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

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.

Figure 1

(a) Example ZF spectra above and below the magnetic ordering temperature of Cu-PM. (b) Temperature dependence of the (left axis) precession frequencies and (right axis) initial asymmetry.

Figure 2

Low-energy muon sites in Cu-PM. Lighter spheres represent the ionic positions in the unit cell without the muon. H atoms have been omitted for clarity where appropriate. (a) The nitrate site. (b) The ${\mathrm{H}}_2\mathrm{O}$ site. (c) the N(pym) site.

Figure 3

(a) Field dependence of the LF relaxation rate in Cu-PM at $T=1.6$ K with fits appropriate for either diffusive or ballistic spin transport. (b) Field dependence of relaxation rate and fits describing ballistic spin transport. Field dependence of the LF relaxation rate for $\mathrm{[}\mathrm{Cu}\left(\mathrm{pym}\right){\left({\mathrm{H}}_2\mathrm{O}\right)}_4]{\mathrm{SiF}}_6·{\mathrm{H}}_2\mathrm{O}$ at (c) $T=5$ K, (d) $T=10$ K, and (e) $T=100$ K, with fits to Eq. (2).