High-field magnetic resonance of spinons and magnons in the triangular lattice $S=\frac{1}{2}$ antiferromagnet ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$

The electron spin resonance doublet indicating the width of the two-spinon continuum in a spin-$\frac{1}{2}$ triangular lattice Heisenberg antiferromagnet ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ was studied in high magnetic field. The doublet was found to collapse in a magnetic field of one-half of the saturation field. The collapse of the doublet occurs via vanishing of the high-frequency component in a qualitative agreement with the theoretical prediction for the $S=\frac{1}{2}$ chain. The field of the collapse is, however, much lower than expected for the $S=\frac{1}{2}$ chain. This is proposed to be due to the destruction of frustration of interchain exchange bonds in a magnetic field, which restores the 2D character of this spin system. In the saturated phase the mode with the Larmor frequency and a much weaker mode downshifted for 119 GHz are observed. The weak mode is of exchange origin; it demonstrates a positive frequency shift at heating corresponding to the repulsion of magnons in the saturated phase.

Figure 1

Examples of ESR lines of ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ at $\mathbf{H}\parallel a,T=0.5$ K at different frequencies. The zoom for the area within a circle is 6-fold for vertical scale and 3-fold for horizontal scale.

Figure 2

142 GHz ESR records at $\mathbf{H}\parallel a$ in ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ at several temperatures.

Figure 3

Upper panel: Shift of the resonance frequencies of doublet components A and ${\mathrm{A}}^{\prime }$ relative to paramagnetic resonance. Crossed circles are 35 GHz data [14] for the spin-liquid phase at $T=1.0$ K. Other symbols correspond to $T=0.5$ K. Solid line presents calculation of the continuum boundaries at the wave vector $q_D$ following Ref. [15]. Lower panel: Ratio of amplitudes of the doublet components $u_{A^{\prime }}/u_A$ vs resonance field of A component. Dashed lines in both panels are guides to the eyes.

Figure 4

Frequency-field diagram of ESR response in ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ with magnetic field along the $a$ axis $(T=0.5$ K). Data presented by symbols $▵,◊,\blacksquare$ are taken by use of the waveguide unit, $▿,◯,\square$ by resonator unit. The solid line presents the Larmor frequency $f_0$ (see text). Dashed line is the Larmor frequency downshifted for 119 GHz.

Figure 5

Temperature evolution of line B at the frequency 197 GHz and $\mathbf{H}\parallel b$. Solid lines are Lorenz fits for experimental curves.

Figure 6

Upper panel: Temperature-induced shift of the resonance fields of line B at the frequency 197 GHz, $\mathbf{H}\parallel b$. The reference field ${\mu }_0{H}_{B0}=11$ T is the ESR field for mode B at $T=0.5$ K. Solid line presents the theoretical calculation according to relation (3). Lower panel: Temperature dependence of the integral intensity (triangles) and linewidth (squares) of mode B at 197 GHz. Dashed lines are guides to the eyes.

Figure 7

Sketch of the exchange paths of ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ within a $bc$ layer. Large circles mark Cu ions. $J$ and $J^{\prime }$ are exchange integrals for two kinds of bonds. ${\mathbf{D}}_{1,2}$ and ${\mathbf{D}}_{1-4}^{\prime }$ are Dzyaloshinsky-Moriya vectors according to Ref. [4]. Out-of-plane components of vectors are marked by points and crosses. Translations ${\delta }_{1,2}$ are periods for exchange bond structure.