Dzyaloshinski-Moriya Interaction in the 2D Spin Gap SystemSrCu2(BO3)2

Abstract

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...

Magnon dispersion and anisotropies inSrCu2(BO3)2

“…[18][19][20] The model contains isotropic couplings 4 and both interdimer 9,12 and intradimer Dzyaloshinskii-Moriya interactions. 14 It reads…”

“…It was for this reason that they were neglected in the original interpretation of the neutron inelastic scattering. 9 Nonetheless, because the symmetry is slightly broken, these interactions are expected to be present and define a smaller energy scale.…”

“…The dispersion of the triplet states of the Shastry-Sutherland model, taken alone, is very small, and this is why smaller interactions are relevant, and even turn out to be dominant. 9 It is natural to consider Dzyaloshinskii-Moriya interactions since they are linear in the ratio of the spin-orbit coupling to the crystal-field splitting , which is estimated from the g factor, i.e., g−2 g , to be about 0.1. They are, however, peculiar in that they are usually expected to have little effect on the spectrum, at most 2 .…”

“…For instance, the splitting of the q = 0 triplet energy is given by ␦ = D Ќ Ј g͑JЈ / J͒, which is linear in D Ќ Ј and involves a function g͑JЈ / J͒ with g͑0͒ = 4, but g͑JЈ / J͒ = 2.0 for JЈ / J = 0.62. 9 This is difficult to calculate by perturbative techniques because of the proximity with the quantum critical point. Therefore, in order to explain the dispersion of the first-triplet states in SrCu 2 ͑BO 3 ͒ 2 , we need not only to include the relevant Dzyaloshinskii-Moriya interactions, but also to go beyond the perturbative techniques used earlier for the dispersion.…”

Effects of an external magnetic field on the gaps and quantum corrections in an ordered Heisenberg antiferromagnet with Dzyaloshinskii-Moriya anisotropy

“…This has made possible the observations of condensation of triplet excitations in a variety of chain, ladder, and weakly-coupled dimer compounds, 1,2,3 magnetization plateaux in frustrated magnets, 4 and other new effects. 5,6 It turned out that in many cases experimental data deviate significantly from the theoretical predictions based on the pure isotropic Heisenberg model in external field. 6,7,8 Such deviations are due to anisotropies, most notably the Dzyaloshinskii-Moriya (DM) anisotropy, which are usually small and often neglected from zero-field considerations.…”