The spin-dependent tunnelling of two-dimensional electrons through a magnetic barrier can be substantially enhanced by the addition of an electric barrier. The spin polarization is found to be strongly dependent on the incident wave vector parallel to the barrier, the incident electron energy, and the height of the electric barrier. The conductance for the spin-up and spin-down electrons can be tuned with this electrical barrier.

Scanning gate experiments on a two-dimensional electron gas in the regime of the classical Hall effect are presented. The Hall resistance is recorded while tuning the local potential by applying a voltage to the metallic tip of a scanning force microscope. In diffusive samples and at zero magnetic field an intriguing Hall resistance pattern arises that is attributed to tip-induced inhomogeneous current flow. Measurements at small, i.e., nonquantizing, magnetic fields reveal an additional Hall resistance pattern due to the tip-induced inhomogeneous electron density in the Hall cross. Deviations of the measurements on higher-mobility samples from expectations based on symmetry arguments are used to distinguish the diffusive from the mesoscopic transport regime. Finite-element-method modeling for the diffusive regime and trajectory calculations for ballistic electrons allow a concise interpretation of the measurements.

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The temperature-dependent giant magnetoresistance effect is investigated in a magnetically modulated two-dimensional electron gas, which can be realized by depositing two parallel ferromagnets on the top and bottom of a heterostructure. The effective potential for electrons arising for parallel magnetization allows the electrons to resonantly tunnel through the magnetic barriers, while this is excluded in the anti-parallel situation. Such a discrepancy results in a giant magnetoresistance ratio (MRR), which can be up to 1031%. The MRR shows a strong dependence on temperature, but our study indicates that for realistic parameters for a GaAs heterostructure the effect can be as high as 104% at 4 K.