A new method of four-wave-mixing spectroscopy in GaAs quantum wells reveals spectral hole burning due to spin relaxation of magnetoexcitons. The measurements resolve the Zeeman doublet of the lowest-energy heavy-hole exciton where the doublet splitting is much less than the exciton inhomogeneous width. The Zeeman splitting depends nonlinearly on the magnetic field and is small compared with that of bulk GaAs. The results reflect effects of the complex band structure of quantum wells. Information on exciton spin relaxation is also provided by the hole-burning measurements.The electronic energy spectrum of quantum well structures is fully quantized under a magnetic field parallel to the growth axis. Optical absorption reveals a ladder of magnetoexcitons corresponding to transitions between electron and hole Landau levels [1]. Magnetic fields also lift the Kramers degeneracy with the resultant Zeeman splitting depending on details of the band structure. The removal of this degeneracy is also expected to lead to a substantial increase of the spin relaxation time between Zeeman-split Landau levels since now spin relaxation can only take place via inelastic processes.The electron g factor in GaAs heterostructures has been extensively studied. Earlier magnetotransport measurements have shown large exchange-induced enhancement of the electron g [2]. Recent electron-spinresonance studies have revealed the magnetic field dependence of the electron g for different Landau levels [3]. These results were explained in terms of the nonparabolicity of the conduction band [4]. Determination of the exciton Zeeman splitting has proven to be more elusive [5][6][7]. Earlier magnetoreflectance measurements were able to resolve Zeeman splittings for the light-hole but not the heavy-hole exciton [5]. More recent measurements have inferred the exciton g from nonlinear quantum-beat spectroscopy [6]. A precise determination of the exciton Zeeman splitting in a quantum well using linear optical spectroscopy is difficult since interface disorder leads to exciton localization and subsequent inhomogeneous broadening of the absorption profile [8]; the resultant inhomogeneous broadening varies from 1 meV to several meV, much larger than the splitting in moderate fields.A related area is relaxation of carrier and exciton spins in semiconductor heterostructures. Polarization-dependent measurements of interband optical transitions have shown an interesting dependence of spin relaxation on growth conditions, carrier confinement, and temperature [9]. Various physical mechanisms for spin relaxation have also been discussed [9,10]. In addition, luminescence measurements at high magnetic fields have revealed a much larger spin relaxation time due to the full quantization of the energy spectrum [11].In this paper, we report frequency-domain nonlinear optical studies of exciton Zeeman splitting and spin relaxation in GaAs quantum wells. Using selective optical excitation and nonlinear optical methods similar to spectral hole burning (SHB, also referred to ...