Direct determination of zero-field splitting for single Co$^{2+}$ ion embedded in a CdTe/ZnTe quantum dot

When Co$^{2+}$ impurity is embedded in semiconductor structure, crystal strain strongly influences zero-filed splitting between Co$^{2+}$ states with spin projection $S_z = \pm 3/2$ and $S_z = \pm 1/2$. Experimental evidences of this effect have been given in previous studies, however direct measurement of the strain induced zero-field splitting has been inaccessible so far. Here this splitting is determined thanks to magneto-optical studies of individual Co$^{2+}$ ion in epitaxial CdTe quantum dot in ZnTe barrier. Using partially allowed optical transitions we measure strain induced zero-field splitting of Co$^{2+}$ ion directly on excitonic photoluminescence spectrum. Moreover, by observation of anticrossing of $S_z = + 3/2$ and $S_z = - 1/2$ Co$^{2+}$ spin states in magnetic field, we determine axial and in-plane components of crystal field acting on Co$^{2+}$. Proposed technique can be applied for optical determination of zero-field splitting of other transition metal ions in quantum dots.