Correlated Decay of Triplet Excitations in the Shastry-Sutherland Compound ${\mathbf{\text{SrCu}}}_2({\mathrm{BO}}_3{)}_2$

The temperature dependence of the gapped triplet excitations (triplons) in the 2D Shastry-Sutherland quantum magnet ${\text{SrCu}}_2({\mathrm{BO}}_3{)}_2$ 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.

Figure 1

Temperature dependence of the excitation spectrum of ${\text{SrCu}}_2({\mathrm{BO}}_3{)}_2$, measured by neutron time-of-flight spectroscopy on the FOCUS spectrometer at SINQ on a powder sample. (a),(b) Energy-momentum $(E,Q)$ map at 2 and 15 K. (c) $Q$ dependence of the integrated intensity around the gap energy ($E=[2.8–3.2]\mathrm{meV}$, full symbols) and away from the gap energy ($E=[3.8–4.2]\mathrm{meV}$ and $E=[1.5–2.2]\mathrm{meV}$ combined, open symbols). (d) $Q$-integrated excitation spectra. (e) Partial spectral weight in the [0.5 meV-$E$] range as a function of $E$. The dashed line at 4.4 meV marks the onset of the two-triplet bound state. (f) Scaled spectral weights from Gaussian fits to (d) showing the peak intensity and the energy-independent component, as well as the integrated spectral weight in the [0.5–4.4] meV range. The black line is the $\mathrm{\Delta }=35\mathrm{K}$ isolated singlet population (see the text), and colored lines are guides to the eye.

Figure 2

INS spectra at $Q=(1.5,0.5,0)$ measured on a single crystal sample. (a) $H=0\mathrm{T}$, measured on the TASP spectrometer at SINQ. A two-stage intensity scale is used to visualize both the peak and the tails of the signal. (b) Data of (a) at $T=8\mathrm{K}$ with fits: the red line is the total fit function consisting of a sharp component in green and a broad component in orange. The black line is a fit to a single DHO which fails to match the data. (c) $H=8\mathrm{T}$, measured on the PANDA spectrometer at FRM-2 with the $H\parallel c$ axis. (d) $H=8\mathrm{T}$ at $T=7\mathrm{K}$, with lines as in (b). The fitting procedure is described in the text, and the DHO is convolved with the instrument resolution.

Figure 3

Fit parameters: (a),(d) line shift $\delta {\omega }_Q$, (b),(e) spectral weights $I$, and (c),(f) damping parameter $\mathrm{\Gamma }$ as a function of temperature for several momenta (left) and magnetic fields (right). In (b) and (e), open (closed) symbols refer to the broad (sharp) components. The dashed blue line is the isolated singlet population at zero field. Full lines are the probabilities $P_s(T)$ and $P_b(T)$ discussed in the text, and additional predictions are given for 12 and 16 T ($g=2.22$, $\mathrm{\Delta }=35\mathrm{K}$). Lines in (a), (c), (d), and (f) are guides to the eye. In (f), LM, CM, and UM are the lower, center, and upper triplet modes, respectively.

Figure 4

Real space sketch of two overlapping triplons (blue disks) with radius 1.3 lattice units on the Shastry-Sutherland lattice. The magnetization pattern around the central triplet is shown by up and down arrows with lengths proportional to the magnetization [20]. The dashed blue square indicates a unit cell.