Transient Nuclear Magnetic Resonance Study of the Conduction Band of MetallicNaxWO3:Na23Relaxation

The spin-lattice relaxation time $T_1$ of the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ nuclear magnetization in the cubic sodium-tungsten bronzes ${\mathrm{Na}}_x\mathrm{W}{\mathrm{O}}_3$ has been measured as a function of $x$ value (0.56-0.89) and temperature (1.4-298°K). There is evidence that more than 10% of the sodium nuclei aggregate into sodium-vacancy-free ($x=1\mathrm{}$) regions. The temperature dependence of the data shows that the relaxation rate of ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ nuclei outside the vacancy-free regions is determined largely by a conduction-electron mechanism at 20 and 76°K, but that a quadrupolar mechanism becomes important at 298°K and spin diffusion to paramagnetic impurities begins to limit $T_1$ at 4°K. For $x=0.73\mathrm{}$, $T_{1}T=74\mathrm{}$ min-°K for conduction-electron relaxation, $T_1=18\mathrm{}$ min for spin-diffusion-limited paramagnetic-impurity relaxation, and $T_1=7.7\mathrm{}$ sec at 298°K for quadrupolar relaxation. The relaxation rate for the conduction-electron mechanism does not vary markedly with $x$ value; the relaxation rates for the quadrupolar and paramagnetic-impurity mechanisms tend to decrease with increasing $x$ value. The measured value of the conduction-electron contribution to the sodium nuclear relaxation is combined with an estimate of $T_1$ for relaxation through sodium $3p$ conduction electrons to give a conservative upper limit estimate of 33% for the density of sodium states at the Fermi surface.