Magnetic order and ballistic spin transport in a sine-Gordon spin chain

We report the results of muon-spin spectroscopy $({\ensuremath{\mu}}^{+}\mathrm{SR})$ measurements on the staggered molecular spin chain [pym-$\mathrm{Cu}{({\mathrm{NO}}_{3})}_{2}{({\mathrm{H}}_{2}\mathrm{O})}_{2}]$ (pym = pyrimidine), a material previously described using sine-Gordon field theory. Zero-field ${\ensuremath{\mu}}^{+}\mathrm{SR}$ reveals a long range magnetically ordered ground state below a transition temperature ${T}_{\mathrm{N}}=0.23(1)$ K. Using longitudinal-field (LF) ${\ensuremath{\mu}}^{+}\mathrm{SR}$ we investigate the dynamic response in applied magnetic fields $0lBl500$ mT and find evidence for ballistic spin transport. Our LF ${\ensuremath{\mu}}^{+}\mathrm{SR}$ measurements on the chiral spin chain $\mathrm{[}\mathrm{Cu}(\mathrm{pym}){({\mathrm{H}}_{2}\mathrm{O})}_{4}]{\mathrm{SiF}}_{6}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$ instead demonstrate one-dimensional spin diffusion, and the distinct spin transport in these two systems suggests that additional anisotropic interactions play an important role in determining the nature of spin transport in $S=1/2$ antiferromagnetic chains.