Electron-spin resonance in the two-dimensional electron gas of GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures

Electron-spin resonance affects the magnetoresistivity of GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures. With microwave frequencies of up to 70 GHz we studied systematically the spin splitting of the Landau levels in magnetic fields up to 14.5 T. The resonances within a certain Landau level are only observed at magnetic field values where the Fermi level is located between the corresponding spin levels. The spin splitting of a Landau level is an exact quadratic function of the magnetic field and its extrapolation to zero magnetic field leads to vanishing spin splitting. The g factors depend on the magnetic field and the Landau level index as follows: g(B,N)=$g_0$-c(N+(1/2)B, where $g_0$ and c are sample-dependent constants.