We present de Haas-van Alphen ͑dHvA͒ measurements on high-mobility two-dimensional electron systems formed in modulation-doped Si/ SiGe ͑100͒ quantum wells and demonstrate directly the manifestation of the valley splitting in the magnetization. We resolve sawtoothlike magnetization oscillations at even filling factors which reflect the Landau quantization and the spin splitting of Landau levels in the electronic energy spectrum. At odd filling factors we observe the lifting of the valley degeneracy in Si at high magnetic field. The magnetization is a thermodynamic quantity that at low temperature reflects the ground-state energy of the interacting electron system. We can thus determine quantitatively the energetic splitting of the two occupied conduction-band valleys directly from the oscillation amplitude. Both valley and spin splitting are found to be enhanced by electron-electron interactions. The energy gap due to valley splitting is found to be ജ0.8 meV at high perpendicular field B Ќ . From studies in tilted magnetic fields we find that the valley splitting is governed solely by B Ќ . From the spin splitting we recalculate an enhanced g factor g * = 2.9 at = 2 including the influence of disorder. This is significantly larger than the band-structure g factor of 2 in Si. We have successfully applied the coincidence technique for the dHvA effect and thus obtained a complementary means to determine the g factor. It yields a constant value g * Х 3.2 for filling factors ജ 10. A detailed analysis of the magnetization traces enabled us also to determine quantitatively the residual level broadening ⌫ in this highmobility Si/ SiGe system. We obtain a small value of ⌫ = 0.15 meVϫ B Ќ ͓T͔ 1/2 for the Si/ SiGe heterostructure of 200 000 cm 2 / ͑V s͒ mobility at 0.3 K.

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We have fabricated highly sensitive micromechanical cantilever magnetometers and, by this means, investigated the de Haas-van Alphen effect of a two-dimensional electron system in a modulation-doped Si/SiGe heterostructure. As a function of perpendicular magnetic field component B ⊥ we observe at low temperature sawtooth-like oscillations of the magnetization M. These are found at even integer filling factors ν = n s /(eB ⊥ /h) = 4(N + 1) with N = 0, 1, 2..., when the chemical potential is in the Landau energy gap, and at ν = (4N + 2) where the spin splitting of the Landau levels occurs. In particular, we also observe oscillations at odd ν where the valley degeneracy is lifted. This signal increases significantly with B ⊥. We discuss our findings in the framework of electron-electron interaction in the presence of disorder.