Elementary excitations of theS=12one-dimensional antiferromagnetKCuGaF6in a magnetic field and quantum sine-Gordon model

Abstract

Elementary excitations of the $S=\frac{1}{2}$ one-dimensional Heisenberg antiferromagnet ${\text{KCuGaF}}_{6}$ with exchange constant $J/{k}_{B}=103\text{ }\text{K}$ were investigated by high-frequency electron spin resonance (ESR) measurements combined with a pulsed high magnetic field. When an external magnetic field $H$ is applied in ${\text{KCuGaF}}_{6}$, a staggered magnetic field $h$ is induced perpendicular to $H$ owing to the staggered $\mathbit{g}$ tensor and the Dzyaloshinsky-Moriya (DM) interaction with an alternating $\mathbit{D}$ vector. Consequently, ${\text{KCuGaF}}_{6}$ in a magnetic field is represented by the quantum sine-Gordon (SG) model. We observed many resonance modes including a soliton resonance, breathers, interbreather transitions, and two-breather excitation. Their resonance conditions are beautifully described by the quantum SG field theory with one adjustable parameter ${c}_{s}=h/H$. To investigate the relationship between the Curie term due to the DM interaction and the proportionality coefficient ${c}_{s}$, magnetic susceptibility measurements were also performed varying the external field direction.