Excitation Hierarchy of the Quantum Sine-Gordon Spin Chain in a Strong Magnetic Field

The magnetic excitation spectrum of copper pyrimidine dinitrate, a material containing $S=\frac{1}{2}$ antiferromagnetic chains with alternating $g$ tensor and the Dzyaloshinskii-Moriya interaction and exhibiting a field-induced spin gap, is probed using submillimeter wave electron spin resonance spectroscopy. Ten excitation modes are resolved in the low-temperature spectrum, and their frequency-field diagram is systematically studied in magnetic fields up to 25 T. The experimental data are sufficiently detailed to make a very accurate comparison with predictions based on the quantum sine-Gordon field theory. Signatures of three breather branches and a soliton, as well as those of several multiparticle excitation modes, are identified.

Figure 1

The frequency-field dependence of the ESR modes in Cu-PM at $T=1.6\mathrm{K}$. Symbols denote the experimental results, and lines correspond to contributions from specific excitations as predicted by the sine-Gordon theory (see text for details).

Figure 2

The ESR transmission spectra in Cu-PM, taken in the Faraday configuration at a frequency of $429.3\mathrm{G}\mathrm{H}\mathrm{z}$ at $T=1.6\mathrm{K}$ (for explanations, see text). 2,2-Diphenyl-1-picrylhydrazyl (DPPH) was used as a marker.

Figure 3

A schematic view of low-energy excitations contributing to the transverse (left panel) and longitudinal (right panel) dynamic susceptibilities; $\overline{S}$ ($S$) denotes (anti)solitons and $B$ labels denote breathers.