phys. stat. sol. (b) 243, No. 4, 858 – 862 (2006) / DOI 10.1002/pssb.200564737
Nanosecond spin memory of electrons in CdTe/CdMgTe quantum wells G. V. Astakhov*, 1, 3, T. Kiessling1, D. R. Yakovlev2, 3, E. A. Zhukov2, 4, M. Bayer2, W. Ossau1, B. P. Zakharchenya3, G. Karczewski5, T. Wojtowicz5, and J. Kossut5 1 2 3 4 5
Physikalisches Institut der Universität Würzburg, 97074 Würzburg, Germany Experimentelle Physik 2, Universität Dortmund, 44221 Dortmund, Germany A.F. Ioffe Physico-Technical Institute, Russian Academy of Sciences, 194021 St.Petersburg, Russia Faculty of Physics, M.V. Lomonosov Moscow State University, 119992 Moscow, Russia Institute of Physics, Polish Academy of Sciences, 02668 Warsaw, Poland
Received 12 September 2005, revised 3 October 2005, accepted 2 January 2006 Published online 6 February 2006 PACS 76.30.Pk, 78.47.+p, 78.66.Hf, 78.67.De We report on spin memory relaxation time τ s of free electrons in CdTe-based quantum wells which is found to be in the nanosecond range. In these studies two different techniques have been exploited: (i) the Hanle effect under cw excitation and (ii) the time-resolved pump-&-probe Kerr rotation measured under excitation by 1.8-ps optical pulses. These independent techniques give very close results τ s = 19 ns and τ s = 14 ns, respectively. To our knowledge this is by two orders of magnitude longer than the electron spin relaxation times reported for CdTe-based quantum wells so far. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction Rising interest to spin-related phenomena in semiconductors is governed by possible application in information processing. It requires preparation of a given spin state of a carrier and its subsequent manipulation. Diluted magnetic semiconductors, containing magnetic impurities, are very perspective materials for spintronics. Due to giant Zeeman splitting spin-up (≠) and spin-down (Ø) states of conducting electrons can be separated in relatively low magnetic fields and these spin polarized electrons can be injected into a nonmagnetic semiconductor [1, 2]. II–VI semiconductors (as CdTe) are most attractive for these purposes as magnetic impurities (i.e., Mn) can be introduced isoelectronically, which leads to a better quality of the semiconductor host. At the same time, the long-lived spin coherence is essential for subsequent spin manipulation. Indeed, long spin coherence of electrons exceeding 100 ns has been found in bulk GaAs [3–5]. Recently, spin relaxation time τ s = 10 ns was also reported for n-doped GaAs quantum wells (QWs) [6]. The longest time reported for CdTe QWs so far is 200 ps [7]. In these paper we report a very long spin memory of free electrons τ s = 19 ns in CdTe QWs. This value is even larger than that in similar GaAs QWs [6]. Our findings suggest that spintronic devises fabricated on all-made II–VI semiconductor heterostructures could be as promising as their III–V analogs. We have investigated structures with a single 80-Å CdTe/Cd0.7Mg0.3Te QW grown by molecular beam epitaxy on (001)GaAs substrate. Free electrons are provided due to modulation doping by iodine impurities in the Cd0.7Mg0.3Te barrier at the distance of 100 Å from the CdTe QW. An electron density in the QW of ne = 8 × 1010 cm–2 was evaluated by means of an optical method [8]. *
Corresponding author: e-mail:
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© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Original Paper
phys. stat. sol. (b) 243, No. 4 (2006)
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Fig. 1 (online colour at: www.pss-b.com) (a) Photoluminescence spectrum of 80-Å CdTe/Cd0.7Mg0.3Te QW under quasi-resonant excitation with Pexc = 2 mW. Excitation energy is set to Eexc = 1.648 eV and shown by the arrow. Two peaks attributed to the neutral exciton (X) and the negatively charged trion (T) are well resolved. B = 0 T and T = 2 K. (b) The Hanle curves measured at the X and T are shown by open and solid symbols, respectively. Solid lines are fits with B1/ 2 = 278 mT for the exciton and B1/ 2 = 237 mT for the trion. The Hanle curves in the range from –4 to +4 mT are enlarged in Fig. 2.
All experiments reported here were carried out at a temperature of 2 K, samples were immersed in pumped liquid helium. For Hanle experiments magnetic fields provided by an electromagnet were applied in the sample plane (Voigt geometry). For continuous wave (cw) excitation we used a dye-laser (pumped by an Ar-ion laser) focused to a 100 µm spot. Excitation power was in the range from 2 to 18 mW. In order to prevent nuclei spin contribution to the optical orientation signal [9] the circular polarized excitation was modulated at a frequency of 50 kHz using photoelastic quartz modulator. Circular polarization degree of emission was detected by an avalanche Si-based photodiode and a two channel photon counter. For time-resolved experiments we used the pump-&-probe technique with polarization sensitivity for detection of the spin beats (see e.g. [10]). Magnetic fields in the Voigt geometry were provided by a superconducting solenoid. Ti:sapphire laser with 1.8-ps pulses at a frequency of 75.6 MHz was tuned in the resonance with the QW excitonic transition. The pump beam was circularly polarized again by means of photoelastic quartz modulator operating at 50 kHz. Its excitation power was kept close to the low possible limit in the range from 1 to 3 mW. The probe beam was linearly polarized and its intensity was 10–20% of the pump beam. The photoinduced Kerr rotation of the reflected probe beam was detected by a balanced diode detector and a lock-in amplifier. We used this effect to monitor net spin polarization as a function of time delay between pump and probe beams. Typical photoluminescence (PL) spectrum is presented in Fig. 1(a). It consists of a line doublet separated by 4 meV. The high-energy resonance is attributed to the neutral exciton (X). The low-energy resonance originates from the negatively charged trion (T), consisting of a hole and two electrons [11]. Detailed investigations show that this is the singlet state of the +trion -[12], +i.e., total electron spin is zero σ σ σ σP = ( I I ) / ( I + I ) the degree of circular polarization of these states in emisSe = 0 . We measure ± sion. Here, I σ is the PL intensity under σ ± excitation (it is always detected in σ + ). Due to optical selection rules P is proportional to the spin polarization. In order to measure spin memory we exploit the Hanle effect, which is suppression of the optically created spin polarization induced by in-plane magnetic fields in steady-state conditions. Electron spins precess around magnetic field direction with the Larmor frequency ω L = g e µ B B/ . As a result, the mean value of the electron spin continuously decreases with increasing magnetic fields and the decrease is described by Lorentz curve [9]. When ω LTs = 1 the spin polarization is reduced by 50%. This condition defines characteristic magnetic field B1/ 2 = / ( µ B g eTs ) allowing to obtain spin life time Ts if g-factor is known. In the studied sample the electron g-factor is g e = -1.35 according to the time-resolved Kerr www.pss-b.com
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Fig. 2 (online colour at: www.pss-b.com) Hanle curves related to the spin depolarization of free electrons in 80-Å CdTe/Cd0.7Mg0.3Te QW. (a), (b) detection at the neutral exciton (X) emission and (c) detection at the negatively charged trion (T) emission. Excitation energy is t he same as in Fig. 1(a). Excitation power: (a) Pexc = 18 mW, (b) Pexc = 2 mW, and (c) Pexc = 13 mW. Symbols are experimental data and C , Eqs. (1) and (2). (d) The characteristic maglines are fits assuming classical Lorentz curve A + 1 + ( B/B1/ 2 ) 2 netic fields B1/ 2 = / ( µ B g eτ s ) found from these fits (solid symbols correspond to the exciton, and an open symbol corresponds to the trion) are shown as a function of excitation power. Extrapolation to the Pexc Æ 0 gives B1/ 2 = 0.45 mT. With electron g-factor g e = -1.35 it corresponds to the spin relaxation time of free electrons τ s = 19 ns.
rotation as we show in Fig. 3(a). It is worth to note that in-plane hole g-factor is supposed to be zero and, therefore, holes do not contribute to the Hanle effect. The Hanle curve detected at the X-line is shown in Fig. 1(b). The observed incomplete depolarization of the exciton is probably caused by the hole contribution which polarization is not affected by in-plane magnetic fields. From the best fit (solid line) we found B1/ 2 = 278 mT, corresponding to Ts = 31 ps. For -1 -1 -1 the case of exciton Ts = τ J + τ s , and such a short Ts we ascribe to the exciton life time τ J . From the simple point of view trions should not contribute to the Hanle effect because their total electron spin is zero (singlet state). However, this is not the case, as one can see in Fig. 1(b) where a strong optical orientation of 15% is shown. From the Hanle curve B1/ 2 = 237 mT and Ts = 36 ps, which is very close to that of the exciton. The point is that the trion is formed from the exciton and an electron X + e Æ T . Hence, polarizations of trions, excitons and free electrons appear to be interconnected. In order to describe such a behavior we use a qualitative approach developed by Dzhioev et al. [6]: PX ª Pin - fPe
and
PT ª PX + Pe .
(1)
Here, Pin is initial polarization of excitons, PX and PT are polarizations of the exciton and the trion emission, respectively. It is important that these values are contributed by the polarization of free elec© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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Original Paper
phys. stat. sol. (b) 243, No. 4 (2006)
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Fig. 3 (online colour at: www.pss-b.com) (a) Dynamics of the Kerr rotation signal measured in 250 mT for a 80- Å CdTe/Cd0.7Mg0.3Te QW with resonant trion excitation (symbols). Fit (solid curve) allows Ê t ˆ gµ B to determine elecron g-factor assuming A exp Á - ˜ cos Ê e B t ˆ , | g e | = 1.35 . Oscillations at negative Ë ¯ * Ë T ¯ 2
delays to the pump pulses evidence that the spin relaxation time is longer than 13.2 ns. (b) Resonance spin amplification signal measured at a delay ∆t = -1.12 ns. Insert shows a fit based on Eq. (3) allowing to determine the spin relaxation time of free electrons τ s = 14 ns. T = 2 K.
trons Pe . This contribution differs by a factor f and opposite in the case of X and T. Depolarization of free electrons in magnetic fields is described by a standard expression (see Ref. [9]) Pe ( B ) =
Pe (0) , 1 + ( B/B1/ 2 ) 2
(2)
and allows directly to obtain spin relaxation time of free electrons τ s . Indeed, we observe the behavior in accordance with Eqs. (1) and (2) in the field range from –4 to +4 mT. This is most clearly seen in the enlarged scale presented in Fig. 2. We conclude from Eq. (1) that Pe < 0. From the best fit we found characteristic magnetic fields for different excitation power and extrapolation to zero gives B1/ 2 = 0.45 mT as shown in Fig. 2(d). It corresponds to the spin relaxation time of unperturbed electrons τ s = / ( g e µ B B1/ 2 ) = 19 ns. The spin relaxation time can be independently measured using pump-&-probe technique. Figure 3(a) displays the typical time-resolved Kerr signal α (t ) measured at a magnetic field B = 250 mT and pump power of 3 mW. Characteristic spin beats originate from the coherent precession of the spin oriented Ê t ˆ gµ B electrons around the magnetic field direction. It is fitted by the expression A exp Á - ˜ cos Ê e B t ˆ Ë ¯ * Ë T ¯ 2
with electron g-factor g e = -1.35 and T2* = 3 ns. However, at such relatively high magnetic field the spin decay T2* is dominated by inhomogeneous dephasing due to differences in electron precession frequencies. It gives spin memory T2* Æ τ s in the limit of low (by order of mT) magnetic fields B Æ 0. We note that a signal is still observed at negative time delays (Fig. 3(a)). This confirms that τ s should be not shorter than the time period Trep = 13.2 ns between the pump pulses. In this case it is much more convenient to use a resonant spin amplification (RSA) technique [4]. An essential of RSA is excitation of spin precession by a pump pulse which is in phase with precessing spin polarization induced by previous pump pulses. It was measured for scanning magnetic field at a fixed negative delay ∆t = -1.12 ns. At resonant conditions sharp peaks appear in RSA signal as shown in Fig. 3(b). The smaller peak linewidth the more pump pulses are coming in phase to contribute to the www.pss-b.com
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G. V. Astakhov et al.: Nanosecond spin memory of electrons
RSA signal, and therefore the longer spin relaxation time is. We use the following equation from Ref. [4] to fit experimental data as shown in the insert of Fig. 3(b) Ê Trep ˆ cos (ω L ∆t ) - exp Á ˜ cos [ω L (∆t + Trep )] Ê Dt + Trep ˆ Ë T2* ¯ α = A + B exp Á . ˜ Ê Trep ˆ Ë T2* ¯ cos (ω LTrep ) - cosh Á ˜ Ë T2* ¯
(3)
In the limit of low magnetic field it gives spin relaxation time of free electrons τ s = 14 ns. In conclusion, long electron spin memory as long as 19 ns is measured in II–VI QWs by two different techniques. We suppose that electrons are localized at low temperatures and, therefore, fluctuations of nuclei field is a mechanism of spin relaxation [13]. However, it requires a careful analysis which is beyond the scope of this paper. Acknowledgements The authors thank V. L. Korenev for fruitful and stimulating discussions, and R. I. Dzhioev, K. V. Kavokin, M. V. Lazarev for cooperation on initial stage. This work was supported by the Deutsche Forschungsgemeinschaft via SFB 410 and RFBR, as well as by the grant 436 RUS17/93/05 for the research stay of EAZ in Dortmund. Also support of BMBF nanoquit is acknowledged.
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