Two-dimensional electron gas under a spatially modulated magnetic field: A test ground for electron-electron scattering in a controlled environment

We have studied the electronic transport in a two-dimensional electron gas (2DEG) subjected to a spatially modulated magnetic field and electrostatic potential. Independent control of the magnetic field components parallel and perpendicular to the 2DEG plane allows us to manipulate the amplitude of the magnetic modulation independently of the normal field component relevant to the magnetotransport in the 2DEG. The amplitudes of the magnetic and electrostatic modulations can be evaluated from an analysis of the commensurability oscillation of magnetoresistance. The increase of resistivity in the presence of a modulated magnetic field at a zero uniform magnetic field is found to be quadratic in the modulation amplitude and to vary as ${\mathrm{AT}}^2+C$ at low temperatures. This is a signature of the electron-electron scattering in the presence of a spatially modulated magnetic field. The present system provides an ideal test ground for theories of electron-electron-scattering-induced resistivity.