Optical control of spins in condensed matter systems such as semiconductor nanostructures requires precise knowledge of the polarization properties of the associated optical transitions subject to an external magnetic field. Here, we demonstrate that coherent optical spectroscopy in the form of photon echoes can be successfully used to evaluate the magnetic anisotropies of valence-band states. It manifests in drastic changes of the transient signals when the orientation of the magnetic field with respect to the crystallographic axes is varied. In particular, we use the two-pulse spin-dependent photon echo to study the in-plane hole spin anisotropy in a 20-nm-thick CdTe/Cd_{0.76}Mg_{0.24}Te single quantum well by exciting the donor-bound exciton resonance. We take advantage of the photon echo sensitivity to the relative phase of the electron and hole spin precession in the ground and excited states, respectively, and study various interactions contributing to the hole in-plane spin properties. The main contribution is found to arise from the crystal cubic symmetry described by the Luttinger parameter q=0.095±0.005, which is substantially larger than the one theoretically expected for CdTe or found in other quantum well structures. Another contribution is induced by the strain within the quantum well. These two contributions lead to different harmonics of the spin precession frequencies in the photon echo experiment, when the strength and orientation of the Voigt magnetic field are varied. The magnitude of the effective in-plane hole g factor is found to vary in the range |g_{h}[over ̃]|=0.125–0.160 in the well plane.
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