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

Competing interactions and geometric frustration provide favourable conditions for exotic states of matter. Such competition often causes multiple phase transitions as a function of temperature and can lead to magnetic structures that break inversion symmetry, thereby inducing ferroelectricity [1-4]. Although this phenomenon is understood phenomenologically [3-4], it is of great interest to have a conceptually simpler system in which ferroelectricity appears coincident with a single magnetic phase transition. Here we report the first such direct transition from a paramagnetic and paraelectric phase to an incommensurate multiferroic in the triangular lattice antiferromagnet RbFe(MoO4)2 (RFMO). A magnetic field extinguishes the electric polarization when the symmetry of the magnetic order changes and ferroelectricity is only observed when the magnetic structure has chirality and breaks inversion symmetry. Multiferroic behaviour in RFMO provides a theoretically tractable example of ferroelectricity from competing spin interactions. A Landau expansion of symmetry-allowed terms in the free energy demonstrates that the chiral magnetic order of the triangular lattice antiferromagnet gives rise to a pseudoelectric field, whose temperature dependence agrees with that observed experimentally.Comment: 16 pages pdf including 3 figure

Successive Magnetic Transitions of the Kagome Staircase Compound Co3V2O8 Studied in Various Magnetic Fields

For the spin-3/2 kagome staircase system Co3V2O8, magnetic field (H)-temperature (T) phase diagrams have been constructed for the fields along three principal directions up to 5 T, using results of various macroscopic measurements on single crystal samples and also using neutron diffraction data taken on both powder and single crystal samples under H along c. In zero magnetic field, the system exhibits three transitions at temperatures Tc1~11.2 K, Tc2~8.8 K and Tc3~ (6.0-7.0) K. The single crystal data present clear evidence for the noncollinear nature of the magnetic structures in all magnetically ordered phases below Tc1. The sinusoidal nature of the incommensurate modulation of the ordered moment reported in the former work has been confirmed between Tc1 and Tc2, that is, no higher harmonics of the modulation have been detected even for the present large single crystal. Even in the phase of commensurate modulation between Tc2 and Tc3, we have not detected any higher harmonics of the modulation. The phase diagrams show that the magnetically ordered phases sensitively change to other phases with H, indicating that the geometrical frustration inherent in this system is important for the determination of the phase diagram. No evidence for ferroelectric transitions has been observed in the measurements of the dielectric constant applying the electric fields along three crystallographic axes, a, b and c. Only small dielectric anomalies closely connected with the magnetic phase transitions have been found.Comment: 5 pages, 10 figures, submitted to JPS

Competing Magnetic Phases on a "Kagome Staircase"

We present thermodynamic and neutron data on Ni_3V_2O_8, a spin-1 system on a kagome staircase. The extreme degeneracy of the kagome antiferromagnet is lifted to produce two incommensurate phases at finite T - one amplitude modulated, the other helical - plus a commensurate canted antiferromagnet for T ->0. The H-T phase diagram is described by a model of competing first and second neighbor interactions with smaller anisotropic terms. Ni_3V_2O_8 thus provides an elegant example of order from sub leading interactions in a highly frustrated systemComment: 4 pages, 3 figure

Magnetically driven ferroelectric order in Ni3_3V2_2O8_8

We show that for Ni$_3$V$_2$O$_8$ long-range ferroelectric and incommensurate magnetic order appear simultaneously in a single phase transition. The temperature and magnetic field dependence of the spontaneous polarization show a strong coupling between magnetic and ferroelectric orders. We determine the magnetic symmetry of this system by constraining the data to be consistent with Landau theory for continuous phase transitions. This phenomenological theory explains our observation the spontaneous polarization is restricted to lie along the crystal b axis and predicts that the magnitude should be proportional to a magnetic order parameter.Comment: 11 pages, 3 figure

Field dependence of magnetic ordering in Kagome-staircase compound Ni3V2O8

We present powder and single-crystal neutron diffraction and bulk measurements of the Kagome-staircase compound Ni3V2O8 (NVO) in fields up to 8.5T applied along the c-direction. (The Kagome plane is the a-c plane.) This system contains two types of Ni ions, which we call "spine" and "cross-tie". Our neutron measurements can be described with the paramagnetic space group Cmca for T < 15K and each observed magnetically ordered phase is characterized by the appropriate irreducible representation(s). Our zero-field measurements show that at T_PH=9.1K NVO undergoes a transition to an incommensurate order which is dominated by a longitudinally-modulated structure with the spine spins mainly parallel to the a-axis. Upon further cooling, a transition is induced at T_HL=6.3K to an elliptically polarized incommensurate structure with both spine and cross-tie moments in the a-b plane. At T_LC=4K the system undergoes a first-order phase transition, below which the magnetic structure is a commensurate antiferromagnet with the staggered magnetization primarily along the a-axis and a weak ferromagnetic moment along the c-axis. A specific heat peak at T_CC'=2.3K indicates an additional transition, which we were however not able to relate to a change of the magnetic structure. Neutron, specific heat, and magnetization measurements produce a comprehensive temperature-field phase diagram. The symmetries of the two incommensurate magnetic phases are consistent with the observation that only one phase has a spontaneous ferroelectric polarization. All the observed magnetic structures are explained theoretically using a simplified model Hamiltonian, involving competing nearest- and next-nearest-neighbor exchange interactions, spin anisotropy, Dzyaloshinskii-Moriya and pseudo-dipolar interactions.Comment: 25 pages, 19 figure

Complex magnetic order in the kagome staircase compound Co3V2O8

Co3V2O8 (CVO) has a geometrically frustrated magnetic lattice, a Kagome staircase. The crystal structure consists of two inequivalent Co sites, one-dimensional chains of Co(2) spine sites, linked by Co(1) cross-tie sites. Neutron powder diffraction has been used to solve the basic magnetic and crystal structures of this system, while polarized and unpolarized single crystal diffraction measurements have been used to reveal a variety of incommensurate phases, interspersed with lock-in transitions to commensurate phases. CVO initially orders magnetically at 11.3 K into an incommensurate, transversely polarized, spin density wave state, with wave vector k=(0,delta,0) with delta=0.55 and the spin direction along the a axis. Delta is found to decrease monotonically with decreasing temperature, and then it locks into a commensurate antiferromagnetic structure with delta=0.5 for 6.9<T<8.6 K. Below 6.9 K the magnetic structure becomes incommensurate again. Delta continues to decrease with decreasing temperature, and locks-in again at delta=1/3 over a narrow temperature range (6.2<T<6.5 K). The system then undergoes a strongly first order transition to the ferromagnetic ground state (delta=0) at Tc=6.2 K. A dielectric anomaly is observed around the ferromagnetic transition temperature of 6.2 K, demonstrating a significant spin-charge coupling present in CVO. A theory based on group theory analysis and a minimal Ising model with competing exchange interactions can explain the basic features of the magnetic ordering

Relationship between Magnetic Structure and Ferroelectricity of LiVCuO4

Neutron scattering studies and measurements of the dielectric susceptibility and ferroelectric polarization P have been carried out in various magnetic fields H for single-crystal samples of the multiferroic system LiVCuO4 with quasi one-dimensional spin 1/2 Cu2+ chains formed of edge-sharing CuO4 square planes, and the relationship between the magnetic structure and ferroelectricity has been studied. The ferroelectric polarization is significantly suppressed by the magnetic field H above 2 T applied along a and b axes. The helical magnetic structure with the helical axis parallel to c has been confirmed in H=0, and for H//a, the spin flop transition takes place at H=2 T with increasing H, where the helical axis changes to the direction parallel to H. The ferroelectric polarization along a at H=0 is found to be proportional to the neutron magnetic scattering intensity, indicating that the magnetic order is closely related to the appearance of the ferroelectricity. The relationship between the magnetic structure and ferroelectricity of LiVCuO4 is discussed by considering the existing theories.Comment: 4 pages (5 figures), submitted to J. Phys. Soc. Jp

Magnetically driven ferroelectric order in Ni3V2O8

We show that long-range ferroelectric and incommensurate magnetic order appear simultaneously in a single phase transition in Ni3V2O8. The temperature and magnetic-field dependence of the spontaneous polarization show a strong coupling between magnetic and ferroelectric orders. We determine the magnetic symmetry using Landau theory for continuous phase transitions, which shows that the spin structure alone can break spatial inversion symmetry leading to ferroelectric order. This phenomenological theory explains our experimental observation that the spontaneous polarization is restricted to lie along the crystal b axis and predicts that the magnitude should be proportional to a magnetic order parameter