Optically probing the fine structure of a single Mn atom in an InAs quantum dot
We report on the optical spectroscopy of a single InAs/GaAs quantum dot (QD) doped with a single Mn atom in a longitudinal magnetic field of a few Tesla. Our findings show that the Mn impurity is a neutral acceptor state whose effective spin is significantly perturbed by the QD potential and its associated strain field. The spin interaction with photo-carriers injected in the quantum dot is shown to be ferromagnetic for holes, with an effective coupling constant of a few hundreds of eV, but vanishingly small for electrons.
The spin state of a single magnetic impurity could be envisaged as a primary building
block of a nanoscopic spin-based device Efros et al. (2001); Fernandez-Rossier and Aguado (2007) in particular for the
realization of quantum bits Leuenberger and Loss (2001). However probing and manipulating such a system
require extremely high sensitivity. Several techniques have been successfully developed over
the last few years to address a single or few coupled spins: electrical detection Xiao et al. (2004); Elzerman et al. (2004), scanning tunneling microscopy (STM) Manassen et al. (1989); Heinrich et al. (2004); Hirjibehedin et al. (2006); Kitchen et al. (2006), magnetic resonance force microscopic Rugar et al. (2004), optical spectroscopy
Gruber et al. (1997). Recently, Besombes et al. Besombes et al. (2004, 2005); Léger et al. (2005, 2006) have
investigated the spin state of a single Mn ion embedded in a single II-VI self-assembled
quantum dot (QD). In this system the magnetic impurity is an isoelectronic center in a
configuration with spin . The large exchange interaction between the spin of the
photocreated carriers confined inside the dot and the Mn magnetic moment induces strong
modifications of the QD photoluminescence (PL) spectrum:
discrete lines are observed, reflecting the Mn spin state at the instant when the exciton recombines.
The case of the Mn ion is different in GaAs, since the impurity is an acceptor in this matrix with a rather large activation energy (113 meV). Two types of Mn centers exist in GaAs, the and the states. In low doped GaAs (below cm), the former is dominant. It corresponds to the configuration, where is a hole bound to the Mn ion with a Bohr radius around 1 nm Schneider et al. (1987). When considering a single Mn impurity in InAs QD several issues arise: the impurity configuration, its possible change when photo-carriers are captured, the influence on the binding energy of excitonic complexes, the strength and sign of the effective exchange interaction with each of the carriers (electron or hole) in the QD -shell. In this Letter, we report the first evidences of a single Mn impurity in an individual InAs QD which enable us to answer most of the above questions. In particular, we find that the formation of excitons, biexciton and trions is weakly perturbed by the impurity center, whereas the effective exchange coupling with the Mn impurity (found in the configuration) is ferromagnetic for holes (a few 100 eV’s) and almost zero for the electrons.
The sample was grown by molecular beam epitaxy on a semi-insulating GaAs  substrate. The Mn-doped quantum layer was embedded inbetween an electron reservoir and a Schottky gate. This design gave us the possibility to observe both neutral and charged excitons. It consists of a 200 nm thick -doped GaAs layer ( cm) followed by a non-intentionally doped (n-i-d) 20 nm GaAs layer, the Mn-doped QD layer, and capped with a n-i-d GaAs (30 nm)/ GaAlAs (100 nm)/ GaAs (20 nm) structure. The QD layer was formed by the deposition of 1.7 ML of InAs during 5 s. The substrate temperature was set to 500 C (optimal for QD) during the growth of the whole structure. The Mn doping was carried out by opening the Mn cell shutter during the QD growth. The cell temperature was set to 590 C. The precise determination of the Mn atom density is difficult in this material because of the large segregation of Mn atoms at these growth temperatures as observed by STM [J.-C. Girard, unpublished]. Estimations from Hall effect measurements in thick and uniformly Mn doped GaAs layers grown at the same temperature yielded a density of approximatively Mn atoms per cm, giving a probability of Mn per dot. However, in -PL measurements on a large collection of single QDs we observed only rare occurrences of Mn doping (0.1%), likely due to the Mn segregation away from the QD layer. Samples grown at higher Mn cell temperature (660 C) showed a much larger probability (1%) of finding dots containing a single Mn atom.
The -PL spectroscopy of individual InAs:Mn QDs was carried out with a split-coil magneto-optic cryostat. A 2 mm focal length aspheric lens (N.A. 0.5) was used to focus the He-Ne excitation beam and to collect the PL from the sample, while the relative positioning in all three directions was ensured by Attocube piezo-motors. All measurements presented in this Letter were performed at low temperature (T=2 K) and the magnetic field was applied parallel to the optical axis (Faraday configuration). The PL was dispersed by a 0.6 m-focal length double spectrometer and detected by a Nitrogen-cooled CCD array camera.
We first present the optical signature in zero magnetic field of a single Mn atom uncovered by our experiments in the PL spectrum of about 10 different QDs. A characteristic spectrum is shown in Fig. 1(a). It consists of two bright doublets labelled and separated by an energy of the order of a few 100 eV, and of a weaker central line denoted by . The splitting of the doublets is the same for both lines and and typically amounts to a few tens of eV.
A simple interpretation of this spectral feature can be constructed by assuming that the QD
contains a Mn impurity in the configuration, i.e. a hole bound to an
center Schneider et al. (1987); Bhattacharjee and à la
Guillaume (1999); Govorov (2004). This acceptor state is characterized in
bulk GaAs by an anti-ferromagnetic “-” exchange between the 3 Mn spin and
the hole spin . The latter takes the form of a Heisenberg Hamiltonian Bhattacharjee and à la
Guillaume (1999) (with 5 meV), giving
rise to splittings of eigenstates as a function of the total angular momentum
: the triplet ground state
() turns out to be well separated from the higher levels by at
least meV. Therefore, at low temperature when the
Mn impurity is completely thermalized in its ground state. Assuming similar “-” exchange
in InAs QDs, we may consider that the photo-carriers captured by the QD interact with an
effective spin . Such a situation is depicted in Fig. 1(b) in the
case of an electron-hole pair (or neutral exciton ) in its ground state. We focus here only
on the exciton bright states with projection of angular momentum , since
the dark states () do not contribute to the PL signal. A natural basis to
describe the initial states of the excitonic transition reads thus
. In case of exchange interaction between and , these levels
are split into three doubly degenerate levels which read , , corresponding to a ferromagnetic (), “orthogonal” (),
and anti-ferromagnetic () spin configuration, respectively. If the final states were
perfectly degenerate, as predicted for the acceptor level in bulk GaAs, then we should observe
in the PL spectrum three lines equally spaced and of identical intensity, similar to the six
lines observed in CdTe QDs doped with a single Mn atom Besombes et al. (2004). Actually, due to its
hole component, the state is sensitive to local variations of composition and strain
over a typical distance of 1 nm from the impurity center Schneider et al. (1987); Govorov (2004); Yakunin et al. (2007).
In self-assembled InAs QDs which ressemble a flat lens of 4 nm height, the most important
perturbation of the bulk potential occurs along the growth direction, . Such a perturbation
of symmetry shifts the level to higher energy with respect to the
states. The same effect occurs for the level in the
complex as this perturbation is diagonal in the basis we have chosen. If in addition the
potential experienced by the impurity has some in-plane anisotropy (with
symmetry or lower), then the are further split by an energy . Such an
effect is expected because the Mn impurity is very likely not in the center of the QD.
Note that this anisotropy acts perturbatively as an off-diagonal term for the
levels which are already split by . Following this scheme, the optical
transitions from the and levels appear as doublets due to the final state
splitting, whereas the level may recombine only to the state because of
orthogonality of its component () with the states. The shift of
the level does not reflect in the transition energy, since it appears in both the
initial and final states,
however it explains the weaker intensity observed experimentally for the line because of thermalization
in the levels.
The main support to this interpretation comes from the evolution in a longitudinal magnetic field. Thanks to the Zeeman effect it is possible to restore the eigenstates to . The and doublets should transform to single lines for a field where is the factor in the spin configuration and is the Bohr magneton. Taking the value found for GaAs:Mn Schneider et al. (1987) the typical magnetic field required amounts to only 230 mT for the QD shown in Fig. 1. In parallel, the magnetic field splits the and levels by the sum of Zeeman effects for and . Therefore, the Zeeman splitting of does not reflect straightforwardly in the PL spectra apart for the “forbidden” transitions involving a spin-flip of and represented by dashed arrows in Fig. 1(b). When the magnetic field reaches the value (1 T in our case) the and states are now brought into coincidence. Since they are formed with the same exciton spin, the anisotropic interaction between the levels splits the levels by the same energy splitting as in zero field. For this very specific field the PL spectrum should thus be quite similar to the spectrum in zero field as illustrated in Fig. 1(b), with the splitting () in the final (initial) states.
To study the magnetic field dependence of the -to- coupling, we recorded a
series of 121 -PL spectra over a 10 meV-energy range, by varying the magnetic field
from T to T with a step of 50 mT. The detection was set to help
identify the different levels and their interactions. The -PL intensity was
plotted on a color-scale against magnetic field and energy-detection, using an
interpolating function for graphical rendering. To focus on the spin-dependent
interactions we subtracted the diamagnetic-shift . Figure 2
displays three spectral regions of this contour-plot, showing clearly correlated spectral
lines that could be identified (after a careful analysis) as the three excitonic features
, and originating all from the same individual QD. Remarkably, the
and set of lines are separated from by roughly the same binding
energies than in undoped InAs QDs emitting at 1.25 eV Eble et al. (2006). Note Fig. 1(a) is the cross-section at T of the contour-plot.
The main feature common to the plots of Fig. 2 is a very peculiar pattern
resulting from the evolution of the zero-field doublets to another pair of doublets at
T. The resulting crossing lines correspond to the “forbidden” transitions
involving spin-flip from to respectively. Obviously these
transitions are not strictly forbidden because of the anisotropic coupling either in the final
state (at 0), or in the initial state (at 0.75 T). Focusing on the
feature, we clearly observe a strong evolution of the intensity ratio between the and
lines due to the thermalization on one of the levels depending on the field
direction 111Thermalization effects are assumed negligible in the excitonic states due to
a long spin lifetime compared to the recombination time. See also Ref. Besombes et al. (2004).. For
, the () population should decrease (increase).
Actually, it is this simple feature which
allowed us to ascribe confidently the low energy doublet to the ferromagnetic
configuration. We note that such an effective ferromagnetic coupling was
already reported by J. Szczytko et al. Szczytko et al. (1996) in very
dilute GaMnAs ().
In each case shown in Fig. 2, an exact replica of the main pattern is found at lower energy. We ascribe them to temporal electrostatic fluctuations of the QD environment which rigidly shift all the excitonic lines, e.g. due to charge trapping and detrapping in the QD vicinity. Since these replica were not found for other Mn-doped QDs that we have examined (and showing also the same cross-like patterns) we conclude that they are not related to the intrinsic signature of a Mn-impurity. We chose to show this particular dot because three excitonic complexes were simultaneously visible with a high signal to noise ratio.
Another striking feature is the symmetry between and . It results from the polarization correlation in the biexciton cascade imposed by the Pauli principle. As we detect only photons the measured transitions from lead to the polarized , which obviously has the same field dependence as the polarized but for . This observation strongly supports the line identification and actually indicates that the biexciton (with both holes and electrons in singlet spin configuration) has no spin interaction with the Mn impurity. Note that the very same symmetry has been observed in Mn-doped CdTe QDs Besombes et al. (2005).
Finally, the position of the cross-like pattern for the case is very instructive. It reveals that one of the electron- or hole- exchange integrals must be vanishingly small with respect to the other. If not the mixing at between the states would be reduced both in the initial state (due to hole- exchange) and final state (due to electron- exchange). There would be no splitting and the cross-like pattern would be shifted to a different field. Since it appears at the same positive field as for , the transitions must be described by the diagram of Fig. 1(b), yet with - as the final state. We can therefore conclude that the electron- coupling is negligible as compared to (actually below 20 eV from a precise comparison of the spectra at ).
To support the above discussion, we have modeled the spin interactions with the Mn impurity for the three excitonic configurations. To reproduce all details of our experimental results, it appeared necessary to include not only the states of but also the states. Our model includes the Zeeman Hamiltonian for a single particle (Mn, bound hole , QD -shell hole and electron ), strain Hamiltonian for Yakunin et al. (2007), valence band mixing between light- and heavy-components for Kowalik et al. (2007), and exchange interaction within each pair of particles. A detailed discussion of this model will be published elsewhere. We present in Fig. 3 the contour plot of theoretical PL spectra corresponding to the - configuration. By adjusting strain and exchange parameters, our model reproduces remarkably well the cross-like pattern, the effect of Mn thermalization (=10 K) as well as the anticrossing observed at -2 T. The latter results from a coupling between the bright exciton and the dark exciton when they are brought into coincidence by the field. Our model reveals that this is a resonant third order coupling involving the valence band mixing, a shear strain (which also contributes to ) and the effective - exchange constant between the spin subspaces and . It reads where is the exchange integral between the spins and . To reproduce our experimental results we found that the - splitting is dominated by this exchange term while the exchange term within the subspace contributes less than 10% of .
In conclusion, the successful
-PL investigation in a longitudinal magnetic field of a single Mn-doped InAs quantum
dots reveals remarkable features bringing new insights into the spin interactions between
carriers and a Mn impurity in a III-V matrix. The anti-ferromagnetic coupling between the
hole bound to the magnetic impurity and the Mn electrons is confirmed. In
contrast, the effective coupling of the Mn impurity as a whole () with a hole
confined in an InAs QD is proven to be ferromagnetic, while it essentially vanishes for a
confined electron. The influence of the strain field on the Mn acceptor level is clearly
evidenced, and gives rise to a very specific spectral signature of the Mn doping. Our
results reveal that the Mn spin in configuration represents a two-level system
well separated from higher energy levels which opens new outlooks for spin-based quantum
e.g. by exploiting the exchange interaction with optically polarized carriers.
Acknowledgements.This work was partly supported by the European Network of Excellence SANDIE, the ANR contracts BOITQUANT and MOMES.
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