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We study the fractionally quantized $Z_N$ Berry phase, $\gamma_N=0, {2\pi \over N}, {4\pi \over N},\ldots, {2(N-1)\pi \over N}$, to characterize local $N$-mer spin structures at magnetization plateaux in spin-1/2 Heisenberg multimer ($N$-mer) models, i.e., highly frustrated $N$-leg ladder models, which are generalizations of an orthogonal dimer chain and have exact ground states in the strong multimer coupling region. We demonstrate that all $N$ types of Berry phases, which characterize magnetization-plateau phases, appear in a magnetic phase diagram when $N=2$ and $4$. We show that magnetization plateau with magnetization $\langle m\rangle$ and $D$-fold degenerated states has $\gamma_N=\pi (\langle m\rangle-1) D$, except for the Haldane phase with $\gamma_N=0$. In addition, we find that a complementary $Z_N$ Berry phase becomes non-zero in the $S=N/2$ Haldane phase for $N=2$ and 4. Because the exact quantization of the $Z_N$ Berry phases is protected by the translational (or rotational) symmetry along the rung direction, the $Z_N$ Berry phase has the potential to be applied for a wide class of magnetization plateaux in coupled multimer systems., Comment: 5 pages, 4 figures

Femoral head fracture associated with hip dislocation is relatively rare but very severe injury. Due to its severity and the need of joint exposure for the reduction of femoral head fracture, the surgical treatment cannot but accompany many complications, including the osteonecrosis of the femoral head, heterotopic ossification, and post-traumatic osteoarthritis. We report a case of less invasive percutaneous screw fixation for the femoral head fracture with excellent clinical result. Post operatively, the fracture was healed, and no acute complication was observed. At 4 years post operation, full Harris hip score was achieved, and there were no osteonecrosis of the femoral head, no heterotopic ossification, and no post-traumatic osteoarthritis. We suggest attempting less invasive percutaneous screw fixation for the femoral head fracture.

Frustrated metals are investigated by numerical methods. In the absence of fermionic dynamics, the models are equivalent to a frustrated Ising model on a geometrically frustrated lattice, where macroscopic degeneracies are observed in the ground states. By taking into account fermionic hoppings, the models show partial loss of degeneracy, but still remains to be frustrated. Various properties of the system, including charge correlations, are also examined.

A V 4+ pyrochlore Lu 2 V 2 O 7 is a ferromagnetic Mott insulator with T c = 73 K. The electronic configuration of the V 4+ ions is ( t 2 g ) 1 , and the orbital ordering pattern was determined by the polarized neutron diffraction measurements. To discuss the stability of the ferromagnetic state in this compound, we treat the Hubbard Hamiltonian with 3d orbitals in the small hopping amplitude limit. We found that the hopping from t 2 g orbitals to e g orbitals, which is normally neglected in t 2 g electron system, plays an important role to stabilize the ferromagnetic state for observed orbital ordering structure. Spin wave spectrum has been calculated and the effects of the anisotropy are also discussed.

In order to study effects of frustration in an itinerant electron system, we investigate ground states of the antiferromagnetic double-exchange model on a triangular lattice. In this model, pseudo-spins are coupled to electron transfer integrals in such a way that antiparallel configurations of pseudo-spins gain kinetic energies. Although the antiferromagnetic Ising model on a triangular lattice shows macroscopic dengenerate ground states, the present model shows that the degeneracy is lifted due to long-range natures of the double exchange interactions. Spin ordering at the ground state is also discussed.

We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied to two- and three-dimensional systems. We show examples of partial line graphs of square and cubic lattices. The method is useful in providing a guideline for synthesizing materials with flat energy bands, since the tight-binding models on the partial line graphs provide us a large room for modification, maintaining the flat energy dispersions., 9 pages, 4 figures

We investigate a detail of a dodecamer cluster ordering in a double-exchange spin ice model on a kagom\'e lattice. In frustrated systems, ordinary spin orderings are suppressed and macroscopic degeneracy remains down to low temperatures. In some frustrated systems, the degeneracy is lifted due to residual interactions and cluster orderings are stabilized. In the present model, the spin ice state is first formed at intermediate temperatures, and further entropies are released at lower temperatures as the dodecamer phase emerges. Since the spin symmetry is not broken in the dodecamer phase, there still exists macroscopic degeneracy. At further low temperatures, a possible spin ordering due to inter-dodecamer interactions is proposed. We discuss that such a multiple-site clustering larger than a bond-pair might be generic to frustrated systems where macroscopic degeneracy is lifted by residual interactions., Comment: 18 pages, 11 figures

The new two-dimensional spin-gap system SiCu 2 (BO 3 ) 2 shows unique physical properties because of its low-dimensionality character and of strong quantum fluctuations due to frustration. The magnetic properties of the material, e.g. dirner singlet ground state, an almost localized triplet and magnetization plateaus, are well described by a spin-1/2 antiferromagnetic Heisenberg model on the orthogonal dimer lattice. However, in the presence of an external magnetic field, unusual magnetic properties, which cannot be explained by the Heisenberg model alone, have been observed in several experiments: (1) a field induced staggered moment, (2) the persistence of an excitation gap at around the critical field, and (3) a finite magnetization below the critical field. We include intra- and inter-dimer Dzyaloshinsky-Moriya interactions and the staggered gyromagnetic tensors in the orthogonal dimer Heisenberg model, and show that these unusual behaviors with the external field in the z direction can be well described with physically reasonable values of the parameters.

We report the NMR observation of spin superstructure in the 1 8 magnetization plateau phase of SrCu2(BO3)2, a quasi-2D dimer singlet spin system, at high magnetic fields near 28 T . The 1 8 phase is characterized by crystalization of triplets in a rhomboid unit cell with oscillating magnetization and separated from uniform phase by a first-order transition. Comparison between the Cu and B NMR spectra and theoretical calculations on the Shastry–Sutherland model enabled us to determine the three-dimensional spin superstructure. We also found that subtle structural feature of the buckling of magnetic layers produces anisotropic interactions, which lead to field-induced staggered magnetization.

The magnetic properties of SrCu2 (BO3)2 are reviewed from a theoretical point of view. SrCu2 (BO3)2 is a new two-dimensional spin gap system and its magnetic properties are well described by a spin-1/2 antiferromagnetic Heisenberg model of the orthogonal dimer lattice. The model has a dimer singlet ground state whose exactness was proven by Shastry and Sutherland for a topologically equivalent model more than 20 years ago. The exactness of the ground state is maintained even if interlayer couplings are introduced for SrCu2 (BO3)2. In the two-dimensional model, quantum phase transitions take place between different ground states for which three phases are expected: a gapped dimer singlet state, a plaquette resonating valence bond state and a gapless magnetic ordered state. Analysis of the experimental data shows that the dimer singlet ground state is realized in SrCu2 (BO3)2. The orthogonality of the dimer bonds, which is the underlying symmetry of the exactness of the ground state, also leads to an unusual property of elementary excitations, namely the almost localized nature of the triplet excitations. Application of an external magnetic field changes the density of the triplet excitations. In general, there is competition between kinetic energies and interaction energies between triplets. The almost localized nature of the triplets makes it easy to form regular lattices. In fact, at certain densities, where the commensurability energy is significant, the triplet excitations form superstructures and plateaux appear at 1/2, 1/3, 1/4 and 1/8 in the magnetization curve. In high-magnetic-field experiments, magnetic plateaux at magnetizations of 1/3, 1/4 and 1/8 have been observed. Translational symmetry of the lattice is spontaneously broken at the plateaux, except for the 1/2 plateau. The 1/3 and 1/4 plateaux are expected to have magnetic superstructures of stripe form while the 1/2 plateau has a square unit cell and the 1/8 plateau a rhomboid cell. Especially at the 1/8 plateau, nuclear magnetic resonance experiments indicate the presence of at least 11 distinct Cu sites with different spin polarizations, which is the first evidence of breaking of the translational symmetry at the plateau phase. The spin texture calculated on the basis of a Heisenberg model with adiabatic spin–phonon coupling is consistent with the experimental results.

The two dimensional Heisenberg model for ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ has an exact dimer ground state which was proven by Shastry and Sutherland almost twenty years ago. The critical value of the quantum phase transition from the dimer state to the N\'eel ordered state is determined. Analysis of the experimental data shows that $\mathrm{SrCu}{}_{2}(\mathrm{BO}{}_{3}{)}_{2}$ has the dimer ground state but its coupling constants are close to the transition point, which leads to an unusual temperature dependence of the susceptibility. The almost localized nature of the triplet excitations explains the plateaus observed in the magnetization curve.

Extensions of the Shastry-Sutherland model are possible in various ways. In particular, it is possible to construct a natural model in three dimensions which has the exact dimer ground state. Recently found spin gap system SrCu_2(BO_3)_2 has this structure. The exchange constants between the layers is expected to be smaller than the intra-layer couplings. However, the exactness of the dimer state for the three dimensional structure is important to understand why magnetic properties of SrCu_2(BO_3)_2 are described well by the two dimensional model., 3 pages, 5 figures, to appear in Journal of Physics: Condensed Matter

We have investigated the magnetoelectric properties originating from the spin-dependent hybridization between transition metal ($X$) $d$ orbital and ligand ion $p$ orbitals in the noncentrosymmetric crystals Ba${}_{2}X$Ge${}_{2}$O${}_{7}$ ($X=\text{Mn}$, Co, Cu). The novel magnetic-field responses of the electric polarization observed in the staggered antiferromagnets Ba${}_{2}$MnGe${}_{2}$O${}_{7}$ ($S=5/2$) and Ba${}_{2}$CoGe${}_{2}$O${}_{7}$ ($S=3/2$) can be accounted for by the mean-field approximation based on the $d$-$p$ hybridization mechanism. In the case of the $S=1/2$ helimagnet Ba${}_{2}$CuGe${}_{2}$O${}_{7}$, we have found the metamagnetic transition to the staggered spin state in the high magnetic field region and observed an electric polarization originating from the $d$-$p$ hybridization mechanism. Especially, the observation of electric polarization not only in the fully spin-polarized state at high magnetic field in Ba${}_{2}$MnGe${}_{2}$O${}_{7}$ but also in all the compounds, under applied external magnetic field, strongly supports the single-spin mechanism of the $d$-$p$ hybridization as the origin of ferroelectricity in this class of materials. We have examined the transition-metal dependence of the polarization magnitude in Ba${}_{2}X$Ge${}_{2}$O${}_{7}$ in terms of the electronic configuration in $d$ levels and found that the unquenched orbital angular momentum determines the magnitude of the electric polarization.

We investigate a dynamical magnetoelectric effect due to a magnetic resonance in helical spin structures through the coupling between magnetization and electric polarization via a spin current mechanism. We show that the magnon has both the dynamical magnetic moment $\Delta M^\omega$ and the electric moment $\Delta P^\omega$ ($\perp \Delta M^\omega$), i.e., a dynamical toroidal moment, under external magnetic fields, and thus it is named the {\em toroidalmagnon}. The toroidalmagnon exists in most conical spin structures owing to the generality of the spin current mechanism. In the absorption of electromagnetic waves, the toroidalmagnon excitation process generally induces a nonreciprocal directional dichroism as a consequence of an interference of the magnetic and electric responses., Comment: 5 pages, 2 figures

Right- and left-handed circularly polarized light interact differently with electronic charges in chiral materials. This asymmetry generates the natural circular dichroism and gyrotropy, also known as the optical activity. Here we demonstrate that optical activity is not a privilege of the electronic charge excitations but it can also emerge for the spin excitations in magnetic matter. The square-lattice antiferromagnet Ba$_2$CoGe$_2$O$_7$ offers an ideal arena to test this idea, since it can be transformed to a chiral form by application of external magnetic fields. As a direct proof of the field-induced chiral state, we observed large optical activity when the light is in resonance with spin excitations at sub-terahertz frequencies. In addition, we found that the magnetochiral effect, the absorption difference for the light beams propagating parallel and anti-parallel to the applied magnetic field, has an exceptionally large amplitude close to 100%. All these features are ascribed to the magnetoelectric nature of spin excitations as they interact both with the electric and magnetic components of light.

Most of the exact results in frustrated spin systems have for a long time been regarded as of purely academic interest, being realized only due to the special geometry of the lattices concerned. However, recent developments in material design offer the genuine possibility of producing such exact states in real materials. In fact, the exact dimer singlet state of the two-dimensional Shastry–Sutherland model has already been found as the ground state of the quasi-two-dimensional material SrCu2(BO3)2. The cooperation between experimentalists and theorists in investigating this material has caused rapid development in the understanding of low-dimensional frustrated spin systems in general, due to the extreme utility of cases where the ground state is known exactly. This fact provides information essential to recognizing novel magnetic behavior in external magnetic fields, at finite temperatures, and in other regimes. In this chapter, we introduce spin-1 ∕ 2 models which have an exact ground state, considering first exactly solvable spin-1 ∕ 2 Heisenberg models, exemplified by the sawtooth–chain model, the Majumdar–Ghosh model, the two-dimensional Shastry–Sutherland model, and a frustrated ladder model. Such exact states can be realized due to special symmetries on geometrically frustrated lattices. As a second class of examples, we introduce also some exact ground states in spin-1/2 models with multiple-spin interactions.

We have investigated the variation of induced ferroelectric polarization under a magnetic field with various directions and magnitudes in a staggered antiferromagnet Ba₂CoGe₂O₇. While the ferroelectric polarization cannot be explained by the well-accepted spin current model nor the exchange striction mechanism, we have shown that it is induced by the spin-dependent p-d hybridization between the transition metal (Co) and ligand (O) via the spin-orbit interaction. On the basis of the correspondence between the direction of electric polarization and the magnetic state, we have also demonstrated the electrical control of the magnetization direction.

We have investigated electrically-active magnetic excitations (electromagnons) in perovskite manganites with the $E$-type (up-up-down-down) spin structure by terahertz spectroscopy. Eu$_{1-x}$Y$_x$MnO$_3$ (0.1$\le x\le$1) and Y$_{1-y}$Lu$_y$MnO$_3$ (0$\le y\le$1) without magnetic $f$-moments, which host collinear sinusoidal, $A$-type, cycloidal, and $E$-type spin orders, are used to examine the systematics of possible electromagnons. Three-peak structures (23, 35, 45 cm$^{-1}$) of magnetic origin show up in the $E$-type phase with little composition ($y$) dependence of frequencies, making a contrast with the electromagnons observed in the cycloidal-spin ($x\le0.8$) phases. One of these electromagnon is ascribed to the zone-edge magnon mode based on the calculated magnon dispersions., Comment: 5 pages, 4 figures

Electromagnon, magnetic excitation driven by an electric field of light, has been investigated for a series of perovskite manganites $R{\text{MnO}}_{3}$. Two distinct excitations commonly appear in the spiral spin-ordered state, and systematic changes in their peak positions and spectral weights were observed as a function of the radius of the $R$-ion or equivalently of spin-exchange interaction energies. By comparing the results with the spin-wave calculation based on the Heisenberg model, the higher-lying excitation is assigned to the zone-edge magnon. The strong electric-dipole activity of these magnetic excitations is discussed in terms of dynamic coupling among the collective modes.

Recent spectroscopic studies at terahertz frequencies for a variety of multiferroics endowed with both ferroelectric and magnetic orders have revealed the possible emergence of a new collective excitation, frequently referred to as electromagnon. It is magnetic origin, but becomes active in response to the electric field component of light. Here we give an overview on our recent advance in the terahertz time-domain spectroscopy of electromagnons or electric-dipole active magnetic resonances, focused on perovskite manganites--$R$MnO$_3$ ($R$ denotes rare-earth ions). The respective electric and magnetic contributions to the observed magnetic resonance are firmly identified by the measurements of the light-polarization dependence using a complete set of the crystal orientations. We extract general optical features in a variety of the spin ordered phases, including the $A$-type antiferromagnetic, collinear spin ordered, and ferroelectric $bc$ and $ab$ spiral spin ordered phases, which are realized by tuning the chemical composition of $R$, temperature, and external magnetic field. In addition to the antiferromagnetic resonances of Mn ions driven by the magnetic field component of light, we clarify that the electromagnon appears only for light polarized along the a-axis even in the collinear spin ordered phase and grows in intensity with evolution of the spiral spin order, but independent of the direction of the spiral spin plane ($bc$ or $ab$) or equivalently the direction of the ferroelectric polarization $P_{\rm s}$ ($P_{\rm s}\| c$ or $P_{\rm s}\| a$). A possible origin of the observed magnetic resonances at terahertz frequencies is discussed by comparing the systematic experimental data presented here with theoretical considerations based on Heisenberg model., 19 pages including 15 figures and 2 tables; Invited Paper in Special Issue on Terahertz Wave Photonics in J. Opt. Soc. Am. B (Accepted for publication)

The wide range optical spectra on a multiferroic prototype TbMnO3 have been investigated to clarify the origin of spin excitations observed in the far-infrared region. We elucidate the full band structure, whose high energy edge (133 cm;{-1}) exactly corresponds to twice of the highest-lying magnon energy. Thus the origin of this absorption band is clearly assigned to two-magnon excitation driven by the electric field of light. There is an overlap between the two-magnon and phonon energy ranges, where the strong coupling between them is manifested by the frequency shift and transfer of oscillator strength of the phonon mode.

In this paper, we carry out a new technique named projection ED and indicate that it is applicable to the frustrated models, e.g., XXZ spin-1/2 Heisenberg and spinless fermion t-V models, in the strong coupling limit with highly degenerate ground states in a general way. As an example, we deal with a spinless fermion t-V model on a triangular lattice and show the usefulness of the method., Comment: 2 pages, 3 figures, to be published in Journal of the Physical Society of Japan (JPSJ) Vol.77 No.8

We analyze a model of spinless fermions on a triangular lattice at half-filling interacting via strong nearest-neighbor repulsive interactions, V, using the variational Monte Carlo simulation technique. The existence of three-sublattice long-range order is confirmed by the finite-size scaling analysis of the charge structural factor at V_c/t > 12. This ordered phase shows characteristics expected for a so called "pinball liquid" state, which has the spontaneous separation of fermionic degrees of freedom into coexisting Wigner crystal-like charge order (pin) and a metal (ball). The pins are fixed in order to maximize the kinetic energy gain of balls which move almost freely. The Fermi surface is reconstructed at V=V_c and remains towards the strong coupling limit. These features reminiscent of the strong correlation together with the large value of V_c/t distinguishes the pinball liquid from the conventional charge-density-wave., 7 pages, 7 figures

We examine the influence of weak anisotropic interactions on the T=0 phase diagram of the frustrated two-leg Heisenberg ladder, a well-studied spin model exhibiting integer and fractional magnetization plateaux separated by gapless incommensurate states. We find that the Dzyaloshinskii--Moriya coupling may substantially modify the phase diagram so that the half-integer plateau and the surrounding gapless phases merge into a single Ising-ordered phase breaking the translational symmetry of the lattice. A different Ising order is found for a weakly frustrated ladder. Implications for experimental ladder and dimer systems are discussed., Comment: 5 pages, 5 figures

We investigate the interplay of Dzyaloshinskii-Moriya interactions and an external field in spin-$1∕2$ dimers. For isolated dimers and at low field, we derive simple expressions for the staggered and uniform magnetizations which show that the orientation of the uniform magnetization can deviate significantly from that of the external field. In fact, in the limit where the $\mathbf{D}$ vector of the Dzyaloshinskii-Moriya interaction is parallel to the external field, the uniform magnetization actually becomes perpendicular to the field. For larger fields, we show that the staggered magnetization of an isolated dimer has a maximum close to one-half the polarization, with a large maximal value of $0.35g{\ensuremath{\mu}}_{B}$ in the limit of very small Dzyaloshinskii-Moriya interaction. We investigate the effect of interdimer coupling in the context of ladders with density-matrix renormalization-group (DMRG) calculations and show that, as long as the values of the Dzyaloshinskii-Moriya interaction and of the exchange interaction are compatible with respect to the development of a staggered magnetization, the simple picture that emerges for isolated dimers is also valid for weakly coupled dimers with minor modifications. The results are compared with torque measurements on ${\mathrm{Cu}}_{2}{({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2})}_{2}{\mathrm{Cl}}_{4}$.

We present a 2D NMR investigation of the gapped spin-1/2 compound Cu2(C5H10N2D2)2Cl4. Our measurements reveal the presence of a magnetic field-induced transverse staggered magnetization (TSM) which persists well below and above the field-induced 3D long-range magnetically ordered (FIMO) phase. The symmetry of this TSM is different from that of the TSM induced by the order parameter of the FIMO phase. Its origin, field dependence, and symmetry can be explained by an intradimer Dzyaloshinskii-Moriya interaction, as shown by DMRG calculations on a spin-1/2 ladder. This leads us to predict that the transition into the FIMO phase is not in the BEC universality class.

We investigated the double-exchange spin ice model on a kagom\'e lattice by Monte Carlo simulation in order to study a mechanism for lifting the degeneracy in frustrated electron systems. We show specific heat and vector spin chirality data on a finite lattice. Specific heat has a double-peak structure: A broad peak and a sharp peak are at $k_{\rm B}T/t \sim 0.15$ and 0.015, respectively, where $t$ is the transfer integral of electrons. The broad peak corresponds to a crossover to the spin ice-like state, on the other hand, the sharp one a transition to a dodecagonal spin cluster (dodecamer) state. We discuss the interplay between the formation of the dodecamer state and the lifting of the macroscopic degeneracy., Comment: 3 pages, 2 figures, to be published in Physica B (as the proceedings of SCES'04)

In order to study effects of frustration in an itinerant electron system, we investigate ground states of the antiferromagnetic double-exchange model on a triangular lattice. In this model, pseudo-spins are coupled to electron transfer integrals in such a way that antiparallel configurations of pseudo-spins gain kinetic energies. Although the antiferromagnetic Ising model on a triangular lattice shows macroscopic dengenerate ground states, the present model shows that the degeneracy is lifted due to long-range natures of the double exchange interactions. Spin ordering at the ground state is also discussed., Comment: 8 pages, 5 figures, Proceedings for SPQS2004

We have observed the orbital ordering in the ferromagnetic Mott-insulator Lu2V2O7 by the polarized neutron diffraction technique. The orbital ordering pattern determined from the observed magnetic form factors can be explained in terms of a linear combination of wave functions |yz>, |zx> and |xy>; |0> = (1/3)^(1/2) |xy> + (1/3)^(1/2)|yz> + (1/3)^(1/2) |zx> which is proportional to |(x + y + z)^2 - r^2>; where each orbital is extended toward the center-of-mass of the V tetrahedron. We discuss the stability of the ferromagnetic Lu2V2O7, using a Hubbard Hamiltonian with these three orbitals., 17pages. to be published in J. Phys. Soc. Jpn. 74 (2005)

We investigated the double-exchange spin ice (DESI) model on a kagom\'e lattice by Monte Carlo simulation to study the effects of a geometrical frustration, and the mechanism that generates an ordered state in a metallic system. The DESI model on the kagom\'e lattice is a frustrated metallic system due to an effective ferromagnetic interaction between localized spins caused by the double-exchange (DE) mechanism and a uniaxial anisotropy for the localized spins. A dodecagonal spin cluster (named dodecamer), which consists of twelve localized spins, appears at low temperature when the number of particles per site $n \simeq 1/3 \sim 1/2$. Such a dodecamer order is driven by both the kinetic energy gain due to the DE mechanism and the geometrical frustration. We discuss that cluster orders, in general, may be a common feature in itinerant electron systems coupled with frustrated adiabatic fields., Comment: 9 pages, 6 figures, to be published in J. Phys. Soc. Jpn

The magnetic properties of SrCu2 (BO3)2 are reviewed from a theoretical point of view. SrCu2 (BO3)2 is a new two-dimensional spin gap system and its magnetic properties are well described by a spin-1/2 antiferromagnetic Heisenberg model of the orthogonal dimer lattice. The model has a dimer singlet ground state whose exactness was proven by Shastry and Sutherland for a topologically equivalent model more than 20 years ago. The exactness of the ground state is maintained even if interlayer couplings are introduced for SrCu2 (BO3)2. In the two-dimensional model, quantum phase transitions take place between different ground states for which three phases are expected: a gapped dimer singlet state, a plaquette resonating valence bond state and a gapless magnetic ordered state. Analysis of the experimental data shows that the dimer singlet ground state is realized in SrCu2 (BO3)2. The orthogonality of the dimer bonds, which is the underlying symmetry of the exactness of the ground state, also leads to an unusual property of elementary excitations, namely the almost localized nature of the triplet excitations. Application of an external magnetic field changes the density of the triplet excitations. In general, there is competition between kinetic energies and interaction energies between triplets. The almost localized nature of the triplets makes it easy to form regular lattices. In fact, at certain densities, where the commensurability energy is significant, the triplet excitations form superstructures and plateaux appear at 1/2, 1/3, 1/4 and 1/8 in the magnetization curve. In high-magnetic-field experiments, magnetic plateaux at magnetizations of 1/3, 1/4 and 1/8 have been observed. Translational symmetry of the lattice is spontaneously broken at the plateaux, except for the 1/2 plateau. The 1/3 and 1/4 plateaux are expected to have magnetic superstructures of stripe form while the 1/2 plateau has a square unit cell and the 1/8 plateau a rhomboid cell. Especially at the 1/8 plateau, nuclear magnetic resonance experiments indicate the presence of at least 11 distinct Cu sites with different spin polarizations, which is the first evidence of breaking of the translational symmetry at the plateau phase. The spin texture calculated on the basis of a Heisenberg model with adiabatic spin–phonon coupling is consistent with the experimental results.

The two-dimensional spin-gap system ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}$ shows unique physical properties due to the low-dimensionality character and the strong quantum fluctuations. Experimentally, $1/8,1/4,\mathrm{and}1/3$ plateaus have been observed in the magnetization curve under magnetic fields up to 70 T, and the 1/2 plateau is expected to be stabilized at higher magnetic fields. We argue that spin-lattice effects are necessary to describe the spin density profile at the plateaus, and we propose a simple microscopic model of spins interacting adiabatically with the lattice to reproduce the main features of the recent experimental results by nuclear magnetic resonance.

By using perturbation calculation and numerical diagonalization, low-energy spin dynamics of the Shastry-Sutherland model is investigated paying particular attention to the two-particle coherent motion. In addition to spin-singlet- and triplet bound states, we find novel branches of coherent motion of a bound quintet pair, which are usually unstable because of repulsion. Unusual dispersion observed in neutron-scattering measurements are explained by the present theory. The importance of the effects of phonon is also pointed out., 4 pages, 6 figures combined into 1 PSfile. Final version to appear in Phys.Rev.Lett. (Jan. 2000)

We investigated the effects of charge frustration in the spinless fermion system on a triangular lattice with bond anisotropies under strong intersite Coulomb interactions. Using the exact diagonalization method, we calculated the density of states for various values of bond anisotropies. Results indicate a partial melting of charge ordering by increasing the amount of frustrations (from a square lattice to an isotropic triangular lattice), which leads to the formation of a midgap states. Due to the midgap states, the system seems to be metallic.

It is important to study the many-body effects of the electrons on the flat band lattice, since the flatness of the dispersion may lead to instabilities in the presence of interactions. To clarify the effects of flat dispersion for superconductivity, we investigate a simple two-band BCS Hamiltonian, where one of the bands has a flat dispersion, in the mean field approximation. A superconducting gap Δ and a critical temperature Tc strongly depend on the pairing coupling constant V. Especially, for small coupling constant, Δ and Tc are proportional to V, which are quite different from the single band BCS cases. Higher Tc, compared to the normal BCS system, are realized due to the existence of the flat band.

Cs2CuBr4 is a new two-dimensional spin- 1 2 system, where 1 3 -plateau has been observed in external magnetic fields for H ∥ b and H ∥ c . It is expected that magnetic behaviors of the material are well explained by a two-dimensional antiferromagnetic Heisenberg model on a distorted triangular lattice. In the model, there are two types of interactions, J 1 and J 2 , where J 1 chains are coupled with interchain interactions J 2 . Using an exact diagonalization method, we investigate magnetic properties, especially magnetization curve. In the magnetization, 1 3 -plateau appears for 0.7 ≲ J 2 / J 1 ≲ 1.3 . In the plateau phase, three-fold degenerate translational symmetry broken ground state is realized. Our results indicate that the material has a more frustrated character than what has been expected from a classical theory.

Recently, we have proposed a new class of lattice structures called generalized partial line graph, on which flat dispersions of energy bands are realized in tight-binding models. We investigate in this paper the possibility of ferromagnetism in the Hubbard model on generalized partial line graphs. Numerical diagonalizations show that the ground states with large total spin quantum numbers are realized in finite-size systems.

We investigate magnetic excitations in an $S=3/2$ Heisenberg model representing two-dimensional antiferromagnet ${\rm Ba_2CoGe_2O_7}$. In terahertz absorption experiment of the compound, Goldstone mode as well as novel magnetic excitations, conventional magnetic resonance at 2 meV and both electric- and magnetic-active excitation at 4 meV, have been observed. By introducing a hard uniaxial anisotropy term $\Lambda (S^z)^2$, three modes can be explained naturally. We also indicate that, via the spin-dependent metal-ligand hybridization mechanism, the 4 meV excitation is an electric-active mode through the coupling between spin and electric-dipole. Moreover, at 4 meV excitation, an interference between magnetic and electric responses emerges as a cross correlated effect. Such cross correlation effects explain the non-reciprocal linear directional dichroism observed in ${\rm Ba_2CoGe_2O_7}$., Comment: 5 pages, 3 figures

Recently, a novel one-magnon excitation induced by electric components of light, so called electromagnon, has been paid attention. Theoretically, a mechanism to induce a one-magnon excitation by electric component of light has been proposed. Such a magnetic excitation can be possible in spins with noncollinear structures due to the couplings between symmetric spin-dependent electric polarizations and electric fields. We adopt the mechanism to one-dimensional frustrated Heisenberg systems, where cycloidal spin states are the ground state in highly frustrated parameter region, and discuss the possible electromagnon processes.

SrCu2(BO3)2 is a unique two-dimensional spin gap system. Furthermore, two magnetization plateaus corresponding to 1 4 and 1 8 of the full Cu moment are observed. We present a theoretical model of these plateaus. In the Heisenberg model for this material triplet excitations are almost localized, which makes them easy to crystallize, leading to the magnetization plateaus. For small magnetization we can map this Heisenberg model to an Ising model and the magnetization curve is calculated. We find 1 2 -, 1 3 -, 1 4 - and 1 8 -plateaus.

Spinless fermion t-V model on a triangular lattice has been studied. In the model, the presence of a novel metallic charge-ordered ground state named a pinball liquid state has been proposed. To clarify the metallic features in the pinball state, we calculate the momentum distribution function of the model. For comparison, we also analyze a corresponding model where charge ordering is strongly pinned. The results are consistent with the picture expected for the pinball liquid, where an insulating ordered state (pin) and a metallic state on the honeycomb lattice (ball) coexist.

The full-potential linear augmented plane-wave calculations have been applied to investigate the systematic change of electronic structures in CaAlSi due to different stacking sequences of AlSi layers. The present ab-initio calculations have revealed that the multistacking, buckling and 60 degrees rotation of AlSi layer affect the electronic band structure in this system. In particular, such a structural perturbation gives rise to the disconnected and cylindrical Fermi surface along the M-L lines of the hexagonal Brillouin zone. This means that multistacked CaAlSi with the buckling AlSi layers increases degree of two-dimensional electronic characters, and it gives us qualitative understanding for the quite different upper critical field anisotropy between specimens with and without superstructure as reported previously., Comment: 4 pages, 4 figures, to be published in J. Phys. Soc. Jpn

We observed a field-induced staggered magnetization in the 2D frustrated dimer-singlet spin system SrCu2(BO3)2 by 11B NMR, from which the magnitudes of the intradimer Dzyaloshinsky-Moriya interaction and the staggered g-tensor were determined. These anisotropic interactions cause singlet-triplet mixing and eliminate a quantum phase transition at the expected critical field Hc for gap closing. They also provide a quantitative account for some puzzling phenomena such as the onset of a uniform magnetization below the and the persistence of the excitation gap above Hc. The gap was accurately determined from the activation energy of the nuclear relaxation rate., Comment: 8 pages, 5 figures, published version

We discuss high-field magnetic properties of the quasi two dimensional frustrated dimer spin system SrCu2(BO3)2, which is a realization of the Shastry-Sutherland spin model and shows magnetization plateaus at 1/8, 1/4 and 1/3 of the saturated magnetization. Based on the results of 11B NMR experiments, we discuss (1) the spin superstructure in the plateau phases, (2) the effects of anisotropic interactions such as the Dzyaloshinski-Moriya interaction, and (3) nature of the phases above the 1/8 plateau.

LaTiO 3 is a Mott insulator with a G-type antiferromagnetic ordered ground state and a Neel temperature about 135 K. Recently, Keimer et al. have shown that t 2 g orbital degrees of freedom of Ti 3 + are missing in LaTiO 3 , although the crystal field acting on Ti 3 + is nearly cubic. In addition to that, magnon spectra observed in neutron scattering experiments are fitted well by a spin-half isotropic Heisenberg model on a cubic lattice. Nevertheless, no evidence of static orbital order was observed in anomalous x-ray scattering experiment. To explain the quenching of the orbital degrees of freedom is one of the stimulating problems in this material. Using exact diagonalizations of finite clusters, we study the interplay of spin-orbit interactions and superexchange in the Kugel-Khomskii model of LaTiO 3 . Spin-orbit interaction leads to a non degenerate ground state. However, the Kugel-Khomskii model with spin-orbit interaction does not describe well the spectrum observed in neutron scattering.

We study the spin-1/2 trellis lattice Heisenberg model, a coupled spin ladder system, both by perturbation around the dimer limit and by quantum Monte Carlo simulations. We discuss the influence of the inter-ladder coupling on the spin gap and the dispersion, and present results for the temperature dependence of the uniform susceptibility. The latter was found to be parameterized well by a mean-field type scaling ansatz. Finally we discuss fits of experimental measurements on SrCu$_2$O$_3$ and CaV$_2$O$_5$ to our results., Comment: 7 pages, 8 figures