H−Impurity States and Nuclear Magnetic Relaxation

It is shown that a hydrogenic impurity will bind a second electron in high magnetic fields, because of contraction of the electron wave functions about the lattice sites. The binding energy of the second electron exceeds $\mathrm{kT}$ for semiconductors at helium temperatures when $\gamma =\frac{\hslash {\omega }_c}{2} \mathrm{Ry}\gg 1$. This ${\mathrm{H}}^{-}$ ion may then provide a new density of states $g^{+}\mathrm{}\left(E\right)\mathrm{}$ for electrons with spin "up" ($\sigma =1\mathrm{}$). Nuclei which relax by mutual spin-flip processes with conduction electrons have a relaxation rate $\frac{1}{T_1}$ proportional to $g^{+}\mathrm{}\left(E\right)\mathrm{}$. In the last Landau state $n=0\mathrm{}$, $\sigma =-1\mathrm{}$, the conduction electron $g^{+}\mathrm{}\left(E\right)\mathrm{}$ vanishes so the additional $g^{+}\mathrm{}\left(E\right)\mathrm{}$ from the ${\mathrm{H}}^{-}$ state can produce a large change in $T_1$. The magnitude of this effect is estimated for InSb and comparison is made with the experiments of Bridges and Clark, with some success. Alternative explanations involving plasma modes are investigated and found wanting. The presence of ${\mathrm{H}}^{-}$ impurities in concentrations on the order of one-tenth of the conduction electron concentration may also affect the negative magnetoresistance and the theory of scattering from localized spins.