$\mu^+$SR study of spin dynamics in the one dimensional Heisenberg antiferromagnet Cu(pyz)(NO$_3$)$_2$

We present the results of longitudinal-field muon spin relaxation ($\mu^+$SR) measurements on the one-dimensional quantum Heisenberg antiferromagnet (1DQHAF) Cu(pyz)(NO$_3$)$_2$ (pyz=pyrazine). The intrachain coupling strength $J/k_{\mathrm{B}}$ in this compound is 10.6 K and the ordering temperature $T_{\mathrm{N}}$ is 0.11 K. Spin dynamics were studied with $\mu^+$SR using applied longitudinal fields at two temperatures ($T$=0.33 K and 1.4 K) between $T_{\mathrm{N}}$ and $J/k_{\mathrm{B}}$. For $B>5$ mT, the nuclear contribution to the relaxation rate is quenched and the data can be fitted to an exponential decay along with a background correction. The relaxation rate $\lambda$ was found to follow a $\lambda\propto B^{-1/2}$ power law between 10 mT and 100 mT at both temperatures, suggesting diffusive spin transport of excitations in this 1DQHAF.