enhance the stability of a ferroelectric AF2 phase at the expense of a non-ferroelectric AF1 phase. This work suggests that electric field induced electrostatic energy, although small due to weak magnetically induced electric polarization, may effectively tune ferroelectric domain structures, and thus the magnetic structure of highly frustrated multiferroic materials.

Multiferroics of spin origin

Multiferroics, compounds with both magnetic and ferroelectric orders, are believed to be a key material system to achieve cross-control between magnetism and electricity in a solid with minute energy dissipation. Such a colossal magnetoelectric (ME) effect has been an issue of keen interest for a long time in condensed matter physics as well as a most desired function in the emerging spin-related electronics. Here we begin with the basic mechanisms to realize multiferroicity or spin-driven ferroelectricity in magnetic materials, which have recently been clarified and proved both theoretically and experimentally. According to the proposed mechanisms, many families of multiferroics have been explored, found (re-discovered), and newly developed, realizing a variety of colossal ME controls. We overview versatile multiferroics from the viewpoints of their multiferroicity mechanisms and their fundamental ME characteristics on the basis of the recent advances in exploratory materials. One of the new directions in multiferroic science is the dynamical ME effect, namely the dynamical and/or fast cross-control between electric and magnetic dipoles in a solid. We argue here that the dynamics of multiferroic domain walls significantly contributes to the amplification of ME response, which has been revealed through the dielectric spectroscopy. Another related issue is the electric-dipole-active magnetic resonance, called electromagnons. The electromagnons can provide a new stage of ME optics via resonant coupling with the external electromagnetic wave (light). Finally, we give concluding remarks on multiferroics physics in the light of a broader perspective from the emergent electromagnetism in a solid as well as from the possible application toward future dissipationless electronics.

Bond distortion effects and electric orders in spiral multiferroic magnets

In this paper we study the bond distortion effect on the electric polarization in spiral multiferroic magnets based on cluster and chain models. The bond distortion breaks the inversion symmetry and modifies the d-p hybridization. Consequently, it will affect the electric polarization, which can be divided into the spin-current part and the lattice-mediated part. The spin-current polarization can be written in terms of [Formula: see text] with anisotropic amplitude, and the lattice-mediated polarization exists only when the M-O-M bond is distorted. The electric polarization for three-atom M-O-M and four-atom M-O2-M clusters is calculated. We also study possible electric ordering in three kinds of chains made of different clusters. We apply our theory to multiferroic cuprates and find that the results are qualitatively in agreement with experimental observations.

Giant tunability of ferroelectric polarization in GdMn2O5

Giant tunability of ferroelectric polarization (ΔP=5000  μC/m2) in the multiferroic GdMn2O5 with external magnetic fields is discovered. The detailed magnetic model from x-ray magnetic scattering results indicates that the Gd-Mn symmetric exchange striction plays a major role in the tunable ferroelectricity of GdMn2O5, which is in distinction from other compounds of the same family. Thus, the highly isotropic nature of Gd spins plays a key role in the giant magnetoelectric coupling in GdMn2O5. This finding provides a new handle in achieving enhanced magnetoelectric functionality.

Hexagonal Manganites—(RMnO3): Class (I) Multiferroics with Strong Coupling of Magnetism and Ferroelectricity

Hexagonal manganites belong to an exciting class of materials exhibiting strong interactions between a highly frustrated magnetic system, the ferroelectric polarization, and the lattice. The existence and mutual interaction of different magnetic ions (Mn and rare earth) results in complex magnetic phase diagrams and novel physical phenomena. A summary and discussion of the various properties, underlying physical mechanisms, the role of the rare earth ions, and the complex interactions in multiferroic hexagonal manganites, are presented in this paper.

Observation of multiferroic properties in pyroxene NaFeGe2O6

We report the observation of multiferroicity in a clinopyroxene NaFeGe(2)O(6) polycrystal from the investigation of its electrical and magnetic properties. Following the previously known first magnetic transition at T(N1) = 13 K, a second magnetic transition appears at T(N2) = 11.8 K in the temperature dependence of the magnetization. A ferroelectric polarization starts to develop clearly at T(N2) rather than T(N1) and its magnitude increases up to ~13 μC m(-2) at 5 K, supporting the idea that the ferroelectric state in NaFeGe(2)O(6) stems from a helical spin order stabilized below T(N2). When a magnetic field of 90 kOe is applied, the electric polarization decreases to 9 μC m(-2) and T(N2) slightly increases by 0.5 K. At intermediate magnetic fields, around 28 and 78 kOe, anomalies in the magnetoelectric current, magnetoelectric susceptibility, and field derivative of magnetization curves are found, indicating field-induced spin-state transitions. Based on these electrical and magnetic properties, we provide a detailed low temperature phase diagram up to 90 kOe, and discuss the nature of each phase of NaFeGe(2)O(6).

The magnetoelectric effect due to local noncentrosymmetry

Magnetoelectrics often possess ions located in noncentrosymmetric surroundings. Based on this fact we suggest a microscopic model of magnetoelectric interaction and show that the spin-orbit coupling leads to spin-dependent electric dipole moments of the electron orbitals of these ions, which results in non-vanishing polarization for certain spin configurations. The approach accounts for the macroscopic symmetry of the unit cell and is valid for both commensurate and complex incommensurate magnetic structures. The model is illustrated by the examples of MnWO(4), MnPS(3) and LiNiPO(4). Application to other magnetoelectrics is discussed.

CuBr2--a new multiferroic material with high critical temperature

A new multiferroic material, CuBr(2) , is reported for the first time. CuBr(2) has not only a high transition temperature (close to liquid nitrogen temperature) but also low dielectric loss and strong magnetoelectric coupling. These findings reveal the importance of anion effects, in the search for the high temperature multiferroics materials among these low-dimensional spin systems.

Quantum spin liquid in frustrated one-dimensional LiCuSbO4

A quantum magnet, LiCuSbO4, with chains of edge-sharing spin-1/2 CuO6 octahedra is reported. While short-range order is observed for T<10  K, no zero-field phase transition or spin freezing occurs down to 100 mK. Specific heat indicates a distinct high-field phase near the 12 T saturation field. Neutron scattering shows incommensurate spin correlations with q=(0.47±0.01)π/a and places an upper limit of 70  μeV on any spin gap. Exact diagonalization of 16-spin easy-plane spin-1/2 chains with competing ferro- and antiferromagnetic interactions (J1=-75  K, J2=34  K) accounts for the T>2  K data.

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.

Unusually large magnetic anisotropy in a CuO-based semiconductor Cu5V2O10

A CuO-based material Cu(5)V(2)O(10) was successfully grown in a closed crucible using Sr(OH)(2)·8H(2)O as flux. The structure of Cu(5)V(2)O(10) can be viewed as being composed of two types of zigzag Cu-O chains running along the b- and c-axes, which shows a two-dimensional crosslike framework with 12-column square tunnels along the a-axis. Magnetic measurements show that Cu(5)V(2)O(10) exhibits unexpected large magnetic anisotropy, which is the first time magnetic anisotropy energy of ∼10(7) erg/cm(3) in the CuO-based materials has been observed. The origins of large anisotropy are suggested to arise from strong anisotropic exchanges due to the particular bonding geometry and the Jahn-Teller distortion of Cu(2+) ions. Further, the band structure investigated by the GGA+U method suggests that Cu(5)V(2)O(10) is a semiconductor.

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.

Chiral order and electromagnetic dynamics in one-dimensional multiferroic cuprates

We show by unbiased numerical calculations that the ferromagnetic nearest-neighbor exchange interaction stabilizes a vector spin chiral order against the quantum fluctuation in a frustrated spin-1/2 chain relevant to multiferroic cuprates, LiCu2O2 and LiCuVO4. Our realistic semiclassical analyses for LiCu2O2 resolve controversies on the helical magnetic structure and unveil the pseudo-Nambu-Goldstone modes as the origin of experimentally observed electromagnons.

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.

Spiral correlations in frustrated one-dimensional spin-1/2 Heisenberg J1-J2-J3 ferromagnets

We use the coupled cluster method for infinite chains complemented by exact diagonalization of finite periodic chains to discuss the influence of a third-neighbor exchange J(3) on the ground state of the spin-½ Heisenberg chain with ferromagnetic nearest-neighbor interaction J(1) and frustrating antiferromagnetic next-nearest-neighbor interaction J(2). A third-neighbor exchange J(3) might be relevant to describe the magnetic properties of the quasi-one-dimensional edge-shared cuprates, such as LiVCuO(4) or LiCu(2)O(2). In particular, we calculate the critical point J(2)(c) as a function of J(3), where the ferromagnetic ground state gives way for a ground state with incommensurate spiral correlations. For antiferromagnetic J(3) the ferro-spiral transition is always continuous and the critical values J(2)(c) of the classical and the quantum model coincide. On the other hand, for ferromagnetic J3 is < or approximately equal to -(0.01...0.02)|J1|. the critical value J(2)(c) of the quantum model is smaller than that of the classical model. Moreover, the transition becomes discontinuous, i.e. the model exhibits a quantum tricritical point. We also calculate the height of the jump of the spiral pitch angle at the discontinuous ferro-spiral transition.

Theory of magnetic switching of ferroelectricity in spiral magnets

We propose a microscopic theory for magnetic switching of electric polarization (P) in the spin-spiral multiferroics by taking TbMnO3 and DyMnO3 as examples. We reproduce their phase diagrams under a magnetic field Hex by Monte Carlo simulation of an accurate spin model and reveal that competition among the Dzyaloshinskii-Moriya interaction, spin anisotropy, and spin exchange is controlled by the applied Hex, resulting in magnetic transitions accompanied by reorientation or vanishing of P. We also discuss the relevance of the proposed mechanisms to many other multiferroics such as LiCu2O2, MnWO4, and Ni3V2O4.

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.

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.

Exciton doublet in the Mott-Hubbard insulator LiCuVO4 identified by spectral ellipsometry

Spectroscopic ellipsometry was used to study the dielectric function of LiCuVO4, a compound comprised of chains of edge-sharing CuO4 plaquettes, in the spectral range 0.75-6.5 eV at temperatures 7-300 K. For photon polarization along the chains, the data reveal a weak but well-resolved two-peak structure centered at 2.15 and 2.95 eV whose spectral weight is strongly enhanced upon cooling near the magnetic ordering temperature. We identify these features as an exciton doublet in the Mott-Hubbard gap that emerges as a consequence of the Coulomb interaction between electrons on nearest and next-nearest-neighbor sites along the chains. Our results and methodology can be used to address the role of the long-range Coulomb repulsion for compounds with doped copper-oxide chains and planes.

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.

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.

Quantum theory of multiferroic helimagnets: collinear and helical phases

We study the quantum fluctuation in the cycloidal helical magnet in terms of the Schwinger boson approach. In sharp contrast to the classical fluctuation, the quantum fluctuation is collinear in nature which gives rise to the collinear spin density wave state slightly above the helical cycloidal state as the temperature is lowered. Physical properties such as the reduced elliptic ratio of the spiral, the neutron scattering and infrared absorption spectra are discussed from this viewpoint with the possible relevance to the quasi-one dimensional LiCu2O2 and LiCuVO4.

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 ground state and transition of a quantum multiferroic LiCu2O2

Based on resonant soft x-ray magnetic scattering, we report that LiCu2O2 exhibits a large interchain coupling which suppresses quantum fluctuations along spin chains, and a quasi-2D short-range magnetic order prevails at temperatures above the magnetic transition. These observations unravel the fact that the ground state of LiCu2O2 possesses long-range 2D-like incommensurate magnetic order rather than being a gapped spin liquid as expected from the nature of quantum spin-1/2 chains. In addition, the spin coupling along the c axis is found to be essential for inducing electric polarization.