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

When a ${\mathrm{Co}}^{2+}$ impurity is embedded in a semiconductor structure, crystal strain strongly influences the zero-field splitting between ${\mathrm{Co}}^{2+}$ states with spin projection $S_z=\pm 3/2$ and $S_z=\pm 1/2$. Experimental evidence of this effect has 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 an individual ${\mathrm{Co}}^{2+}$ ion in an epitaxial CdTe quantum dot in a ZnTe barrier. Using partially allowed optical transitions, we measure the strain-induced zero-field splitting of the ${\mathrm{Co}}^{2+}$ ion directly in the excitonic photoluminescence spectrum. Moreover, by observation of anticrossing of $S_z=+3/2$ and $S_z=-1/2{\mathrm{Co}}^{2+}$ spin states in a magnetic field, we determine the axial and in-plane components of the crystal field acting on the ${\mathrm{Co}}^{2+}$. The proposed technique can be applied to optical determination of the zero-field splitting of other transition-metal ions in quantum dots.

Figure 1

Typical photoluminescence spectrum of a neutral exciton in a CdTe/ZnTe QD with a single ${\mathrm{Co}}^{2+}$ ion at $T=3$ K. This ${\mathrm{Co}}^{2+}$ ion has a ground state with spin projection $\pm 3/2$, and as a consequence, the outer lines related to such spin states are much more pronounced than the inner emission lines related to the $\pm 1/2$ states.

Figure 2

Schematic diagram of the zero-field optical transitions between the energy levels of a singly ${\mathrm{Co}}^{2+}$-doped quantum dot with and without a neutral exciton. Numbers indicate the main ${\mathrm{Co}}^{2+}$ spin wave function. Red solid arrows denote the transitions for which ${\mathrm{Co}}^{2+}$ spin is conserved: the only allowed optical transitions of a bright exciton if the ${\mathrm{Co}}^{2+}$ states are pure. Blue and green dashed arrows denote transitions partially allowed due to ${\mathrm{Co}}^{2+}$ spin-state mixing. The energy differences between the strongest emission lines in the spectrum (red outer lines) and the weak, partially allowed lines at lower energy (blue lines) are exactly equal to the cobalt zero-field splitting ${\mathrm{\Delta }}_{\mathrm{Co}}$.

Figure 3

(a) Polarization-resolved PL intensity map of a neutral exciton in a CdTe/ZnTe QD with a single ${\mathrm{Co}}^{2+}$ ion as a function of the magnetic field in the Faraday configuration at $T=1.5$ K. (b) Corresponding simulation of the optical transitions with the model described in the text. There are four main emission lines [red lines in (b)] corresponding to the bright-exciton transition with conserved spin of ${\mathrm{Co}}^{2+}$ and three weak emission lines: one associated with the dark-exciton recombination [black line in (b)] which does not carry information about the zero-field splitting and two lines related to the transitions allowed by cobalt $\pm 3/2$ and $\mp 1/2$ spin-state mixing [blue lines in (b)]. As explained in Fig. 2, the zero-field splitting of cobalt (${\mathrm{\Delta }}_{\mathrm{Co}}=3.13$ meV) is determined by subtraction of the energies for pairs of transitions for which the initial state is the same ($\pm 3/2$) but the final state is different ($\pm 3/2$ and $\mp 1/2$). The values of the ${\mathrm{\Delta }}_{\mathrm{Co}}$ parameter estimated from two pairs of emission lines are the same.

Figure 4

(a) Polarization-resolved magneto-PL intensity map in the Faraday configuration at $T=1.5$ K for a CdTe/ZnTe QD with a single ${\mathrm{Co}}^{2+}$ ion exhibiting within the experimental range an anticrossing of 3/2 and $-1/2$ spin states. (b) Corresponding simulation of the optical spectra. (c) Corresponding simulation of the energies of the initial state (exciton plus ${\mathrm{Co}}^{2+}$ system) and final state (empty dot with a single ${\mathrm{Co}}^{2+}$ ion) of the optical transition. Anticrossing between $+3/2$ and $-1/2$ cobalt spin states in the absence of an exciton appears four times in the spectra, at a magnetic field of about 7.5 T, and is denoted in (b) and (c) by black circles. Red and blue squares in (b) and (c) represent anticrossings of cobalt spin states modified by the presence of a neutral exciton which acts on ${\mathrm{Co}}^{2+}$ as an effective magnetic field. As a consequence, such anticrossings are shifted to about 4.5 and 10.5 T for ${\sigma }^{+}$ and ${\sigma }^{-}$ polarizations, respectively.

Figure 5

Points: energy difference between mixed $\pm 3/2$ and $\mp 1/2$ spin states of various ${\mathrm{Co}}^{2+}$ ions in CdTe/ZnTe QDs, determined from PL spectra as a function of the magnetic field, near the anticrossing. Solid lines: fit to the ${\mathrm{Co}}^{2+}$ state splitting given by Eq. (2) with the fitting parameters summarized in Table 1.