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arXiv:cond-mat/0204465 · Physical review. B, Condensed matter

Instability of isolated triplet excitations on the Shastry-Sutherland lattice

Andreas Fledderjohann, K.-H. Mütter

Published May 20, 2002• 2 citations
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Abstract

Configurations of singlets and triplets on the Shastry-Sutherland lattice (SSL) have been proposed in the literature as variational ground states of the Shastry-Sutherland model at a fixed magnetization M. We prove that isolated triplet excitations on the SSL are unstable if the coupling $\ensuremath{\alpha}$ falls below a critical value ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}2.0.$ The instability should be visible in the compound ${\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2},$ where a coupling ${\ensuremath{\alpha}}^{*}=1.48$ is realized.

DOI
10.1103/physrevb.65.212406

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Configurations of singlets and triplets on the Shastry-Sutherland lattice (SSL) have been proposed in the literature as variational ground states of the Shastry-Sutherland model at a fixed magnetization M. We prove that isolated triplet excitations on the SSL are unstable if the coupling \ensuremathα\ensuremath{\alpha}\ensuremathα falls below a critical value \ensuremathαc\ensuremath≈2.0.{\ensuremath{\alpha}}_{c}\ensuremath{\approx}2.0.\ensuremathαc​\ensuremath≈2.0. The instability should be visible in the compound SrCu2(BO3)2,{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2},SrCu2​(BO3​)2​, where a coupling \ensuremathα∗=1.48{\ensuremath{\alpha}}^{*}=1.48\ensuremathα∗=1.48 is realized.
We use the nonperturbative Contractor-Renormalization method (CORE) in order to derive an effective model for triplet excitations on the Shastry-Sutherland lattice. For strong enough magnetic fields, various magnetization plateaux are observed, e.g., at 1/8, 1/4, 1/3 of the saturation, as found experimentally in a related compound. Moreover, other stable plateaux are found at 1/9, 1/6, or 2/9. We give a critical review of previous works and try to resolve some apparent inconsistencies between various theoretical approaches.
Using variational algorithm on an infinite Shastry-Sutherland (SS) lattice we show that the introduction of a static nonmagnetic impurity into a dimerized ground state leads to a formation of a small, localized spin polaron surrounding the impurity site. Due to a particular symmetry of the SS lattice, the polaron is extremely anisotropic with a short spatial extent. The presence of nonmagnetic impurities leads to a formation of pronounced in-gap peaks in the dynamical spin structure factor, which we attribute to the spin-doublet excitations of a single unpaired spin S=1∕2S=1∕2S=1∕2 surrounded by triplet fluctuations. Our results are relevant for the description of SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}SrCu2​(BO3​)2​ compound when doped with nonmagnetic atoms at Cu sites.
Bound states made from two triplet excitations on the Shastry-Sutherland lattice are investigated. Based on the perturbative unitary transformation by flow equations quantitative properties like dispersions and qualitative properties like symmetries are determined. The high order results [up to (J2/J1)14({J}_{2}/{J}_{1}{)}^{14}(J2​/J1​)14] permit one to fix the parameters of SrCu2(BO3)2{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}SrCu2​(BO3​)2​ precisely: J1=6.16(10)meV{J}_{1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6.16(10)\mathrm{meV}J1​=6.16(10)meV, $x\ensuremath{\mathrel{:=}}{J}_{2}/{J}_{1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.603(3)$, ${J}_{\ensuremath{\perp}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.3(2)\mathrm{meV}$. At the border of the magnetic Brillouin zone a general double degeneracy is derived. An unexpected instability in the triplet channel at x=0.63x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.63x=0.63 indicates a transition towards another phase. The possible nature of this phase is discussed.
The temperature dependence of the gapped triplet excitations (triplons) in the 2D Shastry-Sutherland quantum magnet SrCu(2)(BO(3))(2) is studied by means of inelastic neutron scattering. The excitation amplitude rapidly decreases as a function of temperature, while the integrated spectral weight can be explained by an isolated dimer model up to 10 K. Analyzing this anomalous spectral line shape in terms of damped harmonic oscillators shows that the observed damping is due to a two-component process: one component remains sharp and resolution limited while the second broadens. We explain the underlying mechanism through a simple yet quantitatively accurate model of correlated decay of triplons: an excited triplon is long lived if no thermally populated triplons are nearby but decays quickly if there are. The phenomenon is a direct consequence of frustration induced triplon localization in the Shastry-Sutherland lattice.
Magnetization plateaus in the Shastry-Sutherland model for SrCu2(BO3)2{\rm SrCu_2(BO_3)_2}SrCu2​(BO3​)2​ are studied by the perturbation expansion method. The fourth-order effective Hamiltonian which describes the dynamics of triplet dimers (TD's) with Sztot=1S^{\rm tot}_z=1Sztot​=1 in the singlet sea is derived and then partially diagonalized for the space that consists of the TD configurations with the lowest second-order energy. The fourth-order terms are treated within a low-density approximation. Our procedure makes clear how TD interactions are responsible for the formation of magnetization plateaus. Particularly, the 1/4-plateau is obtained by the fourth-neighbor TD repulsion in the fourth-order perturbation, and a diagonal stripe arrangement of TD's appears at this plateau.
Spin-1/2 Heisenberg model on the Shastry-Sutherland lattice is considered within the many-body perturbation theory developed from the exactly solved spin-1/2 Ising-Heisenberg model with the Heisenberg intradimer and Ising interdimer interactions. The former model is widely used for a description of magnetic properties of the layered compound SrCu _2 2 (BO _3 3 ) _2 2 , which exhibits a series of fractional magnetization plateaux at sufficiently low temperatures. Using the novel type of many-body perturbation theory we have found the effective model of interacting triplet excitations with the extended hard-core repulsion, which accurately recovers 1/8, 1/6 and 1/4 magnetization plateaux for moderate values of the interdimer coupling. A possible existence of a striking quantum phase of bound triplons is also revealed at low enough magnetic fields.