Temperature-dependent23NaKnight shifts and sharply peaked structure in the electronic densities of states of Na-Si clathrates

We have measured the temperature and frequency dependences of large (1600–2000 ppm) shifts in the ${}^{23}\mathrm{Na}$ NMR frequencies observed for sodium atoms encapsulated in silicon cages of three clathrate compounds: ${\mathrm{Na}}_x@{\mathrm{Si}}_{136},$ ${\mathrm{Na}}_x@{\mathrm{Si}}_{46},$ and $(\mathrm{N}\mathrm{a},\mathrm{B}\mathrm{a}{)}_x@{\mathrm{Si}}_{46}$ $(7\mathrm{}<~x<~9).$ Sample temperature was varied between 77 and 500 K and two values of NMR spectrometer operating frequency were employed, near 79.4 and 23.8 MHz. The shifts in ${\mathrm{Na}}_x@{\mathrm{Si}}_{136}$ and ${\mathrm{Na}}_x@{\mathrm{Si}}_{46}$ decrease strongly with increasing temperature from 140 to 500 K and show activated temperature dependences in this region. Activation energies range from 37 to 105 meV and values differ for each of the two cage sizes present (large and small) in each compound. Below 140 K the NMR shift for Na in the small cages of ${\mathrm{Na}}_x@{\mathrm{Si}}_{136}$ changes its temperature behavior, decreasing as $T$ is lowered to 77 K, while the large-cage shift continues its increase. Shifts in this compound are proportional to the NMR frequency, showing that their origin is magnetic. In the mixed $(\mathrm{N}\mathrm{a},\mathrm{B}\mathrm{a}{)}_x@{\mathrm{Si}}_{46}$ clathrate the position of the ${}^{23}\mathrm{Na}$ line is shifted by 1205 ppm, independent of temperature from 300 to 500 K. We interpret all shifts as Knight shifts arising from delocalized electrons, the novel activated temperature dependences in the pure-Na compounds being due to two sharp peaks in the density of states that lie within $\sim k_{B}T$ of the Fermi level. Band-structure calculations reveal such peaks and show that the Fermi level varies little with temperature, remaining within the lower-lying peak that is associated with the presence of Na atoms in the clathrate cages. The calculations also yield estimates of average peak separations, which may be compared with the experimental activation energies.