Low-Temperature Dynamics of Magnons in a Spin-$1/2$ Ladder Compound

We have used a combination of neutron resonant spin-echo and triple-axis spectroscopies to determine the energy, fine structure, and linewidth of the magnon resonance in the model spin-$1/2$ ladder antiferromagnet $\mathrm{IPA}\mathrm{\text{−}}{\mathrm{CuCl}}_3$ at temperatures $T\ll {\Delta }_0/k_B$, where ${\Delta }_0$ is the spin gap at $T=0$. In this low-temperature regime we find that the results deviate substantially from the predictions of the nonlinear sigma model proposed as a description of magnon excitations in one-dimensional quantum magnets and attribute these deviations to real-space and spin-space anisotropies in the spin Hamiltonian as well as scattering of magnon excitations from a dilute density of impurities. These effects are generic to experimental realizations of one-dimensional quantum magnets.

Figure 1

(a) Schematic view of the $a\mathrm{\text{−}}c$ plane of $\mathrm{IPA}\mathrm{\text{−}}{\mathrm{CuCl}}_3$. The red balls represent spin-$1/2$ ${\mathrm{Cu}}^{2+}$ ions, the arrows show the dominant exchange interactions as discussed in the text. (b) Color plot of the magnon dispersion from Ref. 16.

Figure 2

Neutron beam polarization as a function of spin-echo time measured at $T=0.5\mathrm{K}$ at the bottom of the magnon dispersion at $\mathbf{q}=(0.5,0,0)$. The line is the result of a fit to three Lorentzian modes. The inset shows the spectrum extracted from the fit.

Figure 3

Temperature dependence of the $S^z=0$ magnon line width $\Gamma$. Red (light) symbols are results of the current NRSE-TAS study. Blue (dark) symbols are TAS results from Ref. 12 assuming one Lorentzian mode only. The line represents $\mathrm{NL}\sigma \mathrm{M}$ calculations [4] with ${\Delta }_0=1.44\mathrm{meV}$. Below $T=5\mathrm{K}$, the magnon modes are significantly broadened relative to the theoretical predictions. The inset shows the temperature dependence of $\Gamma$ over a broad temperature range.

Figure 4

Magnon gap energy as a function of temperature. Red (light) symbols are the current NRSE-TAS results. Blue (dark) symbols mark data points from Ref. 12. The red dotted and green dashed lines are results of the $1\mathrm{D}\mathrm{\text{−}}\mathrm{NL}\sigma \mathrm{M}$ with ${\Delta }_0=0.87\mathrm{meV}$ and ${\Delta }_0=1.17\mathrm{meV}$ respectively. The blue line is the result of a calculation based on a $\mathrm{NL}\sigma \mathrm{M}$ with ${\Delta }_0=1.44\mathrm{meV}$ and interladder interaction $J_{\perp }/J=0.1$, following Ref. 25 as described in the text. The inset shows a blowup of the NRSE-TAS data set at low temperatures. Note the small ($\sim 8\mu \mathrm{eV}$) dip at $T=2\mathrm{K}$.