Static and Dynamical Dzyaloshinsky-Moriya interactions in gapped spin systems

Anisotropic spin-spin interactions of Dzyaloshinsky and Moriya symmetry are generally considered weak, as they depend on the spin-orbit couplings. In spin systems with gapped ground states they can, however, have rather strong effects. We will discuss recent results related to the results of neutron scattering and ESR for $\rm SrCu_2(BO_3)_2$. Inclusion of the Dzyaloshinsky-Moriya interactions can explain much of the dynamics of the systems discussed, in particular the splitting and dispersion of the triplet modes. Some effects remain to be explained, however. Symmetries of the crystal lead to the prediction of zero intensity for transitions, for example between the ground state and the triplets observed in ESR. We present recent calculations of the effects of anisotropic terms generated dynamically, ie linearly in the phonon coordinates. We discuss how this leads to a novel mechanism to explain the ESR intensities. For polarized neutron scattering experiments, we can calculate the mixing of nuclear and magnetic scattering amplitudes by such a term and how such mixing should be observed.