${}_{}{}^{17}{}_{}{}^{}O$ NMR Study of $\mathit{q}=0\mathrm{}$ Spin Excitations in a Nearly Ideal $\mathit{S}=\frac{1}{2}$ 1D Heisenberg Antiferromagnet, ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$, up to 800 K

We used ${}^{17}\mathrm{O}$ NMR to probe the uniform (wave vector $q=0\mathrm{}$) electron spin excitations up to 800 K in ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$ and separate the $q=0\mathrm{}$ from the $q=\pm \frac{\pi }{a}$ staggered components. Our results support the logarithmic decrease of the uniform spin susceptibility below $T\sim 0.015J$, where $J=2200\mathrm{}\mathrm{K}$. From measurement of the dynamical spin susceptibility for $q=0\mathrm{}$ by the spin-lattice relaxation rate ${1/T}_1$, we demonstrate that the $q=0\mathrm{}$ mode of spin transport is ballistic at the $T=0\mathrm{}$ limit, but has a diffusion-like contribution at finite temperatures even for $T\ll J$.