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

The identification of high-pressure phase transition sequence in selected tungstates and molybdates

Tungstates and molybdates possessing the scheelite- and wolframite-type (if present) structures hold a significant functional value. Their high-pressure phase diagrams are very complicated and controversial, and even some parts have not been characterized yet. In this study, we investigate the sequence of pressure driven structural phase transitions up to 100 GPa in these tungstate and molybdate families via first-principles structure predictions. Based on our structural predictions, it is possible for isostructural tungstates and molybdates to exhibit a phase transition sequence that is either similar or identical. Examples of these compounds are CaWO4, CaMoO4, and CdMoO4, in addition to EuWO4 and EuMoO4. However, the phase transition sequences of some tungstates and molybdates, especially those with different divalent cations, display noteworthy variations, revealing the intricate influence of ionic radii and electronic properties on crystal configurations. To obtain a deeper understanding of the high-pressure phase transition behavior of tungstates and molybdates, we analyze the high-pressure phase diagrams of MgWO4, SrWO4, and CaMoO4, representative examples of wolframite-type tungstate, scheelite-type tungstate, and scheelite-type molybdate, respectively, using x-ray powder diffraction. Our x-ray diffraction experiments and structure predictions consistently verify that the orthorhombic Cmca phase is a high-pressure phase of SrWO4. Structural configurations and mechanical properties of these predicted structures are discussed, and electronic properties are given. This study could have important implications for the fields of seismology and geophysics, as well as the utilization of these materials in various capacities, such as photocatalysts, photoanodes, and phosphors.

High-field magnetization and electronic spin resonance study in the twisted honeycomb latticeα-Mn2V2O7

We report the single-crystal growth of Mn₂V₂O₇and the results of magnetic susceptibility, high-field magnetization up to 55 T and high-frequency electric spin resonance (ESR) measurements for its low-temperatureαphase. Two antiferromagnetic (AFM) ordering at 17.5 K and 3 K and obvious magnetic anisotropy are observed inα-Mn₂V₂O₇upon cooling. In pulsed high magnetic fields, the compound reaches the saturation magnetic moment of ∼10.5μ_Bfor each molecular formula at around 45 T after two undergoing AFM phase transitions atH_c1≈ 16 T,H_c2≈ 34.5 T forH//[11-0] andH_sf1= 2.5 T,H_sf2= 7 T forH//[001]. In these two directions, two and seven resonance modes are detected by ESR spectroscopy, respectively. Theω₁andω₂modes ofH//[11-0] can be well described by two-sublattice AFM resonance mode with two zero-field gaps at 94.51 GHz and 169.28 GHz, indicating a hard-axis feature. The seven modes forH//[001] are partially separated by the critical fields ofH_sf1andH_sf2, displaying the two signs of spin-flop transition. The fittings ofω_c1andω_c2modes yield zero-field gaps at 69.50 GHz and 84.73 GHz forH//[001], confirming the axis-type anisotropy. The saturated moment and gyromagnetic ratio indicate the Mn²⁺ion inα-Mn₂V₂O₇is in a high spin state with orbital moment completely quenched. A quasi-one-dimensional magnetism with a zig-zag-chain spin configuration is suggested inα-Mn₂V₂O₇, due to the special neighbor interactions caused by a distorted network structure with honeycomb layer.

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.

Writing of strain-controlled multiferroic ribbons into MnWO4

Local and low-dimensional structures, such as interfaces, domain walls and structural defects, may exhibit physical properties different from the bulk. Therein, a wide variety of local phases were discovered including conductive interfaces, sheet superconductivity, and magnetoelectric domain walls. The confinement of combined magnetic and electric orders to spatially selected regions may be particularly relevant for future technological applications because it may serve as basis of electrically controllable magnetic memory devices. However, direct observation of magnetoelectric low-dimensional structures cannot readily be done partly because of the lack of experimental techniques locally probing their physical nature. Here, we report an observation of multiferroic ribbon-like domains in a non-multiferroic environment in MnWO₄. Using optical second harmonic generation imaging, we reveal that a multiferroic phase is stabilized by locally generated strain while the bulk magnetic structure is non-multiferroic. We further find that the confined multiferroic state retains domains with different directions of electric polarization and we demonstrate deterministic writing of a multiferroic state embedded in a non-multiferroic environment.

Spin-phonon coupling and thermodynamic behaviour in YCrO3and LaCrO3: inelastic neutron scattering and lattice dynamics

We report detailed temperature-dependent inelastic neutron scattering andab initiolattice dynamics investigation of magnetic perovskites YCrO₃and LaCrO₃. The magnetic neutron scattering from the Cr ions exhibits significant changes with temperature and dominates at low momentum transfer regime.Ab initiocalculations performed including magnetic interactions show that the effect of magnetic interactions is very significant on the low- as well as high-energy phonon modes. We have also shown that the inelastic neutron spectrum of YCrO₃mimics the magnon spectrum from a G-type antiferromagnetic system, which is consistent with previously reported magnetic structure in the compound. The pressure-dependentab initiolattice dynamics calculations are used to calculate the anisotropic thermal expansion behaviour in orthorhombic YCrO₃, which is in excellent agreement with the available experimental data in the paramagnetic phase. We identify that the low energy anharmonic phonon modes involving Y vibrations contribute maximum to the thermal expansion behaviour.

Enhancement of magnetoelectric coupling in Cr doped Mn2O3

The effect of Cr doping has been undertaken to investigate its effect on the structural, magnetic, dielectric and magnetoelectric properties of newly discovered multiferroics material α-Mn₂O₃. The Cr doping modifies the room temperature crystal symmetry i.e. transforms from orthorhombic to cubic symmetry. Similar to α-Mn₂O₃, two magnetic transitions have been observed in all Cr doped samples. The effect of Cr doping manifested on the low temperature transition. The lower magnetic transition shifted toward higher temperature (25 K for pristine to 40 K for Cr = 10%) whereas the high temperature transition decreases slightly with increasing Cr content. A clear frequency independent transition is observed in temperature dependent complex dielectric measurements for Mn_2-x Cr _x O₃ (0 ⩽ x ⩽ 0.10) samples around high temperature magnetic ordering ∼80 K which corroborate the magnetoelectric coupling in these samples. Interestingly, the magnetodielectric value enhanced significantly with Cr doping and a maximum increase of ∼21% is observed for 10% Cr doped sample at 5 K around 70 kOe magnetic field.

Antiferromagnetism of Double Molybdate LiFe(MoO4)2

The magnetic properties of the spin-5/2 double molybdate LiFe(MoO₄)₂ have been characterized by heat capacity, magnetic susceptibility, and neutron powder diffraction techniques. Unlike the multiferroic system LiFe(WO₄)₂ which exhibits two successive magnetic transitions, LiFe(MoO₄)₂ undergoes only one antiferromagnetic transition at T_N ∼ 23.8 K. Its antiferromagnetic magnetic structure with the commensurate propagation vector k = (0, 0.5, 0) has been determined. Density functional theory calculations confirm the antiferromagnetic ground state and provide a numerical estimate of the relevant exchange coupling constants.

Domains and domain walls in multiferroics

Multiferroics are materials combining several ferroic orders, such as ferroelectricity, ferro- (or antiferro-) magnetism, ferroelasticity and ferrotoroidicity. They are of interest both from a fundamental perspective, as they have multiple (coupled) non-linear functional responses providing a veritable myriad of correlated phenomena, and because of the opportunity to apply these functionalities for new device applications. One application is, for instance, in non-volatile memory, which has led to special attention being devoted to ferroelectric and magnetic multiferroics. The vision is to combine the low writing power of ferroelectric information with the easy, non-volatile reading of magnetic information to give a “best of both worlds” computer memory. For this to be realised, the two ferroic orders need to be intimately linked via the magnetoelectric effect. The magnetoelectric coupling – the way polarization and magnetization interact – is manifested by the formation and interactions of domains and domain walls, and so to understand how to engineer future devices one must first understand the interactions of domains and domain walls. In this article, we provide a short introduction to the domain formation in ferroelectrics and ferromagnets, as well as different microscopy techniques that enable the visualization of such domains. We then review the recent research on multiferroic domains and domain walls, including their manipulation and intriguing properties, such as enhanced conductivity and anomalous magnetic order. Finally, we discuss future perspectives concerning the field of multiferroic domain walls and emergent topological structures such as ferroelectric vortices and skyrmions.

Comprehensive inelastic neutron scattering study of the multiferroic M n 1 - x C o x W O 4

Using high-resolution inelastic neutron scattering, we examine the spin dynamics ofM n 1 - x C o x W O 4 in the collinear AF1, the a c - b spiral AF2, and the a c cycloidal AF5 phases. The spin wave excitations are well described by a Heisenberg model with competing long-range exchange interactions (J i up to 12th nearest neighbors) and the single-ion anisotropy K induced by the spin-orbit interaction. While the exchange constants are relatively unchanged, the dominant effect of doping is to change the single-ion anisotropy from easy axis ( K > 0 ) in the collinear AF1 phase to easy plane ( K < 0 ) in the two multiferroic phases.

Electronic structure of Pr2MnNiO6 from x-ray photoemission, absorption and density functional theory

The electronic structure of double perovskite Pr₂MnNiO₆ was studied using core x-ray photoelectron spectroscopy and x-ray absorption spectroscopy. The 2p x-ray absorption spectra show that Mn and Ni are in 4+  and 2+  states respectively. Based on charge transfer multiplet analysis of the 2p XPS spectra of both ions, we find charge transfer energies [Formula: see text] of 3.5 and 2.5 eV for Ni and Mn respectively. The ground state of Ni²⁺ and Mn⁴⁺ ions reveal a higher d electron count of 8.21 and 3.38 respectively as compared to the ionic values. The partial density of states clearly show a charge transfer character of the system for U  -  J [Formula: see text] 2 eV. The O 1s edge absorption spectra reveal a band gap of 0.9 eV, which is close to the value estimated from analysis of Ni and Mn 2p photoemission and absorption spectra. The combined analysis of nature of spectroscopic data and first principles calculations reveal that the material is a p  -  d type charge transfer insulator with an intermediate covalent character according to the Zannen-Sawatzy-Allen phase diagram.

Theoretical spin-wave dispersions in the antiferromagnetic phase AF1 of MnWO4 based on the polar atomistic model in P2

The spin wave dispersions of the low temperature antiferromagnetic phase (AF1) MnWO₄ have been numerically calculated based on the recently reported non-collinear spin configuration with two different canting angles. A Heisenberg model with competing magnetic exchange couplings and single-ion anisotropy terms could properly describe the spin wave excitations, including the newly observed low-lying energy excitation mode [Formula: see text] meV appearing at the magnetic zone centre. The spin wave dispersion and intensities are highly sensitive to two differently aligned spin-canting sublattices in the AF1 model. Thus this study reinsures the otherwise hardly provable hidden polar character in MnWO₄.

Switching of the Chiral Magnetic Domains in the Hybrid Molecular/Inorganic Multiferroic (ND4)2[FeCl5(D2O)]

(ND₄)₂[FeCl₅(D₂O)] represents a promising example of the hybrid molecular/inorganic approach to create materials with strong magneto-electric coupling. Neutron spherical polarimetry, which is directly sensitive to the absolute magnetic configuration and domain population, has been used in this work to unambiguously prove the multiferroicity of this material. We demonstrate that the application of an electric field upon cooling results in the stabilization of a single-cycloidal magnetic domain below 6.9 K, while poling in the opposite electric field direction produces the full population of the domain with opposite magnetic chirality. We prove the complete switchability of the magnetic domains at low temperature by the applied electric field, which constitutes a direct proof of the strong magnetoelectric coupling. Additionally, we refine the magnetic structure of the ordered ground state, deducing the underlying magnetic space group consistent with the direction of the ferroelectric polarization, and we provide evidence of a collinear amplitude-modulated state with magnetic moments along the a-axis in the temperature region between 6.9 and 7.2 K.

Two spin-canting textures in the antiferromagnetic phase AF1 of MnWO4 based on the new polar atomistic model in P2

The low temperature antiferromagnetic (AF) phase of MnWO₄ (the so-called AF1 phase) exhibits different spin-canting configurations at two Mn²⁺ sublattices of the (3  +  1)-dimensional magnetic structure. The suggested superspace group [Formula: see text] is a significant consequence of the polar space group [Formula: see text]2 true for the nuclear structure of MnWO₄. Density functional theory calculations showed that its ground state prefers this two spin-canting system. The structural difference between two independent atomic sites for Mn (Mn _a , Mn _b ) is too small to allow microscopically detectable electric polarisation. However, this hidden intrinsic polar character allows AF1 two commensurately modulated spin-canting textures. This is considered as the prerequisite onset of the improper ferroelectricity enhanced by the helical spin order in the multiferroic phase AF2 of MnWO₄.

Control of Chiral Magnetism Through Electric Fields in Multiferroic Compounds above the Long-Range Multiferroic Transition

Polarized neutron scattering experiments reveal that type-II multiferroics allow for controlling the spin chirality by external electric fields even in the absence of long-range multiferroic order. In the two prototype compounds TbMnO_{3} and MnWO_{4}, chiral magnetism associated with soft overdamped electromagnons can be observed above the long-range multiferroic transition temperature T_{MF}, and it is possible to control it through an electric field. While MnWO_{4} exhibits chiral correlations only in a tiny temperature interval above T_{MF}, in TbMnO_{3} chiral magnetism can be observed over several kelvin up to the lock-in transition, which is well separated from T_{MF}.

Magnetoelectric Coupling through the Spin Flop Transition in Ni_{3}TeO_{6}

We combined high field optical spectroscopy and first principles calculations to analyze the electronic structure of Ni_{3}TeO_{6} across the 53 K and 9 T magnetic transitions, both of which are accompanied by large changes in electric polarization. The color properties are sensitive to magnetic order due to field-induced changes in the crystal field environment, with those around Ni1 and Ni2 most affected. These findings advance the understanding of magnetoelectric coupling in materials in which magnetic 3d centers coexist with nonmagnetic heavy chalcogenide cations.

Phase transitions and magnetic structures in MnW1-x Mo x O4 compounds (x ⩽ 0.2)

Temperature-dependent specific heat, magnetization and neutron diffraction data have been collected in zero magnetic field for polycrystalline samples of MnW1-x Mo x O4 (x  ⩽  0.2) solid solution whose end-member MnWO4 exhibits a magnetoelectric multiferroic phase (AF2 phase) between T 1  ≈  8 K and T 2  =  12.5 K. In MnW1-x Mo x O4, diamagnetic W(6+) are replaced with diamagnetic Mo(6+) cations and magnetic couplings among Mn(2+) (3d (5), S  =  5/2) ions are modified due the doping-induced tuning of the orbital hybridization between Mn 3d and O 2p states. It was observed that magnetic phase transition temperatures which are associated with the second-order AF3-to-paramagnetic (T N) and AF2-to-AF3 (T 2) transitions in pure MnWO4 slightly increase with the Mo content x. Magnetic specific heat data also indicate that the first-order AF1-to-AF2 phase transition at T 1 survives a weak doping x  ⩽  0.05. This latter phase transition becomes invisible above the base temperature 2 K for higher level of doping x  ⩾  0.10. Neutron powder diffraction datasets collected above 1.5 K for a sample of MnW0.8Mo0.2O4 were analyzed using the Rietveld method. The magnetic structure below  ≈  14 K is a helical incommensurate spin order with a temperature-independent propagation vector k  =  (-0.217(6), 0.5, 0.466(4)). This cycloidal magnetic structure is similar to the polar AF2 structure observed in MnWO4. The AF1 up-up-down-down collinear spin arrangement observed in MnWO4 is absent in our MnW0.8Mo0.2O4 sample.

Magnetic Reversal of Electric Polarization with Fixed Chirality of Magnetic Structure in a Chiral-Lattice Helimagnet MnSb_{2}O_{6}

The correlation between magnetic and dielectric properties has been investigated for the single crystal of the chiral triangular-lattice helimagnet MnSb_{2}O_{6}. We found that the spin-spiral plane in the ground state has a considerable tilting from the (110) plane and that the sign of the spin-spiral tilting angle is coupled to the clockwise or counterclockwise manner of spin rotation and accordingly to the sign of magnetically induced electric polarization. This leads to unique magnetoelectric responses such as the magnetic-field-induced selection of a single ferroelectric domain as well as the reversal of electric polarization just by a slight tilting of the magnetic field direction, where the chiral nature of the crystal structure plays a crucial role through the coupling of the chirality between the crystal and magnetic structures. Our results demonstrate that crystallographic chirality can be an abundant source of novel magnetoelectric functions with coupled internal degrees of freedom.

Comparative study of the field-induced and spontaneous AF2′ multiferroic phases in MnWO4and Mn0.90Co0.10WO4within the magnetic symmetry framework

(Mn,Co)WO4compounds are regarded as reference spin-induced multiferroics. A comparative study is presented here, within the magnetic symmetry framework, of the incommensurate magnetic orders responsible for the ferroelectric phases of (i) MnWO4under a magnetic field (H||b) and (ii) Mn0.90Co0.10WO4in the absence of an external field. On the one hand, although these two ferroelectric phases are stabilized under different external physical conditions, both present the sameXc1′(α0γ)ssmagnetic symmetry and practically the same modulation vector. The magnetic ordering in both phases is an elliptical helix with the magnetic moments (as the polarization vector,P) perpendicular to thebaxis, although in most of the ferroelectric compositions of the (Mn,Co)WO4family the spins rotate in planes containingb(and haveP||b). On the other hand, the anisotropy of the resulting magnetic modulations is extraordinarily different in the two phases. This is described and explained in the light of the different anisotropies of Co and Mn ions.

Two-Step Antiferromagnetic Transitions and Ferroelectricity in Spin-1 Triangular-Lattice Antiferromagnetic Sr3NiTa2O9

We report the low-temperature characterizations on structural, specific heat, magnetic, and ferroelectric behaviors of transition metal oxide compound Sr3NiTa2O9. It is suggested that Sr3NiTa2O9 is a spin-1 triangular lattice Heisenberg quantum antiferromagnet which may have weak easy-axis anisotropy. At zero magnetic field, a two-step transition sequence at T(N1) = 3.35 K and T(N2) = 2.74 K, respectively, is observed, corresponding to the up-up-down (uud) spin ordering and 120° spin ordering, respectively. The two transition points shift gradually with increasing magnetic field toward the low temperature, accompanying an evolution from the 120° spin structure (phase) to the normal oblique phases. Ferroelectricity in the 120° phase is clearly identified. The first-principles calculations confirm the 120° phase as the ground state whose ferroelectricity originates mainly from the electronic polarization.

Functional domain walls in multiferroics

During the last decade a wide variety of novel and fascinating correlation phenomena has been discovered at domain walls in multiferroic bulk systems, ranging from unusual electronic conductance to inseparably entangled spin and charge degrees of freedom. The domain walls represent quasi-2D functional objects that can be induced, positioned, and erased on demand, bearing considerable technological potential for future nanoelectronics. Most of the challenges that remain to be solved before turning related device paradigms into reality, however, still fall in the field of fundamental condensed matter physics and materials science. In this topical review seminal experimental findings gained on electric and magnetic domain walls in multiferroic bulk materials are addressed. A special focus is put on the physical properties that emerge at so-called charged domain walls and the added functionality that arises from coexisting magnetic order. The research presented in this review highlights that we are just entering a whole new world of intriguing nanoscale physics that is yet to be explored in all its details. The goal is to draw attention to the persistent challenges and identify future key directions for the research on functional domain walls in multiferroics.

Control of multiferroic domains by external electric fields in TbMnO₃

The control of multiferroic domains through external electric fields has been studied by dielectric measurements and by polarized neutron diffraction on single-crystalline TbMnO3. Full hysteresis cycles were recorded by varying an external field of the order of several kV mm(-1) and by recording the chiral magnetic scattering as well as the charge in a sample capacitor. Both methods yield comparable coercive fields that increase upon cooling.

Piezomagnetoelectric Effect of Spin Origin in Dysprosium Orthoferrite

The piezomagnetoelectric effect, namely, the simultaneous induction of both the ferromagnetic moment and electric polarization by an application of uniaxial stress, was demonstrated in the nonferroelectric antiferromagnetic ground state of DyFeO(3). The induced electric polarization and ferromagnetic moment are coupled with each other, and monotonically increase with increasing uniaxial stress. The present work provides a new guiding principle for designing multiferroics where its magnetic symmetry is broken by external uniaxial stress.

Magnetically-induced ferroelectricity in the (ND4)2[FeCl5(D2O)] molecular compound

The number of magnetoelectric multiferroic materials reported to date is scarce, as magnetic structures that break inversion symmetry and induce an improper ferroelectric polarization typically arise through subtle competition between different magnetic interactions. The (NH4)2[FeCl5(H2O)] compound is a rare case where such improper ferroelectricity has been observed in a molecular material. We have used single crystal and powder neutron diffraction to obtain detailed solutions for the crystal and magnetic structures of (NH4)2[FeCl5(H2O)], from which we determined the mechanism of multiferroicity. From the crystal structure analysis, we observed an order-disorder phase transition related to the ordering of the ammonium counterion. We have determined the magnetic structure below TN, at 2 K and zero magnetic field, which corresponds to a cycloidal spin arrangement with magnetic moments contained in the ac-plane, propagating parallel to the c-axis. The observed ferroelectricity can be explained, from the obtained magnetic structure, via the inverse Dzyaloshinskii-Moriya mechanism.

Electric polarization of magnetic domain walls in magnetoelectrics

Two prominent magnetoelectrics MnWO4 and CuO possess low-temperature commensurate paraelectric magnetically ordered phase. Here using Monte Carlo simulations we show that the walls between the domains of this phase are ferroelectric with the same electric polarization direction and value as those in the magnetoelectric phases of these compounds. We also suggest that experimental observation of electric polarization of domain walls in MnWO4 should help to determine the macroscopic interactions responsible for its magnetoelectric properties.

An organic approach for nanostructured multiferroics

Multiferroics are materials that simultaneously exhibit more than one ferroic order parameters, such as ferroelectricity, ferroelasticity and ferromagnetism. Recently, multiferroicity has received a significant revival of interest due to the colossal magnetoelectric coupling effect for the development of nano-ferronics. In this mini-review, we focus on a recent study of ferroelectricity, magnetism and magnetoelectric coupling within the newly discovered organic charge-transfer complexes. A systemic understanding of the origin of organic ferroelectricity and magnetism is provided. Furthermore, based on the recent mechanism of the magnetoelectric coupling effect: spin-ordering-induced electric polarization and ferroelectricity-induced spin alignment, we further present the recent progress in organic charge-transfer multiferroics and metal-organic framework multiferroics. The coexistence of polarization and magnetism at room temperature of organic charge-transfer complexes will be critical for the development of all-organic multiferroics.

Polarization control at spin-driven ferroelectric domain walls

Unusual electronic states arise at ferroelectric domain walls due to the local symmetry reduction, strain gradients and electrostatics. This particularly applies to improper ferroelectrics, where the polarization is induced by a structural or magnetic order parameter. Because of the subordinate nature of the polarization, the rigid mechanical and electrostatic boundary conditions that constrain domain walls in proper ferroics are lifted. Here we show that spin-driven ferroelectricity promotes the emergence of charged domain walls. This provides new degrees of flexibility for controlling domain-wall charges in a deterministic and reversible process. We create and position a domain wall by an electric field in Mn0.95Co0.05WO4. With a magnetic field we then rotate the polarization and convert neutral into charged domain walls, while its magnetic properties peg the wall to its location. Using atomistic Landau-Lifshitz-Gilbert simulations we quantify the polarization changes across the two wall types and highlight their general occurrence.

Magnetic origin of giant magnetoelectricity in doped Y-type hexaferrite Ba(0.5)Sr(1.5)Zn(2)(Fe(1-x)Al(x))(12)O(22)

We investigated site-specific magnetic behaviors of multiferroic Ba(0.5)Sr(1.5)Zn(2)(Fe(1-x)Al(x))(12)O(22) using Fe L(2,3)-edge x-ray magnetic circular dichroism. The Al dopants mostly replace the Fe(3+) ions at octahedral (O(h)) sites, which contribute unquenched angular momenta through off-centering displacements. This replacement greatly reduces the magnetic anisotropy energy to change the magnetic order from a helical to a heliconical type with enhanced magnetoelectric susceptibility (α(ME)). The tetrahedral (T(d)) Fe sites exhibit magnetic hysteresis distinguishable from that of the O(h) sites, especially at low magnetic fields. These results provide essential clues for the heliconical order with a giant α(ME) and multibit memory effects in the Al-doped Y-type hexaferrite.

Uniaxial-stress control of spin-driven ferroelectricity in multiferroic Ba(2)CoGe(2)O(7)

We have demonstrated that spin-driven ferroelectricity in a tetragonal multiferroic Ba(2)CoGe(2)O(7) is controlled by applying uniaxial stress. We found that the application of compressive stress along the [110] direction leads to a 45° or 135° rotation of the sublattice magnetization of the staggered antiferromagnetic order in this system. This allows the spontaneous electric polarization to appear along the c axis. The present study suggests that an application of anisotropic stress, which is the simplest way to control symmetry of matter, can induce a variety of cross-correlated phenomena in spin-driven multiferroics.

Critical slowing down near the multiferroic phase transition in MnWO4

By using broadband dielectric spectroscopy in the radio frequency and microwave range, we studied the magnetoelectric dynamics in the multiferroic chiral antiferromagnet MnWO_{4}. Above the multiferroic phase transition at T_{N2}≈12.6  K we observe a critical slowing of the corresponding magnetoelectric fluctuations resembling the soft-mode behavior in canonical ferroelectrics. This electric-field-driven excitation carries much less spectral weight than ordinary phonon modes. Also, the critical slowing down of this mode scales with an exponent larger than 1, which is expected for magnetic second-order phase transition scenarios. Therefore, the investigated dynamics have to be interpreted as the softening of an electrically active magnetic excitation, an electromagnon.

High pressure and multiferroics materials: a happy marriage

The community of material scientists is strongly committed to the research area of multiferroic materials, both for the understanding of the complex mechanisms supporting the multiferroism and for the fabrication of new compounds, potentially suitable for technological applications. The use of high pressure is a powerful tool in synthesizing new multiferroic, in particular magneto-electric phases, where the pressure stabilization of otherwise unstable perovskite-based structural distortions may lead to promising novel metastable compounds. The in situ investigation of the high-pressure behavior of multiferroic materials has provided insight into the complex interplay between magnetic and electronic properties and the coupling to structural instabilities.

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.

Interpretation of magnetoelectric phase states using the praphase concept and exchange symmetry

The majority of magnetoelectric crystals show complex temperature-magnetic field or temperature-pressure phase diagrams with alternating antiferromagnetic incommensurate, magnetoelectric, and commensurate phases. Such phase diagrams occur as a result of successive magnetic instabilities with respect to different order parameters, which usually transform according to different irreducible representations (IRs) of the space group of the crystal. Therefore, in order to build a phenomenological theory of phase transitions in such magnetoelectrics one has to employ several order parameters and assume the proximity of various instabilities on the thermodynamic path. In this work we analyze the magnetoelectrics MnWO4, CuO, NaFeSi2O6, NaFeGe2O6, Cu3Nb2O8, α-CaCr2O4 and FeTe2O5Br using the praphase concept and the symmetry of the exchange Hamiltonian. We find that in all the considered cases the appearing magnetic structures are described by IRs entering into a single exchange multiplet, whereas in the cases of MnWO4 and CuO by a single IR of the space group of the praphase structure. Therefore, one can interpret the complex phase diagrams of magnetoelectrics as induced by a single IR either of the praphase or of the symmetry group of the exchange Hamiltonian. Detailed temperature-magnetic field phase diagrams of MnWO4 and CuO for certain field directions are obtained and the magnetic structures of the field-induced phases are determined.

Sorption of dyes and Cu(ii) ions from wastewater by sonochemically synthesized MnWO4 and MnMoO4 nanostructures

Sonochemically synthesized MnWO₄ and MnMoO₄ nanomaterials with superior sorption for cationic dyes like Rhodamine B and Methylene Blue.

Charge carriers and small-polaron migration as the origin of intrinsic dielectric anomalies in multiferroic TbMnO3 polycrystals

Temperature-dependent and frequency-dependent dielectric investigations have been performed in TbMnO3 polycrystals sintered in either oxidative or reductive atmospheres. The results revealed the occurrence of two dielectric anomalies above 100 K, which are caused by the thermal activation of charge carriers and their motion in grain cores and grain boundaries. The temperature dependence of the bulk dc conductivity was also analysed and indicates that charge carriers move between inequivalent sites according to a variable-range-hopping mechanism. Also, a strong correlation between dielectric properties and crystalline structure was observed. Furthermore, a low-temperature dielectric relaxation, commonly reported in rare-earth manganite crystals, was observed in both samples. This relaxation follows the empirical Cole-Cole model and was attributed to small-polaron tunnelling. Polaron motion was observed to be affected by the magnetic transitions, structural properties and intrinsic anisotropies in TbMnO3. It is also worth mentioning that the dielectric anomaly due to motion of charge carriers in grain boundaries is the only one of extrinsic origin, while the anomalies related to carrier motion in grain cores and small-polaron tunnelling are intrinsic to TbMnO3.

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.

Coexistence of spiral magnetic state and weak ferromagnetism in a multiferroic, cross-controlled by external magnetic and electric fields

The influence of external magnetic and electric fields on the properties of a multiferroic with a helical magnetic structure is described. Thermodynamics of the phase transition from the antiferromagnetic ferroelectric to the new magnetic state is described for a multiferroic with a perovskite-type structure. In this magnetic state a spiral spin structure and weak ferromagnetism can exist simultaneously. Such a state is a result of the first-order phase transition at a certain temperature below T(N) when, due to the Dzyaloshinskii-Moriya effect, a helical magnetic structure occurs. In this state the vectors of electrical polarization and the helicoid of magnetic moments in perovskites are mutually perpendicular and lie in the basic (ab) plane perpendicular to the main c axis. In this case an additional electrical polarization proportional to the square of magnetization appears in the (ab) plane which reduces the common polarization of the ferroelectric. It is shown that a weak ferromagnetic moment m occurs along the c axis in an applied magnetic field in addition to a modulated magnetic structure appearing in the (ab) plane. The dependence of these phenomena on the applied electric field is considered. It is shown that a sign-alternating electric field causes a linear-in-the-field variation of the magnetic moment opposite in sign to the electric field variation (i.e., the greater is the electric field, the smaller is the magnetic moment m). The observed hysteresis phenomena determining the temperature ranges of overheating and overcooling of each phase under applied magnetic and electrical fields are explained.

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.

Low frequency excitations in multiferroic MnWO4

Dynamic anomalies have been found in the magnetically ordered phases of multiferroic MnWO(4) using polarized Raman scattering. Strong phonon damping is observed for several B(g) modes within the ferroelectric phase and has been attributed to spin-phonon interactions. Moreover, a new low frequency excitation was detected near 33 cm(-1) that grows in intensity on cooling into the antiferromagnetic phases. It is argued that this signal is most probably due to a two-magnon process.

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.

Giant ferroelectric polarization of CaMn7O12 induced by a combined effect of Dzyaloshinskii-Moriya interaction and exchange striction

By extending our general spin-current model to noncentrosymmetric spin dimers and performing density functional calculations, we investigate the causes for the helical magnetic order and the origin of the giant ferroelectric polarization of CaMn7O12. The giant ferroelectric polarization is proposed to be caused by the symmetric exchange striction due to the canting of the Mn4+ spin arising from its strong Dzyaloshinskii-Moriya interaction. Our study suggests that CaMn7O12 may exhibit a novel magnetoelectric coupling mechanism in which the magnitude of the polarization is governed by the exchange striction, but the direction of the polarization by the chirality of the helical magnetic order.

Field-induced continuous rotation of the polarization in multiferroic Mn0.95Co0.05WO4

We report the observation of a continuous rotation of the polarization in Mn0.95Co0.05WO4 under magnetic field. At zero field, this compound shows a transition into the spiral magnetic and ferroelectric phase at 12.2 K, which is the ground state, with the polarization oriented along the b-axis. Increasing b-axis magnetic fields rotate the ferroelectric polarization continuously toward the a-axis, indicating a rotation of the spin spiral plane. This rotation extends over a large field and temperature range. At a constant magnetic field of 3 T, the polarization also rotates from the a-axis at the ferroelectric transition toward the b-axis upon decreasing temperature.

Coupling of replicate order-parameters in incommensurate multiferroics

The specific properties of incommensurate multiferroic phases resulting from the coupling of order-parameter replicates are worked out using the illustrative example of iron vanadate. The phase difference between the order-parameter copies induces an additional broken symmetry phase corresponding to the lowest symmetry of the system and varies critically at the transition to the multiferroic phase. It reflects the temperature dependence of the angle between paired spins in the antiferromagnetic spiral structure. Expressing the transition order-parameters in terms of spin-density waves allows us to show that isotropic exchange interactions contribute to the stabilization of the ferroelectric phase.

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.