- Email: [email protected]
Spin relaxation and antiferromagnetic coupling in semiconductor quantum dots
ARTICLE IN PRESS
Physica E 32 (2006) 354–358 www.elsevier.com/locate/physe
Spin relaxation and antiferromagnetic coupling in semiconductor quantum dots A. Tackeuchia,, T. Kurodaa, K. Yamaguchib, Y. Nakatac,1, N. Yokoyamac, T. Takagaharad a
b
Waseda University, Tokyo 169-8555, Japan University of Electro-Communications,Tokyo182-8585, Japan c Fujitsu Laboratories Ltd., Atsugi 243-0197, Japan d Kyoto Institute of Technology, Kyoto 606-8585, Japan Available online 7 February 2006
Abstract We report carrier spin dynamics in highly uniform self-assembled InAs quantum dots and the observation of antiferromagnetic coupling between semiconductor quantum dots. The spin relaxation times in the ground state and the first excited state were measured to be 1.0 and 0.6 ns, respectively, without the disturbance of inhomogeneous broadening. The measured spin relaxation time decreases rapidly from 1.1 ns at 10 K to 200 ps at 130 K. This large change in the spin relaxation time is well-explained in terms of the mechanism of acoustic phonon emission. In coupled quantum dots, the formation of antiferromagnetic coupling is directly observed. Electron spins are found to flip at 80 ps after photoexcitation via the interdot exchange interaction. The antiferromagnetic coupling exists at temperatures lower than 50–80 K. A model calculation based on the Heitler–London approximation supports the finding that the antiferromagnetic coupling is observable at low temperature. These carrier spin features in quantum dots are suitable for the future quantum computation. r 2006 Elsevier B.V. All rights reserved. PACS: 72.25.Rb; 78.67.Hc; 78.47.+p Keywords: Spin relaxation; InAs; D’yakonov–Perel’; Elliott–Yafet; Spin; Antiferromagnetism; Quantum dot; Semiconductor
1. Spin relaxation dynamics in highly uniform InAs quantum dots (QDs) Recently, interesting features of electron spin in III–V semiconductor QDs have been revealed. In this paper, we show that carriers in QDs have a long spin relaxation time of approximately 1 ns or longer [1,2], and that an antiferromagnetic coupling is present between QDs by interdot exchange interaction [3]. These interesting carrier spin features in QDs are suitable for future quantum computation. The spin-related phenomena in quantum-confined structures became observable in the 1990s using a few kinds of Corresponding author. Tel./fax: +81 3 5286 3853.
E-mail address: [email protected] (A. Tackeuchi). Current address. Institute of Industrial Science, Nanoelectronic Collaborative Research Center, University of Tokyo, Tokyo 153-8505, Japan. 1
1386-9477/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2005.12.126
time-resolved measurements [4,5]. We proposed the spindependent pump and probe measurement and directly observed the spin relaxation in GaAs quantum wells in 1990 [4]. However, the inhomogeneous broadening of QDs has made it difficult to observe the clear spin relaxation, because the ground-state energies of some QDs are equal to the first excited state energies of the other QDs. To overcome this problem, we have adopted highly uniform QDs as samples which typically have the narrowest photoluminescence (PL) line width of 18.6 meV [6]. We report the spin relaxation dynamics in QDs revealed by spin-dependent time-resolved PL measurements. The carrier density dependence and the temperature dependence of the spin relaxation times indicate the relevance of the mechanism of acoustic phonon emission. The highly uniform QD sample was grown on semiinsulating GaAs (0 0 1) substrates by MBE [6]. The GaAs buffer layer of 200 nm thickness was prepared at 590 1C. The InAs dots were grown at 500 1C. The growth rate of
ARTICLE IN PRESS A. Tackeuchi et al. / Physica E 32 (2006) 354–358
the InAs was 0.03 monolayer/s. The InAs coverage was 2.65 monolayers. The GaAs cap layer of 120 nm thickness was grown at 460 1C. Enhanced surface migration due to the low arsenic pressure during the capping growth leads to a narrow size distribution. The transient spin polarization was time-resolved by spin-dependent PL measurement. The optical source was a Ti:sapphire laser which generated 100 fs pulses with an 80 MHz repetition rate. To generate and measure the spin polarization of a QD, we used the optical transition selection rule between carrier spin and circularly polarized light. The excitation laser wavelength was tuned to near the band gap of GaAs at 10 K. The incident light was right circularly polarized using a quarter-wave plate in the incident beam. In bulk GaAs, the ideal initial spin polarization of electrons in GaAs is 50%. Here, the spin polarization is defined by (n+–n)/(n++n), where n+ and n are the electron population with up- and down-spin, respectively. The spin-aligned carriers generated in the GaAs barrier layer energetically relax into QDs with spin relaxation and, subsequently, recombine in the lowest energy states. The collected luminescence passes through an analyzer consisting of an achromatic quarter-wave plate (CVI ACWP-series) and a linear polarizer arranged so that right or left circularly polarized emission can be selected. The transmitted light was dispersed in a spectrometer and detected with a synchroscan streak camera (Hamamatsu Photonics C4334-04) with a time resolution of 15 ps. The PL spectra of the highly uniform QDs timeintegrated during 0.9 ns after photoexcitation at 10 K are shown in Fig. 1. Note that the PL peaks of the ground state and the first excited state are clearly separated, and that the full-width at half-maximum of the ground state PL peak is
30
10 K
Ground state
PL intensity (arb. units)
during 0.9 ns 80 W/cm2
20 /+ /10
First excited state
0 1100
1150 Wavelength (nm)
1200
Fig. 1. Time-integrated PL spectra during 0.9 ns after photoexcitation. The black and gray curves indicate the PL intensity of the same (I+) and opposite (I) circular polarizations from the pump laser, respectively. The difference between black and gray curves corresponds to the spin polarization.
355
only 23 meV. Theoretically, the hole spin is expected to have a very short spin relaxation time in III–V compound semi conductors because spin is not a good quantum number except for the G point [7]. Therefore, this spin polarization can be attributed to the electron spin or the exciton spin. The clearly observed spin polarization indicates that the spin-polarized carriers initially photoexcited in the GaAs layer can preserve their spin polarization after their relaxation into QDs. Note that the spin polarization, (I+–I )/(I ++I ), of 16% in the first excited state is greater than that of 5% in the ground state. This indicates directly the existence of the spin Pauli blocking [1]. An electron in the first excited state which has the same spin as that in the ground state cannot relax to the ground state due to the Pauli principle. This results in greater spin polarization in the first excited state. The spin relaxation time is equal to twice the decay time of the spin polarization. The evaluated spin relaxation time is 1.0 ns, which is comparable to that of 1.3 ns in the conventional Stranski–Krastanov (SK) dots with large inhomogeneous broadening [2]. The spin relaxation time in the first excited state was evaluated to be 0.6 ns. These spin relaxation times are much longer than those in quantum wells of several tens of picoseconds [4]. The spin relaxation time is needed to be 103–105 times longer than one spin flip operation for the quantum computation. These long spin relaxation times are preferable for future quantum information processing. In an ideal QD structure, the D’yakonov–Perel’ process [8], which is one of the most significant spin relaxation mechanisms for III–V quantum wells [9] should be suppressed. Also, the spin flip due to scattering would be restricted by the comb-shaped density of states, resulting in the reduction of the Elliott–Yafet (EY) process which is significant in narrow band-gap materials [10,11]. The other candidate is the Bir–Aronov–Pikus (BAP) process [12] which arises from the exchange interaction between electrons and holes, and is dominant in quantum wells at low temperature [13]. This mechanism is stronger at lower temperatures because the overlap of electrons and holes increases. We have investigated the dependence of spin polarization decay time on the excitation power density at 10 K, as shown in Fig. 2. The spin polarization decay time does not depend on the carrier density. The absence of the carrier density dependence of the spin relaxation time indicates that the BAP process is not a significant spin relaxation mechanism at 10 K. The EY process depends on temperature, because some parameters such as the carrier scattering time and the band gap energy change dependent on temperature. The temperature dependence of the spin relaxation time of the highly uniform QDs is plotted in Fig. 3 along with the PL decay time. The measured spin relaxation time decreases rapidly from 1.1ns at 10 K to 200 ps at 130 K. A similar dependence was reported for an InGaAs quantum disk [14]. The change in the spin relaxation time between 10 and
ARTICLE IN PRESS A. Tackeuchi et al. / Physica E 32 (2006) 354–358
356
related mechanisms become significant at high temperature. We have fitted the result under the assumption that the spin relaxation rate is proportional to the acoustic phonon emission rate, as follows:
700 10K Decay time of spin polarization (ps)
600 Ground state
1 1 . /1þ ts expðE=kT Þ 1
500
Here, E is the acoustic phonon energy. The dependence of the spin relaxation time on the temperature is well-fitted by the curve with the energy, E, of 2.7 meV, as shown in Fig. 3. This energy value seems to be reasonable in reference to recent experimental and theoretical results on the exciton fine structures in a single QD [15–17]. Thus, at temperatures from 10 to 130 K, the acoustic phonon process between the exciton ground state and the excited exciton state is shown to be a dominant spin relaxation mechanism.
400
300
First excited state
200
100
0 0
50 100 150 Excitation power density (W/cm2)
200
Fig. 2. Excitation power dependence of the spin polarization decay time in the ground (closed circle) and the first excited (open square) states. Solid lines show the least-square fittings.
1200 Spin relaxation time 1000
Time (ps)
800
600
PL decay time
400
200
0 0
20
40
60 80 100 Temperature (K)
(1)
120
140
Fig. 3. Temperature dependence of the spin relaxation time (closed circle) of the ground state and the PL decay time (open square) for the pumping power density of 80 W/cm2. The solid line shows the least-square fitting assuming acoustic phonon emission.
130 K is significantly larger than that in PL decay time. Since the relatively small change in the PL decay time implies that the overlap of wave functions between an electron and a hole does not change largely, the large change in the spin relaxation time suggests that scattering
2. Electron spin flip by antiferromagnetic coupling between semiconductor QDs There is a possibility of flipping the carrier spin in one QD by controlling the carrier spin in the adjacent QD via the interdot exchange interaction. Such a correlation will be useful in quantum computation [18]. Theoretically, the exchange interaction energy between QDs is predicted to be negative, thereby leading to antiferromagnetism [19]. Experimentally, however, detecting the interdot exchange interaction had remained a formidable challenge. We report that an antiferromagnetic coupling that proves the interdot exchange interaction energy to be negative can be measured in non-magnetic semiconductor-coupled QDs [3]. The vertically aligned asymmetric-coupled QDs (ACQDs) consist of In0.9Al0.1As SK mode dots with 2 MLs deposition, a GaAs barrier layer and InAs SK QDs with 2 ML deposition. The spin polarization of each QD can be separated using the PL energy difference. Fig. 4 shows cross-sectional transmission electron microscope (TEM) dark-field images of samples. The upper InAs QDs are vertically aligned to the positions of lower In0.9Al0.1As QDs. Samples ACQD-A and ACQD-B have GaAs barrier thicknesses, LB, of 10 and 8 nm, respectively. These barrier thicknesses between the top of the InAlAs dots and the bottom of InAs dots are the average values evaluated for several dots in the TEM dark field images. TEM bright field images have average barrier thicknesses of 8.9 and 6.4 nm for ACQD-A and ACQD-B, respectively. The dot density is about 1 1011 cm2 in ACQD-A, which is higher than that in ACQD-B. We have calculated the exchange energy using the Heitler–London approximation according to Itoh et al. [19]. The energy difference between the antiferromagnetic singlet state and the ferromagnetic triplet states is calculated to be 1.61, 0.34 and 0.07 meV for LB ¼ 6, 8 and 10 nm, respectively. These values correspond to kBT of 18.7, 3.9 and 0.8 K, respectively. In actual SK dots, there is a height fluctuation. This calculation supports the
ARTICLE IN PRESS A. Tackeuchi et al. / Physica E 32 (2006) 354–358
Fig. 4. Cross-sectional transmission electron microscope dark-field images of asymmetric-coupled quantum dots B (ACQD-B) with LB ¼ 8 nm. The coupled QDs consist of InAs QDs, a GaAs barrier layer and In0.9Al0.1As QDs, where upper InAs QDs are vertically aligned to the positions of lower In0.9Al0.1As QDs.
500 10K InAs QDs PL intensity (arb. units)
400
300
200
InAlAs QDs
100
357
pling is observed in both ACQDs. The magnetic coupling should disappear as the temperature is raised. The antiferromagnetic behavior disappears between 50 and 80 K for both ACQD-A and ACQD-B. The transient behavior of antiferromagnetism is shown in Fig. 6 as the time evolution of PL polarization. Initially, the spin polarizations of both dots are in the same direction, although greater spin polarization is observed in In0.9Al0.1As QDs than in InAs QDs. The initial degree of polarization of In0.9Al0.1As QDs in ACQD-A is 40%. In contrast, that in InAs QDs is only 20%. This initial difference in the spin polarization might be due to the difference in the energy depth of the lowest energy states, which affects the number of spin flip scattering events during electron relaxation to the lowest energy states. This initial large difference in the spin polarization between In0.9Al0.1As QDs and InAs QDs causes the observable spin flip mainly in InAs QDs. The initial combination of spins in the coupled QDs is aa. Since the probabilities of spin flip by interdot exchange interaction from aa to ab and aa to ba are the same, the spin polarizations after spin flip become (P1–P2)/2 and (P2–P1)/2 from the initial spin polarizations, P1 and P2, of the respective QD. Note that the spin polarization of InAs QDs flips or inverts its sign at 80 ps after photoexcitation. This spin-flip time is the same as that of ACQD-B.
0.3-0.6 ns 900
950 1000 Wavelength (nm)
1050
40
1100
ACQD-A 10K : 890-920 nm
Fig. 5. Time-integrated PL spectra during 0.3–0.6 ns of ACQD-A. The black and gray curves indicate the PL intensity of the same (I+) and opposite (I) circular polarizations from the pump laser, respectively. The difference between black and gray curves corresponds to the spin polarization.
Up Spin polarization (%)
20
0 : 1000-1050 nm 20
InAs QDs
10
0
-10 Down
following experimental finding that the antiferromagnetic coupling is observable at low temperature. The transient spin polarization was time-resolved by spin-dependent PL measurement. The excitation laser wavelength is tuned to near the band gap of GaAs, e.g., 816 nm at 10 K.Fig. 5 shows the time-integrated PL spectra during 0.3 and 0.6 ns after the photoexcitation. In0.9Al0.1As QDs and InAs QDs have PL peaks at 910 and 1020 nm, respectively. The black and gray curves indicate the PL intensity of the same (I+) and opposite (I) circular polarizations from the pump laser, respectively. The difference between the black and gray curves corresponds to the spin polarization. The striking feature is that I+ is higher than I at around 910 nm, and lower than I at around 1020 nm at 10 K, which indicates that the spin polarization of In0.9Al0.1As QDs at around 910 nm is opposite that of InAs QDs at around 1020 nm. This is a direct indication that the antiferromagentic coupling is induced in non-magnetic semiconductor coupled QDs. This antiferromagnetic cou-
InAlAS QDs
Up
0 850
0
0.2
0.4 Time (ns)
0.6
0.8
Fig. 6. Time evolution of the spin polarization at 890–920 nm (upper curve) corresponds to In0.9Al0.1As QDs. Time evolution of the spin polarization at 1000–1050 nm (lower curve) corresponds to InAs QDs. The spin polarization of InAs QD flips.
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The spin polarization of InAs QDs reaches a minimum at 0.8 ns. Then the reversed spin polarization relaxes. The leastsquares fit applying a single exponential decay between 0.8 and 2 ns gives a spin relaxation time of 10 ns. This long relaxation time is in contrast to the spin relaxation time of 1.0 ns in the isolated InAs QDs. This long spin relaxation time implies that the rate of spin alignment by the exchange interaction compensates for the rate of depolarization by other spin relaxation mechanisms when the antiferromagnetic coupling is induced. In application, it may be possible to preserve information in the form of spin polarization under antiferromagnetic coupling. 3. Conclusion We have investigated carrier spin dynamics in highly uniform self-assembled InAs quantum dots. The spin relaxation times in the ground state and the first excited state were measured to be 1.0 and 0.6 ns, respectively, without the disturbance of inhomogeneous broadening. The measured spin relaxation time decreases rapidly from 1.1 ns at 10 K to 200 ps at 130 K. This large change in the spin relaxation time is well-explained in terms of the mechanism of acoustic phonon emission. In the coupled quantum dots, the formation of antiferromagnetic coupling is directly observed. Electron spins are found to flip at 80 ps after photoexcitation via the interdot exchange interaction. The antiferromagnetic coupling exists at temperatures lower than 50–80 K. A model calculation based on the Heitler–London approximation supports the finding that the antiferromagnetic coupling is observable at low temperature. These spin features are suitable for the future quantum computation. Acknowledgment The authors would like to thank Professor S. Muto of Hokkaido University for his useful discussions. This work
was partly supported by the 21st Century COE Program and the High-Tech Research Center Project from the Ministry of Education, Culture, Sports, Science and Technology.
References [1] A. Tackeuchi, R. Ohtsubo, K. Yamaguchi, M. Murayama, T. Kitamura, T. Kuroda, T. Takagahara, Appl. Phys. Lett. 84 (2004) 3576. [2] H. Gotoh, H. Ando, H. Kamada, A. Chavez-Pirson, J. Tem-myo, Appl. Phys. Lett. 72 (1998) 1341. [3] A. Tackeuchi, T. Kuroda, Y. Nakata, M. Murayama, T. Kitamura, N. Yokoyama, Jpn. J. Appl. Phys. 42 (2003) 4278. [4] A. Tackeuchi, S. Muto, T. Inata, T. Fujii, Appl. Phys. Lett. 56 (1990) 2213. [5] M. Kohl, M.R. Freeman, D.D. Awschalom, J.M. Hong, Phys. Rev. B 44 (1991) 5923. [6] K. Yamaguchi, K. Yujobo, T. Kaizu, Jpn. J. Appl. Phys. 39 (2000) L1245. [7] T. Uenoyama, L.J. Sham, Phys. Rev. Lett. 64 (1990) 3070. [8] M.I. D’yakonov, V. Yu. Kachorovski, Sov. Phys. Semicond. 20 (1986) 110. [9] A. Tackeuchi, Y. Nishikawa, O. Wada, Appl. Phys. Lett. 68 (1996) 797. [10] R.J. Elliott, Phys. Rev. 96 (1954) 266. [11] Y. Yafet, Solid State Phys. 14 (1963) 1. [12] G.L. Bir, A.G. Aronov, G.E. Pikus, Sov. Phys. JETP 42 (1976) 705. [13] J. Wagner, H. Schneider, D. Richards, A. Fischer, K. Ploog, Phys. Rev. B 47 (1993) 4786. [14] H. Gotoh, H. Kamada, H. Ando, J. Temmyo, Jpn. J. Appl. Phys. 42 (2003) 3340. [15] D. Gammon, E.S. Snow, B.V. Shanabrook, D.S. Katzer, D. Park, Science 273 (1996) 87. [16] H. Htoon, D. Kulik, O. Baklenov, A.L. Holmes Jr., T. Takagahara, C.K. Shih, Phys. Rev. B 63 (2001) 241303. [17] T. Takagahara, Phys. Rev. B 62 (2000) 16840. [18] D. Loss, D.P. Divincenzo, Phys. Rev. A 57 (1998) 120. [19] S. Itoh, S. Muto, Y. Ebiko, H. Sasakura, K. Shiramine, Jpn. J. Appl. Phys. 38 (1999) L917.
Physica E 32 (2006) 354–358 www.elsevier.com/locate/physe
Spin relaxation and antiferromagnetic coupling in semiconductor quantum dots A. Tackeuchia,, T. Kurodaa, K. Yamaguchib, Y. Nakatac,1, N. Yokoyamac, T. Takagaharad a
b
Waseda University, Tokyo 169-8555, Japan University of Electro-Communications,Tokyo182-8585, Japan c Fujitsu Laboratories Ltd., Atsugi 243-0197, Japan d Kyoto Institute of Technology, Kyoto 606-8585, Japan Available online 7 February 2006
Abstract We report carrier spin dynamics in highly uniform self-assembled InAs quantum dots and the observation of antiferromagnetic coupling between semiconductor quantum dots. The spin relaxation times in the ground state and the first excited state were measured to be 1.0 and 0.6 ns, respectively, without the disturbance of inhomogeneous broadening. The measured spin relaxation time decreases rapidly from 1.1 ns at 10 K to 200 ps at 130 K. This large change in the spin relaxation time is well-explained in terms of the mechanism of acoustic phonon emission. In coupled quantum dots, the formation of antiferromagnetic coupling is directly observed. Electron spins are found to flip at 80 ps after photoexcitation via the interdot exchange interaction. The antiferromagnetic coupling exists at temperatures lower than 50–80 K. A model calculation based on the Heitler–London approximation supports the finding that the antiferromagnetic coupling is observable at low temperature. These carrier spin features in quantum dots are suitable for the future quantum computation. r 2006 Elsevier B.V. All rights reserved. PACS: 72.25.Rb; 78.67.Hc; 78.47.+p Keywords: Spin relaxation; InAs; D’yakonov–Perel’; Elliott–Yafet; Spin; Antiferromagnetism; Quantum dot; Semiconductor
1. Spin relaxation dynamics in highly uniform InAs quantum dots (QDs) Recently, interesting features of electron spin in III–V semiconductor QDs have been revealed. In this paper, we show that carriers in QDs have a long spin relaxation time of approximately 1 ns or longer [1,2], and that an antiferromagnetic coupling is present between QDs by interdot exchange interaction [3]. These interesting carrier spin features in QDs are suitable for future quantum computation. The spin-related phenomena in quantum-confined structures became observable in the 1990s using a few kinds of Corresponding author. Tel./fax: +81 3 5286 3853.
E-mail address: [email protected] (A. Tackeuchi). Current address. Institute of Industrial Science, Nanoelectronic Collaborative Research Center, University of Tokyo, Tokyo 153-8505, Japan. 1
1386-9477/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2005.12.126
time-resolved measurements [4,5]. We proposed the spindependent pump and probe measurement and directly observed the spin relaxation in GaAs quantum wells in 1990 [4]. However, the inhomogeneous broadening of QDs has made it difficult to observe the clear spin relaxation, because the ground-state energies of some QDs are equal to the first excited state energies of the other QDs. To overcome this problem, we have adopted highly uniform QDs as samples which typically have the narrowest photoluminescence (PL) line width of 18.6 meV [6]. We report the spin relaxation dynamics in QDs revealed by spin-dependent time-resolved PL measurements. The carrier density dependence and the temperature dependence of the spin relaxation times indicate the relevance of the mechanism of acoustic phonon emission. The highly uniform QD sample was grown on semiinsulating GaAs (0 0 1) substrates by MBE [6]. The GaAs buffer layer of 200 nm thickness was prepared at 590 1C. The InAs dots were grown at 500 1C. The growth rate of
ARTICLE IN PRESS A. Tackeuchi et al. / Physica E 32 (2006) 354–358
the InAs was 0.03 monolayer/s. The InAs coverage was 2.65 monolayers. The GaAs cap layer of 120 nm thickness was grown at 460 1C. Enhanced surface migration due to the low arsenic pressure during the capping growth leads to a narrow size distribution. The transient spin polarization was time-resolved by spin-dependent PL measurement. The optical source was a Ti:sapphire laser which generated 100 fs pulses with an 80 MHz repetition rate. To generate and measure the spin polarization of a QD, we used the optical transition selection rule between carrier spin and circularly polarized light. The excitation laser wavelength was tuned to near the band gap of GaAs at 10 K. The incident light was right circularly polarized using a quarter-wave plate in the incident beam. In bulk GaAs, the ideal initial spin polarization of electrons in GaAs is 50%. Here, the spin polarization is defined by (n+–n)/(n++n), where n+ and n are the electron population with up- and down-spin, respectively. The spin-aligned carriers generated in the GaAs barrier layer energetically relax into QDs with spin relaxation and, subsequently, recombine in the lowest energy states. The collected luminescence passes through an analyzer consisting of an achromatic quarter-wave plate (CVI ACWP-series) and a linear polarizer arranged so that right or left circularly polarized emission can be selected. The transmitted light was dispersed in a spectrometer and detected with a synchroscan streak camera (Hamamatsu Photonics C4334-04) with a time resolution of 15 ps. The PL spectra of the highly uniform QDs timeintegrated during 0.9 ns after photoexcitation at 10 K are shown in Fig. 1. Note that the PL peaks of the ground state and the first excited state are clearly separated, and that the full-width at half-maximum of the ground state PL peak is
30
10 K
Ground state
PL intensity (arb. units)
during 0.9 ns 80 W/cm2
20 /+ /10
First excited state
0 1100
1150 Wavelength (nm)
1200
Fig. 1. Time-integrated PL spectra during 0.9 ns after photoexcitation. The black and gray curves indicate the PL intensity of the same (I+) and opposite (I) circular polarizations from the pump laser, respectively. The difference between black and gray curves corresponds to the spin polarization.
355
only 23 meV. Theoretically, the hole spin is expected to have a very short spin relaxation time in III–V compound semi conductors because spin is not a good quantum number except for the G point [7]. Therefore, this spin polarization can be attributed to the electron spin or the exciton spin. The clearly observed spin polarization indicates that the spin-polarized carriers initially photoexcited in the GaAs layer can preserve their spin polarization after their relaxation into QDs. Note that the spin polarization, (I+–I )/(I ++I ), of 16% in the first excited state is greater than that of 5% in the ground state. This indicates directly the existence of the spin Pauli blocking [1]. An electron in the first excited state which has the same spin as that in the ground state cannot relax to the ground state due to the Pauli principle. This results in greater spin polarization in the first excited state. The spin relaxation time is equal to twice the decay time of the spin polarization. The evaluated spin relaxation time is 1.0 ns, which is comparable to that of 1.3 ns in the conventional Stranski–Krastanov (SK) dots with large inhomogeneous broadening [2]. The spin relaxation time in the first excited state was evaluated to be 0.6 ns. These spin relaxation times are much longer than those in quantum wells of several tens of picoseconds [4]. The spin relaxation time is needed to be 103–105 times longer than one spin flip operation for the quantum computation. These long spin relaxation times are preferable for future quantum information processing. In an ideal QD structure, the D’yakonov–Perel’ process [8], which is one of the most significant spin relaxation mechanisms for III–V quantum wells [9] should be suppressed. Also, the spin flip due to scattering would be restricted by the comb-shaped density of states, resulting in the reduction of the Elliott–Yafet (EY) process which is significant in narrow band-gap materials [10,11]. The other candidate is the Bir–Aronov–Pikus (BAP) process [12] which arises from the exchange interaction between electrons and holes, and is dominant in quantum wells at low temperature [13]. This mechanism is stronger at lower temperatures because the overlap of electrons and holes increases. We have investigated the dependence of spin polarization decay time on the excitation power density at 10 K, as shown in Fig. 2. The spin polarization decay time does not depend on the carrier density. The absence of the carrier density dependence of the spin relaxation time indicates that the BAP process is not a significant spin relaxation mechanism at 10 K. The EY process depends on temperature, because some parameters such as the carrier scattering time and the band gap energy change dependent on temperature. The temperature dependence of the spin relaxation time of the highly uniform QDs is plotted in Fig. 3 along with the PL decay time. The measured spin relaxation time decreases rapidly from 1.1ns at 10 K to 200 ps at 130 K. A similar dependence was reported for an InGaAs quantum disk [14]. The change in the spin relaxation time between 10 and
ARTICLE IN PRESS A. Tackeuchi et al. / Physica E 32 (2006) 354–358
356
related mechanisms become significant at high temperature. We have fitted the result under the assumption that the spin relaxation rate is proportional to the acoustic phonon emission rate, as follows:
700 10K Decay time of spin polarization (ps)
600 Ground state
1 1 . /1þ ts expðE=kT Þ 1
500
Here, E is the acoustic phonon energy. The dependence of the spin relaxation time on the temperature is well-fitted by the curve with the energy, E, of 2.7 meV, as shown in Fig. 3. This energy value seems to be reasonable in reference to recent experimental and theoretical results on the exciton fine structures in a single QD [15–17]. Thus, at temperatures from 10 to 130 K, the acoustic phonon process between the exciton ground state and the excited exciton state is shown to be a dominant spin relaxation mechanism.
400
300
First excited state
200
100
0 0
50 100 150 Excitation power density (W/cm2)
200
Fig. 2. Excitation power dependence of the spin polarization decay time in the ground (closed circle) and the first excited (open square) states. Solid lines show the least-square fittings.
1200 Spin relaxation time 1000
Time (ps)
800
600
PL decay time
400
200
0 0
20
40
60 80 100 Temperature (K)
(1)
120
140
Fig. 3. Temperature dependence of the spin relaxation time (closed circle) of the ground state and the PL decay time (open square) for the pumping power density of 80 W/cm2. The solid line shows the least-square fitting assuming acoustic phonon emission.
130 K is significantly larger than that in PL decay time. Since the relatively small change in the PL decay time implies that the overlap of wave functions between an electron and a hole does not change largely, the large change in the spin relaxation time suggests that scattering
2. Electron spin flip by antiferromagnetic coupling between semiconductor QDs There is a possibility of flipping the carrier spin in one QD by controlling the carrier spin in the adjacent QD via the interdot exchange interaction. Such a correlation will be useful in quantum computation [18]. Theoretically, the exchange interaction energy between QDs is predicted to be negative, thereby leading to antiferromagnetism [19]. Experimentally, however, detecting the interdot exchange interaction had remained a formidable challenge. We report that an antiferromagnetic coupling that proves the interdot exchange interaction energy to be negative can be measured in non-magnetic semiconductor-coupled QDs [3]. The vertically aligned asymmetric-coupled QDs (ACQDs) consist of In0.9Al0.1As SK mode dots with 2 MLs deposition, a GaAs barrier layer and InAs SK QDs with 2 ML deposition. The spin polarization of each QD can be separated using the PL energy difference. Fig. 4 shows cross-sectional transmission electron microscope (TEM) dark-field images of samples. The upper InAs QDs are vertically aligned to the positions of lower In0.9Al0.1As QDs. Samples ACQD-A and ACQD-B have GaAs barrier thicknesses, LB, of 10 and 8 nm, respectively. These barrier thicknesses between the top of the InAlAs dots and the bottom of InAs dots are the average values evaluated for several dots in the TEM dark field images. TEM bright field images have average barrier thicknesses of 8.9 and 6.4 nm for ACQD-A and ACQD-B, respectively. The dot density is about 1 1011 cm2 in ACQD-A, which is higher than that in ACQD-B. We have calculated the exchange energy using the Heitler–London approximation according to Itoh et al. [19]. The energy difference between the antiferromagnetic singlet state and the ferromagnetic triplet states is calculated to be 1.61, 0.34 and 0.07 meV for LB ¼ 6, 8 and 10 nm, respectively. These values correspond to kBT of 18.7, 3.9 and 0.8 K, respectively. In actual SK dots, there is a height fluctuation. This calculation supports the
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Fig. 4. Cross-sectional transmission electron microscope dark-field images of asymmetric-coupled quantum dots B (ACQD-B) with LB ¼ 8 nm. The coupled QDs consist of InAs QDs, a GaAs barrier layer and In0.9Al0.1As QDs, where upper InAs QDs are vertically aligned to the positions of lower In0.9Al0.1As QDs.
500 10K InAs QDs PL intensity (arb. units)
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pling is observed in both ACQDs. The magnetic coupling should disappear as the temperature is raised. The antiferromagnetic behavior disappears between 50 and 80 K for both ACQD-A and ACQD-B. The transient behavior of antiferromagnetism is shown in Fig. 6 as the time evolution of PL polarization. Initially, the spin polarizations of both dots are in the same direction, although greater spin polarization is observed in In0.9Al0.1As QDs than in InAs QDs. The initial degree of polarization of In0.9Al0.1As QDs in ACQD-A is 40%. In contrast, that in InAs QDs is only 20%. This initial difference in the spin polarization might be due to the difference in the energy depth of the lowest energy states, which affects the number of spin flip scattering events during electron relaxation to the lowest energy states. This initial large difference in the spin polarization between In0.9Al0.1As QDs and InAs QDs causes the observable spin flip mainly in InAs QDs. The initial combination of spins in the coupled QDs is aa. Since the probabilities of spin flip by interdot exchange interaction from aa to ab and aa to ba are the same, the spin polarizations after spin flip become (P1–P2)/2 and (P2–P1)/2 from the initial spin polarizations, P1 and P2, of the respective QD. Note that the spin polarization of InAs QDs flips or inverts its sign at 80 ps after photoexcitation. This spin-flip time is the same as that of ACQD-B.
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Fig. 5. Time-integrated PL spectra during 0.3–0.6 ns of ACQD-A. The black and gray curves indicate the PL intensity of the same (I+) and opposite (I) circular polarizations from the pump laser, respectively. The difference between black and gray curves corresponds to the spin polarization.
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following experimental finding that the antiferromagnetic coupling is observable at low temperature. The transient spin polarization was time-resolved by spin-dependent PL measurement. The excitation laser wavelength is tuned to near the band gap of GaAs, e.g., 816 nm at 10 K.Fig. 5 shows the time-integrated PL spectra during 0.3 and 0.6 ns after the photoexcitation. In0.9Al0.1As QDs and InAs QDs have PL peaks at 910 and 1020 nm, respectively. The black and gray curves indicate the PL intensity of the same (I+) and opposite (I) circular polarizations from the pump laser, respectively. The difference between the black and gray curves corresponds to the spin polarization. The striking feature is that I+ is higher than I at around 910 nm, and lower than I at around 1020 nm at 10 K, which indicates that the spin polarization of In0.9Al0.1As QDs at around 910 nm is opposite that of InAs QDs at around 1020 nm. This is a direct indication that the antiferromagentic coupling is induced in non-magnetic semiconductor coupled QDs. This antiferromagnetic cou-
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Fig. 6. Time evolution of the spin polarization at 890–920 nm (upper curve) corresponds to In0.9Al0.1As QDs. Time evolution of the spin polarization at 1000–1050 nm (lower curve) corresponds to InAs QDs. The spin polarization of InAs QD flips.
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The spin polarization of InAs QDs reaches a minimum at 0.8 ns. Then the reversed spin polarization relaxes. The leastsquares fit applying a single exponential decay between 0.8 and 2 ns gives a spin relaxation time of 10 ns. This long relaxation time is in contrast to the spin relaxation time of 1.0 ns in the isolated InAs QDs. This long spin relaxation time implies that the rate of spin alignment by the exchange interaction compensates for the rate of depolarization by other spin relaxation mechanisms when the antiferromagnetic coupling is induced. In application, it may be possible to preserve information in the form of spin polarization under antiferromagnetic coupling. 3. Conclusion We have investigated carrier spin dynamics in highly uniform self-assembled InAs quantum dots. The spin relaxation times in the ground state and the first excited state were measured to be 1.0 and 0.6 ns, respectively, without the disturbance of inhomogeneous broadening. The measured spin relaxation time decreases rapidly from 1.1 ns at 10 K to 200 ps at 130 K. This large change in the spin relaxation time is well-explained in terms of the mechanism of acoustic phonon emission. In the coupled quantum dots, the formation of antiferromagnetic coupling is directly observed. Electron spins are found to flip at 80 ps after photoexcitation via the interdot exchange interaction. The antiferromagnetic coupling exists at temperatures lower than 50–80 K. A model calculation based on the Heitler–London approximation supports the finding that the antiferromagnetic coupling is observable at low temperature. These spin features are suitable for the future quantum computation. Acknowledgment The authors would like to thank Professor S. Muto of Hokkaido University for his useful discussions. This work
was partly supported by the 21st Century COE Program and the High-Tech Research Center Project from the Ministry of Education, Culture, Sports, Science and Technology.
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