Dzyaloshinsky-Moriya interaction in the $S=\frac{1}{2}$ quasi-one-dimensional antiferromagnet ${\text{Cu}}_2{\text{Cl}}_4\cdot {\text{H}}_8{\text{C}}_4{\text{SO}}_2$ as determined via high-frequency ESR

High-frequency ESR measurements have been performed on the $S=\frac{1}{2}$ quasi-one-dimensional antiferromagnet ${\text{Cu}}_2{\text{Cl}}_4\cdot {\text{H}}_8{\text{C}}_4{\text{SO}}_2$ in the frequency range up to 360 GHz and the field range up to 12 T. Reflecting the small alternation of exchange interaction along the chain direction, very peculiar temperature dependences of $g$ value and linewidth are observed. Moreover, we have observed the direct transition between the singlet ground state and triplet excited states in ${\text{Cu}}_2{\text{Cl}}_4\cdot {\text{H}}_8{\text{C}}_4{\text{SO}}_2$ at $T=1.7\text{K}$ and determined the excitation gap (for $c$ axis) $\Delta /k_{\text{B}}=7.9\pm 0.4\text{K}$. Considering the observed anisotropic nature of the direct transition and applying the selection rules of the direct transition proposed by Sakai [J. Phys. Soc. Jpn. 72, Suppl. B 53 (2003)], we have come to the conclusion that the direct transition is caused by the Dzyaloshinsky-Moriya interaction and are able to determine the $D$ vector in ${\text{Cu}}_2{\text{Cl}}_4\cdot {\text{H}}_8{\text{C}}_4{\text{SO}}_2$ as $D_{a^{\ast }}:D_b:D_c=1.0:0.0:2.3\pm 0.1$.

Figure 1

Temperature dependence of ESR spectra observed at 240 GHz for $B\parallel c$ axis. The sharp absorption line is the DPPH signal, which is the standard of $g=2$. Arrows indicate the direct transition.

Figure 2

Temperature dependence of (a) the magnetic susceptibility, (b) the $g$ value, and (c) the linewidth for $B\parallel c$ axis.

Figure 3

Typical ESR spectra at $T=1.7\text{K}$ for $B\parallel a^{\ast }$, $B\parallel b$, and $B\parallel c$ axes. The sharp absorption line is the DPPH signal.

Figure 4

Frequency-field diagram at $T=1.7\text{K}$ for $B\parallel c$ axis. The solid lines are the fitting. The inset shows a schematic energy diagram of spin-gap system under the magnetic field. $|S,S^z⟩$ is the wave function with the spin quantum number $S$ and the $z$ component of spin quantum number $S^z$. The arrows mean the direct transition between the singlet ground state and triplet excited states in gapped spin systems.