${}^{11}$B and ${}^{27}$Al NMR spin-lattice relaxation and Knight shift study of Mg${}_{1-x}$Al${}_x$B${}_2$. Evidence for anisotropic Fermi surface

We report a detailed study of ${}^{11}$B and ${}^{27}$Al NMR spin-lattice relaxation rates ($1\mathrm{/}{T}_1$), as well as of ${}^{27}$Al Knight shift (K) of Mg${}_{1-x}$Al${}_x$B${}_2$, $0\le x\le 1$. The obtained ($1\mathrm{/}{T}_{1}T$) and K vs. x plots are in excellent agreement with ab initio calculations. This asserts experimentally the prediction that the Fermi surface is highly anisotropic, consisting mainly of hole-type 2-D cylindrical sheets from bonding $2p_{x,y}$ boron orbitals. It is also shown that the density of states at the Fermi level decreases sharply on Al doping and the 2-D sheets collapse at $x\approx 0.55$, where the superconductive phase disappears.