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

The Cr${}^{5+}$ ions in Sr${}_3$Cr${}_2$O${}_8$ constitute a strongly correlated spin-1/2 dimer system. Experiments show that the collective singlet-triplet excitations in this system are well defined in the zero-temperature limit, but, when heated, the inelastic neutron scattering peaks decrease rapidly in intensity and acquire a nonzero line width. When including the fluctuations to leading order in $1/z$, where $z$ is the coordination number, the diagrammatic high-density expansion is found to offer an accurate description of the singlet-triplet excitations. The theory explains not only the temperature dependencies of the intensities and line widths, but also that strong correlation causes the lineshapes to become asymmetric at temperatures comparable to the excitation energies.

Figure 1

The density of states of singlet-triplet excitations in Sr${}_3$Cr${}_2$O${}_8$ in the zero temperature limit. It is determined from the RPA model in Ref. [3] as an average over the three twinned domains. The inset shows the spin-dimer structure in Sr${}_3$Cr${}_2$O${}_8$. The dimer units are the Cr${}^{5+}$ pairs of nearest neighbors connected by the blue-red vertical bonds, and the intradimer exchange interaction is denoted by $J_0=\Delta$. A detailed description of the magnetic exchange interactions in Sr${}_3$Cr${}_2$O${}_8$  can be found in Ref. [3].

Figure 2

Constant $Q$ scans at $(0.5,0.5,3)$ measured at different temperatures on V2-FLEX. The solid lines are the calculated response functions assuming the fitted experimental resolution function to be independent of temperature. The three peaks derive from the three equivalent crystallographic twins.

Figure 3

The intrinsic shapes of each of the three peaks considered in Fig. 2 calculated at (a) 20 and (b) 40 K. The correlation function corresponding to the peak at the lowest energy has been divided by two in (a).

Figure 4

Constant $Q$ scans performed at TASP. The temperature variation of the low energy peak at $(0.5,0.5,3)$ is shown in (a), and of the single excitation at $(0,0,7.5)$ in (b). The solid lines are the calculated response functions using experimental resolution functions determined by the scans at 1.6 K.

Figure 5

Constant $Q$ scan at $(0,0,3)$ measured at different temperatures on V2-FLEX. The solid lines are the calculated response functions assuming the smooth but nonlinear background indicated by the dashed line.