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Time-resolved magnetophotoluminescence studies of magnetic polaron dynamics in type-II quantum dots

We used continuous wave photoluminescence (cw-PL) and time resolved photoluminescence (TR-PL) spectroscopy to compare the properties of magnetic polarons (MP) in two related spatially indirect II-VI epitaxially grown quantum dot systems. In the ZnTe/(Zn,Mn)Se system the holes are confined in the non-magnetic ZnTe quantum dots (QDs), and the electrons reside in the magnetic (Zn,Mn)Se matrix. On the other hand, in the (Zn,Mn)Te/ZnSe system, the holes are confined in the magnetic (Zn,Mn)Te QDs, while the electrons remain in the surrounding non-magnetic ZnSe matrix. The magnetic polaron formation energies in both systems were measured from the temporal red-shift of the band-edge emission. The magnetic polaron exhibits distinct characteristics depending on the location of the Mn ions. In the ZnTe/(Zn,Mn)Se system the magnetic polaron shows conventional behavior with decreasing with increasing temperature T and increasing magnetic field B. In contrast, in the (Zn,Mn)Te/ZnSe system has unconventional dependence on temperature T and magnetic field B; is weakly dependent on T as well as on B. We discuss a possible origin for such a striking difference in the MP properties in two closely related QD systems.

The majority of published work describe studies of magnetic QDs with type-I band alignment, 7,39 where the location of electrons and holes coincide spatially. In this work, we investigate TR-PL measurements in QD structures with type-II band alignment where the holes are confined in the QDs while the electrons reside in the surrounding matrix. Schematic diagrams of type-I and type-II alignment are shown in Fig. 2(a) and Fig. 2(b) respectively. We have studied two closely related ZnTe/ZnSe QD systems, grown using the same MBE process. In sample 1, Mn 2+ ions are incorporated in the matrix: ZnTe/(Zn,Mn)Se, while in sample 3, Mn 2+ ions are in the QDs region: (Zn,Mn)Te/ZnSe. These type-II structures offer two clear advantages for the study of MP dynamics over type-I QDs: (i) In type-II QDs, the photoexcited electrons and holes are spatially separated, i.e., have a small wavefunction overlap. As a result, the recombination time is comparable to or exceeds the MP formation time, and thus the MP has sufficient time to develop before electron-hole recombination takes place. (ii) The energy of the spatially-indirect interband transitions in 4 (Zn,Mn)Te/ZnSe and ZnTe/(Zn,Mn)Se QDs is 1.9 eV, i.e., it lies below the competing Mn internal transition at 2.2 eV. 7 Thus, most of the luminescence intensity appears in the interband recombination channel.
Our experimental results show that the MP in the closely related ZnTe/(Zn,Mn)Se and (Zn,Mn)Te/ZnSe QD structures show a strikingly different dependence on temperature and magnetic field. This difference in MP properties in the two systems is attributed to the difference in the location and magnetic susceptibility of the Mn ions.

II. EXPERIMENTAL
We have used 4 samples in this study. Sample 1 is a ZnTe/(Zn,Mn)Se QD structure while sample 3 is a (Zn,Mn)Te/ZnSe QD structure. Samples 2 and 4 are the non-magnetic references for samples 1 and 3 respectively, grown in the same growth runs as their magnetic counterparts. In samples 1 and 3, the average Mn composition is 5.2% as measured by Energy Dispersive X-Ray Spectroscopy. All samples were grown by MBE on (100) GaAs substrates. The details of sample growth have been given elsewhere 33 . All the QDs have a disk shape with an average 20nm base diameter and a height of 3nm as determined from cross sectional transmission electron microscopy studies. In Fig. 3(a) we show a schematic of the disk-shaped QDs. The samples have been placed in a variable temperature optical magnet cryostat operating in the 5-140 K temperature range. The magnetic field was applied along the direction perpendicular to the QD layers, defined as the z-axis, as is shown in Fig. 3(a). The Faraday geometry was used, with the emitted light propagating along the magnetic field. The possible interband recombination channels in the Faraday geometry are illustrated in Fig. 3 Fig. 3 we have included only the heavy holes. The strong valence-band confinement drives the lighthole levels well below the heavy-hole levels. As a result, the light holes do not contribute to the PL spectra. 46 A combination of quarter-wave plate and linear polarizer was placed in appropriate configurations before the spectrometer entrance slit to separate the from the components of the emission. The continuous wave (cw) PL was excited by the linearly polarized 488 nm (2.54 eV) line of an argon-ion laser. The cw PL was analyzed by a single monochromator equipped with a charged coupled device (CCD) multichannel detector. The TR-PL was excited at 400 nm by a frequency doubled pulsed laser system (repetition rate = 250 kHz, pulse duration ~200 fs). The TR-PL was spectrally resolved by a monochromator and temporally analyzed by a streak camera having a temporal resolution of 40 ps. The TR-PL data were divided into time slices. Each slice was fitted with a Gaussian that yielded the peak position and the intensity as a function of time delay .

III. RESULTS
We first discuss the cw PL results. In Fig. 4 we plot the peak position energies of the PL from sample 1 (triangles) and sample 3 (circles) as function of applied magnetic field B. Sample 1 has a red shift of 12 meV at B = 6 tesla. In this sample the emission is due to recombination of electrons in the magnetic (Zn,Mn)Se matrix with holes confined in the ZnTe QDs. Therefore the red shift is mainly due to the exchange interaction of electron spins with the spins of the Mn ions in the matrix. An additional contribution to the red shift due to the interaction of holes in the ZnTe QDs with Mn that diffused into the non-magnetic QDs cannot be excluded. 47 The red shift of PL in sample 1 decreases with increasing temperature. These data strongly indicate that the (Zn,Mn)Se matrix in sample 1 is in the paramagnetic phase with large, temperature-sensitive, band Zeeman splittings. In contrast, sample 3 exhibits a smaller red shift of 4 meV at B = 6 tesla even though the holes are confined in the magnetic (Zn,Mn)Te quantum dots. The unusual result for sample 3 shown in Fig. 4 will be discussed in Section IV.
We next turn to the time-resolved measurements. In Fig. 5(a) and 5(b), we show the Gaussian fits derived from the TR-PL spectra in cascade form from sample 1 and sample 3, respectively recorded at B =0 and T = 7K. The exciting laser pulse arrived at t = 1.96 ns for both spectra.
Photon collection was chosen to always start earlier than the pulse arrival to ensure that the entire Additional information about the time-resolved measurements is shown in Fig. 6 where we plot the peak energies for our samples as function of time delay t  . The magnetic samples 1 and 3 show large red shifts (tens of meV) with t  as shown in the lower panels of Fig. 6. For the laser powers used in our experiments the peak energy of the non-magnetic samples 2 and 4 exhibit a smaller but sizeable red shift as shown in the upper panels of Fig. 6(a) and Fig. 6(b). The data from samples 2 and 4 were fitted by a single exponential time evolution with time constants 2 16 ns   and 4 6.9 ns   , respectively. In order to obtain fits for the magnetic samples 1 and 3 [solid yellow lines in Fig. 6  Given the similarity of 1S  with 2  on one hand, and the similarity of 3S  with 4  on the other, we attribute the entire red shift of the peak position in the non-magnetic samples 2 and 4, and the slower component of the red shift in the magnetic samples 1 and 3 to the same spinindependent mechanism. A possible mechanism could be electric-dipole layer formation at the wetting layer/ZnSe matrix interface. Such dipole layers have been predicted and studied by other groups in ZnSeTe multilayers and type-II GaSb/GaAs quantum wells. 48,49 The total temporal red shifts 1 R and 3 R of the TR-PL for samples 1 and 3 was determined from the sum of the two energy parameters in the bi-exponential fit of the peak position energy described above.

IV. DISCUSSION
In Fig. 7 (a) [Fig. 7 Fig. 1(c). 9 The hole-Mn spin exchange interaction is stronger in sample 3 due to the fact that Mn and holes The MP energies, MP E , for zero magnetic field are plotted as function of temperature in Fig. 8(a) and Fig. 8  Due to this alignment, the temporal red-shift of PL, for 0 B  , identified as the MP formation energy MP E , is smaller than for B = 0. This is because recombination events at zero delay time occur for carrier energies defined by Mn spins partially aligned by B, while events at long delay times occur for full Mn spin alignment, as they did for B=0. Therefore, the energy difference between the zero-delay and long-delay recombination events (i.e., MP E ) must be smaller than the same difference at B = 0, in agreement with the results of Fig. 9(a).

11
(1) and the assumption of antiferromagnetic coupling of the Mn spins which would give a weak dependence of  on T. However, additional measurements in the present work suggest a different and a more plausible explanation realizing that from (b) and (c) we should expect that this robust MP behavior is a consequence of a large molecular (exchange) field. Following this motivation, we use Eq. (2) from the paper by Dietl et al. 55  suggested by the data from sample 3 shown in Fig. 8(b) and Fig. 9(b), we chose d to be equal to  is the hole spin density, and  is the oscillator frequency that describes the lateral confinement of the holes. In Eq. (4) the first two terms represent the kinetic energy, the third term is the potential energy, and the fourth term comes from hole degeneracy. The final term is the exchange energy between hole and Mn spins. For the calculation of the average MP energy, because of the initial localization of the hole, it is sufficient to consider only the last term in Eq. (4). The average MP energy can be obtained from, In Fig. 11 we plot MP E (T) for 20,10,5, and 3 d  nm. The effective MP temperature MP T can be higher than the lattice temperature of 7 K. The elevated MP T could be due to the high-peak power of the pulsed laser used to excite the TR-PL spectra. 58 In Fig. 11, if we consider T > 7 K, we have a weak dependence of MP E (T) , close to the results of Fig. 8  In order to understand the MP properties in sample 3 we performed calculations of the molecular magnetic field Bm , as well as the dependence of the MP energy MP E on T and B. If we assume strong hole localization due to alloy and spin disorder scattering, 55 our calculations suggest a large molecular field Bm (>20 tesla). If we make the additional assumption that the pulsed laser excitation resulted in an increase of the hole-Mn system effective temperature above the lattice temperature, our calculations describe adequately the behavior of sample 3 as shown in Fig. 8(b) and Fig. 9(b). 15 Additional guidance for a suitable theoretical description would come with the availability of new materials systems. Just as in other prior DMS work, we anticipate a transition from bulk-like systems to structures of reduced dimensionality. 7 One important example would be to realize QDs from novel Mn-doped II-II-V DMS which can have independent charge and spin doping and would therefore be suitable to test the MP formation for a wide range of parameters. 60 Fig.   1(a) and Fig. 1(b) depict the situation at early times (∆t ≪ ) following photoexcitation and before MP is formed. The lower panels in Fig. 1(a) and Fig. 1