Ordering in Spatially Anisotropic Triangular Antiferromagnets

We investigate the phase diagram of the anisotropic spin-$1/2$ triangular lattice antiferromagnet, with interchain diagonal exchange $J^{\prime }$ much weaker than the intrachain exchange $J$. We find that fluctuations lead to a competition between (commensurate) collinear antiferromagnetic and (zigzag) dimer orders. Both states differ in symmetry from the spiral order known to occur for larger $J^{\prime }$, and are therefore separated by quantum phase transitions from it. The zero-field collinear antiferromagnet is succeeded in a magnetic field by magnetically ordered spin-density-wave and cone phases, before reaching the fully polarized state. Implications for the anisotropic triangular magnet ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ are discussed.

Figure 1

Left: The triangular lattice, showing ($J$, $J^{\prime }$, $J_2$) exchange interactions, and integer coordinates $x$, $y$. Black (red or gray) arrows indicate spin order in the CAF phase on odd (even) chains ($J_2=0$ section). Solid ovals show the strong bonds in the ordered zigzag dimer state ($J_2=0.241$ section). Right: suggested zero-field phase diagram (solid points indicate position of phase boundaries on the axes).

Figure 2

Left panel: Comparison of experimental [solid black line—obtained by scanning Fig. 2(a), $B\parallel a$, of Ref. [7] ] and theoretical (dashed red line) magnetization curves for ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$, $J^{\prime }/J=0.34$. The experimental (and theoretical) $M(h)$ is nearly direction-independent apart from $g$-factor rescaling. Right panel: $T=0$ phase diagram of $J-J^{\prime }$ model (top line) and ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ ($h\parallel a$ and $h\perp a$ lines). $h_{\mathrm{sat}}$ is the field at which $M=1/2$ is reached.