Muon-spin relaxation measurements on the dimerized spin-1/2 chains NaTiSi2O6 and TiOCl

We report muon spin relaxation $(\ensuremath{\mu}\mathrm{SR})$ and magnetic susceptibility investigations of two ${\mathrm{Ti}}^{3+}\phantom{\rule{0.3em}{0ex}}(S=1∕2)$ chain compounds, $\mathrm{Na}\mathrm{Ti}{\mathrm{Si}}_{2}{\mathrm{O}}_{6}$ and TiOCl, each of which exhibits a spin gap at low temperature. From these we conclude that the spin gap in $\mathrm{Na}\mathrm{Ti}{\mathrm{Si}}_{2}{\mathrm{O}}_{6}$, which arises from orbital ordering at ${T}_{\mathrm{O}\mathrm{O}}=210\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, is temperature independent below ${T}_{\mathrm{O}\mathrm{O}}$, with a value of $2\ensuremath{\Delta}=700(100)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. In TiOCl, we find thermally activated spin fluctuations corresponding to a spin gap $2\ensuremath{\Delta}=440(60)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ below ${T}_{c1}=67\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. We can describe both the $\ensuremath{\mu}\mathrm{SR}$ and susceptibility data in terms of a model based on the dimerization of the ${\mathrm{Ti}}^{3+}$ chains. We also compare the methods used to extract the spin gap and the concentration of free spins within the samples from $\ensuremath{\mu}\mathrm{SR}$ and magnetic susceptibility data.