Thermal Tuning and Inversion of Excitonic Zeeman Splittings in

Apr 24, 2012 - Thermal Tuning and Inversion of Excitonic Zeeman Splittings in Colloidal Doped ... Quantum Confinement-Controlled Exchange Coupling in ...
0 downloads 0 Views 268KB Size
Download PDF
Letter pubs.acs.org/JPCL

Thermal Tuning and Inversion of Excitonic Zeeman Splittings in Colloidal Doped CdSe Quantum Dots Alina M. Schimpf and Daniel R. Gamelin* Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States S Supporting Information *

ABSTRACT: Variable-temperature magnetic circular dichroism (MCD) spectroscopy is used to measure excitonic Zeeman splittings in colloidal Co2+- and Mn2+-doped CdSe quantum dots with low dopant concentrations. The data demonstrate that the competition between intrinsic and exchange contributions to the excitonic Zeeman splittings in doped quantum dots can be tuned using temperature, from being dominated by exchange at low temperatures to being dominated by intrinsic Zeeman interactions at room temperature, with inversion at easily accessible temperatures and fields. These results may have relevance to spin-based information processing technologies that rely on manipulating carrier spins in quantum dots.

SECTION: Spectroscopy, Photochemistry, and Excited States

T

Figure 1 shows room-temperature absorption and variabletemperature MCD spectra of Cd1−xMnxSe and Cd1−xCoxSe QDs (x = 0.005 ± 0.001). For the MCD measurements, an external field of 0.63 T was applied using a small electromagnet. At 28 K, the MCD spectrum of the Cd0.995Mn0.005Se QDs shows a large derivative-shaped feature at the CdSe absorption edge. This feature has its positive intensity at lowest energy, indicative of a negative excitonic Zeeman splitting, ΔEZeeman.11 The excitonic MCD intensity decreases with increasing temperature, reflecting loss of Mn2+ magnetization (vide infra). At ∼80 K, this intensity passes through zero, and its sign is inverted at higher temperatures. We note that the MCD intensity does not pass through zero simultaneously at all wavelengths within the excitonic band, in part because of inhomogeneities in the dopant concentration and nanocrystal diameter. Similar results are obtained for Cd0.995Co0.005Se QDs. The large, positive excitonic MCD feature dominant at 33 K loses its intensity with increasing temperature. In this sample, the excitonic MCD intensity inverts closer to room temperature. The structured MCD feature centered at ∼13500 cm−1 derives from the 4A2(F) → 4T1(P) ligand field transition of tetrahedral Co2+ in CdSe.12 This MCD intensity also decreases with increasing temperature, approaching zero at high temperatures but not inverting. The strong temperature dependence and inversion of the excitonic MCD intensities in these DMS QDs can be

he defining physical characteristic of diluted magnetic semiconductors (DMSs) is the so-called “giant” Zeeman splitting of their band structure, which arises from sp−d exchange coupling between delocalized charge carriers and localized spins on magnetic impurity ions embedded within the semiconductor.1 These splittings lend DMSs a variety of extraordinary magnetic, magneto-optical, and magneto-transport properties that make them attractive for semiconductorbased spintronics or spin-photonics technologies.2 Giant Zeeman splittings of excitons give rise to the so-called giant Faraday rotation effect,3−5 useful in Faraday optical isolators, and to spin-polarized excitonic photoluminescence,6 in which magnetic fields control luminescence polarizations. Giant Zeeman splittings are also responsible for the spontaneous zero-field magnetization observed in excitonic magnetic polarons.7−10 Here, we demonstrate tuning and inversion of the excitonic Zeeman splittings in colloidal Mn2+- and Co2+-doped CdSe quantum dots (QDs) at small magnetic fields, using temperature as the external variable. Excitonic Zeeman splittings probed by MCD spectroscopy are shown to follow a Curie temperature dependence, except that at elevated temperatures, they pass through zero and actually invert in sign, in contrast with the MCD intensities of simple Curie paramagnets (like the Co2+ ligand field MCD in the same Co2+-doped CdSe quantum dots). Fitting the excitonic MCD temperature dependence allows quantitative parametrization of the microscopic factors underpinning this sign inversion. Specifically, these measurements yield an unusually clear illustration of the competition between intrinsic and exchange contributions to the excitonic Zeeman splittings of DMS QDs. © 2012 American Chemical Society

Received: March 15, 2012 Accepted: April 24, 2012 Published: April 24, 2012 1264

dx.doi.org/10.1021/jz300320y | J. Phys. Chem. Lett. 2012, 3, 1264−1268

The Journal of Physical Chemistry Letters

Letter

term of eq 1b, ΔEsp−d depends on the mole fraction of the magnetic ion (x), the cation density (N0), the exciton-impurity overlap (γ), the s−d and p−d exchange energies (α and β, respectively), and the spin expectation value of the magnetic ions (⟨Sz⟩). For magnetic transition-metal impurity ions with spin-only ground states, such as tetrahedral Mn2+ and Co2+ (S = 5/2 and 3/2 Curie paramagnets, respectively), ⟨Sz⟩ follows Brillouin magnetization, as represented by eq 2, where gTM is the effective g value of the impurity’s ground state, kB is the Boltzmann constant, and T is temperature. At small magnetic fields, this function is inversely proportional to T (Curie behavior). The strong temperature dependence seen in Figure 1 is thus consistent with excitonic Zeeman splittings dominated by ΔEsp−d. ⎡ 2S + 1 ⎛ 2S + 1 g TM μB H ⎞ coth⎜ ⟨Sz⟩ = −⎢ ⎟ ⎢⎣ 2 kBT ⎠ ⎝ 2 −

understood by examination of the microscopic contributions to the excitonic Zeeman splittings. Formally, the magnitudes of the excitonic Zeeman splittings are determined by a competition between the intrinsic excitonic Zeeman splitting of the parent semiconductor (ΔEint) and that arising from sp−d exchange (ΔEsp−d), as described by eq 1a.1 (1a)

= gμB H + xγN0(α − β)⟨Sz⟩ (1b) = gexcμB H

(2)

An interesting feature of DMSs is that ΔEint and ΔEsp−d usually have opposite signs and thus compete with one another. Typically, ΔEZeeman is measured at low temperatures where ΔEsp−d may become extremely large due to the inverse temperature dependence of ⟨Sz⟩. In this regime, there is little evidence of ΔEint, and consequently, it is widely neglected. For a particular magnetic field, however, eq 1 predicts the existence of a unique temperature for any given DMS at which ΔEint = −ΔEsp−d, and hence, ΔEZeeman = 0. Similarly, eq 1 predicts that at fixed temperature, the g value can be inverted by application of a magnetic field. Whereas inversion of DMS spin splittings has indeed been demonstrated at cryogenic temperatures using large magnetic fields and low dopant concentrations,3,4,14,15 the use of temperature for this purpose has not been explored. The data in Figure 1 were analyzed by plotting the integrated intensities of the first excitonic MCD peaks (Iexc) versus temperature for each sample. These plots are shown in Figure 2. The ligand field MCD intensity (ILF) in the Cd0.995Co0.005Se spectra is also plotted versus temperature in Figure 2b. The inset in Figure 2b plots the ratio of excitonic to ligand field MCD intensities (Iexc /ILF) versus temperature for the Cd0.995Co0.005Se QDs. This ratio is linear over a broad temperature range. The temperatures at which the excitonic MCD intensities invert are more clearly seen from these plots than from those in Figure 1. This crossing point occurs at ∼80 K for the Cd0.995Mn0.005Se QDs and at ∼160 K for the Cd0.995Co0.005Se QDs. At these crossing points, the two contributions to ΔEZeeman cancel one another (i.e., ΔEsp−d = −ΔEint). Doped QDs with small values of x were used for these measurements because their MCD inversion occurs at relatively low temperatures. This inversion temperature can be adjusted by altering x (eq 1). The solid curves in Figure 2 were obtained by fitting these data to eqs 3a and 3b.

Figure 1. Representative absorption and variable-temperature MCD spectra of colloidal (a) Cd0.995Mn0.005Se and (b) Cd0.995Co0.005Se QDs, collected at H = 0.63 T. The bold red and blue MCD spectra represent the highest and lowest temperatures, respectively. Absorption spectra were collected on colloidal suspensions, and MCD spectra were collected on films drop-coated from these suspensions.

ΔEZeeman = ΔE int + ΔEsp−d

⎛ 1 g μ B H ⎞⎤ 1 coth⎜ TM ⎟⎥ 2 ⎝ 2 kBT ⎠⎥⎦

(1c)

These two contributions are expanded in eq 1b, and in the Curie regime, their sum may be conveniently represented by a single (temperature-dependent) effective excitonic g value, gexc (eq 1c). In eq 1b, ΔEint is described by a simple Zeeman perturbation term, where g is the intrinsic Landé g factor of the exciton (gCdSe = +1.41 [ref 13.]), μB is the Bohr magneton, and H is the external magnetic field. To first order, ΔEint is thus independent of temperature and of the magnetic impurity ion concentration or magnetization. On the other hand, ΔEsp−d reflects the splitting of the exciton induced by the collective action of an ensemble of magnetic impurity ions simultaneously exchange coupled with the exciton. As shown in the second

Iexc(T ) = AΔEZeeman(T ) = A(gCdSeμB H + xγN0(α − β)⟨Sz⟩)

ILF(T ) = B⟨Sz⟩

(3a) (3b)

Equation 3a describes the excitonic Zeeman splitting, and therefore the excitonic MCD signal intensity, as a function of 1265

dx.doi.org/10.1021/jz300320y | J. Phys. Chem. Lett. 2012, 3, 1264−1268

The Journal of Physical Chemistry Letters

Letter

QDs, respectively. Because of the propensity for crystal nucleation to exclude dopants, colloidal DMS QDs appear to generally have undoped cores,18,19 precisely where the exciton probability density is greatest. The values of γ determined here are consistent with undoped cores of ∼2 nm in both samples, similar to the values measured in previous experiments.18 The influence of such nonstatistical dopant distributions is exacerbated in QDs because of the tight exciton confinement. Although some research20−23 may suggest that γ should instead be interpreted in terms of confinement-induced changes in N0α,20 recent theoretical work suggests that these QDs are too large to display significant kinetic s−d exchange.24,25 It should be noted that the literature values for N0α and N0β in bulk Cd1−xMnxSe and Cd1−xCoxSe show substantial variance (up to ∼15%; see the Supporting Information). Similarly, the value of gCdSe taken from bulk may not be accurate for QDs,26 and at such small x, even small experimental uncertainties (x = 0.005 ± 0.001) translate to large uncertainties in γ. The specific values of γ in Table 1 are thus influenced by uncertainties in N0(α − β), gCdSe, and x and hence should not be overinterpreted. The primary finding from these data, namely, of inversion of the sign of ΔEZeeman using temperature, is valid regardless of the value or interpretation of γ and provides a particularly clear experimental validation of the competition between ΔEint and ΔEsp−d formulated in eq 1. From eq 1c, these results further demonstrate that the effective excitonic g values (gexc) of these nanocrystals also invert over the temperature range explored here. At the crossing point, where Iexc = 0, gexc is tuned to zero. In the hightemperature limit, gexc = gCdSe ≈ +1.41. At ∼30 K, gexc ≈ −3gCdSe (−4.2) for the Cd0.995Mn0.005Se, and gexc ≈ −8gCdSe (−11.3) for the Cd0.995Co0.005Se QDs. At the liquid helium temperatures (4.2 K), these gexc values increase to −25.9 and −50.2, respectively. In summary, variable-temperature MCD spectroscopy at small magnetic fields has been used to measure excitonic Zeeman splittings in colloidal Co2+- and Mn2+-doped CdSe quantum dots. The results clearly illustrate a competition between intrinsic and exchange contributions to these Zeeman splittings and demonstrate that the exciton spin polarizations can be tuned and inverted within easily accessible temperature and magnetic field ranges, a finding that may be relevant to future spin-photonic information processing technologies reliant upon spin manipulation within quantum dots. Used in this way, variable-temperature MCD spectroscopy is demonstrated as a valuable tool for probing magnetic exchange interactions in DMSs.

Figure 2. Temperature dependence of the MCD signal intensities in colloidal (a) Cd0.995Mn0.005Se and (b) Cd0.995Co0.005Se QDs, normalized at room temperature. The plus signs and open diamonds are the integrated MCD intensities of the lowest-energy feature for the exciton and d−d transitions, respectively. The solid lines show fits to the data using eq 3. The right axes show the corresponding excitonic Zeeman splittings. The inset in (b) plots the ratio of excitonic to ligand field MCD intensities in the Cd0.995Co0.005Se QDs.

temperature, where A is a proportionality constant that relates the observed MCD signal intensity (in mdeg) to the actual Zeeman splitting energy (in eV). Similarly, B is the proportionality constant relating the ligand field MCD intensity to Co2+ ground-state magnetization. When determining the fits, A, B, and the overlap factor γ were floated, while all other values were held constant. gCdSe and N0(α − β) were fixed at their bulk values, and x was fixed to the value determined analytically. The linearity of Iexc/ILF versus T (Figure 2, inset) is consistent with a temperature-independent value of gCdSe. From these fits, the values of ΔEZeeman at saturation may be determined by taking the limit as T → 0 (eq 4). Plots showing the temperature dependence of ΔEZeeman extended to saturation are provided in the Supporting Information, and the analysis is summarized in Table 1. ⎛ I (T ) ⎞ sat ΔEZeeman = lim ⎜ exc ⎟ T → 0⎝ A ⎠

■

METHODS Cd1−xTM x Se QD Synthesis. Colloidal DMS QDs were synthesized by cluster thermolysis (for Cd1−xMnxSe)11 and hot injection (for Cd1−xCoxSe)27 methods, as described previously. Briefly, for the cluster thermolysis synthesis, a solution of 0.015 mmol of manganese chloride tetrahydrate in 11 g of hexadecylamine (HDA) was degassed under vacuum at

(4)

ΔEsat Zeeman

The values of extracted from the data in Figure 2 are smaller than expected from bulk exchange energies, yielding γ = 0.61 and 0.23 for the Cd0.995Co0.005Se and Cd0.995Mn0.005Se Table 1. Results from Analysis of Excitonic Zeeman Splittings

a

sample

experimental ΔEsat Zeeman (meV)

a predicted ΔEsat Zeeman (meV)

Cd0.995Mn0.005Se Cd0.995Co0.005Se

−4 −10

−17 −16

experimental γN0(α − β) (eV)

literature N0(α − β) (eV) b

0.35 1.32

1.50 2.15c

overlap (γ) 0.23 0.61

Predicted values are calculated using eq 1 based on literature values of N0(α − β). bReference 16. cReference 17. 1266

dx.doi.org/10.1021/jz300320y | J. Phys. Chem. Lett. 2012, 3, 1264−1268

The Journal of Physical Chemistry Letters

Letter

130 °C for 1.5 h. The reaction flask was placed under N2 and the temperature reduced to below 80 °C for the addition of 0.093 mmol of (Me4N)2[Cd4(SePh)10] and 0.260 mmol of Se powder. The temperature was increased to 130 °C and maintained for 1.5 h and then increased to 220 °C and maintained for 1 h. After growth, the solution was rapidly cooled using a water bath. The nanocrystals were suspended with the addition of ∼4 mL of toluene when the temperature dropped to ∼70 °C. For the hot injection synthesis, a solution of the following was prepared and degassed at 130 °C: 80 mmol of octadecene, 1.7 mmol of oleic acid, 2.1 mmol of HDA, 0.312 mmol of cadmium acetate dehydrate, and 23 μmol of cobalt(II) acetate tetrahydrate. A separate air-free solution of 25 mmol of Se powder in 1 mL of tributylphosphine was prepared. The former solution was heated to 310 °C, and the latter solution was added quickly via a syringe with vigorous stirring. The nanocrystals were allowed to grow for ∼7 min, after which they were cooled with a water bath. Nanocrystals prepared by both methods were washed with ethanol, followed by centrifugation and resuspension in toluene. They were then sonicated in toluene with excess trioctylphosphine oxide to remove surface cations, washed again, and resuspended, as described above. Concentrated suspensions of each were dropcoated onto quartz substrates for spectroscopic measurements. Physical Characterization. The TM2+ mole fraction (x) was determined by inductively coupled plasma mass spectrometry (ICP-MS). Absorption spectra (295 K) were collected using 1 mm cuvettes and a Cary 500 (Varian) spectrophotometer. For MCD experiments, a Janis ST-300MS cryostat with a custommade coldfinger was mounted between the poles of a GMW 45 mm electromagnet. The temperature of the coldfinger near the sample was read with a Lakeshore CX-1030-SD-1.4 L temperature sensor. MCD spectra were collected using an Aviv 40DS spectropolarimeter. All spectra were obtained at 0.63 T. MCD data are reported as θ(mdeg) = 32980ΔA, where ΔA = AL − AR. AL and AR refer to the absorption of left and right circularly polarized photons, respectively, following the sign convention of Piepho and Schatz.28

■

(2) Beaulac, R.; Archer, P. I.; Ochsenbein, S. T.; Gamelin, D. R. Mn2+-Doped CdSe Quantum Dots: New Inorganic Materials for SpinElectronics and Spin-Photonics. Adv. Funct. Mater. 2008, 18, 3873− 3891. (3) Yasuhira, T.; Uchida, K.; Matsuda, Y. H.; Miura, N.; Twardowski, A. Giant Faraday Rotation Spectra of Zn1−xMnxSe Observed in High Magnetic Fields Up To 150 T. Phys. Rev. B 2000, 61, 4685−4688. (4) Yasuhira, T.; Uchida, K.; Matsuda, Y. H.; Miura, N.; Twardowski, A. Magnetic and Non-Magnetic Faraday Rotation in ZnMnSe in High Magnetic Fields. Semicond. Sci. Technol. 1999, 14, 1161−1164. (5) Bartholomew, D. U.; Furdyna, J. K.; Ramdas, A. K. Interband Faraday-Rotation in Diluted Magnetic Semiconductors: Zn1−xMnxTe and Cd1−xMnxTe. Phys. Rev. B 1986, 34, 6943−6950. (6) Beaulac, R.; Archer, P. I.; Liu, X.; Lee, S.; Salley, G. M.; Dobrowolska, M.; Furdyna, J. K.; Gamelin, D. R. Spin-Polarizable Excitonic Luminescence in Colloidal Mn2+-Doped CdSe Quantum Dots. Nano Lett. 2008, 8, 1197−1201. (7) Harris, J. H.; Nurmikko, A. V. Formation of the Bound Magnetic Polaron in (Cd,Mn)Se. Phys. Rev. Lett. 1983, 51, 1472−1475. (8) Merkulov, I. A.; Yakovlev, D. R.; Kavokin, K. V.; Mackh, G.; Ossau, W.; Waag, A.; Landwehr, G. Hierarchy of Relaxation Times in the Formation of an Excitonic Magnetic Polaron in (CdMn)Te. JETP Lett. 1995, 62, 335−339. (9) Beaulac, R.; Schneider, L.; Archer, P. I.; Bacher, G.; Gamelin, D. R. Light-Induced Spontaneous Magnetization in Colloidal Doped Quantum Dots. Science 2009, 325, 973−976. (10) Sellers, I. R.; Oszwałdowski, R.; Whiteside, V. R.; Eginligil, M.; Petrou, A.; Zutic, I.; Chou, W.-C.; Fan, W. C.; Petukhov, A. G.; Kim, S. J.; et al. Robust Magnetic Polarons in Type-II (Zn,Mn)Te/ZnSe Quantum Dots. Phys. Rev. B 2010, 82, 195320. (11) Archer, P. I.; Santangelo, S. A.; Gamelin, D. R. Direct Observation of sp−d Exchange Interactions in Colloidal Mn2+- and Co2+-doped CdSe Quantum Dots. Nano Lett. 2007, 7, 1037−1043. (12) Archer, P. I.; Santangelo, S. A.; Gamelin, D. R. Inorganic Cluster Syntheses of TM2+-Doped Quantum Dots (CdSe, CdS, CdSe/CdS): Physical Property Dependence on Dopant Locale. J. Am. Chem. Soc. 2007, 129, 9808−9818. (13) Madelung, O. Semiconductors: Data Handbook; Springer: New York, 2004. (14) Wojtowicz, T.; Kutrowski, M.; Karczewski, G.; Kossut, J.; Konig, B.; Keller, A.; Yakovlev, D. R.; Waag, A.; Geurts, J.; Ossau, W.; et al. II−VI Quantum Structures with Tunable Electron g-Factor. J. Cryst. Growth 2000, 214/215, 378−386. (15) Wojtowicz, T.; Kutrowski, M.; Karczewski, G.; Kossut, J.; Teran, F. J.; Potemski, M. g-Factor Ddependence of the Evolution of Magneto-Optical Spectra with the Density of Quasi-Two-Dimensional Electrons in Cd1−xMnxTe/Cd1−yMgyTe Heterostructures. Phys. Rev. B 1999, 59, 10437−10440. (16) Arciszewska, M.; Nawrocki, M. Determination of the BandStructure Parameters of Cd0.95Mn0.05Se from Magnetoabsorption Measurements. J. Phys. Chem. Solids 1986, 47, 309−314. (17) Nawrocki, M.; Hamdani, F.; Lascaray, J. P.; Golacki, Z.; Deportes, J. Ion-Carrier Electron Exchange Constants for CdCoSe Semimagnetic Semiconductor. Solid State Commun. 1991, 77, 111− 114. (18) Norberg, N. S.; Parks, G. L.; Salley, G. M.; Gamelin, D. R. Giant Excitonic Zeeman Splittings in Co2+-Doped ZnSe Quantum Dots. J. Am. Chem. Soc. 2006, 128, 13195−13203. (19) Beaulac, R.; Ochsenbein, S. T.; Gamelin, D. R. Colloidal Transition Metal Doped Quantum Dots. In Semiconductor Quantum Dots, 2nd ed.; Klimov, V. I., Ed.; CRC Press: Boca Raton, FL, 2010, pp 397−453. (20) Merkulov, I. A.; Yakovlev, D. R.; Keller, A.; Ossau, W.; Geurts, J.; Waag, A.; Landwehr, G.; Karczewski, G.; Wojtowicz, T.; Kossut, J. Kinetic Exchange Between the Conduction Band Eelectrons and Magnetic Ions in Quantum-Confined Structures. Phys. Rev. Lett. 1999, 83, 1431−1434. (21) Bussian, D. A.; Crooker, S. A.; Yin, M.; Brynda, M.; Efros, A. L.; Klimov, V. I. Tunable Magnetic Exchange Interactions in Manganese-

ASSOCIATED CONTENT

S Supporting Information *

A collection of literature sp−d exchange energies and plots of the ΔEZeeman temperature dependence extended to saturation (one table and one figure). This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support from the U.S. National Science Foundation (DMR-0906814, DMR-1206221 to D.R.G. and Graduate Research Fellowship DGE-0718124 to A.M.S.) is gratefully acknowledged.

■

REFERENCES

(1) Furdyna, J. K.; Kossut, J. Diluted Magnetic Semiconductors. In Semiconductors and Semimetals; Willardson, R. K., Beer, A. C., Eds.; Academic Press: New York, 1988; Vol. 25. 1267

dx.doi.org/10.1021/jz300320y | J. Phys. Chem. Lett. 2012, 3, 1264−1268

The Journal of Physical Chemistry Letters

Letter

Doped Inverted Core−Shell ZnSe−CdSe Nanocrystals. Nat. Mater. 2009, 8, 35−40. (22) Yu, J. H.; Liu, X. Y.; Kweon, K. E.; Joo, J.; Park, J.; Ko, K.-T.; Lee, D.; Shen, S.; Tivakornsasithorn, K.; Son, J. S.; et al. Giant Zeeman Splitting in Nucleation-Controlled Doped CdSe:Mn2+ Quantum Nanoribbons. Nat. Mater. 2010, 9, 47−53. (23) Myers, R. C.; Poggio, M.; Stern, N. P.; Gossard, A. C.; Awschalom, D. D. Antiferromagnetic s−d Exchange Coupling in GaMnAs. Phys. Rev. Lett. 2005, 95, 017204. (24) Beaulac, R.; Gamelin, D. R. Two-Center Formulation of Mn2+Electron s−d Exchange Coupling in Bulk and Quantum-Confined Diluted Magnetic Semiconductors. Phys. Rev. B 2010, 82, 224401. (25) Beaulac, R.; Feng, Y.; May, J. W.; Badaeva, E.; Gamelin, D. R.; Li, X. S. Orbital Pathways for Mn2+-Carrier sp−d Exchange in Diluted Magnetic Semiconductor Quantum Dots. Phys. Rev. B 2011, 84, 195324. (26) Kuno, M.; Nirmal, M.; Bawendi, G.; Efros, A.; Rosen, M. Magnetic Circular Dichroism Study of CdSe Quantum Dots. J. Chem. Phys. 1998, 108, 4242−4247. (27) Santangelo, S. A.; Hinds, E. A.; Vlaskin, V. A.; Archer, P. I.; Gamelin, D. R. Bimodal Bond-Length Distributions in Cobalt-Doped CdSe, ZnSe, and Cd1−xZnxSe Quantum Dots. J. Am. Chem. Soc. 2007, 129, 3973−3978. (28) Piepho, S. B.; Schatz, P. N. Group Theory in Spectroscopy with Applications to Magnetic Circular Dichroism; Wiley: New York, 1983.

■

NOTE ADDED AFTER ASAP PUBLICATION This paper was published ASAP on April 30, 2012. Equation 3b was corrected. The revised paper was reposted on May 2, 2012.

1268

dx.doi.org/10.1021/jz300320y | J. Phys. Chem. Lett. 2012, 3, 1264−1268