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Hanle effect and spin-dependent recombination at deep centers in GaAsN
ARTICLE IN PRESS Physica B 404 (2009) 4929–4932
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Physica B journal homepage: www.elsevier.com/locate/physb
Hanle effect and spin-dependent recombination at deep centers in GaAsN V.K. Kalevich a,, A.Yu. Shiryaev a, E.L. Ivchenko a, M.M. Afanasiev a, A.Yu. Egorov a, V.M. Ustinov a, Y. Masumoto b a b
A.F. Ioffe Physico-Technical Institute, St. Petersburg 194021, Russia University of Tsukuba, Tsukuba 305-8571, Japan
a r t i c l e in fo
Keywords: Spin-dependent recombination Optical orientation
abstract The peculiarities of Hanle effect (i.e., the depolarization of edge photoluminescence in a transverse magnetic field) in semiconductors, brought about by spin-dependent recombination of free electrons with deep paramagnetic centers, have been investigated in GaAs0.979N0.021 alloy at room temperature. The measured Hanle curve consists of narrow and wide parts with the widths at the half-height being 100 and 120000 G. The difference between the widths by three orders of magnitude results from strongly differing spin lifetimes of bound and free electrons, Tsc and Ts. Using g-factor values +2 and +1 for bound and free electrons, respectively, we have found that Tsc E700 ps and Ts E2 ps. Thus obtained values of Tsc and Ts allow us to describe theoretically the experimental Hanle curve as well as its dependence on the pump intensity. & 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental results
The paper is devoted to a study of giant electron spin polarization achieved in nonmagnetic semiconductors at room temperature due to spin-dependent recombination through deep paramagnetic centers. Recently, the extremely high optical spin polarization (about 90%) and spin memory ( 1 ns) of free electrons was found in GaAsN alloys at room temperature [1–7]. These results have been explained by formation of nonlinear coupled system of free and localized spins and its dynamic polarization [2–4]. The system arises due to spin-dependent capture of free electrons on deep paramagnetic centers, which are formed under incorporation of nitrogen into GaAs [2,7]. The proposed theoretical model [2,4] qualitatively well describes the coupled spin-system. However, the model includes eight parameters and a careful fitting of the parameters is needed to describe the system quantitatively. In this work, we have measured spin lifetimes of free electrons and electrons bound on paramagnetic centers in GaAs0.979N0.021 using the Hanle effect (the depolarization of free electrons by a magnetic field B directed perpendicularly to the continuous-wave pump beam). The measured spin lifetimes allowed us to simulate the main experimental dependences.
We studied the undoped 0.1 mm thick GaAs0.979N0.021 layer grown by rf-plasma-assisted molecular-beam epitaxy on semi-insulating (0 0 1) GaAs substrate [1]. Free-electron spin polarization P was created upon the interband absorption of circularly polarized light [8]. We measured the steady-state degree r of circular polarization of the edge photoluminescence (PL), which is proportional to free-electron polarization [8]: r = QP, where the numerical factor Qr1, the polarization r is defined as r = (I + I )/I, I + and I are the right (s + ) and left (s ) circularly polarized PL components, I=(I + + I ) is the total PL intensity. Continuous-wave tunable Ti:sapphire laser was used for PL excitation. The value r and PL intensity were measured using a high-sensitive polarization analyser [9]. The measurements were carried out at 300 K. Circles in Fig. 1 show the typical experimental Hanle curve in GaAsN alloy. One can see that the curve is superimposition of the narrow and wide contours with the half-widths being different by more than two orders of magnitude. It is reasonably fitted by the solid curve, which is the sum of two Lorentzians r(B) = r0c/[1+(B/Bc1/2)2]+ r0/[1+ (B/B1/2)2] + rres, where Bc1/2 185 G and B1/2 25000 G, r0c and r0 are half-widths at half-maximum and maxima of the narrow and wide parts, respectively, and rres is a contribution independent of the magnetic field [10]. The experimental r(B) curve strongly depends on the excitation power. In particular, with increasing excitation intensity its narrow part becomes wider while its wide part becomes narrower, as one can see in Fig. 2. Experimental dependences of Bc1/2 and B1/2 on pump intensity J are shown by squares
Corresponding author. Tel.: + 7 812 2927140; fax: + 7 812 2971017.
E-mail address: [email protected] (V.K. Kalevich). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.08.234
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Fig. 1. Typical Hanle curve in GaAs0.979N0.021 alloy measured near the PL band maximum at a moderate pump density. T= 300 K. hvexc = 1.312 eV, hvdet = 1.163 eV. Insert shows the initial part of the Hanle curve in extended scale.
in Fig. 3a and b, respectively. They are fitted by calculated curves (solid, details of calculation see below), which show that min = 85 G while B1/2-Bmax Bc1/2-Bc1/2 1/2 = 60 kG when J tends to zero. In other words, the half-widths of the narrow and wide parts of the experimental Hanle curve differ by 3 orders of magnitude at extremely low excitation.
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0 30000 -30000 Transverse magnetic field (Gauss) Fig. 2. Narrow (a) and wide (b) parts of the experimental Hanle curves in GaAs0.979N0.021 at different excitation powers. J: ’—220 mW, B—100 mW, X—50 mW, m—25 mW. Solid curves in (b) are the result of fitting by Lorentzians r(B)= r0/(1/B2/B21/2)+ rres with rres = 3.3%.
3.1. Free electrons 3. Discussion Hanle effect is a depolarization of photoluminescence by a magnetic field B directed perpendicular to continuous-wave pump beam [8]. The effect originates from Larmor precession of electron spins, which destroys electron polarization. In the simplest case, Hanle effect is described by Lorentzian r(B)= r(B =0)/(1 +B2/B21/2) with half-width at half-maximum B1/2 = _/gmBTs, where g is the electron Lande g-factor, mB is the Bohr magneton, and Ts is the electron spin-polarization lifetime. Spin lifetime of electrons bound on paramagnetic centers, Tsc, can exceed spin lifetime of free electrons, Ts, by orders of magnitude at room temperature. Therefore, the half-width of Hanle curve of bound electrons, Bc1/2 = _/gcmBTsc (gc is the gyromagnetic g-factor of bound electrons [11]), should be far less than the half-width of Hanle curve of free electrons B1/2. As noted above, the spin-dependent recombination results in formation of a strongly coupled spin-system of free and bound electrons, where a variation of the polarization of the centers is accompanied by the changing free-electron polarization. As a result, the function r(B) is a sum of two terms with strongly different half-widths, a narrow contour presenting the Hanle effect on bound electrons and a wide contour describing the depolarization of free electrons [6], see also Ref. [12]. c min allow us to estimate the The found values of Bmax 1/2 and B1/2 spin lifetimes of both free and bound electrons at the low pump limit, Ts min and Tsc max, respectively.
For Bmax 1/2 =60 kG, taking into account that in GaAs0.979N0.021 gE + 1 [6], we found Ts min = 1.9E2 ps. Spin lifetime is determined as the least of lifetime and spin relaxation time: 1/Ts = 1/t + 1/ts [8]. In GaAs0.979N0.021 alloy under study, due to effective capture of free electrons by deep centers, t 5 ts [4]. Therefore, t = Ts and tmin = Ts min E2 ps. It is instructive to introduce explicitly in our model [4] the lifetimes of free electrons (t) and holes (th): 1/t = ReN1(14PPc)/2 and 1/th = RhN2 where Re and Rh are the constants of recombination of free electrons and holes with deep centers, N1 and N2 are the densities of centers occupied by one and two electrons, respectively, and Pc is the polarization of single-electron centers. In the limit of weak pumping, J-0, one has N1-Nc (Nc is the total density of the paramagnetic centers), Pc-0 and t 11 tmin = ReNc/2. As a consequence, ReNc = 2/tmin E1 ps 1. In the opposite limit of strong pumping, J-N, one has N2-Nc, and 1/th-1/th min =RhNc. The strong pumping regime was realized at pulse excitation in Ref. [4] where it was found that th min = (3071) ps. Therefore, we can use the estimations RhNc = (3.370.1) 10 2 ps 1 and Re/Rh =2th min/tmin E30. 3.2. Bound electrons The dependence of Bc1/2 on pump intensity gives a possibility to find the spin relaxation time of bound electrons tsc. Indeed, Bc1/2-
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J (mW) Fig. 3. Dependence of the Hanle curve half-width for bound (a) and free (b) electrons on excitation power. The data for J =150 mW and J =50 mW are obtained from the fitting of the experimental Hanle curves, which are not presented in Fig. 2 for the sake of simplicity.
min Bc1/2 and, consequently, Tsc-Tsc max when J-0. At the same time, the bound-electron lifetime tc-N, and, as a consequence, Tsc max E tsc. Using the valueBc1/2min E 85 G found above and g = +2 [2,6,7], we obtained tsc E700 ps. We applied the obtained values tsc = 700 ps, ReNc = 1 ps 1 to simulate spin-system of free and bound electrons by solving the set of nonlinear equations given in Ref. [4]. Others model parameters used are the following: g= + 1 [6], gc = + 2 [6,7], RhNc = 0.033 ps 1 [4], ts = 140 ps [4], Nc = 1.8 1015 cm 3, Q=0.24, the initial photoelectron polarization Pi = 0.5P0, where P0 E0.5 is the fitting constant taking into account depolarization of light inside the sample. It is worth to note that the values of Nc, Pi and Q were found by fitting the experimental dependences r(B = 0) and I(B =0) on excitation power (the analysis of the experimental dependences r(B =0, J) and I(B =0, J) and their model simulation will be published elsewhere). Solid curves in Fig. 4 present the Hanle curves calculated at different pump powers. One can see, that the calculated r(B) dependences demonstrate the main features observed experimentally. Namely, they have the narrow and wide parts with the half-widths that are different by two orders of magnitude. With increasing pump intensity the narrow part broadens, its amplitude rapidly grows, while the wide part narrows, just slightly decreasing in height.
0 30000 -30000 Transverse magnetic field (Gauss) Fig. 4. Model calculated Hanle curves at different excitation powers for small (a) and large (b) magnetic fields. For comparison, dashed lines show Lorentzians for J= 220 mW (see text for details). J: 1—25 mW, 2—50 mW, 3—100 mW, 4—220 mW.
It is worth noting that a Hanle curve has Lorentzian shape only if the spin lifetime is independent of the magnetic field. Strictly speaking, this condition is not fulfilled for the narrow part of the dependence r(B) in the magnetic field range |B| 3 kG. This part of the Hanle curve, as shown above, originates from the decoherence of dynamic polarization of centers. As a consequence, the lifetimes of bound and free electrons vary with B [13]. For this reason, the calculated Hanle curve is not Lorentzian (see Fig. 4a where a Lorentzian is shown by dashed line for comparison). To compare with experiment we used the half-with at half-maximum of the calculated narrow part of the Hanle curve as Bc1/2. The calculated dependence Bc1/2(J) is shown by solid line in Fig. 3a. It has nearly horizontal part at Jr40 mW which is due to the fact that, in this intensity range, the lifetime of bound electrons tc is so long that their spin lifetime Tsc is controlled only by their spin relaxation time tsc, which does not depend on J: Tsc = tsc. Therefore, the value of Bc1/2 on the horizontal part can be used to measure tsc. The calculated curve Bc1/2(J) in Fig. 3a is obtained at tsc = 700 ps. In strong magnetic fields, |B|43 kG, the dynamic polarization of the centers is destroyed and variation of r is due to depolarization of free electrons only. In this case the lifetime of free electrons is unchanged and their depolarization is described well by a Lorentzian (as an example, dashed curve in Fig. 4b is a Lorentzian approximation of curve 4). The half-width of the Lorentzian was used as a model value of B1/2. The half-width B1/2, determined in this way from the wide part of the calculated r(B) curves, is shown by solid line in Fig. 3b as a function of the pump
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power. One can see that it describes well the experimental dependence in Fig. 3b. The extrapolation of the calculated values of B1/2 to J=0 gives Ts(J=0) = 1.9 ps [14]. Thus, under conditions of spin-dependent recombination the Hanle-effect depolarization of free electrons contains, in addition to the wide part, a narrow contour due to slow spin relaxation of deep centers. Under weak pumping, the spin lifetime of free electrons is determined by their lifetime (of the order of 1 ps), in contrast to the spin lifetime of bound electrons (of the order of 1 ns) controlled by their spin relaxation. The measured values of spin lifetimes have enabled us to simulate Hanle effect and its dependence on pump intensity in the presence of spin-dependent recombination.
Acknowledgements This work was financially supported by the RFBR, JSPS and programs of RAS. References [1] A.Yu. Egorov, V.K. Kalevich, M.M. Afanasiev, A.Yu. Shiryaev, V.M. Ustinov, M. Ikezawa, Y. Masumoto, J. Appl. Phys. 98 (2005) 13539.
[2] V.K. Kalevich, E.L. Ivchenko, M.M. Afanasyev, A.Yu. Shiryaev, A.Yu. Egorov, V.M. Ustinov, B. Pal, Y. Masumoto, JETP Lett. 82 (2005) 455. [3] L. Lombez, P.-F. Braun, H. Carre re, B. Urbaszek, P. Renucci, T. Amand, X. Marie, J.C. Harmand, V.K. Kalevich, Appl. Phys. Lett. 87 (2005) 252115. [4] V.K. Kalevich, E.L. Ivchenko, A.Yu. Shiryaev, A.Yu. Egorov, L. Lombez, D. Lagarde, X. Marie, T. Amand, JETP Lett. 85 (2007) 174. [5] X. Marie, V.K. Kalevich, D. Lagarde, T. Amand, in: A. Erol (Ed.), Dilute III–V Nitride Semiconductors and Material Systems, vol. 105, Springer, BerlinHeidelberg-New York, 2008, pp. 283–299 (Springer Series in Material Science, Chapter. 11). [6] V.K. Kalevich, E.L. Ivchenko, A.Yu. Shiryaev, M.M. Afanasiev, A.Yu. Egorov, M. Ikezawa, Y. Masumoto, Semicond. Sci. Technol. 23 (2008) 114008. [7] X.J. Wang, I.A. Buyanova, F. Zhao, D. Lagarde, A. Balocchi, X. Marie, C.W. Tu, J.C. Harmand, W.M. Chen, Nat. Mater. 8 (2009) 198. [8] F. Meier, B. Zakharchenya (Eds.), Optical Orientation, North-Holland, Amsterdam, 1984. [9] V.D. Kulkov, V.K. Kalevich, Instrum. Exp. Tech. 24 (1981) 1265. [10] The origin of rres is not clear now. To elucidate it, the additional experiments are necessary. [11] In GaAs0.979N0.021 alloy, g E + 1 [6], gc = + 2 [2,6,7]. [12] C. Weisbuch, G. Lampel, Solid State Commun. 14 (1974) 141. [13] We believe that spin relaxation times of both localized and free electrons are independent of the magnetic field or pump intensity. [14] The Hanle effect measured under continuous-wave excitation gives a simple way to estimate bound-electron spin relaxation time tsc. On the other hand, time-resolved PL measurements give no information about tsc since kinetics of r after pulse pumping is insensitive to tsc [4].
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Hanle effect and spin-dependent recombination at deep centers in GaAsN V.K. Kalevich a,, A.Yu. Shiryaev a, E.L. Ivchenko a, M.M. Afanasiev a, A.Yu. Egorov a, V.M. Ustinov a, Y. Masumoto b a b
A.F. Ioffe Physico-Technical Institute, St. Petersburg 194021, Russia University of Tsukuba, Tsukuba 305-8571, Japan
a r t i c l e in fo
Keywords: Spin-dependent recombination Optical orientation
abstract The peculiarities of Hanle effect (i.e., the depolarization of edge photoluminescence in a transverse magnetic field) in semiconductors, brought about by spin-dependent recombination of free electrons with deep paramagnetic centers, have been investigated in GaAs0.979N0.021 alloy at room temperature. The measured Hanle curve consists of narrow and wide parts with the widths at the half-height being 100 and 120000 G. The difference between the widths by three orders of magnitude results from strongly differing spin lifetimes of bound and free electrons, Tsc and Ts. Using g-factor values +2 and +1 for bound and free electrons, respectively, we have found that Tsc E700 ps and Ts E2 ps. Thus obtained values of Tsc and Ts allow us to describe theoretically the experimental Hanle curve as well as its dependence on the pump intensity. & 2009 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental results
The paper is devoted to a study of giant electron spin polarization achieved in nonmagnetic semiconductors at room temperature due to spin-dependent recombination through deep paramagnetic centers. Recently, the extremely high optical spin polarization (about 90%) and spin memory ( 1 ns) of free electrons was found in GaAsN alloys at room temperature [1–7]. These results have been explained by formation of nonlinear coupled system of free and localized spins and its dynamic polarization [2–4]. The system arises due to spin-dependent capture of free electrons on deep paramagnetic centers, which are formed under incorporation of nitrogen into GaAs [2,7]. The proposed theoretical model [2,4] qualitatively well describes the coupled spin-system. However, the model includes eight parameters and a careful fitting of the parameters is needed to describe the system quantitatively. In this work, we have measured spin lifetimes of free electrons and electrons bound on paramagnetic centers in GaAs0.979N0.021 using the Hanle effect (the depolarization of free electrons by a magnetic field B directed perpendicularly to the continuous-wave pump beam). The measured spin lifetimes allowed us to simulate the main experimental dependences.
We studied the undoped 0.1 mm thick GaAs0.979N0.021 layer grown by rf-plasma-assisted molecular-beam epitaxy on semi-insulating (0 0 1) GaAs substrate [1]. Free-electron spin polarization P was created upon the interband absorption of circularly polarized light [8]. We measured the steady-state degree r of circular polarization of the edge photoluminescence (PL), which is proportional to free-electron polarization [8]: r = QP, where the numerical factor Qr1, the polarization r is defined as r = (I + I )/I, I + and I are the right (s + ) and left (s ) circularly polarized PL components, I=(I + + I ) is the total PL intensity. Continuous-wave tunable Ti:sapphire laser was used for PL excitation. The value r and PL intensity were measured using a high-sensitive polarization analyser [9]. The measurements were carried out at 300 K. Circles in Fig. 1 show the typical experimental Hanle curve in GaAsN alloy. One can see that the curve is superimposition of the narrow and wide contours with the half-widths being different by more than two orders of magnitude. It is reasonably fitted by the solid curve, which is the sum of two Lorentzians r(B) = r0c/[1+(B/Bc1/2)2]+ r0/[1+ (B/B1/2)2] + rres, where Bc1/2 185 G and B1/2 25000 G, r0c and r0 are half-widths at half-maximum and maxima of the narrow and wide parts, respectively, and rres is a contribution independent of the magnetic field [10]. The experimental r(B) curve strongly depends on the excitation power. In particular, with increasing excitation intensity its narrow part becomes wider while its wide part becomes narrower, as one can see in Fig. 2. Experimental dependences of Bc1/2 and B1/2 on pump intensity J are shown by squares
Corresponding author. Tel.: + 7 812 2927140; fax: + 7 812 2971017.
E-mail address: [email protected] (V.K. Kalevich). 0921-4526/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2009.08.234
ARTICLE IN PRESS 4930
V.K. Kalevich et al. / Physica B 404 (2009) 4929–4932
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Fig. 1. Typical Hanle curve in GaAs0.979N0.021 alloy measured near the PL band maximum at a moderate pump density. T= 300 K. hvexc = 1.312 eV, hvdet = 1.163 eV. Insert shows the initial part of the Hanle curve in extended scale.
in Fig. 3a and b, respectively. They are fitted by calculated curves (solid, details of calculation see below), which show that min = 85 G while B1/2-Bmax Bc1/2-Bc1/2 1/2 = 60 kG when J tends to zero. In other words, the half-widths of the narrow and wide parts of the experimental Hanle curve differ by 3 orders of magnitude at extremely low excitation.
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0 30000 -30000 Transverse magnetic field (Gauss) Fig. 2. Narrow (a) and wide (b) parts of the experimental Hanle curves in GaAs0.979N0.021 at different excitation powers. J: ’—220 mW, B—100 mW, X—50 mW, m—25 mW. Solid curves in (b) are the result of fitting by Lorentzians r(B)= r0/(1/B2/B21/2)+ rres with rres = 3.3%.
3.1. Free electrons 3. Discussion Hanle effect is a depolarization of photoluminescence by a magnetic field B directed perpendicular to continuous-wave pump beam [8]. The effect originates from Larmor precession of electron spins, which destroys electron polarization. In the simplest case, Hanle effect is described by Lorentzian r(B)= r(B =0)/(1 +B2/B21/2) with half-width at half-maximum B1/2 = _/gmBTs, where g is the electron Lande g-factor, mB is the Bohr magneton, and Ts is the electron spin-polarization lifetime. Spin lifetime of electrons bound on paramagnetic centers, Tsc, can exceed spin lifetime of free electrons, Ts, by orders of magnitude at room temperature. Therefore, the half-width of Hanle curve of bound electrons, Bc1/2 = _/gcmBTsc (gc is the gyromagnetic g-factor of bound electrons [11]), should be far less than the half-width of Hanle curve of free electrons B1/2. As noted above, the spin-dependent recombination results in formation of a strongly coupled spin-system of free and bound electrons, where a variation of the polarization of the centers is accompanied by the changing free-electron polarization. As a result, the function r(B) is a sum of two terms with strongly different half-widths, a narrow contour presenting the Hanle effect on bound electrons and a wide contour describing the depolarization of free electrons [6], see also Ref. [12]. c min allow us to estimate the The found values of Bmax 1/2 and B1/2 spin lifetimes of both free and bound electrons at the low pump limit, Ts min and Tsc max, respectively.
For Bmax 1/2 =60 kG, taking into account that in GaAs0.979N0.021 gE + 1 [6], we found Ts min = 1.9E2 ps. Spin lifetime is determined as the least of lifetime and spin relaxation time: 1/Ts = 1/t + 1/ts [8]. In GaAs0.979N0.021 alloy under study, due to effective capture of free electrons by deep centers, t 5 ts [4]. Therefore, t = Ts and tmin = Ts min E2 ps. It is instructive to introduce explicitly in our model [4] the lifetimes of free electrons (t) and holes (th): 1/t = ReN1(14PPc)/2 and 1/th = RhN2 where Re and Rh are the constants of recombination of free electrons and holes with deep centers, N1 and N2 are the densities of centers occupied by one and two electrons, respectively, and Pc is the polarization of single-electron centers. In the limit of weak pumping, J-0, one has N1-Nc (Nc is the total density of the paramagnetic centers), Pc-0 and t 11 tmin = ReNc/2. As a consequence, ReNc = 2/tmin E1 ps 1. In the opposite limit of strong pumping, J-N, one has N2-Nc, and 1/th-1/th min =RhNc. The strong pumping regime was realized at pulse excitation in Ref. [4] where it was found that th min = (3071) ps. Therefore, we can use the estimations RhNc = (3.370.1) 10 2 ps 1 and Re/Rh =2th min/tmin E30. 3.2. Bound electrons The dependence of Bc1/2 on pump intensity gives a possibility to find the spin relaxation time of bound electrons tsc. Indeed, Bc1/2-
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J (mW) Fig. 3. Dependence of the Hanle curve half-width for bound (a) and free (b) electrons on excitation power. The data for J =150 mW and J =50 mW are obtained from the fitting of the experimental Hanle curves, which are not presented in Fig. 2 for the sake of simplicity.
min Bc1/2 and, consequently, Tsc-Tsc max when J-0. At the same time, the bound-electron lifetime tc-N, and, as a consequence, Tsc max E tsc. Using the valueBc1/2min E 85 G found above and g = +2 [2,6,7], we obtained tsc E700 ps. We applied the obtained values tsc = 700 ps, ReNc = 1 ps 1 to simulate spin-system of free and bound electrons by solving the set of nonlinear equations given in Ref. [4]. Others model parameters used are the following: g= + 1 [6], gc = + 2 [6,7], RhNc = 0.033 ps 1 [4], ts = 140 ps [4], Nc = 1.8 1015 cm 3, Q=0.24, the initial photoelectron polarization Pi = 0.5P0, where P0 E0.5 is the fitting constant taking into account depolarization of light inside the sample. It is worth to note that the values of Nc, Pi and Q were found by fitting the experimental dependences r(B = 0) and I(B =0) on excitation power (the analysis of the experimental dependences r(B =0, J) and I(B =0, J) and their model simulation will be published elsewhere). Solid curves in Fig. 4 present the Hanle curves calculated at different pump powers. One can see, that the calculated r(B) dependences demonstrate the main features observed experimentally. Namely, they have the narrow and wide parts with the half-widths that are different by two orders of magnitude. With increasing pump intensity the narrow part broadens, its amplitude rapidly grows, while the wide part narrows, just slightly decreasing in height.
0 30000 -30000 Transverse magnetic field (Gauss) Fig. 4. Model calculated Hanle curves at different excitation powers for small (a) and large (b) magnetic fields. For comparison, dashed lines show Lorentzians for J= 220 mW (see text for details). J: 1—25 mW, 2—50 mW, 3—100 mW, 4—220 mW.
It is worth noting that a Hanle curve has Lorentzian shape only if the spin lifetime is independent of the magnetic field. Strictly speaking, this condition is not fulfilled for the narrow part of the dependence r(B) in the magnetic field range |B| 3 kG. This part of the Hanle curve, as shown above, originates from the decoherence of dynamic polarization of centers. As a consequence, the lifetimes of bound and free electrons vary with B [13]. For this reason, the calculated Hanle curve is not Lorentzian (see Fig. 4a where a Lorentzian is shown by dashed line for comparison). To compare with experiment we used the half-with at half-maximum of the calculated narrow part of the Hanle curve as Bc1/2. The calculated dependence Bc1/2(J) is shown by solid line in Fig. 3a. It has nearly horizontal part at Jr40 mW which is due to the fact that, in this intensity range, the lifetime of bound electrons tc is so long that their spin lifetime Tsc is controlled only by their spin relaxation time tsc, which does not depend on J: Tsc = tsc. Therefore, the value of Bc1/2 on the horizontal part can be used to measure tsc. The calculated curve Bc1/2(J) in Fig. 3a is obtained at tsc = 700 ps. In strong magnetic fields, |B|43 kG, the dynamic polarization of the centers is destroyed and variation of r is due to depolarization of free electrons only. In this case the lifetime of free electrons is unchanged and their depolarization is described well by a Lorentzian (as an example, dashed curve in Fig. 4b is a Lorentzian approximation of curve 4). The half-width of the Lorentzian was used as a model value of B1/2. The half-width B1/2, determined in this way from the wide part of the calculated r(B) curves, is shown by solid line in Fig. 3b as a function of the pump
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power. One can see that it describes well the experimental dependence in Fig. 3b. The extrapolation of the calculated values of B1/2 to J=0 gives Ts(J=0) = 1.9 ps [14]. Thus, under conditions of spin-dependent recombination the Hanle-effect depolarization of free electrons contains, in addition to the wide part, a narrow contour due to slow spin relaxation of deep centers. Under weak pumping, the spin lifetime of free electrons is determined by their lifetime (of the order of 1 ps), in contrast to the spin lifetime of bound electrons (of the order of 1 ns) controlled by their spin relaxation. The measured values of spin lifetimes have enabled us to simulate Hanle effect and its dependence on pump intensity in the presence of spin-dependent recombination.
Acknowledgements This work was financially supported by the RFBR, JSPS and programs of RAS. References [1] A.Yu. Egorov, V.K. Kalevich, M.M. Afanasiev, A.Yu. Shiryaev, V.M. Ustinov, M. Ikezawa, Y. Masumoto, J. Appl. Phys. 98 (2005) 13539.
[2] V.K. Kalevich, E.L. Ivchenko, M.M. Afanasyev, A.Yu. Shiryaev, A.Yu. Egorov, V.M. Ustinov, B. Pal, Y. Masumoto, JETP Lett. 82 (2005) 455. [3] L. Lombez, P.-F. Braun, H. Carre re, B. Urbaszek, P. Renucci, T. Amand, X. Marie, J.C. Harmand, V.K. Kalevich, Appl. Phys. Lett. 87 (2005) 252115. [4] V.K. Kalevich, E.L. Ivchenko, A.Yu. Shiryaev, A.Yu. Egorov, L. Lombez, D. Lagarde, X. Marie, T. Amand, JETP Lett. 85 (2007) 174. [5] X. Marie, V.K. Kalevich, D. Lagarde, T. Amand, in: A. Erol (Ed.), Dilute III–V Nitride Semiconductors and Material Systems, vol. 105, Springer, BerlinHeidelberg-New York, 2008, pp. 283–299 (Springer Series in Material Science, Chapter. 11). [6] V.K. Kalevich, E.L. Ivchenko, A.Yu. Shiryaev, M.M. Afanasiev, A.Yu. Egorov, M. Ikezawa, Y. Masumoto, Semicond. Sci. Technol. 23 (2008) 114008. [7] X.J. Wang, I.A. Buyanova, F. Zhao, D. Lagarde, A. Balocchi, X. Marie, C.W. Tu, J.C. Harmand, W.M. Chen, Nat. Mater. 8 (2009) 198. [8] F. Meier, B. Zakharchenya (Eds.), Optical Orientation, North-Holland, Amsterdam, 1984. [9] V.D. Kulkov, V.K. Kalevich, Instrum. Exp. Tech. 24 (1981) 1265. [10] The origin of rres is not clear now. To elucidate it, the additional experiments are necessary. [11] In GaAs0.979N0.021 alloy, g E + 1 [6], gc = + 2 [2,6,7]. [12] C. Weisbuch, G. Lampel, Solid State Commun. 14 (1974) 141. [13] We believe that spin relaxation times of both localized and free electrons are independent of the magnetic field or pump intensity. [14] The Hanle effect measured under continuous-wave excitation gives a simple way to estimate bound-electron spin relaxation time tsc. On the other hand, time-resolved PL measurements give no information about tsc since kinetics of r after pulse pumping is insensitive to tsc [4].