Negative magnetoresistance in p -type β−FeSi2 single crystals in two regimes of variable-range hopping

Single crystals of $p$-type $\ensuremath{\beta}$-FeSi${}_{2}$ demonstrate the negative magnetoresistance below 40 K that increases with decreasing temperature and does not reach either a maximum or a saturation up to at least 12 kOe. This effect is observed in both the Mott and the Shklovskii-Efros variable-range hopping regimes. At fields below approximately 3--5 kOe (depending on the temperature) the magnetoresistance displays a quadratic dependence on the magnetic field, while at higher fields the dependence is linear. The experimental data are analyzed using two different approaches to the interference effects in hopping conductivity in a magnetic field.