Electron spin resonance modes in a strong-leg ladder in the Tomonaga-Luttinger liquid phase

Magnetic excitations in the strong-leg quantum spin ladder compound ${\left({\mathrm{C}}_7{\mathrm{H}}_{10}\mathrm{N}\right)}_2{\mathrm{CuBr}}_4$ (known as DIMPY) in the field-induced Tomonaga-Luttinger spin-liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual nonlinear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact-diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe their ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

Figure 1

Schematic view of the crystal structure of DIMPY [36]. The copper (Cu) ions form a ladderlike structure with the dominant exchange couplings indicated in the figure.

Figure 2

Left panel: Examples of ESR spectra obtained at a frequency of 324 GHz at 1.5, 2, 2.8, and 4.6 K. Right panel: Examples of pulsed-field ESR spectra obtained at the frequencies 189, 235, 280, and 314 GHz ($T=1.5$ K).

Figure 3

(a) Temperature dependence of the line-width of mode B at a frequency of 328.8 GHz. (b) Linewidth of mode B for different resonance fields ($T=1.5$ K). Lines are guides to the eye.

Figure 4

The frequency-field diagram of magnetic excitations in DIMPY. Data of the structure factors $S_{\pi }^{zz}$ and $S_0^{\pm }$ obtained by use of exact-diagonalization calculations for chains from $N=32$ to $N=64$ sites are given in bright colors [46]. Blue and red solid lines are guides to the eye. The first and second critical fields are denoted by vertical dashed lines.