Negative Magnetoresistance of Neutron‐Transmutation‐Doped Gallium Arsenide at Variable‐Range Hopping

Investigations of anomalous magnetoresistance (mr) in neutron‐transmutation‐doped GaAs are performed at T = 0.05 to 4.2 K in the vicinity of the metal–insulator transition (MIT). Without as well as with magnetic field a variable‐range hopping‐law ϱ( T ) = ϱ 0 exp ( T 1 / T ) 1/2 is found with T 1 → 0 at n → n c . At low magnetic field a negative mr and for the first time T 1 ( H ) < T 1 (0) is found. At higher magnetic fields the negative mr saturates and eventually changes into a positive mr with T 1 ( H ) > T 1 (0). The dependence of T 1 on n as well as on H originates from the scaling behaviour of the localization radius a and the dielectric constant ϵ 0 at the MIT. From the extrapolation of the T 1 ‐curves versus n ( T = 300 K) to zero without and with magnetic field n c ( H ) is determined. In the range of negative mr no shift of n c with H is found. For positive mr, however, n c ( H ) > n c (0) = 2.18 × 10 16 cm −3 is obtained. The scaling behaviour of the conductivity of barely metallic samples extrapolated to T = 0 gives for the critical index v = 0.84 ± 0.05. The comparison of v with the critical index b for the scaling relation of T 1 gives the critical index ξ for the dielectric constant ξ = 1.55 and ξ/ν = 1.94.