Low dimensional quantum magnets which display a collective singlet ground state and a gap in their magnetic excitation spectrum provide a framework for much exotic phase behavior in new materials, with high temperature superconductivity being the best appreciated example. Neutron scattering techniques can be applied to study a wide variety of problems in condensed matter physics. These techniques are particularly useful as applied to understanding the magnetic properties of quantum magnets that display exotic phases. SrCu2(BO3)2, is a rare example of a two-dimensional quantum magnet for which an exact theoretical solution describing its ground state is known to be a collective singlet. Previous high resolution neutron scattering measurements identified the most prominent features of the spin excitation spectrum in SrCu2(BO3)2, including the presence of one and two triplet excitations and weak dispersion characteristic of subleading terms in the spin Hamiltonian. The resemblance between the spin gap behavior in the Mott insulator SrCu2(BO3)2 and that associated with high temperature superconductors motivated the consideration of the significance of doping in order to understand the properties of this quantum magnetic system. For this reason, a series of neutron scattering studies on doped SrCu2(BO3)2 were initiated. These series of investigations began with the performance of neutron scattering measurements on a SrCu(2-x)Mgx(BO3)2 single crystal in order to introduce magnetic vacancies to the system. These results revealed the presence of new spin excitations within the singlet-triplet gap of this system. Application of a magnetic field induces Zeeman-split states associated with un-paired spins which exist as a consequence of doping with quenched non-magnetic impurities. Additional substantial broadening of both the one and two triplet excitations is observed in the doped system as compared to the pure system. Theoretical calculations are shown to qualitatively account for these features. These studies were extended to neutron scattering measurements on Sr(1-x)LaxCu2(BO3)2, with an aim of introducing charged carriers into this system. The broadening of the one and two triplet excitations is observed and compared to the thermally induced finite lifetime of the pure system. The temperature dependence of this broadening in Sr(1-x)LaxCu2(BO3)2 is different compared to that observed in both SrCu2(BO3)2 and SrCu(2-x)Mgx(BO3)2. It has also been suggested that there is a relation between the spin-lattice interaction in SrCu2(BO3)2 and the magnetic dynamics at low temperatures and high magnetic fields. For this reason there has been increased interest in the study of the crystalline structure and vibrational modes of SrCu2(BO3)2. In order to investigate the role of the lattice in the formation of the singlet ground state in SrCu2(BO3)2, a series of low and high energy neutron scattering measurements were carried out on this system to study both the crystalline structure as well as the normal modes of vibration of the lattice, the transverse acoustic and optical phonons. Transverse acoustic phonons with energies comparable to and higher than the onset of the two triplet continuum show substantially increased lifetimes on entering the singlet ground state below ~ 10 K. This may indicate the removal of the decay channel for the phonons due to the gapping of the spin excitation spectrum in SrCu2(BO3)2 at low temperatures. In high energy inelastic neutron scattering we observe broadening of optic phonons in the ~ 52 to 65 meV region on entering the low temperature singlet ground state. Additionally, the magnetic properties of CuMoO4, which is a triclinic quantum magnet system based on S=1/2 moments at the Cu2+ site, were studied using elastic and inelastic neutron scattering experiments. This material exhibits a first order structural phase transition at ~ 190 K as well as a magnetic phase transition at ~ 1.75 K. We were primarily interested in the low temperature magnetic properties of this material. Magnetization and heat capacity measurements as well as elastic and inelastic neutron scattering measurements were conducted on this system within the low temperature ordered phase. These studies confirm that this material has a magnetic phase transition at ~ 1.7 K. Neutron scattering results indicate that this magnetically ordered phase is characterized by a doubling of the a axis. Inelastic neutron scattering measurements revealed a gapped magnetic excitation spectrum in zero magnetic field, which could be filled in by the application of magnetic fields approaching 7 T.
In this letter we report on the high energy-resolution neutron scattering studies on the dynamic structure factor of the two-triplet bound states in the two-dimensional S = 1/2 Shastry–Sutherland system, SrCu 2 (BO 3 ) 2 , in the energy transfer range of 4 to 7 meV. In contrast to the earlier interpretation of the low energy-resolution results, these bound state excitations show hardly any dispersion, but do show a strong wave-vector-dependent structure factor. Although these findings are in overall agreement with the recent theoretical calculation of the 2-triplon dynamic structure factor by Knetter and Uhrig [Phys. Rev. Lett. 92 (2004) 027204], they also show distinct differences, which may be due to some symmetry-breaking terms in the Hamiltonian that are not included in the theory, such as the interdimer Dzyaloshinski–Moriya interactions recently discovered in this compound.
We performed inelastic neutron scattering on the 2D Shastry-Sutherland system SrCu2(11BO3)2 with an exact dimer ground state. Three energy levels at around 3, 5, and 9 meV were observed at 1.7 K. The lowest excitation at 3.0 meV is almost dispersionless with a bandwidth of 0.2 meV at most, showing a significant constraint on a single-triplet hopping owing to the orthogonality of the neighboring dimers. In contrast, the correlated two-triplet excitations at 5 meV exhibit a more dispersive behavior.
We have studied spin excitation spectra in the Shastry-Sutherland model compound
SrCu2(BO3)2 in magnetic fields using far-infrared Fourier spectroscopy. The transitions from the ground singlet state to the triplet state at $24\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ and to several bound triplet states are induced by the electric field component of the far-infrared light. To explain the light absorption in the spin system we invoke a dynamic Dzyaloshinskii-Moriya (DM) mechanism where light couples to a phonon mode, allowing the DM interaction. Two optical phonons couple light to the singlet to triplet transition in
SrCu2(BO3)2. One is
a-polarized and creates an intradimer dynamic DM along the
c axis. The other is
c-polarized and creates an intradimer dynamic DM interaction, it is in the
(ab) plane and perpendicular to the dimer axis. Singlet levels at 21.5 and $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ anticross with the first triplet as is seen in far-infrared spectra. We used a cluster of two dimers with a periodic boundary condition to perform a model calculation with scaled intra- and interdimer exchange interactions. Two static DM interactions are sufficient to describe the observed triplet state spectra. The static interdimer DM in the
c-direction ${d}_{1}=0.7\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ splits the triplet state sublevels in zero field [C\'epas et al., Phys. Rev. Lett. 87, 167205 (2001)]. The static intradimer DM in the
(ab) plane (perpendicular to the dimer axis) ${d}_{2}=1.8\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, allowed by the buckling of
CuBO3 planes, couples the triplet state to the $28.6\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ singlet as is seen from the avoided crossing.
SrCu 2( BO 3)2 is a new two-dimensional spin gap system and the magnetic behaviour of this compound is explained well by the two-dimensional orthogonal dimer Heisenberg model. Recently several excitations have been observed by inelastic neutron scattering and other experiments. We study features of these excitations by Lanczos method and perturbation technique. A triplet excitation has an almost localised nature. This localised character is observed as an almost flat band in neutron scattering. On the other hand, bound states of two triplet excitations, which have dispersive character, are stable in contrast to ordinary magnetic systems. We calculate the dynamic structure factor by a Lanczos method in finite systems and compare our results with experiments.
Using finite temperature Lanczos technique on finite clusters we calculate dynamical spin structure factor of the quasi-two-dimensional dimer spin liquid
SrCu2(BO3)2 as a function of wave vector and temperature. At low temperatures the peak belonging to the lowest spin excitations is split due to spin anisotropy, in accord with the experimental data. Unusual temperature dependence of calculated spectra is as well in agreement with inelastic neutron scattering measurements. Normalized peak intensities of the single-triplet peak are
q independent, their temperature dependence is analyzed in terms of thermodynamic quantities.