Direct transition from a disordered to a multiferroic phase on a triangular lattice

Development of short and long-range magnetic order in the double perovskite based frustrated triangular lattice antiferromagnet Ba[Formula: see text]MnTeO[Formula: see text]

Frustrated magnets based on oxide double perovskites offer a viable ground wherein competing magnetic interactions, macroscopic ground state degeneracy and complex interplay between emergent degrees of freedom can lead to correlated quantum phenomena with exotic excitations highly relevant for potential technological applications. By local-probe muon spin relaxation ([Formula: see text]SR) and complementary thermodynamic measurements accompanied by first-principles calculations, we here demonstrate novel electronic structure and magnetic phases of Ba[Formula: see text]MnTeO[Formula: see text], where Mn[Formula: see text] ions with S = 5/2 spins constitute a perfect triangular lattice. Magnetization results evidence the presence of strong antiferromagnetic interactions between Mn[Formula: see text] spins and a phase transition at [Formula: see text] = 20 K. Below [Formula: see text], the specific heat data show antiferromagnetic magnon excitations with a gap of 1.4 K, which is due to magnetic anisotropy. [Formula: see text]SR reveals the presence of static internal fields in the ordered state and short-range spin correlations high above [Formula: see text]. It further unveils critical slowing-down of spin dynamics at [Formula: see text] and the persistence of spin dynamics even in the magnetically ordered state. Theoretical studies infer that Heisenberg interactions govern the inter- and intra-layer spin-frustration in this compound. Our results establish that the combined effect of a weak third-nearest-neighbour ferromagnetic inter-layer interaction (owing to double-exchange) and intra-layer interactions stabilizes a three-dimensional magnetic ordering in this frustrated magnet.

Crystal symmetry for incommensurate helical and cycloidal modulations

A classification of magnetic superspace groups compatible with the helical and cycloidal magnetic modulations is presented. Helical modulations are compatible with groups from crystal classes 1, 2, 222, 4, 422, 3, 32, 6 and 622, while cycloidal modulations are compatible with groups from crystal classes 1, 2, m and mm2. For each magnetic crystal class, the directions of the symmetry-allowed (non-modulated) net ferromagnetic moment and electric polarization are given. The proposed classification of superspace groups is tested on experimental studies of type-II multiferroics published in the literature.

The crystal growth and properties of novel magnetic double molybdate RbFe5(MoO4)7 with mixed Fe3+/Fe2+ states and 1D negative thermal expansion

Single crystals of new composition RbFe₅(MoO₄)₇ were successfully grown by the flux method, and their crystal structure was determined using the X-ray single-crystal diffraction technique.

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.

Spherical neutron polarimetry under high pressure for a multiferroic delafossite ferrite

The analysis of three-dimensional neutron spin polarization vectors, using a technique referred to as spherical neutron polarimetry (SNP), is a very powerful means of determining complex magnetic structures in magnetic materials. However, the requirement to maintain neutrons in a highly polarized state has made it difficult to use this technique in conjunction with extreme experimental conditions. We have developed a high pressure cell made completely of nonmagnetic materials and having no effect on neutron polarizations. Herein, we report the first SNP analyses under high pressure up to 4.0 GPa in the magnetoelectric multiferroic delafossite CuFeO2. This study also determined the complex spiral magnetic structures in these pressure-induced phases, by measuring the full neutron polarization matrix. The results presented herein demonstrate that the SNP measurements are feasible under high pressure conditions, and that this method is a useful approach to study pressure-induced physical phenomena.

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.

Order by Quenched Disorder in the Model Triangular Antiferromagnet RbFe(MoO_{4})_{2}

We observe a disappearance of the 1/3 magnetization plateau and a striking change of the magnetic configuration under a moderate doping of the model triangular antiferromagnet RbFe(MoO_{4})_{2}. The reason is an effective lifting of degeneracy of mean-field ground states by a random potential of impurities, which compensates, in the low-temperature limit, the fluctuation contribution to free energy. These results provide a direct experimental confirmation of the fluctuation origin of the ground state in a real frustrated system. The change of the ground state to a least collinear configuration reveals an effective positive biquadratic exchange provided by the structural disorder. On heating, doped samples regain the structure of a pure compound, thus allowing for an investigation of the remarkable competition between thermal and structural disorder.

MAGNDATA: towards a database of magnetic structures. II. The incommensurate case

A free web page under the nameMAGNDATA, which provides detailed quantitative information on more than 400 published magnetic structures, has been made available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. In the first article in this series, the information available on commensurate magnetic structures was presented [Gallego, Perez-Mato, Elcoro, Tasci, Hanson, Momma, Aroyo & Madariaga (2016).J. Appl. Cryst.49, 1750–1776]. In this second article, the subset of the database devoted to incommensurate magnetic structures is discussed. These structures are described using magnetic superspace groups,i.e.a direct extension of the non-magnetic superspace groups, which is the standard approach in the description of aperiodic crystals. The use of magnetic superspace symmetry ensures a robust and unambiguous description of both atomic positions and magnetic moments within a common unique formalism. The point-group symmetry of each structure is derived from its magnetic superspace group, and any macroscopic tensor property of interest governed by this point-group symmetry can be retrieved through direct links to other programs of the Bilbao Crystallographic Server. The fact that incommensurate magnetic structures are often reported with ambiguous or incomplete information has made it impossible to include in this collection a good number of the published structures which were initially considered. However, as a proof of concept, the published data of about 30 structures have been re-interpreted and transformed, and together with ten structures where the superspace formalism was directly employed, they form this section ofMAGNDATA. The relevant symmetry of most of the structures could be identified with an epikernel or isotropy subgroup of one irreducible representation of the space group of the parent phase, but in some cases several irreducible representations are active. Any entry of the collection can be visualized using the online tools available on the Bilbao server or can be retrieved as a magCIF file, a file format under development by the International Union of Crystallography. These CIF-like files are supported by visualization programs likeJmoland by analysis programs likeJANAandISODISTORT.

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.

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.

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.

Spin-chirality-driven ferroelectricity on a perfect triangular lattice antiferromagnet

Magnetic field (B) variation of the electrical polarization P(c) (∥c) of the perfect triangular lattice antiferromagnet RbFe(MoO(4))(2) is examined up to the saturation point of the magnetization for B⊥c. P(c) is observed only in phases for which chirality is predicted in the in-plane magnetic structures. No strong anomaly is observed in P(c) at the field at which the spin modulation along the c axis, and hence the spin helicity, exhibits a discontinuity to the commensurate state. These results indicate that the ferroelectricity in this compound originates predominantly from the spin chirality, the explanation of which would require a new mechanism for magnetoferroelectricity. The obtained field-temperature phase diagram of ferroelectricity agree well with those theoretically predicted for the spin chirality of a Heisenberg spin triangular lattice antiferromagnet.

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.

Triangular antiferromagnet with nonmagnetic impurities

The effect of nonmagnetic impurities on the phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice is investigated. We present analytical arguments confirmed by numerical calculations that at zero temperature vacancies stabilize a conical state providing an example of "order by quenched disorder" effect. Competition between thermal fluctuations and the site disorder leads to a complicated H-T phase diagram, which is deduced from the classical Monte Carlo simulations for a representative vacancy concentration. For the XY triangular-lattice antiferromagnet with an in-plane external field, nonmagnetic impurities stabilize the fanlike spin structure. We also briefly discuss the effect of quantum fluctuations.

Successive magnetic phase transitions and multiferroicity in the spin-one triangular-lattice antiferromagnet Ba3NiNb2O9

We report the magnetic and electric properties of Ba3NiNb2O9, which is a quasi-two-dimensional spin-one triangular-lattice antiferromagnet with trigonal structure. At low T and with increasing magnetic field, the system evolves from a 120 degree magnetic ordering phase (A phase) to an up-up-down (uud) phase (B phase) with a change of slope at 1/3 of the saturation magnetization, and then to an "oblique" phase (C phase). Accordingly, the ferroelectricity switches on at each phase boundary with appearance of spontaneous polarization. Therefore, Ba3NiNb2O9 is a unique triangular-lattice antiferromagnet exhibiting both uud phase and multiferroicity.

Electric field control of the magnetic chiralities in ferroaxial multiferroic RbFe(MoO4)2

The coupling of magnetic chiralities to the ferroelectric polarization in multiferroic RbFe(MoO4)2 is investigated by neutron spherical polarimetry. Because of the axiality of the crystal structure below T(c)=190   K, helicity and triangular chirality are symmetric-exchange coupled, explaining the onset of the ferroelectricity in this proper-screw magnetic structure--a mechanism that can be generalized to other systems with ferroaxial distortions in the crystal structure. With an applied electric field, we demonstrate control of the chiralities in both structural domains simultaneously.

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.

Symmetry and magnetic field driven transitions in the 2D triangular lattice compound RbFe(MoO4)2

The temperature versus magnetic field phase diagram of the 2D triangular lattice and multiferroic compound RbFe(MoO(4))(2) is analysed from the point of view of symmetry. The paramagnetic space group and its irreducible representations are used in order to obtain the magnetic symmetry of the possible modulated phases and characterize the restrictions imposed by this symmetry on the corresponding magnetic structures. Superspace symmetry is considered in the case of incommensurate phases. It is shown that the experimentally observed phases correspond to different isotropy subgroups originating in the same irreducible representation of the paramagnetic symmetry group. The relevant couplings between the primary transverse spin modulation and the electric polarization, the in-plane magnetization and the secondary longitudinal magnetic modulation are discussed. The mechanisms for the destabilization of the improper ferroelectric chiral phase and the origin of the different orientation of the spins with respect to the external field in the two collinear phases are analysed from a symmetry based perspective.

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.

Neutron-scattering measurement of incommensurate short-range order in single crystals of the S=1 triangular antiferromagnet NiGa(2)S(4)

Neutron scattering is used to investigate spin correlations in ultrapure single crystals of the S=1 triangular lattice NiGa(2)S(4). Despite a Curie-Weiss temperature of Θ(CW)=-80(2)  K, static (τ>1  ns) short-range (ξ(ab)=26(3)  Å) incommensurate order prevails for T>1.5  K. The incommensurate modulation Q(0)=(0.155(3),0.155(3),0), Θ(CW), and the spin-wave velocity (c=4400  m/s) can be accounted for by antiferromagnetic third-nearest-neighbor interactions J(3)=2.8(6)  meV and ferromagnetic nearest-neighbor coupling J(1)=-0.35(9) J(3). Interplane correlations are limited to nearest neighbors and weakened by an in-plane field. These observations show that the short-range ordered glassy phase that has been observed in a number of highly degenerate systems can persist near the clean limit.

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.

Temperature- and pressure-dependent lattice behaviour of RbFe(MoO4)2

Trigonal RbFe(MoO(4))(2) is a quasi-two-dimensional antiferromagnet on a triangular lattice below T(N) = 3.8 K, The crystal exhibits also a structural phase transition at T(c) = 190 K related to symmetry change from P3m1 to P3. We present the temperature- and pressure-dependent characteristics of this material in the context of ambiguous opinions on the symmetry and crystal properties below T(c). A single-crystal x-ray diffraction shows that the temperature-dependent evolution of the unit cell in the range 100-300 K is strongly anisotropic with markedly discontinuous changes at T(c). The transition is connected with a spontaneous strain developing in effect of the volume decrease. The structure releases the strain by rotation of corner-sharing rigid MoO(4) and FeO(6) polyhedra in the (a,b) basal plane. The temperature dependence of the IR vibrational wavenumbers exhibits weak changes near T(c), which are consistent with the symmetry transformation from P3m1 to P3. High-pressure x-ray powder diffraction indicates that the material is extremely soft but with some stiffening at high pressure. The zero-pressure bulk modulus is B(0) = 7.9(6) GPa and the pressure derivative is B(0)' = 10(1). The compression curve can be described by a single equation of state, corresponding to the trigonal cell, up to 5 GPa. An amorphization appearing above 5 GPa and increasing gradually on further pressure increase suggests the thermodynamic instability of the high-pressure structure.

Development of electrical polarization at an antiferromagnetic transition in FeVO(4)

We have probed changes in the magnetic, electrical, dielectric, optical, and thermodynamic properties of iron vanadate (FeVO(4)) at two magnetic phase transitions. FeVO(4) exhibits two antiferromagnetic transitions at T(N1) = 22 K and T(N2) = 15 K. Below 15 K FeVO(4) develops an electric polarization, concomitant with the second antiferromagnetic transition and indicating strong magnetoelectric coupling. The powder averaged zero field electric polarization for the polycrystalline FeVO(4) sample is 6 µC m(-2) and can be switched by reversing the poling voltage. The peaks for certain Raman modes at larger wavenumbers shift to slightly higher energies in the temperature range between T(N1) and T(N2), but there is practically no change in the Raman spectra between the paramagnetic and ground states. These Raman features help to clarify the microscopic mechanisms for magnetoelectric coupling in FeVO(4).

Spin amplitude modulation driven magnetoelectric coupling in the new multiferroic FeTe2O5Br

The magnetic and ferroelectric properties of the layered geometrically frustrated cluster compound FeTe2O5Br were investigated with single-crystal neutron diffraction and dielectric measurements. An incommensurate transverse amplitude modulated magnetic order with the wave vector q=(1/2,0.463,0) develops below T(N)=10.6(2) K. Simultaneously, a ferroelectric order due to exchange striction involving polarizable Te4+ lone-pair electrons develops perpendicular to q and to Fe3+ magnetic moments. The observed magnetoelectric coupling is proposed to originate from the temperature dependent phase difference between neighboring amplitude modulation waves.

Observation of a multiferroic critical end point

The study of abrupt increases in magnetization with magnetic field known as metamagnetic transitions has opened a rich vein of new physics in itinerant electron systems, including the discovery of quantum critical end points with a marked propensity to develop new kinds of order. However, the electric analogue of the metamagnetic critical end point, a "metaelectric" critical end point, has been rarely studied. Multiferroic materials wherein magnetism and ferroelectricity are cross-coupled are ideal candidates for the exploration of this novel possibility using magnetic-field (H) as a tuning parameter. Herein, we report the discovery of a magnetic-field-induced metaelectric transition in multiferroic BiMn(2)O(5), in which the electric polarization (P) switches polarity along with a concomitant Mn spin-flop transition at a critical magnetic field H(c). The simultaneous metaelectric and spin-flop transitions become sharper upon cooling but remain a continuous cross-over even down to 0.5 K. Near the P = 0 line realized at mu(0)H(c) approximately 18 T below 20 K, the dielectric constant (epsilon) increases significantly over wide field and temperature (T) ranges. Furthermore, a characteristic power-law behavior is found in the P(H) and epsilon(H) curves at T = 0.66 K. These findings indicate that a magnetic-field-induced metaelectric critical end point is realized in BiMn(2)O(5) near zero temperature.

Chiral and collinear ordering in a distorted triangular antiferromagnet

Magnetization, specific heat, and neutron diffraction measurements are used to map out the entire magnetic phase diagram of KFe(MoO4)2. This stacked triangular antiferromagnet is structurally similar to the famous multiferroic system RbFe(MoO4)2. Because of an additional small crystallographic distortion, it contains two sets of inequivalent distorted magnetic triangular lattices. As a result, the spin network breaks down into two intercalated yet almost independent magnetic subsystems. One is a collinear antiferromagnet that shows a simple spin-flop behavior in applied magnetic fields. The other is a helimagnet that instead goes through a series of exotic commensurate-incommensurate phase transformations. In the various phases one observes either true three-dimensional or unconventional quasi-two-dimensional ordering.

Single domain magnetic helicity and triangular chirality in structurally enantiopure Ba3NbFe3Si2O14

A novel doubly chiral magnetic order is found in the structurally chiral langasite compound Ba3NbFe3Si2O14. The magnetic moments are distributed over planar frustrated triangular lattices of triangle units. On each of these they form the same triangular configuration. This ferrochiral arrangement is helically modulated from plane to plane. Unpolarized neutron scattering on a single crystal associated with spherical neutron polarimetry proved that a single triangular chirality together with a single helicity is stabilized in an enantiopure crystal. A mean-field analysis allows us to discern the relevance on this selection of a twist in the plane to plane super-superexchange paths.

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.

Spin-driven ferroelectricity in triangular lattice antiferromagnets ACrO2 (A=Cu, Ag, Li, or Na)

The correlation between the dielectric and magnetic properties is investigated on the triangular-lattice antiferromagnets ACrO2 (A=Cu, Ag, Li, or Na) with a 120-degree spiral structure. For the A=Cu and Ag compounds with a delafossite structure, the ferroelectric polarization emerges with a spiral-spin order, implying strong coupling between ferroelectricity and the spiral-spin structure. For the A=Li and Na compounds with an ordered rock salt structure, on the other hand, no spontaneous polarization is discerned, while the clear anomaly in the dielectric constant can be observed upon the transition to the spiral-spin ordered state. This feature can be ascribed to the possible antiferroelectric state induced by the alternate stacking of the Cr-spin sheet with opposite vector spin chirality.

Order parameters and phase diagram of multiferroic RMn2O5

The generic magnetic phase diagram of multiferroic RMn2O5 (with R=Y, Ho, Tb, Er, Tm), which allows different sequences of ordered magnetic structures for different R's and different control parameters, is described using order parameters which explicitly incorporate the magnetic symmetry. A phenomenological magnetoelectric coupling is used to explain why some of these magnetic phases are also ferroelectric. Several new experiments, which can test this theory, are proposed.