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TbMnO3 is an orthorhombic insulator where incommensurate spin order for temperature T(N)<41 K is accompanied by ferroelectric order for T<28 K. To understand this, we establish the magnetic structure above and below the ferroelectric transition using neutron diffraction. In the paraelectric phase, the spin structure is incommensurate and longitudinally modulated. In the ferroelectric phase, however, there is a transverse incommensurate spiral. We show that the spiral breaks spatial inversion symmetry and can account for magnetoelectricity in TbMnO3.

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.

Hubbard's model for studying correlation effects in systems with narrow energy bands is analyzed by means of a technique which allows the calculation of moments of the individual peaks in the spectral weight function for single-particle excitations. The analysis of the zeroth moments of the peaks shows that the total weight in the bands depends on the strength of the kinetic-energy term in the Hamiltonian even though the bands may be narrow and widely separated. This conclusion is illustrated and verified by an exact calculation for the case when there are only two lattice sites. Analysis of first and higher moments yields results for nonmagnetic or paramagnetic phases which are in qualitative agreement with Hubbard's improved solution. However, we find that (a) there occurs a spin-dependent shift in the band energies which has not been obtained by other treatments of the model and which energetically favors ferromagnetism, and (b) single-particle excitations are more heavily damped in antiferromagnetic than in isomorphic paramagnetic phases. Hubbard's model for studying correlation eGects in systems with narrow energy bands is analyzed by means of a technique which allows the calculation of moments of the individual peaks in the spectral weight function for single-particle excitations. The analysis of the zeroth moments of the peaks shows that the total weight in the bands depends on the strength of the kinetic-energy term in the Hamiltonian even though the bands may be narrow and widely separated. This conc1usion is illustrated and verified by an exact calculation for the case when there are only two lattice sites. Analysis of first and higher moments yields results for nonmagnetic or paramagnetic phases which are in qualitative agreement with Hubbard's improved solution. However, we 6nd that (a) there occurs a spin-dependent shift in the band energies which has not been obtained by other treatments of the model and which energetically favors ferromagnetism, and (b) single-particle excitations are more heavily damped in antiferromagnetic than in isomorphic paramagnetic phases. Disciplines Physics | Quantum Physics

Possible Néel orderings of antiferromagnetically coupled spins on a kagomé lattice are studied using linearspin-wave theory and high-temperature expansions. Spin-wave analysis, applied to q=0 (three spins per magnetic unit cell) and to √3 × √3 (nine spins per cell) Néel orderings yield identical excitation spectra with twofold-degenerate linear modes and a dispersionless zero-energy mode. This dispersionless mode is equivalent to an excitation localized to an arbitrary hexagon of nearest-neighbor spins. Second-(J 2) and third-(J 3) neighbor interactions are shown to stabilize the q=0 state for J 2 >J 3 and the √3 × √3 state for J 2 3. A hightemperature expansion of the spin-spin susceptibility χ αβ (q) is performed to order 1/T 8 , for n-component, classical spins with nearest-neighbor interactions only. To order 1/T 7 the largest eigenvalue of the susceptibility matrix is found to be independent of wave vector with an eigenvector that corresponds to the dispersionless mode of the ordered phase. This degeneracy is removed at order 1/T 8. For n=0, the q=0 mode is favored; for n=1, the band is flat; and, for n>1, the maximum susceptibility is found for a √3 × √3 excitation. Similar results are found for the three-dimensional pyrochlore lattice. The high-temperature expansion is used to interpret experimental data for the uniform susceptibility and powder-neutron-diffraction spectrum for the kagomé-lattice system SrCr 8−x Ga 4+x O 19 .