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

We report the results of muon-spin spectroscopy (${\mu }^{+}$SR) measurements on the staggered molecular spin chain [pym-Cu(NO${}_3$)${}_2$(H${}_2$O)${}_2$] (pym = pyrimidine), a material previously described using sine-Gordon field theory. Zero-field ${\mu }^{+}$SR reveals a long range magnetically-ordered ground state below a transition temperature $T_{\mathrm{N}}=0.22(1)$ K. Using longitudinal-field (LF) ${\mu }^{+}$SR we investigate the dynamic response in applied magnetic fields $0<B<500$ mT and find evidence for ballistic spin transport. Our LF ${\mu }^{+}$SR measurements on the chiral spin chain [Cu(pym)(H${}_2$O)${}_4$]SiF${}_6\cdot$H${}_2$O instead demonstrate one-dimensional spin diffusion and the distinct spin transport in these two systems likely reflects differences in their magnetic excitations.