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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

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.

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

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 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.

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.

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.

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.

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.