Time-resolved magnetophotoluminescence studies of magnetic polaron dynamics
in type-II quantum dots
B. Barman,1R. Oszwałdowski,1,2L. Schweidenback,1A. H. Russ,1J. M. Pientka,1,3Y. Tsai,1W-C. Chou,4W. C. Fan,4 J. R. Murphy,1A. N. Cartwright,5I. R. Sellers,6A. G. Petukhov,2I. ˇZuti´c,1B. D. McCombe,1and A. Petrou1
1Department of Physics, University at Buffalo SUNY, Buffalo, New York 14260, USA
2Department of Physics, South Dakota School of Mines & Technology, Rapid City, South Dakota 57701, USA 3Department of Physics, St. Bonaventure University, St. Bonaventure, New York 14778, USA
4Department of Electro-physics, National Chiao Tung University, Hsinchu 300, Taiwan
5Department of Electrical & Electronic Engineering, University at Buffalo SUNY, Buffalo, New York 14260, USA 6Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73019, USA
(Received 15 January 2013; revised manuscript received 3 April 2015; published 24 July 2015) 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 nonmagnetic 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 nonmagnetic ZnSe matrix. The magnetic polaron formation energies EMP in both systems
were measured from the temporal redshift 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 EMPdecreasing with increasing temperature T and increasing magnetic field B.
In contrast, EMPin the (Zn,Mn)Te/ZnSe system has unconventional dependence on temperature T and magnetic
field B; EMPis 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.
DOI:10.1103/PhysRevB.92.035430 PACS number(s): 78.55.Et, 78.67.Hc, 85.35.Be
I. INTRODUCTION
Quantum dots (QDs), also known as artificial atoms, can allow versatile control of the number of carriers, their spins, Coulomb interactions, and quantum confinement [1–4]. Compared to their bulk counterparts [5–9], magnetically doped semiconductor QDs could provide control of the magnetic or-dering [10–16] with the onset of magnetization at substantially higher temperatures [17–21]. Experiments typically focus on Mn-doped II-VI and III-V QDs, in which it is possible to include both single [22–25] and several magnetic impurities [17–21,26–40], having similarities with nuclear spins [41,42]. In the first case (single magnetic ion), such systems could be considered as potential quantum bits, quantum memories, or probes to detect an unconventional orbital ordering [17,23–
25,43]. In the second case, the presence of several magnetic ions can lead to the formation of a magnetic polaron (MP), a long-standing research topic in magnetic semiconductors [5–8,44].
MP can be viewed as a cluster of localized magnetic ion spins, aligned through an exchange interaction with the spin of a confined carrier. Initial studies in bulk systems involved MPs with a carrier spin bound to an impurity center (donor or acceptor) [8]. In contrast, in semiconductor nanostructures with reduced dimensionality, the confinement removes the need for the presence of impurities and enhances the stability of the MPs [7]. As depicted in Fig.1, after a sufficiently long time interval after photoexcitation (comparable to MP formation time), Mn spins in II-VI systems typically couple ferromag-netically with electron spins and antiferromagferromag-netically with hole spins. The simultaneous presence of carriers and Mn ions in QDs result in the formation of MP through lowering of the
exciton energy by an amount as shown in Fig.1. Two main classes of magnetic QDs have been investigated; those grown using molecular beam epitaxy (MBE) [7,17,20–25,29–35,39] and those that are solution processed, known as colloidal QDs [12,26–28,36,37,40]. Despite entirely different growth procedures, in both classes of QDs the MP formation is asso-ciated with the observed magnetic ordering [12,20–22,30,37]. Several interesting effects have been attributed to MPs in nanostructures, such as the long “spin memory” times in (Cd,Mn)Te QDs [30], giant magnetoresistance in ErAs:GaAs nanocomposites [45], and room-temperature ferromagnetic ordering in MnGe QDs [21]. The temporal evolution of the MP (Fig.1) can be studied using time-resolved photoluminescence spectroscopy (TR-PL) [39]. In these experiments large (tens of meV) redshifts of the photoluminescence (PL) peak energy are observed as a function of time delay between laser excitation and PL detection.
The majority of published work describe studies of mag-netic 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 Figs.2(a)and2(b), respectively. We have studied two closely related ZnTe/ZnSe QD systems, grown using the same MBE process. In sample 1, Mn2+ions are incorporated in the matrix: ZnTe/(Zn,Mn)Se, while in sample 3, Mn2+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 I QDs: (i) In type-II QDs, the photoexcited electrons and holes are spatially
FIG. 1. (Color online) (a) and (b) Schematic diagram of the formation of magnetic polarons (MPs). The red (black) arrows indicate the hole (electron) spin; orange arrows are used for the magnetic ion spins. The hole (electron) spin is antiferromagnetically (ferromagnetically) aligned with the surrounding magnetic ion spins. Here t is the difference between the PL detection time and the pulse arrival time and τMPis the polaron formation time. The upper panels
in (a) and (b) depict the situation at early times (t τMP) following
photoexcitation and before MP is formed. The lower panels in (a) and (b) refer to later times (t ∼= τMP) with the MP fully formed. (c) A
schematic plot of the exciton energy as a function of t.
separated, i.e., have a small wave function 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 (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.
FIG. 2. (Color online) Schematic of the band diagram in: (a) Spatially direct (type-I) quantum dots and (b) spatially indirect (type-II) quantum dots. Here CB and VB indicate the conduction and valence band edges, respectively. Electrons (holes) are denoted by full circles (open circles).
II. EXPERIMENT
We have used four 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 nonmagnetic 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 20 nm base diameter and a height of 3 nm 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(b): Spin-down electrons (ms= −1/2) recombine with spin-up
holes (mj = +3/2) emitting σ+ photons; spin-up electrons
(ms = +1/2) recombine with spin down holes (mj = −3/2)
emitting σ− photons. In Fig.3(b)we have included only the heavy holes. The strong valence-band confinement drives the light-hole levels well below the heavy-hole levels. As a result, the light holes do not contribute to the PL spectra [46]. A combination of a quarter-wave plate and linear polarizer was placed in appropriate configurations before the spectrometer entrance slit to separate the σ+ from the σ− 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
FIG. 3. (Color online) (a) Schematic of the disk-shaped ZnTe/(Zn,Mn)Se and (Zn,Mn)Te/ZnSe quantum dots used in this work in which the dot diameter is much larger than the height. Here B is the externally applied magnetic field and k is the wave vector of the emitted luminescence (Faraday geometry). (b) Allowed interband radiative transitions in the Faraday geometry.
FIG. 4. (Color online) Peak energies of the cw PL at T = 7 K plotted as a function of an externally applied magnetic field in the Faraday geometry. Triangles: sample 1; circles: sample 3.
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 t.
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 a function of applied magnetic field
B. Sample 1 has a redshift of 12 meV at B = 6 T. 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 redshift 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 redshift due
to the interaction of holes in the ZnTe QDs with Mn that diffused into the nonmagnetic QDs cannot be excluded [47]. The redshift 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 redshift of 4 meV at B= 6 T 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 Sec.IV.
We next turn to the time-resolved measurements. In Figs.5(a) and5(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 = 7 K. 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 PL time evolution was recorded. The time delay t in the remainder of the text is defined as the difference between the detection time and the pulse arrival time (i.e., difference between the detection time and the photon-collection start time reduced by 1.96 ns in Fig.5). Immediately after the pulse arrival, the PL peak in Figs.5(a)
and 5(b) is at 1.96 eV. The peak energies redshift with increasing time delay reaching a value of 1.91 eV for sample 1 and 1.89 eV for sample 3, at t ≈ 18 ns.
Additional information about the time-resolved measure-ments is shown in Fig.6, where we plot the peak energies for our samples as a function of time delay t. The magnetic samples 1 and 3 show large redshifts (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 nonmagnetic samples 2 and 4 exhibit a smaller but sizable redshift as shown in the upper panels of Figs.6(a) and6(b). The data from samples 2 and 4 were fitted by a single exponential time evolution with time constants τ2= 16 ns and τ4= 6.9 ns, respectively.
In order to obtain fits for the magnetic samples 1 and 3 [solid yellow lines in Figs.6(a)and6(b)], we had to use two decaying exponentials with two corresponding time constants: a fast time constant τ1F(τ3F) for sample 1 (sample 3) and a slow
FIG. 5. Time-resolved photoluminescence spectra in cascade form recorded at B= 0, T = 7 K for time delays t between 0 and 20 ns. (a) Sample 1. (b) Sample 3.
FIG. 6. (Color online) Peak energy from TR-PL spectra plotted as a function of delay time t at T = 7 K. (a) Upper panel: Nonmagnetic sample 2; lower panel: magnetic sample 1. (b) Upper panel: Nonmagnetic sample 4; lower panel: magnetic sample 3. The solid yellow lines are exponential fits to the data discussed in the text.
time constant τ1S(τ3S). Times τ1Sand τ3Sare comparable to τ2
and τ4, respectively. The fitted time constants for all samples
are summarized in TableI.
Given the similarity of τ1S with τ2 on one hand, and the
similarity of τ3S with τ4 on the other, we attribute the entire
redshift of the peak position in the nonmagnetic samples 2 and 4, and the slower component of the redshift in the magnetic samples 1 and 3 to the same spin-independent 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 redshifts R1 and R3 of the TR-PL for
samples 1 and 3 were determined from the sum of the two energy parameters in the biexponential fit of the peak position energy described above. For the nonmagnetic samples 2 and 4 there was only one component contributing to the temporal redshifts R2and R4.
Even though the redshifts, of samples 1 and 2 on one hand and samples 3 and 4 on the other, depend strongly on laser power, the differences R1− R2and R3− R4remain constant
over a wide range of laser powers, indicating that R1− R2and R3− R4 are not related to the spin-independent mechanism
responsible for the slow redshift. Therefore, we identify the faster components τ1Fand τ3Fof the redshifts in samples 1 and
3 as the MP formation times (τ1MP = τ1F and τ3MP = τ3F). In
a similar fashion we identify the energy differences R1− R2
and R3− R4 as the MP formation energies E1MP and E3MP,
respectively, in the magnetic samples.
TABLE I. Zero field TR-PL parameters.
Sample τF(ns) τS(ns) τ(ns) EMP(meV) 1 0.35 17.2 25.4 2 16 3 0.48 7 34.4 4 6.9 IV. DISCUSSION
In Fig. 7(a) and 7(b) we show a schematic of the MP formation for sample 1 (sample 3) for the spin-up holes and spin-down electrons (σ+polarization recombination channel). The picture with all spins reversed (Mn, electrons, and holes) would correspond to the σ− polarization. Top panels correspond to the picture before electron-hole photoexcitation. The Mn spins, indicated by the orange arrows, are randomly oriented. Middle panels describe the system immediately after photoexcitation and before the MP had time to form. Thus the Mn spins continue to be randomly oriented. The electron spins in both samples are also randomly oriented; in contrast the direction of the hole spins in our flat disk-shaped QDs (height much smaller than the diameter) is determined by the strong confinement and by the spin-orbit interaction to be oriented either parallel or antiparallel with the QD axis (z axis) [32,50]. Bottom panels show the spin orientation for the Mn, the electron, and the hole spins after the MP formation. In both
FIG. 7. (Color online) Schematic diagram of magnetic polaron formation in: (a) ZnTe/(Zn,Mn)Se sample 1 and (b) (Zn,Mn)Te/ZnSe sample 3. The red (black) arrows indicate the hole (electron) spin; orange arrows are used for the manganese ion spins. The blue boxes represent the ZnTe and (Zn,Mn)Te QDs, respectively.
FIG. 8. Magnetic polaron energy plotted as a function of temper-ature at B= 0. (a) Circles: Sample 1. (b) Squares: Sample 3.
samples the direction of the hole spins defines the orientation of the Mn ion spins which are oriented antiferromagnetically with the hole spins [6]. The electron spins orient themselves ferromagnetically with the Mn spins. The MP formation results in the reduction in energy of the Mn-hole-electron complex by an amount EMPas shown in Fig.1(c).
The hole-Mn spin exchange interaction is stronger in sample 3 due to the fact that Mn and holes occupy the same space [the (Zn,Mn)Te QDs]. In sample 1 the hole-Mn interaction is weaker and is present due to the penetration of the hole wave function in the (Zn,Mn)Se matrix and possible diffusion of Mn in the ZnTe QDs. Therefore, it is expected that
E1MP< E3MP; this is indeed the case as can be seen from the EMPvalues listed in TableI. It is clear that the ratio E3MP/E1MP
is not equal to the ratio of the exchange constants for holes and electrons β/α [47,51]. This indicates that in sample 1 we may have some diffusion of Mn from the (Zn,Mn)Se matrix into the ZnTe QDs.
The MP energies EMPfor zero magnetic field are plotted as a
function of temperature in Figs.8(a)and8(b)for samples 1 and 3, respectively. EMPof sample 1 shows the typical temperature
dependence, i.e., it decreases with increasing temperature [39]. Surprisingly, EMP of sample 3 has a weak temperature
dependence.
The dependencies of EMPon magnetic field B, at constant
temperature, differ between samples 1 and 3 as well, see Fig.9. Sample 1 [Fig.9(a)] exhibits the conventional trend, i.e., EMP
decreases with increasing B [52]. In contrast, EMPin sample
3 is roughly independent of B. Weak B-field dependence has been reported in CdTe/(Cd,Mn)Te superlattices [53] and also presented in Figs.7–16 of Ref. [7].
FIG. 9. Magnetic polaron energy plotted as a function of magnetic field at T = 7 K. (a) Circles: Sample 1. (b) Squares: Sample 3.
An important model of magnetic polaron formation in DMS was used to successfully analyze spin-flip data of donor bound electrons in (Cd,M)nSe [44,54],
EMP= μ−10 (Jex
2gμBN0)2η(EMP/kBT) −1effχ(T ), (1)
where Jexis the exchange integral for carriers, N0is the cation
density, g= 2,μBis the Bohr magneton, and effis the
effec-tive MP volume. The term η(EMP/kBT) = tanh(EMP/kBT)
[20]. As can be seen from Eq. (1) the magnetic susceptibility
χhas a strong influence on the properties of MPs in (Cd,Mn)Se and DMS systems in general [44]. The use of Eq. (1) is appropriate only if the molecular field Bm is small so that it
does not saturate the Mn spins. This is the case for sample 1 which incorporates a (Zn,Mn)Se matrix, characterized by conventional paramagnetic susceptibility that decreases quickly with increasing temperature. From the typical strong temperature dependence (∼1/T ) of χ, the trend in Fig.8(a)
is consistent with Eq. (1). At the same time, the conventional values of χ at low temperatures are sufficiently high to allow for significant alignment of the Mn spins in the presence of an applied magnetic field of a few tesla [6]. Due to this alignment, the temporal redshift of PL, for B= 0, identified as the MP formation energy EMP, 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., EMP) must be smaller than the same
difference at B= 0, in agreement with the results of Fig.9(a). Turning to sample 3 we see significant differences in
EMP(T ,B) as compared to sample 1, as well as what would be expected for the MP energy from Eq. (1). Our theoretical description of sample 3 should then reconcile: (a) small redshift with B of the cw-PL peak energy, (b) weak dependence of EMP on T , and (c) weak dependence of EMP on B. In
an earlier work [20], which included the results for EMP(T )
from Fig.8(b), but neither EMP(B), nor the measurements on
samples 1 and 2, an attempt was made to explain aspects (a) and (b) using Eq. (1) and the assumption of antiferromagnetic coupling of the Mn spins which would give a weak dependence of χ 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] and Eq. (7.3) in Ref. [7], to calculate the molecular field Bmand its mean-field approximation value
Bm= 1 3μBg βJ|ψ(−→r )|2≈ 1 3μBg βJ 1 eff , (2)
where β is the exchange constant for holes in (Cd,Mn)Te,
J = 3/2 is the hole spin, and ψ is the hole wave function.
Since the hole localization diameter can be smaller than the QD diameter due to alloy and spin disorder scattering [7,56,57], we treat the effective QD diameter dand effective QD height h as adjustable parameters for the eff, given by the expression
eff = πh d 3 2 m∗EVB , (3)
FIG. 10. Molecular field Bm as a function of the effective QD diameter dwith the effective QD height h= 1.5, 2, and 3 nm.
where m∗= 0.19me is the hole effective mass, and EVB= 1 eV is the valence band offset. The calculated values
of Bmare plotted in Fig.10as a function of dfor three values
of h. It is clear that Bmincreases with decreasing values of dand h. In order to obtain the high values of Bm suggested
by the data from sample 3 shown in Figs.8(b)and9(b), we chose dto be equal to 5 nm and h= h = 3 nm. This gives a value of Bm≈ 20 T. The high value of Bmwould also explain
the small redshift in sample 3 due to the application of an external magnetic field shown in Fig. 4. Since sample 3 is a type-II heterostructure with an exciton lifetime longer than the MP formation time, the hole has enough time to polarize the surrounding Mn spins. This results in a relatively small redshift induced by the externally applied magnetic field.
The free energy functional of the magnetic polaron can be expressed as [44,58] FMP = 2 2m∗L2MP + 2π2 2m∗h2 + m∗ω2 2 L 2 MP− kBT ln 2− kBT × NMn j=1 ln sinh2S2+1[βρMP(Rj) 3kBT] sinh1 2[βρMP(Rj) 3kBT] , (4)
where LMPis a free parameter that describes the lateral extent
of the MP wave function ψMP, ρMP= (3/2)|ψMP(−→r )|2 is
the hole spin density, and ω 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
FIG. 11. Average magnetic polaron energy as a function of temperature with the QD diameter d= 3, 5, 10, and 20 nm.
FIG. 12. Average magnetic polaron energy as a function of applied magnetic field at T = 7, 14, and 25 K.
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
EMP=FMP− T∂FMP
∂T . (5)
In Fig.11 we plot EMP(T ) for d= 20, 10, 5, and 3 nm.
The effective MP temperature TMP can be higher than the
lattice temperature of 7 K. The elevated TMPcould be due to
the high-peak power of the pulsed laser used to excite the TR-PL spectra [59]. In Fig.11, if we consider T > 7 K, we have a weak dependence of EMP(T ), close to the results of
Fig.8(b).
In order to calculate EMP(B), we rewrite Eq. (2) as βρMP(−→r )
3 =
βJ|ψ(−→r )|2
3 = gμBBm(−
→r). (6) In Eq. (4) we express βρMP(−→r ) in terms of Bm( r) and
substitute Bm( r) with Bm( r) + B. Using Eq. (5) we calculate
the average MP energy and subtract the Zeeman shift [60] to obtain EMP. In Fig.12we plot EMP(B) at T = 7, 14, and 25 K.
If we assume that TMP is higher than the lattice temperature
of 7 K, we observe: (i) a weak dependence of EMP(B) in
agreement with Fig.9(b); and (ii) EMP for 0 < B < 4 T is
close to the experimental value of 35 meV. V. CONCLUSIONS
We have performed magneto-optical studies of magnetic polaron formation in two closely related type-II (spatially indirect) QD systems: ZnTe/(Zn,Mn)Se (sample 1) and (Zn,Mn)Te/ZnSe (sample 3). These were grown by the same experimental group using the same procedures. Likewise, the optical measurements and the corresponding data analysis were also performed in the same way. MP formation was observed in both systems; nevertheless, there are striking differences in their properties. In sample 1, where the magnetic ions are located outside of the QDs in the surrounding matrix, the MP formation energy has a strong temperature and magnetic field dependence, similar to previously studied type-I QDs [39].
Electrons, which are mostly responsible for the MP forma-tion in sample 1, are not strongly localized in the magnetic matrix. Therefore, we would expect that properties of such samples would resemble those of extensively studied bulk systems. Indeed, the MP formation picture developed for donors in bulk DMS provides a very good description for MP properties in sample 1. In contrast, in sample 3 we expect more pronounced quantum confinement effects where the magnetic ordering would arise from exchange interaction of Mn ion spins with the spin of holes that are strongly localized within the QDs.
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 EMPon 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 T). 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 Figs.8(b)and9(b).
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 bulklike 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 [61–63].
ACKNOWLEDGMENTS
This work was supported by US DOE, Office of Science BES, under Award DE-SC0004890 (I.Z., J.M.P., A.G.P), NSF DMR-1305770 and US ONR N000141310754 (R.O.).
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