An enhancement of spin polarization by multiphoton pumping in semiconductors

Materials Chemistry and Physics 128 (2011) 548–551

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An enhancement of spin polarization by multiphoton pumping in semiconductors M. Idrish Miah a,b,∗ a b

Queensland Micro- and Nanotechnology Centre, Griffith University, Nathan, Brisbane, QLD 4111, Australia Department of Physics, University of Chittagong, Chittagong 4331, Bangladesh

a r t i c l e

i n f o

Article history: Received 8 August 2010 Received in revised form 12 February 2011 Accepted 22 March 2011 Keywords: Semiconductors Optical materials Spectroscopy Optical properties

a b s t r a c t A pump–probe spectroscopic study has been carried out in zinc-blende bulk semiconductors. In the semiconductor samples, a spin-polarized carrier population is produced by the absorption of a monochromatic circularly polarized light beam with two-photon energy above the direct band gap in bulk semiconductors. The production of a carrier population with a net spin is a consequence of the optical selection rules for the heavy-hole and light-hole valence-to-conduction band transitions. This production is probed by the spin-dependent transmission of the samples in the time domain. The spin polarization of the conduction-band-electrons in dependences of delay of the probe beam as well as of pumping photon energy is estimated. The spin polarization is found to depolarize rapidly for pumping energy larger than the energy gap of the split-off band to the conduction band. From the polarization decays, the spin relaxation times are also estimated. Compared to one-photon pumping, the results, however, show that an enhancement of the spin-polarization is achieved by multiphoton excitation of the samples. The experimental results are compared with those obtained in calculations using second order perturbation theory of the spin transport model. A good agreement between experiment and theory is obtained. The observed results are discussed in details. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Spin physics has drawn much attention recently [1,2]. This is because of increased interest in the emerging field of spin-sensitive electronics or spintronics [3,4], where the electronic spin is utilized in equal footing as electronic charge. Spin-dependent transport or the transport of spin-polarized electrons, or spin transport in short, is a crucial part of spin physics. Reliable spin transport or spin transport without spin relaxation, or loss of the spin polarization, over distances that are comparable to the device dimensions is required for practical spintronic devices. However, once an electron spin imbalance is injected into (or generated in) a semiconductor, electrons experience spin-dependent interactions with the environment, i.e. with impurities, defects and excitations or phonons, in particular, electron–phonon interactions including the anharmonic ones. This causes the relaxation of the electron spin [4]. Spin relaxation refers to the process which brings a nonequilibrium electronic spin population to a spin equilibrium state. Since this nonequilibrium electronic spin in metals and semiconductors is used to carry the spin-encoded information, which is one of the important steps towards applied spintronics and possible future quantum compu-

∗ Correspondence address: Department of Physics, University of Chittagong, Chittagong 4331, Bangladesh. E-mail address: m.miah@griffith.edu.au 0254-0584/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2011.03.052

tation, it is important to know how long the spin can travel without losing its initial spin orientation, both in distance as well as time. The determination of spin-flip rate is extremely important for electronic applications, because if the spins relax too fast, the distance travelled by the spin-polarized current will be too short to serve any practical purpose. Considerable effort [2–4] has thus been dedicated in understanding the transport of spin-polarized electrons in semiconductors. However, the efficient spin generation/injection still remains a major problem in semiconductor spintronics. For this, for example, the generation/injection of highly polarized spins in/into a semiconductor is essential. Because of the larger absorption depth, multiphoton pumping has widely been used for a long time to study the multiphoton absorption of the optical nonlinear processes, particularly in semiconductors and insulators [5,6]. The multiphoton pumping allows deep-level photo-excitation in a bulk semiconductor. In addition, multiphoton spin-excitation in lead chacogenides has been studied theoretically [7]. They predicted high spinpolarization in these cubic materials having fundamental band gaps. For the class of zinc-blende semiconductors, the similar predictions have also been observed in the earlier theoretical investigations [8–10]. In the present paper, we report the results of an experimental investigation on multiphoton spin-polarization in zinc-blende GaAs. In addition, a comparison with the results obtained in calculations using second order perturbation theory is also reported.

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549

two-photon spin generation rate can be written phenomenologically as dS i j k l∗ m∗ Eω Eω , = ijklm Eω Eω dt

Fig. 1. Energy bands for GaAs: a scheme showing the heavy-hole (HH), light-hole (LH) and split-off (SO) bands of GaAs and their energies, where ESO = Eg + ESO is the SO band to CB energy gap and ESO is the SO splitting energy.

(3)

where ijklm is a fifth rank pseudotensor. The two-photon spin generation rate under the assumptions detailed above has been considered earlier for the doubly degenerate band case and is given [7] dS = dt

 2    L3



ˆ k B  ck|S|c B ı{2ω − ωcv (k)} c ,v,k c,v,k (2)∗

(2)

c,c  ,v,k

(4)





where Sˆ is the spin operator, L3 is a normalized volume, nk is a

2. Experimental

(2)

Samples for the present investigation were bulk GaAs doped with 1.8 × 1016 cm−3 . We performed spin-resolved two-photon pump–probe experiments, where the differential transmission Dt = t/t = (t − t0 )/t [t(t0 ) is the transmission with (without) the pump] of the probe pulses was measured as a function of the delay  between circularly polarized pump and probe pulses for the same and opposite circularly polarizations. To satisfy that L(˛ − ˛0 )  1 and to maximize the magnitude of Dt , L = 1 ␮m was chosen. The probe beam (ωPr ) was resonant with the bandgap energy Eg , and the pump beam (ω) had an excess energy ¯ 2ω − h ¯ ωPr  h ¯ 2ω − Eg of ∼100 meV. However, the excess photon energy E2ω = h was varied for the measurements of its dependence. The probe pulse was tuned to the bandgap excitation resonance (¯hωPr ≈ Eg ). A scheme showing the heavy-hole (HH), light-hole (LH) and split-off (SO) bands of GaAs and their energies, where ESO = Eg + ESO is the SO band to CB energy gap and ESO is the SO splitting energy, is given Fig. 1. The generated electron spins were in a direction parallel (antiparallel) to the direction of light propagation for right (left) circularly polarized light  + ( − ) beam. Transmission measurements were performed at 4.2 K by placing the sample in a temperature-regulated cryostat and using fs pulses from an optical parametric amplifier pumped by a regeneratively amplified Ti:sapphire laser operating at 250 kHz. The laser system was tuned to produce ∼150 fs pulses (signal and idler). A beta barium borate crystal was used to generate pulses from the signal and idler. The second harmonic and fundamental pulses were then separated using a dichroic beamsplitter. We used ∼150 fs pulses to excite the sample by two-photon absorption and 825 nm pulses to probe the transmission of the sample. Broadband quarter wave plates were used to transform pump and probe beams from linear to (right/left) circularly polarized light. Since, for probe pulses near the band edge, (t/t) +  + ∝ 3n↓ + n↑ and (t/t) +  − ∝ 3n↑ + n↓ , as a result of the selection rules, one can determine the polarization, defined as P(r , t) =

n↓ (r , t) − n↑ (r , t) , n↓ (r , t) + n↑ (r , t)

(1)

(Dt ) +  + − (Dt ) +  − , (Dt ) +  + + (Dt ) +  −

(2)

Bc,v,k =

 e 2  {E · v (k)}{E · v (k)} ω c,n ω n,v h ¯ω

ωnv − ω(k)

n



.

(5)



Here vn,m (k) = nk|ˆv|mk and vˆ is the velocity operator. In the Fermi’s golden rule, the photo-generation rate is time-dependent and can be simplified if the spin–split bands are well-separated. For GaAs, the spin–split pairs of bands should be treated as quasidegenerate in Fermi’s golden rule as the splitting is at most a few meV [13]. Thus dS = dt

 2    L3

c,c  ,v,k

 1 (2) ˆ  k B(2)∗ ck|S|c B × [ı{2ω − ωcv (k)} c  ,v,k c,v,k 2

+ ı{2ω − ωc v (k)}].

(6)

Similarly, the optical generation rate of electron–hole pairs can be obtained as dn = dt

  2     (2) 2 Bc,v,k  ı{2ω − ωcv (k)}. 3 L

(7)

c,v,k

Using the parameters’ values for GaAs, the spin polarization as a function of the pumping photon energy can be calculated from Eqs. (6) and (7). 4. Results and discussion

from the relation P=2

Bloch state with energy h ¯ ωn (k) and Bc,v,k is the two-photon amplitude given by

(2)

by measuring the differential transmission for pump and probe pulses having the same [(Dt ) +  + ] and opposite [(Dt ) +  − ] circular polarizations. Here n↓ (n↑ ) is the density of spin-down (spin-up) conduction-band-electrons. However, for the determination of the spin polarization, Eq. (2) can only be used if the sample is thin enough or the absorbance change induced by the pump is small, i.e. l(˛ − ˛0 )  1, where l is the sample thickness and ˛(˛0 ) is the absorption coefficient with (without) the pump.

3. Theoretical The spin polarization due to multiphoton (two-photon) spin generation has been calculated using the eight band Kane model in the limit large spin-orbit splitting [7–9]. Here we estimate the spin polarization by calculating the photo-generation rate of electron spin density (dS/dt) using the second order perturbation theory of the spin transport model in the long wavelength limit, where electron–electron and electron–phonon interactions are ignored [10]. As optically excited hole spin relaxation is extremely fast, their polarization is effectively zero. We therefore neglect the hole spin polarization [11,12]. For an electric field E(t) = Eω (e−iωt + eiωt ) the

Typical differential transmissions measured by multiphoton pumping with excess photon energy in a sample using probe pulses with the same and opposite circularly polarizations are shown in Fig. 2. As can be seen, there is a difference between the different spin polarization conditions, which is caused by spin-dependent phase-space filling [14,15]. The resulting electron spin polarization, as measured using probe pulses with the same and opposite circularly polarization, as a function of the pump–probe delay is shown in Fig. 3. The polarization decays with a time constant of  = 225 ps, giving a value for the spin relaxation time of  S = 2 = 450 ps. Fig. 4 shows the spin relaxation as a function of the excess photon energy. As can be seen, the spin relaxation time depends strongly on the pumping photon energy. The decay of the polarization might be due to the randomization of the initial spin polarization by the Dyakonov–Perel (DP) spin relaxation mechanism [1,2]. The DP spin relaxation occurs in semiconductors lacking inversion symmetry due to the spin precession

k))

induced by the presence about an intrinsic magnetic field (h( of the spin–orbit interactions in a zinc-blende structure, and the resulting spin precession or spin relaxation is modelled by the rela k)

× P,

= (e/m∗)h(

is the intrinsic

where ωL (k) tion dP/dt = ωL (k) Larmor frequency, P is electron spin-polarization vector, m* = mcv

550

M.I. Miah / Materials Chemistry and Physics 128 (2011) 548–551

1.5

ΔDt (%)

1.2

0.9

0.6

0.3

.............. ............. . . . . ... ................. . ........................... ...................................................... . . . . . . . . . . ....................... .. ..................... .... 0

25

50

75

100

Δτ (ps) Fig. 2. Differential transmissions measured by multiphoton pumping with excess photon energy in a sample using probe pulses with the same (top) and opposite (bottom) circularly polarizations.

(=0.076 for GaAs, for example) is the effective electron mass and mcv is a constant close in magnitude to free electron mass (m0 ). The corresponding Hamiltonian term, known as the DP Hamiltonian, due to spin–orbital splitting of the conduction band describing the precession of electrons in the conduction band [12] is

100

P (%)

80

60

40

20

.................... ................................... .................................. 0

20

40

60

80

100

Δτ (ps)

Spin relaxation time (ps)

104 103 102 101 100 10-1

100

200

= HDP (k)

300

400

500

Excess photon energy (meV) Fig. 4. Dependence of spin relaxation on the excess photon energy. Spin relaxation times are calculated from the polarization decays.

h ¯

· ωL (k),

2

(8)

is the vector of Pauli spin matrices. Momentum-dependent where  spin procession described by the DP Hamiltonian, Eq. (8), together with momentum scattering characterized by momentum relaxation time p (Ek ) leads to DP spin relaxation. Since the magnitude and the direction of k changes in an uncontrolled way owing to electron scattering by the environment, this process contributes to a spin relaxation given by [12]

1 s

Fig. 3. Measured spin polarization in dependence of the delay time. A solid line is drawn through the mean of the experimental data. The initial polarization decays exponentially with time.

10-2

Fig. 5. Spin polarization in dependences of the photon energy: (a) experimental (down triangle) and (b) theoretical values calculated using second order perturbation theory (blue solid line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

DP

=

 ˛ 2 h ¯



p

E 3

k

Eg



,

(9)

where Ek = kB Te and is a dimensionless factor that ranges from 0.8 to 2.7, depending on the dominant momentum relaxation process. For example, for scattering by polar optical or piezoelectric phonons ≈ 0.8, while scattering by ionized impurities gives ≈ 1.5, and scattering by acoustic phonons ≈ 2.7. For bulk materials, the spin–orbit interaction is only due to the bulk inversion asymmetry and the Hamiltonian is composed of the Dresselhaus term [16]. However, in a quantum well (QW), for example, the Hamiltonian is composed of the Dresselhaus [16] and Rashba terms [17]. The Rashba term appears if the self-consistent potential within a QW is asymmetric along the growth direction and is therefore referred to as structural inversion asymmetry contribution. The transmissions pumped with different excess multiphoton energies were measured. Fig. 5 shows the results, where the initial polarization is plotted as a function of the excess energies of the multiphoton excitation. As can be seen, the initial polarization remains almost constant up to ∼200 meV, and then decreases. However, the maximum is obtained for the excess energy considerably less than the SO splitting energy (340 meV). The maximum value is ∼50%. For the higher excess energy, the polarization decreases rapidly due to the mixture of LH and HH states with the SO valence band states which have an opposite sign. The LH and SO band transitions create the same electron spin orientation and the sum of their inter-band matrix elements is equal to the HH inter-band dipole-transition matrix element. It should be

M.I. Miah / Materials Chemistry and Physics 128 (2011) 548–551

noted that some photo-induced processes may cause a transfer of the excited energies between the multi-excited states. As can be seen, there is still a sizeable degree of electron spin polarization even at excess energy higher than the spin–orbit splitting energy, consisting with the earlier investigations [12]. Based on the optical selection rules for inter-band transitions, although the maximum optical spin-polarization for an unstrained bulk sample is expected to be 50% in theory, the maximum has experimentally been observed to be much less [11,18,19]. In the earlier spin polarization measurements, they used one-photon excitation. In a bulk sample there are usually some background unpolarized electrons, which are not photo-excited. If there is a background density of unpolarized electrons nup in the sample, the electronic-spin polarization would be P(0) = 0.5/(1 + nup /n0 ) for an optically generated electron density n0 = n↓ (0) + n↑ (0) [19]. The two-photon pumping enhances the spin polarization because it takes the advantages over one-photon spin generation due to a much longer absorption depth, which allows spin excitation in the deep level, i.e. throughout the volume of a thin bulk sample. The 1␮m thick samples used for this investigation are reasonably thin enough, and so the absorbance change induced by the pump is considered to be small. On comparison with results of the onephoton excitation [20], it can be concluded that due to a much longer absorption depth highly spin-polarized conduction-bandelectrons can be produced optically by the multiphoton HH and LH states excitation of the bulk semiconductors. A calculation using second order perturbation theory of the spin transport model for the spin-polarization was performed. The parameters’ values for GaAs used in the calculation were taken from Adachi [21]. Fig. 5 (blue solid line) shows the calculated results. The experimental results are compared with those obtained in the calculations [from Eqs. (6) and (7)]. As can be seen, over the whole range of the pumping photon energy, a good agreement between experiment and theory is achieved. 5. Conclusions A multiphoton pump–probe spin-polarization investigation in zinc-blende semiconductor GaAs was performed using the transmission spectroscopy in the time domain. The generation of the

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electronic spins in the samples were achieved by optical twophoton pumping with circularly polarized light beam and was probed by the time- and polarization-resolved transmissions of the samples. The conduction-band-electron spin-polarization was found to depend on the delay of the probe beam as well as on the pumping energy. The electron spin-polarization was found to depolarize rapidly for pumping energy larger than the energy gap of the split-off band to the conduction band. The spin relaxation times were also estimated and were found to depend strongly on the pumping photon energy. A theoretical spin-polarization calculation was performed using the spin transport and band-energy models. A good agreement between experimental and theoretical results was obtained. References [1] M.I. Dyakonov, V.I. Perel, Sov. Phys. JETP 33 (1971) 1053. [2] M.I. Dyakonov, A.V. Khaetskii, in: M.I. Dyakonov (Ed.), Spin Hall Effect (Spin Physics in Semiconductors), Springer-Verlag, Berlin, 2008. [3] D.D. Awschalom, D. Loss, N. Samarth (Eds.), Semiconductor Spintronics and Quantum Computation, Springer, Berlin, 2002. ´ J. Fabian, S.D. Sarma, Rev. Mod. Phys. 76 (2004) 323. [4] I. Zˇ utic, [5] H. Haug (Ed.), Optical Nonlinearities and Instabilities in Semiconductors, Academic Press, New York, 1988. [6] M.I. Miah, Opt. Mater. 18 (2001) 231. [7] E.L. Ivchenko, Sov. Phys. Solid State 14 (1973) 2942. [8] T. Matsuyama, H. Horinaka, W. Wada, T. Kondo, M. Hangyo, T. Nakanishi, S. Okumi, K. Togawa, Jpn. J. Appl. Phys. 40 (2001) L555. [9] A.M. Danishevskii, E.L. Ivchenko, S.F. Kochegarov, M.I. Stepanova, Sov. Phys. JETP 16 (1972) 440. [10] S.B. Arifzhanov, E.L. Ivchenko, Sov. Phys. Solid State 17 (1975) 46. [11] D.T. Pierce, F. Meier, Phys. Rev. B 13 (1976) 5484. [12] G.E. Pikus, A.N. Titkov, in: F. Meier, B.P. Zakharchenya (Eds.), Optical Orientation, Modern Problems in Condensed Matter Science, vol. 8., North-Holland, Elsevier, Amsterdam, 1984. [13] M. Cardona, N.E. Christensen, G. Fasol, Phys. Rev. B 38 (1988) 1806. [14] I.A. Avrutsky, A.V. Vosmishev, Phys. Low-Dimens. Struct. 10 (11) (1995) 257. [15] T. Wang, A. Li, Z. Tan, Proc. SPIE 6838 (2007) 683814. [16] G. Dresselhaus, Phys. Rev. 100 (1955) 580. [17] Y.A. Bychkov, E.I. Rashba, J. Phys. C: Solid State Phys. 17 (1984) 6039. [18] H. Sanada, I. Arata, Y. Ohno, Z. Chen, K. Kayanuma, Y. Oka, F. Matsukura, H. Ohno, The Second International Conference on Physics and Application of Spin Related Phenomena in Semiconductors, Würzburg, Germany, 2002. [19] M.I. Miah, J. Appl. Phys. 103 (2008) 123711. [20] M.I. Miah, E.M. Gray, Curr. Opin. Solid State Mater. Sci. 14 (2010) 49. [21] S. Adachi, GaAs and Related Materials: Bulk Semiconducting and Superlattice Properties, World Scientific, Singapore, 1994.