Modes of Magnetic Resonance in the Spin-Liquid Phase of ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$

We report the observation of a frequency shift and splitting of the electron spin resonance (ESR) mode of the low-dimensional $S=1/2$ frustrated antiferromagnet ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ in the spin-correlated state above the ordering temperature 0.62 K. The shift and splitting exhibit strong anisotropy with respect to the direction of the applied magnetic field and do not vanish in a zero field. The low-temperature evolution of the ESR is a result of the modification of the one-dimensional spinon continuum by the uniform Dzyaloshinskii-Moriya interaction within the spin chains.

Figure 1

ESR frequency at $T=1.3\mathrm{K}$ for $H\parallel \mathbf{b}$. Dotted line is paramagnetic resonance with $g=2.08$, solid line—theory (see text). Empty circles stand for resonances losing intensity with cooling. Upper insert: gap vs temperature, various symbols correspond to different cryostats. Lower insert: evolution of the resonance line with cooling.

Figure 2

ESR frequencies at $T=1.3\mathrm{K}$ for $H\parallel \mathbf{a}$. Dotted line is the paramagnetic resonance with $g=2.20$, dashed line—theory (see text). Upper insert: line shape at $T=1.3\mathrm{K}$, $\nu =27\mathrm{GHz}$. Points—experimental data, solid line is the result of a fit by the sum of two Lorentzians (dashed lines). Lower insert: evolution of the resonance line with cooling.

Figure 3

The angular dependence of the resonance field $H_r$ in the $\mathbf{a}\mathbf{b}$ plane for $\nu =27\mathrm{GHz}$ at $T=1.3\mathrm{K}$. Thick line is the theoretical prediction with $D_a/(4\hslash )=8$ and $D_c/(4\hslash )=11\mathrm{GHz}$. The measured values of the resonance field deep in the paramagnetic phase (at $T=10\mathrm{K}$) are presented by crosses, the dashed line is a theoretical fit of a paramagnetic resonance with $g_{a,b,c}$ of ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$.

Figure 4

The polarization effect at $\nu =14.44\mathrm{GHz}$ for $H\to 0$. Circles with error bars show the uncertainty resulting from normalizing the signals to zero absorption at $H>1.5\mathrm{T}$.

Figure 5

Spinon spectrum of the $S=1/2$ Heisenberg chain for $\mathbf{q}\sim 0$ with (solid lines) and without (dashed lines) DM interaction. When $\mathbf{D}\parallel \mathbf{H}$, momentum is boosted by $q=D/J{a}_0$.