High-Resolution Study of Spin Excitations in the Singlet Ground State ofSrCu2(BO

Abstract

High resolution, inelastic neutron scattering measurements on SrCu2(BO3)2 reveal the dispersion of the three single triplet excitations continuously across the (H,0) direction within its tetragonal basal plane. These measurements also show distinct Q dependencies for the single and multiple triplet excitations, and that these excitations are largely dispersionless perpendicular to this plane. The temperature dependence of the intensities of these excitations is well described as the complement of the dc-susceptibility of SrCu2(BO3)2 .PACS numbers: 75.10. Jm, 75.25.+z, 75.40.Gb Quantum magnets which display collective singlet ground states have been of much recent interest 1 . Several of these, such as CuGeO 3 2 , MEM-(TCNQ) 2 3 , and NaV 2 O 5 4 result from spin-Peierls phenomena in low dimensions where the lattice combines with s=1/2 spin degrees of freedom to break translational symmetry below some characteristic phase transition temperature, and a non-magnetic ground state with a characteristic energy gap is observed. A related state is observed in the s=1 antiferromagnetic chain compounds, such as CsNiCl 3 5 and NENP 6 , where a non-magnetic ground state with an energy gap, the Haldane gap, forms in the absence of translational symmetry breaking.SrCu 2 (BO 3 ) 2 has been proposed 7,8 as a realization of the Shastry-Sutherland model 9 of interacting dimers in two dimensions. This material crystallizes 10 into the tetragonal space group I42m with lattice parameters a=8.995Å, c=6.649Å. Magnetically, it can be thought of in terms of well isolated basal planes populated by antiferromagnetically coupled s=1/2 moments on the Cu 2+ sites. These are arranged in dimers at right angles to each other and forming a square lattice. The microscopic Hamiltonian appropriate to this system is based on:It is known that both interactions, J and J', are antiferromagnetic and similar in strength, such that the system is not far removed from the critical value of x=J'/J known to be appropriate to the quantum phase transition which separates a 4 sublattice Neel state from a collective singlet ground state.The estimated values of J and J' have evolved over time as both theory and experiment have improved. Early estimates of J and x were J=8.6 meV and x=0.687 , very close to the critical value x c =0.6911 , where the single triplet excitation goes soft. More recently Miyahara and Ueda 12 found J=7.3 meV and x=0.635 from fits to the magnetic susceptibility. Somewhat smaller values were obtained by Knetter et al 13 who compared theoretical and experimental ratios of the energy of the lowest S=1 two triplet bound state to the single triplet gap, to obtain J=6.16 meV and x=0.603. Note that within this theory 13 , the collective singlet ground state becomes unstable when the lowest energy two triplet bound state goes soft.Earlier, relatively low resolution inelastic neutron scattering measurements 14,15,16 have directly identified three bands of excitations corresponding to single (n=1) triplet excitations, as well as to two (n=2), and...

Magnon dispersion and anisotropies inSrCu2(BO3)2

“…͑18͒. Note that the renormalization at q = ͑ ,0͒ is, in fact, very small compared to that at q = 0, and solves the puzzle previously noticed, 13 as we shall explain below.…”

“…12,13 This is the value we extracted before relying on the perturbative expression. 12 We have here calculated the renormalization coefficient at ͑ ,0͒, and shown that coefficient is quite different from that at ͑0,0͒; therefore, applying the same renormalization to both splittings 13 leads to an artificially large in-plane Dzyaloshinskii-Moriya coupling. This explains why the ratio appeared so large previously.…”

“…This is consistent with the observation of vanishing intensity for the middle mode in neutron scattering. 12,13 The splitting seen at q = ͑ ,0͒ can therefore be interpreted as the gap between the lower and upper states. As we have seen, the splitting at q = ͑ ,0͒ is given by D ʈ f͑JЈ / J͒, with f͑0͒ =2 ͱ 2 and f͑0.62͒ = 2.80 ͑which is, in fact, within 1% of the perturbative result͒.…”

“…While spin-orbit interactions always introduce anisotropies at some energy scale, it was a surprise that in a frustrated model they could dominate the dispersion which generally arises from larger, isotropic couplings. More recently, other components of the vectors were argued to be required to explain further experimental findings: another splitting was observed at q = ͑ ,0͒, 12,13 and was subsequently associated with in-plane components of the Dzyaloshinskii-Moriya interactions. In addition, there is an avoided level crossing when the first-triplet state is about to cross the ground state for magnetic fields applied along c. This is not compatible with a single-axis anisotropy along the same direction and requires additional forms of anisotropy.…”

Order–disorder effects on the elastic properties of CuMPt6 (M=Cr and Co) compounds

“…Temperature was varied between ambient and 25 K with a helium cooled cryostat. Two types of samples where used : [28]. The single crystals are naturally cleaved along the a À b plane.…”