We argue that the S =1/ 2 kagome antiferromagnet undergoes a quantum phase transition when the Dzyaloshinskii-Moriya coupling is increased. For D Ͻ D c the system is in a moment-free phase, and for D Ͼ D c the system develops antiferromagnetic long-range order. The quantum critical point is found to be D c Ӎ 0.1J using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ZnCu 3 ͑OH͒ 6 Cl 3 may be in a quantum critical region controlled by this fixed point.

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. PACS numbers:Strontium Copper Borate (SrCu 2 (BO 3 ) 2 ) is a new example of a magnetic oxide with a spin gap [1], with a ground state well described as simply a product of magnetic dimers in two dimensions on the bonds giving the strongest magnetic exchange [2]. The weaker exchanges are frustrated by the geometry and, as shown by Shastry and Sutherland [3], the ground state of the isotropic Hamiltonian is independent of the value of the weaker exchange, up to a critical value. The excitations, however, are not purely local and cannot be explicitly given. Recent experiments by ESR [4] and neutron inelastic scattering presented here show how in fact there are spin anisotropies needed for an accurate description of the dynamics. We shall show the corrections to the ground state are needed that, while small, will be necessary to understand many physical properties. For example at finite external magnetic field SrCu 2 (BO 3 ) 2 appears to exhibit a number of finite magnetization plateaux [1,5], and the anisotropies will determine the observability of plateaux in different field directions. Furthermore SrCu 2 (BO 3 ) 2 is believed to be close in parameter space to a quantum critical point whose nature is somewhat controversial, and while the anisotropies are small they may be essential to its nature.For spin 1 2 the leading anisotropic terms are of form Dzyaloshinski-Moriya [6] and exchange anisotropy. The former is particularly relevant, since it may not be frustrated even if the isotropic exchange is. While a small Dzyaloshinski-Moriya interaction should not destroy a gap generated by larger isotropic interactions it modifies the pure locality of the ground state correlations and delocalizes the first triplet excitation. This is because it appears in lower order in perturbation theory than the frustrated isotropic interactions. In this paper we predict the Dzyaloshinski-Moriya interactions that should be expected in SrCu 2 (BO 3 ) 2 from the structure, and show that they do indeed explain new features of the excitations observed with ESR and neutron inelastic scattering experiments. Miyahara and Ueda [2] have introduced the frustrated Shastry-Sutherland modelfor SrCu 2 (BO 3 ) 2 , with S = 1/2 and where nn stands for nearest neighbor spins and nnn for next nearest neighbors. The lattice is shown in fig. 1. J = 85K and J ′ = 54K are antiferromagnetic interactions estimated from the susceptibility and the gap [2]. The spectrum of spin excitations has several interesting f...

We have obtained the zero-temperature phase diagram of the kagomé antiferromagnet with Dzyaloshinskii-Moriya interactions in Schwinger-boson mean-field theory. We find quantum phase transitions (first or second order) between different topological spin liquids and Néel ordered phases (either the √ 3 × √ 3 state or the so-called Q = 0 state). In the regime of small Schwinger-boson density, the results bear some resemblances with exact diagonalization results and we briefly discuss some issues of the mean-field treatment. We calculate the equal-time structure factor (and its angular average to allow for a direct comparison with experiments on powder samples), which extends earlier work on the classical kagomé to the quantum regime. We also discuss the dynamical structure factors of the topological spin liquid and the Néel ordered phase.