Anomalous Excitation Spectra of Frustrated Quantum Antiferromagnets

We use series expansions to study the excitation spectra of spin-$1/2$ antiferromagnets on anisotropic triangular lattices. For the isotropic triangular lattice model (TLM), the high-energy spectra show several anomalous features that differ strongly from linear spin-wave theory (LSWT). Even in the Néel phase, the deviations from LSWT increase sharply with frustration, leading to rotonlike minima at special wave vectors. We argue that these results can be interpreted naturally in a spinon language and provide an explanation for the previously observed anomalous finite-temperature properties of the TLM. In the coupled-chains limit, quantum renormalizations strongly enhance the one-dimensionality of the spectra, in agreement with experiments on ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$.

Figure 1

Excitation spectrum for the TLM ($J_1=J_2$) along the path ABCOAQD shown in Fig. 4. The high-energy spectrum is strongly renormalized downwards compared to the LSWT prediction (solid line). Note the roton minima at B and D and the flat dispersion in the middle parts of CO and OQ.

Figure 2

(a) Exchange constants $J_1$ and $J_2$ for the $S=1/2$ HAFM on the anisotropic triangular lattice. The model can also be viewed as a square lattice with an extra exchange along one diagonal. (b) Brillouin zone for the frustrated SLM, in standard square lattice notation (the frustrating $J_1$ bonds are taken to lie along the $+45°$ directions in real space). The excitation spectra in Fig. 3 are plotted along the bold path. Also shown are the locations of the Bragg vectors (solid squares) and the local roton minima (solid circles) in the $S=1$ dispersion and the global minima of the $S=1/2$ spinon dispersion (open squares) in the Néel phase. Note that the 90° rotation invariance present for $J_1=0$ is lost for $J_1>0$.

Figure 3

Excitation spectra in the Néel phase. As $J_1/J_2$ is increased, the local roton minimum at $(\pi ,0)$ becomes more pronounced, and the energy difference between $(\pi ,0)$ and $(\pi /2,\pi /2)$, which LSWT predicts to be zero, increases.

Figure 4

Brillouin zone diagram for the TLM. Bragg vectors (solid squares), local roton minima (solid circles), and midpoints of flat dispersion regions (stars) for the spin-$1$ dispersion are shown, as well as the global minima of the proposed $S=1/2$ spinon dispersion (open squares). Note that the latter two sets of wave vectors coincide. The excitation spectra in Figs. 1, 5 are plotted along the path ABCOAD.

Figure 5

Excitation spectrum for $J_1/J_2=3$ (solid points from series) along the path ABCOAD in Fig. 4, compared to experimental dispersion in ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ (squares from Ref. 1; dashed line is the experimental fit), where the exchange ratio is similar, $J_2/J_1=0.34(3)$ and $J_2=0.128(5)\mathrm{meV}$. Compared to LSWT for $J_1/J_2=3$ (solid line), these spectra are enhanced along the $J_1$ bonds and decreased perpendicular to them.