Negative magnetoconductance in an Anderson insulator with strong spin-orbit scattering

We have measured the magnetoconductance of amorphous ${\mathrm{Y}}_{\mathit{x}}$ ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ samples in the diffusive, barely, and deeply insulating regimes. Application of a magnetic field decreases the localization length ξ in the barely insulating regime where spin-orbit scattering (SOS) is important. In an insulator without SOS, we see an increase of ξ, indicating that spin-reversal symmetry and time-reversal symmetry control the magnetoconductance in the barely insulating regime, in contrast with predictions obtained by directed-path approximations.