Quasiparticles of Spatially Anisotropic Triangular Antiferromagnets in a Magnetic Field

The spectral properties of the spin-$1/2$ Heisenberg antiferromagnet on an anisotropic triangular lattice in a magnetic field are investigated using a weak-interchain-coupling approach combined with exact solutions of a chain. Dominant modes induced by interchain interactions in a magnetic field behave as quasiparticles which show distinctive features such as anomalous incommensurate ordering and high-energy modes. In terms of them, various unusual features observed in the anisotropic triangular antiferromagnet ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ in a magnetic field are quantitatively explained in a unified manner.

Figure 1

(a) Anisotropic triangular lattice. (b) Momentum regions of $J^{\prime }(\mathit{k})>0$ (light blue) and $J^{\prime }(\mathit{k})<0$ (light yellow) for $J^{\prime }>0$. Solid circles denote ordering momenta for $m=1/16$, which shift towards the center of each light yellow plaquette as the magnetic field increases as indicated by arrows. (c)–(e) Comparisons with experimental results on ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$. Blue solid lines are present results. (c) Magnetization curve. The red dotted line denotes experimental results for $H\parallel c$ in Ref. 15 with $g$ factor $g=2.30$ [34] and $J=0.374\mathrm{meV}$ [6]. $S_{\max }^z$ denotes $S^z$ at $H_s$. (d) Dispersion relation above $H_s$ along red dotted lines in (b). Symbols are experimental results in Ref. 6. (e) Momenta of IC ordering. Symbols are experimental results at $k_y=0$ for $H\parallel c$ in Ref. 2, replotted using the magnetization curve in (c).

Figure 2

$S^{zz}(\mathit{k},\omega )$, $S^{+-}(\mathit{k},\omega )/2$, $S^{-+}(\mathit{k},\omega )/2$, and $\overline{S}(\mathit{k},\omega )$ (from above) at $k_y=0$ for $J^{\prime }/J=0.34$. (a) Results using the RPA at $m=1/8$, $1/4$, and $3/8$ (from the left), broadened in a Lorentzian form with full width at half maximum (FWHM) $0.08J$. (b) Results using the method of Ref. 10 at $m=1/4$. Solid lines above (below) continua denote antibound (bound) states for $0\le k_x<\pi$ ($\pi <k_x\le 2\pi$). The inset shows the line shape at $k_x=1.25\pi$. (c) Single-magnon modes in linear spin-wave theory at $m=1/4$. Here, the modes from two cone states, one with the ordering momentum $+\mathit{Q}$ and the other with $-\mathit{Q}$, are shown, broadened in a Lorentzian form with $\mathrm{FWHM}=0.02J$.

Figure 3

Comparisons of line shapes of $\overline{S}(\mathit{k},\omega )$ with experimental results on ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ at $k_y=0$ for (a) $\omega =0.35\mathrm{meV}$ and (b) $k_x=1.5\pi$. (Left panels) Solid lines are present RPA results of $\overline{S}(\mathit{k},\omega )$ broadened in accordance with the experimental energy resolution [5]. Arrows in (b) indicate peak positions of $S^{\overline{\alpha }\alpha }(\mathit{k},\omega )$, $\alpha =+$, $z$, and $-$ (from the left). Symbols denote experimental results for $H\parallel c$ in Ref. 5. Here, the intensities are rescaled after subtracting backgrounds [5], and the energies are normalized by $J=0.374\mathrm{meV}$ [6]. (Right panels) $\overline{S}(\mathit{k},\omega )$ using the RPA at $k_y=0$ corresponding to the left panels, broadened in a Lorentzian form with $\mathrm{FWHM}=0.08J$. Green dashed lines indicate the scan paths for the left panels.