Abstract
We study the spin-split de Haas--van Alphen oscillations in two-dimensional (2D) conductors whose density of states (DOS) is made of two parts: one is a set of sharp Landau levels and another is a DOS unaffected by the magnetic field. We call the latter the background DOS and denote it by ${\ensuremath{\rho}}_{\mathrm{BG}}.$ We report the analytical formula for the spin factors of all the harmonic components at absolute zero temperature; the formula is valid for any ${\ensuremath{\rho}}_{\mathrm{BG}}$ and for any g value of the quantized band. The obtained spin factors, in particular the ones of the higher-harmonic components, depend complicatedly on ${\ensuremath{\rho}}_{\mathrm{BG}}$ and g, and differ drastically from those in the Lifshitz-Kosevich formula: the values of g (or the magnetic field angles) for which the spin factors become zero vary with ${\ensuremath{\rho}}_{\mathrm{BG}}.$
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