We report the results of muon-spin spectroscopy $\left({\mu }^{+}\mathrm{SR}\right)$ measurements on the staggered molecular spin chain [pym-$\mathrm{Cu}{\left({\mathrm{NO}}_3\right)}_2{\left({\mathrm{H}}_2\mathrm{O}\right)}_2]$ (pym = pyrimidine), a material previously described using sine-Gordon field theory. Zero-field ${\mu }^{+}\mathrm{SR}$ reveals a long range magnetically ordered ground state below a transition temperature $T_{\mathrm{N}}=0.23\left(1\right)$ K. Using longitudinal-field (LF) ${\mu }^{+}\mathrm{SR}$ we investigate the dynamic response in applied magnetic fields $0<B<500$ mT and find evidence for ballistic spin transport. Our LF ${\mu }^{+}\mathrm{SR}$ measurements on the chiral spin chain $\mathrm{[}\mathrm{Cu}\left(\mathrm{pym}\right){\left({\mathrm{H}}_2\mathrm{O}\right)}_4]{\mathrm{SiF}}_6·{\mathrm{H}}_2\mathrm{O}$ 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.

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• Antiferromagnetism
• Magnetism
• 1-dimensional spin chains
• Density functional theory
• Muon spin relaxation & rotation