Hole spin anisotropy in single Mn-doped quantum dots

The anisotropy in the exchange interaction between a single magnetic atom and a single exciton confined in a quantum dot (QD) is revealed experimentally. In a transverse magnetic field we directly observe the orientation of the magnetic ion spin along the resultant direction of the external magnetic field and the hole exchange field. With an increasing transverse magnetic field, this orientation progressively cancels the exchange interaction with the hole and at a high field the fine structure is mainly controlled by the electron-Mn coupling. At intermediate fields, we observe emission replicas caused by multiple spin flips within the Zeeman split ground state of a single Mn. All these features are well modeled by the magnetic field dependence of the stationary states of a single Mn spin in the exchange field of a heavy-hole exciton.

Figure 1

Experimental and calculated spectra at a zero magnetic field for two QDs. QD1 is a dot where there is no experimental evidence of valence band mixing. For QD2, the appearance of dark states at a zero magnetic field is an evidence of valence band mixing.

Figure 2

(Color online) (a) and (b) are contour plots presenting the magnetic field dependence of QD1 emission structure. (a) Voigt configuration, (b) Faraday configuration (yellow or light gray: high intensity; red or dark gray: low intensity). (c) and (d) are schemes of the spin orientations of the electron (blue), the hole (red), and the Mn atom (green) in Voigt and in Faraday configurations, respectively.

Figure 3

PL spectra of QD1 under magnetic field in Voigt geometry. The left inset presents the magnetic field dependence of the energy splitting between the emission replicas $n=1$ and $n=-1$. This linear evolution corresponds to a Mn $g$ factor $g_{Mn}=2.0$. The right inset is an illustration of the precession motion of $S$ in $B_{eff}=B_{ext}+B_{ex,Mn}^h$.

Figure 4

(Color online) (a) Simulation of the magnetic field dependence of QD1 emission in a Voigt configuration. Under a high field, several sets of lines are observed, spaced by the Zeeman energy of the Mn atom. (b) Energy level diagram of the Mn-doped QD in a transverse magnetic field. The quantization axis in the initial state $\left(A\right)$ differs from the quantization axis in the ground state $\left(x\right)$. (c) Illustration of the rotation of a spin $5∕2$ with a projection $S_A=3∕2$ by an angle $\pi ∕2-\alpha$ from an axis $A$ to the $x$ axis.

Figure 5

(Color online) Transverse magnetic field dependence of the experimental $X$-Mn splittings for the central set of lines of QD1 and QD2. QD1 evolution can be well reproduced by the pure heavy-hole model. The inset shows the magnetic field dependence of QD2 emission in a Voigt configuration.