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International Journal of Modern Physics B

MAGNETIC EXCITATION OF ORTHOGONAL DIMER HEISENBERG SPIN SYSTEM FOR SrCu 2( BO 3)2

Shin Miyahara, Kiyohito Totsuka, Kazuhiro Ueda

Published Nov 10, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979203020181

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MAGNETIC EXCITATION OF ORTHOGONAL DIMER HEISENBERG SPIN SYSTEM FOR SrCu 2( BO 3)2

S. MIYAHARA, Kiyohito Totsuka, Kazuhiro Ueda

Recent Progress in Many-Body Theories•Dec 1, 2002•0 citations
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.
The magnetic properties of SrCu 2 (BO 3 ) 2 are reviewed from a theoretical point of view. SrCu 2 (BO 3 ) 2 is a new two-dimensional spin gap system and its magnetic properties are well described by a spin-1/2 antiferromagnetic Heisenberg model of the orthogonal dimer lattice. The model has a dimer singlet ground state whose exactness was proven by Shastry and Sutherland for a topologically equivalent model more than 20 years ago. The exactness of the ground state is maintained even if interlayer couplings are introduced for SrCu 2 (BO 3 ) 2 . In the two-dimensional model, quantum phase transitions take place between different ground states for which three phases are expected: a gapped dimer singlet state, a plaquette resonating valence bond state and a gapless magnetic ordered state. Analysis of the experimental data shows that the dimer singlet ground state is realized in SrCu 2 (BO 3 ) 2 . The orthogonality of the dimer bonds, which is the underlying symmetry of the exactness of the ground state, also leads to an unusual property of elementary excitations, namely the almost localized nature of the triplet excitations. Application of an external magnetic field changes the density of the triplet excitations. In general, there is competition between kinetic energies and interaction energies between triplets. The almost localized nature of the triplets makes it easy to form regular lattices. In fact, at certain densities, where the commensurability energy is significant, the triplet excitations form superstructures and plateaux appear at 1/2, 1/3, 1/4 and 1/8 in the magnetization curve. In high-magnetic-field experiments, magnetic plateaux at magnetizations of 1/3, 1/4 and 1/8 have been observed. Translational symmetry of the lattice is spontaneously broken at the plateaux, except for the 1/2 plateau. The 1/3 and 1/4 plateaux are expected to have magnetic superstructures of stripe form while the 1/2 plateau has a square unit cell and the 1/8 plateau a rhomboid cell. Especially at the 1/8 plateau, nuclear magnetic resonance experiments indicate the presence of at least 11 distinct Cu sites with different spin polarizations, which is the first evidence of breaking of the translational symmetry at the plateau phase. The spin texture calculated on the basis of a Heisenberg model with adiabatic spin–phonon coupling is consistent with the experimental results.
By using the perturbation expansion up to the fifth order, we study the two-triplet-dimer excitation spectra in the Shastry-Sutherland model, where the localized nature of a triplet-dimer, the propagation of a triplet-dimer pair by the correlated hopping and the long-range interactions between triplet-dimers play an essential role. It is found that the dispersion relations for first-neighbor triplet-dimer pair excitations with S=1 and p-type symmetry qualitatively explain the second-lowest branch observed in the neutron inelastic scattering experiment. It is also predicted that the second-lowest branch consists of two components, p_x- and p_y-states, with slightly different excitation energies. The origin of the singlet mode at 3.7meV observed in the Raman scattering experiment is also discussed.
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.
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.
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\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}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\mathbf{q}q independent, their temperature dependence is analyzed in terms of thermodynamic quantities.