Magnetization Plateaus in the Shastry-Sutherland Model for SrCu_2(BO_3)_2: Results of Fourth-Order Perturbation Expansion with a Low-Density Approximation

Magnetization plateaus in the Shastry-Sutherland model for ${\rm SrCu_2(BO_3)_2}$ are studied by the perturbation expansion method. The fourth-order effective Hamiltonian which describes the dynamics of triplet dimers (TD's) with $S^{\rm tot}_z=1$ in the singlet sea is derived and then partially diagonalized for the space that consists of the TD configurations with the lowest second-order energy. The fourth-order terms are treated within a low-density approximation. Our procedure makes clear how TD interactions are responsible for the formation of magnetization plateaus. Particularly, the 1/4-plateau is obtained by the fourth-neighbor TD repulsion in the fourth-order perturbation, and a diagonal stripe arrangement of TD's appears at this plateau.Comment: 8 pages, 12 figure

Instability of isolated triplet excitations on the Shastry-Sutherland lattice (SSL)

Configurations of singlets and triplets on the SSL have been proposed in the literature as variational ground states of the Shastry-Sutherland model at fixed magnetization M. We prove, that isolated triplet excitations on the SSL are unstable if the coupling alpha falls below a critical value alpha_c=2.0 (approx.). The instability should be visible in the compound SrCu_2(BO_3)_2 where a coupling alpha^*=1.48 is realized.Comment: 4 pages, 4 figures, RevTe

Low-Lying Magnetic Excitation of the Shastry-Sutherland Model

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.Comment: 4 pages, 6 figures combined into 1 PSfile. Final version to appear in Phys.Rev.Lett. (Jan. 2000

Field-Induced Effects of Anisotropic Magnetic Interactions in SrCu2(BO3)2

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 versio

Far infrared study of the two dimensional dimer spin system SrCu_2(BO_3)_2

Using far-infrared spectroscopy in magnetic fields up to 12T we have studied a two-dimensional dimer spin gap system SrCu_2(BO_3)_2. We found several infrared active modes in the dimerized state (below 10K) in the frequency range from 3 to 100cm^-1. The measured splitting from the ground state to the excited triplet M_S=0 sublevel is Delta_1=24.2cm^-1 and the other two triplet state sublevels in zero magnetic field are 1.4cm^-1 below and above the M_S=0 sublevel. Another multiplet is at Delta_2=37.6cm^-1 from the ground state. A strong electric dipole active transition polarized in the (ab)-plane is activated in the dimer spin system below 15K at 52cm^-1.Comment: 4 pages including 5 figures, submitted to PRB, instrumental arte facts remove

Numerical Study of Excited States in the Shastry-Sutherland Model

We investigate excited states of the Shastry-Sutherland model using a kind of variational method. Starting from various trial states which include one or two triplet dimers, we numerically pursue the best evaluation of the energy for each set of quantum numbers. We present the energy difference as a function of either the coupling ratio or the momentum and compare them with the perturbative calculations. Our data suggest that the helical order phase exists between the singlet dimer phase and the magnetically ordered phase. In comparison with the experimental data we can estimate the intra-dimer coupling J and the inter-dimer coupling J' for SrCu2(BO3)2 : J'/J =0.65 and J = 87K.Comment: 15pages, 5figures to be published in JPS

Magnetization plateaus of SrCu_2(BO_3)_2 from a Chern-Simons theory

The antiferromagnetic Heisenberg model on the frustrated Shastry-Sutherland lattice is studied by a mapping onto spinless fermions carrying one quantum of statistical flux. Using a mean-field approximation these fermions populate the bands of a generalized Hofstadter problem. Their filling leads to the magnetization curve. For SrCu_2(BO_3)_2 we reproduce plateaus at 1/3 and 1/4 of the saturation moment and predict a new one at 1/2. Gaussian fluctuations are shown to be massive at these plateau values.Comment: 4 pages, 5 figure

Multi-Triplet Magnons in SrCu2_2(BO3_3)2_2 Studied by Thermal Conductivity Measurements in Magnetic Fields

We have measured the thermal conductivity parallel to the a-axis of the Zn-free and 1% Zn-substituted SrCu$_{2-x}$Zn$_x$(BO$_3$)$_2$ in magnetic fields up to 14 T, in order to examine the thermal conductivity due to the multi-triplet magnons. It has been found that the thermal conductivity peak observed in the spin gap state is suppressed by the substitution of Zn for Cu in high magnetic fields above 6 T, while it is not changed in low magnetic fields below 6 T. The results suggest that the thermal conductivity peak in the spin-gap state of SrCu$_2$(BO$_3$)$_2$ is composed of not only thermal conductivity due to phonons but also that due to the multi-triplet magnons in high fields above 6 T.Comment: 7 pages, 2 figure

Dzyaloshinski-Moriya Interaction in the 2D Spin Gap System SrCu2(BO3)2

The Dzyaloshinski-Moriya interaction partially lifts the magnetic frustration of the spin-1/2 oxide SrCu2(BO3)2. It explains the fine structure of the excited triplet state and its unusual magnetic field dependence, as observed in previous ESR and new neutron inelastic scattering experiments. We claim that it is mainly responsible for the dispersion. We propose also a new mechanism for the observed ESR transitions forbidden by standard selection rules, that relies on an instantaneous Dzyaloshinski-Moriya interaction induced by spin-phonon couplings.Comment: 5 pages, 4 figures, symmetries clarified, added references, (v3) correct addres