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Physical Review B

Lineshape of the singlet-triplet excitations in the dimer system Sr 3 Cr 2 O 8 to first order in the high-density 1/z expansion

Jens Jensen, Diana Lucia Quintero-Castro, A. T. M. N. Islam, K. C. Rule, Martin Må̊nsson, B. Lake

Published Apr 11, 2014• 11 citations
Publisher

Abstract

The authors study spin-triplet excitations in the strongly correlated spin-1/2 dimer system Sr${}_{3}$Cr${}_{2}$O${}_{8}$ via inelastic neutron scattering. They find that the thermal broadening of the excitations can be accurately described by going beyond RPA via diagrammatic high-density $1/z$ expansion.

DOI
10.1103/physrevb.89.134407

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The authors study spin-triplet excitations in the strongly correlated spin-1/2 dimer system Sr3{}_{3}3​Cr2{}_{2}2​O8{}_{8}8​ via inelastic neutron scattering. They find that the thermal broadening of the excitations can be accurately described by going beyond RPA via diagrammatic high-density 1/z1/z1/z expansion.
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.
Using single crystal inelastic neutron scattering with and without the application of an external magnetic field and powder neutron diffraction, we have characterized magnetic interactions in Ba3Cr2O8{\mathrm{Ba}}_{3}{\mathrm{Cr}}_{2}{\mathrm{O}}_{8}Ba3​Cr2​O8​. Even without a field, we found that there exist three singlet-to-triplet excitation modes in the (hhh, hhh, lll) scattering plane. Our complete analysis shows that the three modes are due to spatially anisotropic interdimer interactions that are induced by lattice distortions of the tetrahedron of oxygens surrounding the Jahn-Teller active Cr5+(3d1){\mathrm{Cr}}^{5+}(3{d}^{1})Cr5+(3d1). The strong intradimer coupling of J0=2.38(2)  meV{J}_{0}=2.38(2)\text{ }\text{ }\mathrm{meV}J0​=2.38(2)  meV and weak interdimer interactions ($|{J}_{\mathrm{inter}}|\ensuremath{\le}0.52(2)\text{ }\text{ }\mathrm{meV}$) makes Ba3Cr2O8{\mathrm{Ba}}_{3}{\mathrm{Cr}}_{2}{\mathrm{O}}_{8}Ba3​Cr2​O8​ a good model system for weakly coupled s=1/2s=1/2s=1/2 quantum spin dimers.
In this paper we would like to review the zero field inelastic neutron scattering results obtained by using both the thermal and cold neutron triple axis instrument. The first single triplet state at around 3 meV is split due to the Dzyaloshinski-Moriya (DM) inter-dimer interaction with both the out-of-plane and in-plane components. The splitting between the Sz = ±1 states is of the order of 0.3 meV. The two triplets bound states also form a very flat bands at 4.9, 5.5 and 6.3 meV with finite line width of the order and/or twice of the DM splitting. Finally the higher energy range up to 13 meV can be also characterized by three rather broad, but flat bands at around 8, 10 and 12 meV with the line width roughly three times the DM splitting. These excitations can be probably assigned to three and more triplets bound state excitations.
We discuss the transition strength between the disordered ground state and the basic low-lying triplet excitation for interacting dimer materials by presenting theoretical calculations and series expansions as well as inelastic neutron scattering results for the material KCuCl 3 . We describe in detail the features resulting from the presence of two differently oriented dimers per unit cell and show how energies and spectral weights of the resulting two modes are related to each other. We present results from the perturbation expansion in the interdimer interaction strength and thus demonstrate that the wavevector dependence of the simple dimer approximation is modified in higher orders. Explicit results are given in tenth order for dimers coupled in 1D, and in second order for dimers coupled in 3D with application to KCuCl 3 and TlCuCl 3 .
The compound TlCuCl(3) represents a model system of dimerized quantum spins with strong interdimer interactions. We investigate the triplet dispersion as a function of temperature by inelastic neutron scattering experiments on single crystals. By comparison with a number of theoretical approaches we demonstrate that the description of Troyer, Tsunetsugu, and Würtz [Phys. Rev. B 50, 13 515 (1994)10.1103/Phys. Rev. B 50, 13515] provides an appropriate quantum statistical model for dimer spin systems at finite temperatures, where many-body correlations become particularly important.
Motivated by recent experiments on Ba3Cr2O8{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}Ba3​Cr2​O8​, a new spin-dimer compound with spin-1/2 moments of Cr5+{\text{Cr}}^{5+}Cr5+ ions, we theoretically investigate the field-induced magnetic ordering in this material in view of the Bose-Einstein condensation (BEC) of triplet excitations (triplons). We apply the self-consistent Hartree-Fock-Popov (HFP) approach to a microscopic Hamiltonian, using the realistic triplon dispersion measured in an inelastic neutron-scattering experiment. In particular, we ask to what extent the BEC of dilute triplons near the critical field can explain the magnetic ordering in this material. For example, we investigate the temperature range where the BEC picture of triplons can be applied via the HFP approach. We also determine the temperature regime where a quadratic approximation of the triplon dispersion works. It is found that the strength of the effective repulsive interaction between triplons is much weaker in Ba3Cr2O8{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}Ba3​Cr2​O8​ than in the canonical spin-dimer compound TlCuCl3{\text{TlCuCl}}_{3}TlCuCl3​. Small effective repulsive interaction in combination with the narrow band of triplons leads to higher density of triplons ncr{n}_{\text{cr}}ncr​ at the critical point. The combined effect points to a bigger HFP correction UncrU{n}_{\text{cr}}Uncr​ in Ba3Cr2O8{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}Ba3​Cr2​O8​ than in TlCuCl3{\text{TlCuCl}}_{3}TlCuCl3​. Nonetheless, the HFP approach provides a reasonable explanation of the transverse magnetization and the specific-heat data of Ba3Cr2O8{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}Ba3​Cr2​O8​.