Transmission-grating-photomasked transient spin grating and its application to measurement of electron-spin ambipolar diffusion in (110) GaAs quantum wells

doi:10.1364/OE.20.008192

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Transmission-grating-photomasked transient spin grating and its application to measurement of electron-spin ambipolar diffusion in (110) GaAs quantum wells

Ke Chen, Wenfang Wang, Jingda Wu, D. Schuh, W. Wegscheider, T. Korn, and Tianshu Lai »View Author Affiliations

Optics Express, Vol. 20, Issue 7, pp. 8192-8198 (2012)
http://dx.doi.org/10.1364/OE.20.008192

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Abstract

A circular dichromatic transient absorption difference spectroscopy of transmission-grating-photomasked transient spin grating is developed and formularized. It is very simple in experimental setup and operation, and has high detection sensitivity. It is applied to measure spin diffusion dynamics and excited electron density dependence of spin ambipolar diffusion coefficient in (110) GaAs quantum wells. It is found that the spin ambipolar diffusion coefficient of (110) and (001) GaAs quantum wells is close to each other, but has an opposite dependence tendency on excited electron density. This spectroscopy is expected to have extensive applicability in the measurement of spin transport.

1. Introduction

Spin transport, including diffusion and drift, is one way to transfer spin information in spintronic devices. It is one of fundamental issues in spintronics [1

I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys. 76(2), 323–410 (2004). [CrossRef]

] and reflects directly the spatiotemporal evolution of a spin wave packet. Spin transport parameters, such as spin diffusion coefficient and mobility, determine the size and response rate of spintronic devices. Consequently, the measurement of spin transport is important for the development of spintronics. The main optical measurement techniques reported so far may be categorized in three kinds. The first kind is the diffraction detection of transient spin gratings generated by two coherent pump lasers [2

A. R. Cameron, P. Riblet, and A. Miller, “Spin gratings and the measurement of electron drift mobility in multiple quantum well semiconductors,” Phys. Rev. Lett. 76(25), 4793–4796 (1996). [CrossRef] [PubMed]

–5

S. G. Carter, Z. Chen, and S. T. Cundiff, “Optical measurement and control of spin diffusion in n-doped GaAs quantum wells,” Phys. Rev. Lett. 97(13), 136602 (2006). [CrossRef] [PubMed]

]. The main disadvantage of such a kind of technique is low diffraction efficiency of the transient spin grating, and hence very weak diffracted signal. As a result, optical heterodyne amplification had to be used, but considerably adding the complexity of experimental setup and operation [4

C. P. Weber, N. Gedik, J. E. Moore, J. Orenstein, J. Stephens, and D. D. Awschalom, “Observation of spin Coulomb drag in a two-dimensional electron gas,” Nature 437(7063), 1330–1333 (2005). [CrossRef] [PubMed]

, 5

S. G. Carter, Z. Chen, and S. T. Cundiff, “Optical measurement and control of spin diffusion in n-doped GaAs quantum wells,” Phys. Rev. Lett. 97(13), 136602 (2006). [CrossRef] [PubMed]

]. The second kind is the local circular dichromatic absorption detection of the transient spin gratings by a tightly focused time-delayed probe [6

H.-L. Yu, X.-M. Zhang, P.-F. Wang, H.-Q. Ni, Z.-C. Niu, and T. S. Lai, “Measuring spin diffusion of electrons in bulk n-GaAs using circularly dichromatic absorption difference spectroscopy of spin gratings,” Appl. Phys. Lett. 94(20), 202109 (2009). [CrossRef]

], but the limited size of the focused probe spot restricted the detection of small period transient spin gratings. The third kind is tightly focused-probe-spot spatiotemporal scanning detection of a tightly focused pump-spot-injected electron spin pocket by circular dichromatic absorption [7

H. Zhao, M. Mower, and G. Vignale, “Ambipolar spin diffusion and D’yakonov-D’perel’ spin relaxation in GaAs quantum wells,” Phys. Rev. B 79(11), 115321 (2009). [CrossRef]

, 8

H.-L. Yu, X.-M. Zhang, and T. S. Lai, “Study of electron spin diffusion transport in intrinsic GaAs quantum wells by time- and space-resolved absorption spectroscopy,” Acta Phys. Sin. 58, 3543–3547 (2009).

], Faraday [9

D. D. Awschalom and J. M. Kikkawa, “Lateral drag of spin coherence in gallium arsenide,” Nature 397(6715), 139–141 (1999). [CrossRef]

] and Kerr [10

M. Furis, D. L. Smith, S. Kos, E. S. Garlid, K. S. M. Reddy, C. J. Palmstrøm, P. A. Crowell, and S. A. Crooker, “Local Hanle-effect studies of spin drift and diffusion in n:GaAs epilayers and spin transport devices,” New J. Phys. 9(9), 347 (2007). [CrossRef]

] rotations, but measurable lower limit of transport parameters is still restricted to the limited size of focused pump and probe spots and spatial scanning resolution between the two spots. It is very necessary to develop an optical measurement technique with simple experimental setup and operation as well as high detection sensitivity. We have reported such a technique which has such advantages and whose validation also has been proven by measuring carrier diffusion in bulk GaAs films [11

K. Chen, W. Wang, J. Chen, J. Wen, and T. Lai, “A transmission-grating-modulated pump-probe absorption spectroscopy and demonstration of diffusion dynamics of photoexcited carriers in bulk intrinsic GaAs film,” Opt. Express 20(4), 3580–3585 (2012). [CrossRef] [PubMed]

]. In this article, we will further develop the optical technique to measure electron spin diffusion. A circular dichromatic time-resolved pump-probe absorption spectroscopy is developed and formularized. It maintains the advantages expected, such as simple experimental setup and operation, much higher detection sensitivity than the diffraction measurement [12

A. Miller, R. J. Manning, P. K. Milsom, D. C. Hutchings, D. W. Crust‡, and K. Woodbridge, “Transient grating studies of excitonic optical nonlinearities in GaAs/AlGaAs multiple-quantum-well structures,” J. Opt. Soc. Am. B 6(4), 567–578 (1989). [CrossRef]

], no demanding a second pump beam, tightly focused pump and/or probe spots as well as spatially scanning of the spot. A formula is derived to describe circular dichromatic absorption difference experiment signal. Then, the spectroscopy is applied to measure spin diffusion dynamics in a (110) GaAs quantum well film to demonstrate its usage and advantages. The excited electron density dependence of spin diffusion coefficient is obtained, and found to disagree with one in (001) GaAs quantum wells. A brief discussion is made on the difference.

2. Principle and model

The details of experimental setup can be found in Ref. 11

. A change is that two achromatic quarter-wave plates are added, respectively in pump and probe beams, to generate circularly polarized pump and probe light. Figure 1 shows the main idea of our new spectroscopy. In the inset, the details to combine the standard pump-probe absorption spectroscopy with a transmission grating are displayed. A transmission grating is placed in front of and as close as possible to the sample to avoid diffraction effects or even contacted with the sample if the contact does not lead to any side effect. Another combination way (not shown) is back moving the sample away from the transmission grating. An imaging lens is placed between the grating and the sample to image the grating onto the sample. This combination is useful in low temperature measurement where the sample is mounted in a cryostat. The transmission grating is one-dimensional binary opaque/transparent, and fabricated on a Cr plate by photolithography. The Gaussian profile of pump and probe is modulated into a periodic stripe profile (PSP) as they are transmitted through the grating. Circularly polarized PSP pump laser excites the sample, generating one-dimensional transient spin-polarized carrier grating (TSPCG) in the sample, as shown in Fig. 1 with consideration of Gaussian profile of laser beam. The photoinjected TSPCG will evolve with time due to electron-hole recombination, transport and spin relaxation. Circularly polarized PSP probe travels through the sample and monitors the evolution of TSPCG by transient absorption change instead of diffraction intensity change, enhancing detection sensitivity at least by a factor of 300 [12

]. The key idea to measure the spin diffusion transport in the spectroscopy is that circularly polarized PSP probe can see the spin-polarized carriers only in the light area (corresponding to the transparent slits of the grating) of the sample, while the other carriers located in the dark area (corresponding to the opaque area of the grating) of the sample are not seen. However, spin diffusion transport can lead to the transfer of spin polarized carriers from the light to dark areas. The transfer of carriers is equivalent to an additional carrier recombination process occurred in the light area, thus leading to that a transient transmission change of the circularly polarized PSP probe decays faster than one of a normal circularly polarized Gaussian probe with no grating added. Therefore, the transient absorption change of TSPCG reflects the dynamics of not only recombination and relaxation but also spin diffusion of photoexcited spin-polarized carriers. Their quantitative relation will be modeled as follows.

Fig. 1 A profile at y=0 of transient spin-polarized electron distribution excited by a circularly polarized pump pulse through a binary transmission grating. N₊, N₋ and N₋-N₊ denote spin-up, spin-down and spin-polarized electron distribution. The inset shows experimental geometry with the grating in front of the sample. a and d are the transparent slit width and period of the grating, respectively.

Assuming N₊ and N₋ to be spin-up and spin-down electron density in conduction band, respectively, excited by circularly polarized pump light, the absorption coefficient,

α^{\pm}

, of right-handed (σ⁺) and left-handed (σ⁻) circularly polarized probes, may be expressed under the conditions of N₊ <<

N_{+}^{s}

and N₋<<

N_{-}^{s}

by [13

T. S. Lai, X. D. Liu, H. H. Xu, Z. X. Jiao, L. Lei, J. H. Wen, and W. Z. Lin, “Elliptically polarized absorption spectroscopy and observation of spin coherence in intrinsic GaAs,” Appl. Phys. Lett. 87(26), 262110 (2005). [CrossRef]

α^{\pm} (r, t) = \frac{α_{0}}{4} (4 - \frac{3 N_{\mp} (r, t)}{N_{\mp}^{s}} - \frac{N_{\pm} (r, t)}{N_{\pm}^{s}}),

(1)

where

α_{0}

is the linear absorption coefficient without pump.

N_{+}^{s}

and

N_{-}^{s}

are the density of state in |1/2> and |-1/2> spin conduction bands, respectively.

Assuming I₀(r) to be the incident intensity profile of σ⁺ and σ⁻ probes at front plane of the grating and T_G(x) the transmittivity of the binary transmission grating, the transient intensity profile of the transmitted σ⁺ and σ⁻ probes at backplane of the sample may be expressed by, respectively,

I^{\pm} (r, t) = I_{0} (r) T_{G} (x) \exp (- α^{\pm} (r, t) L),

(2)

where L is the thickness of the sample.

Substituting Eq. (1) into Eq. (2), Eq. (2) can be simplified as,

I^{\pm} (r, t) = I_{0} (r) T_{G} (x) e^{- α_{0} L} [1 + \frac{α_{0} L}{4 N^{s}} (N_{\pm} (r, t) + 3 N_{\mp} (r, t)],

(3)

where

N_{+}^{s} = N_{-}^{s} \equiv N^{s}

is applied.

The circular dichromatic transient absorption difference trace can be described by,

Δ P (t) = \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} [I^{+} (r, t) - I^{-} (r, t)] d x d y = F \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} I_{0} (r) T_{G} (x) [N_{-} (r, t) - N_{+} (r, t)] d x d y,

(4)

where F = α₀Lexp(-α₀L)/(2N ^s) is a scaling constant. Obviously, the transient signal, ΔP(t), is dominated by the dynamics of the relaxation and diffusion of spin-polarized electron distribution, N₋(r,t)-N₊(r,t), while spatiotemporal evolution of the spin-polarized electron distribution is controlled by following spin diffusion equation,

\frac{\partial S (r, t)}{\partial t} = D_{a s} \nabla^{2} S (r, t) - \frac{S (r, t)}{τ_{r s}},

(5)

where S(r,t) = N₋(r,t)-N₊(r,t) is spin-polarized electron distribution. D_as is the spin diffusion coefficient of electrons, 1/τ_rs = 1/τ_r + 2/τ_s is the effective spin decay rate with τ_r being the carrier recombination lifetime and τ_s spin relaxation time of electrons. Both τ_r and τ_s can be measured alone by normal circularly-polarized pump-probe transient traces with no grating added [13

]. Therefore, D_as is only unknown parameter in this equation, and just what we intend to measure.

For an initial TSPCG photoexcited by PSP pump pulses, Eq. (5) has no analytical solution. Therefore, numerical solution is necessary. A numerical optimization fitting program is developed based on Eqs. (4) and (5).

3. Sample and experiment

(110) GaAs quantum wells have potential applications in spintronic devices and been paid attention considerably because it has long spin lifetimes up to several nanoseconds due to the suppression of Dyakonov-Perel (DP) spin relaxation mechanism [14

Y. Ohno, R. Terauchi, T. Adachi, F. Matsukura, and H. Ohno, “Spin relaxation in GaAs(110) quantum wells,” Phys. Rev. Lett. 83(20), 4196–4199 (1999). [CrossRef]

–16

R. Völkl, M. Griesbeck, S. A. Tarasenko, D. Schuh, W. Wegscheider, C. Schüller, and T. Korn, “Spin dephasing and photoinduced spin diffusion in a high-mobility two-dimensional electron system embedded in a GaAs-(Al, Ga)As quantum well grown in the [110] direction,” Phys. Rev. B 83(24), 241306 (2011). [CrossRef]

]. Its spin relaxation is dominated by Bir-Aronov-Pikus (BAP) mechanism, and is distinct from one in (001) GaAs quantum wells dominated by the DP mechanism. It is unknown so far whether both (001) and (110) GaAs quantum wells have a same or similar spin transport behavior. Though the former was reported on its spin diffusion coefficient, the latter has not yet. Therefore, here we measure the spin diffusion dynamics of (110) GaAs quantum wells for the first time using the developed spectroscopy. The results obtained are important physically for revealing possible influence of spin relaxation mechanisms on spin diffusion dynamics.

GaAs quantum well sample under study is grown on (110) GaAs substrate by molecular beam epitaxy and consists of ten periods of 15 nm thick GaAs well and 185 nm thick Al_0.3Ga_0.7As barrier with a Si-δ-doped layer located at the centre of each barrier except the second barrier. The Si-δ doping resulted in an electron density of ~3.5x10¹¹ cm⁻² in each quantum well at room temperature. More details on the sample can be found in Ref. 17

V. V. Bel’kov, P. Olbrich, S. A. Tarasenko, D. Schuh, W. Wegscheider, T. Korn, C. Schüller, D. Weiss, W. Prettl, and S. D. Ganichev, “Symmetry and spin dephasing in (110)-grown quantum wells,” Phys. Rev. Lett. 100(17), 176806 (2008). [CrossRef] [PubMed]

(see sample C). GaAs substrate is removed by selectively chemical etching to allow transmission measurement. The sample film is mounted strain-free on a piece of quartz. The details on experimental setup and femtosecond lasers can be found elsewhere [11

]. The central wavelength of laser is tuned at 850 nm to excite carriers above the Fermi energy of the two-dimensional electron gas contained in each QW. Achromatic quarter-wave plates are inserted into pump and probe beams to generate circularly polarized pump and probe. All measurements are performed at room temperature.

4. Demonstration of spin diffusion dynamics and measurement of spin diffusion coefficient

Transient differential transmission with no transmission grating added is first measured for a σ⁺ pump and probe under a pump-injected spin-polarized electron density of ~1.0 × 10¹² cm⁻² per quantum well. The transient trace is plotted in Fig. 2 by open squares (trace A) and shows a slow decay. However, the transient trace B decays significantly faster than the A under the same experimental conditions as the trace A except a transmission grating with parameters, the slit width of a=2 μm and a period of d=6 μm, is placed in front of the sample, indicating out spin diffusion effect. This obvious diffusion effect is enhanced just by the introduction of the transmission grating because spin diffusion length is usually very small and only a few micrometers [18

M. Q. Weng and M. W. Wu, “Kinetic theory of spin transport in n-type semiconductor quantum wells,” J. Appl. Phys. 93(1), 410–420 (2003). [CrossRef]

], so that spin diffusion effect is not evident in normal pump-probe experiments with large pump and probe spots of at least several tens of micrometers. To show the enhancement effect of spin diffusion transport by the introduction of the transmission grating, another transmission grating with narrower 1 μm transparent slits is used. Thetransient trace is taken again under the same excitation conditions as trace B taken, and plotted by trace C in Fig. 2. Obviously, it decays faster than trace B and shows more obvious spin diffusion effect, again showing the key role of the transmission grating in the spectroscopy. With rotating quarter-wave plate by 90 degrees only in the probe to generate a σ⁻ probe, the transient trace is taken again for the 2 μm slit grating and plotted in Fig. 2 by open triangles (trace D). A transient difference trace is obtained by subtracting trace D from the B, and also plotted in Fig. 2 by open circles (trace E), and is called as circular dichromatic transient absorption difference trace which just reflects the dynamics of the relaxation and diffusion of spin-polarized electron distribution described by Eq. (4).

Fig. 2 Circular dichromatic transient differential transmission traces taken under a transmision grating added except the transient trace A. (σ+,σ–) and (σ+,σ+) denote the cross- and co-helicity circularly polarized pump and probe, respectively. The solid line in the transient trace E denotes the best fitting to open circles data with Eq. (4).

A best fitting to transient trace E in Fig. 2 with the optimization fitting program described afore gives D_as = 19.8 cm²/s, and is also plotted in Fig. 2 by a black solid line on trace E. The value of 19.8 cm²/s is slightly larger than the value of ~15 cm²/s [7

H. Zhao, M. Mower, and G. Vignale, “Ambipolar spin diffusion and D’yakonov-D’perel’ spin relaxation in GaAs quantum wells,” Phys. Rev. B 79(11), 115321 (2009). [CrossRef]

] measured at 80 K but smaller than the value of ~37.5 ± 15 cm²/s [8

] measured at room temperature of (001) GaAs quantum wells. With consideration of temperature difference and different well width (10 nm [7

H. Zhao, M. Mower, and G. Vignale, “Ambipolar spin diffusion and D’yakonov-D’perel’ spin relaxation in GaAs quantum wells,” Phys. Rev. B 79(11), 115321 (2009). [CrossRef]

], 6 nm [8

] and 15 nm here) of the samples studied, our result should be reasonable. However, the value of 19.8 cm²/s is much less than the value of ~130 cm²/s measured by the diffraction of transient spin grating in (001) GaAs quantum wells [2

, 4

]. As explained by Zhao et al [7

H. Zhao, M. Mower, and G. Vignale, “Ambipolar spin diffusion and D’yakonov-D’perel’ spin relaxation in GaAs quantum wells,” Phys. Rev. B 79(11), 115321 (2009). [CrossRef]

] and Yu et al [8

], the value of ~130 cm²/s reflects alone spin diffusion of electrons, whereas our value reflects spin ambipolar diffusion of electrons and holes because in our method, TSPCG contains carrier density inhomogeneity. Because of the requirement of local electrical neutrality, spin-polarized electron diffusion must be accompanied by hole diffusion. However, it is well known that holes diffuse much slower than electrons so that Coulomb attraction between holes and electrons leads to a much slower spin ambipolar diffusion than alone electron spin diffusion.

5. Excited electron density dependence of spin diffusion coefficient and discussion

The experimental measurements described in Fig. 2 are repeated for different pump-injected spin-polarized electron density. The experimental data are analyzed as described above. An excited electron density dependence of spin ambipolar diffusion coefficient (D_as), spin (τ_s) and recombination (τ_r) relaxation times is obtained and plotted in Fig. 3 . The τ_s decreases with the increase in excited electron density, agreeing well with the previous report in Ref. 14

Y. Ohno, R. Terauchi, T. Adachi, F. Matsukura, and H. Ohno, “Spin relaxation in GaAs(110) quantum wells,” Phys. Rev. Lett. 83(20), 4196–4199 (1999). [CrossRef]

. This variation tendency was explained by the suppression of DP mechanism and resultant domination of BAP spin relaxation mechanism in (110) GaAs quantum wells [14

Y. Ohno, R. Terauchi, T. Adachi, F. Matsukura, and H. Ohno, “Spin relaxation in GaAs(110) quantum wells,” Phys. Rev. Lett. 83(20), 4196–4199 (1999). [CrossRef]

, 19

M. Q. Weng, M. W. Wu, and H. L. Cui, “Spin relaxation in n-type GaAs quantum wells with transient spin grating,” J. Appl. Phys. 103(6), 063714 (2008). [CrossRef]

]. In contrast, the D_as increases with electron density. Such a dependence is opposite to one in (001) GaAs quantum wells reported by Zhao et al [7

H. Zhao, M. Mower, and G. Vignale, “Ambipolar spin diffusion and D’yakonov-D’perel’ spin relaxation in GaAs quantum wells,” Phys. Rev. B 79(11), 115321 (2009). [CrossRef]

], showing different spin diffusion behavior in (110) and (001) GaAs quantum wells. We conjecture this difference may be related to different spin relaxation mechanisms in (001) and (110) GaAs quantum wells. However, our result is indirectly supported by the increase of a spin diffusion length with excitation density [16

] though no data on spin diffusion coefficient are available for comparison. It has beenreported by Hanle steady-state measurement that spin diffusion length, L_d = (D_asτ_s)^1/2, increases with excitation density in (110) GaAs quantum wells [16

], implying the increase of D_as with excitation density because it is known that τ_s decreases with excitation density. Therefore, such a dependence of D_as on excitation density is convincing. However, completely understanding its origin physically is beyond the scope of this article. A brief discussion is made below on the reasonability of the dependence.

Fig. 3 Spin ambipolar diffusion coefficient, spin and recombination relaxation times as a function of excited electron density per quantum well. The scattered points are experimental data. The lines are guide for eyes.

Based on a microscopic theory of kinetic spin Bloch equations [19

M. Q. Weng, M. W. Wu, and H. L. Cui, “Spin relaxation in n-type GaAs quantum wells with transient spin grating,” J. Appl. Phys. 103(6), 063714 (2008). [CrossRef]

], the spin diffusion coefficient may be expressed by D = <k²τ₁/2m²>, where k denotes electron momentum, τ₁ is the momentum relaxation time due to electron-impurity scattering and m the effective mass of electrons. With increasing excited electron density, the k should increase due to the rise of Fermi level, but τ₁ usually decreases and depends on scattering mechanisms and band structures which are different for (001) and (110) GaAs quantum wells. Therefore, the variation tendency of D with the excited electron density relies on the competition between the changing rates of k and τ₁. If the dropping rate of τ₁ exceeds the rising rate of k², D will decrease with the excited electron density. This case occurs possibly in (001) GaAs quantum wells. Contrarily, D will increase with the excited electron density. This case may just occur in (110) GaAs quantum wells. A quantitative calculation is too complex and beyond the scope of this article.

6. Conclusion

A circular dichromatic transient absorption difference spectroscopy of transmission-grating-photomasked transient spin grating has been developed and used to measure the spin diffusion dynamics of (110) GaAs quantum wells. The excited density dependence of spin ambipolar diffusion coefficient D_as has been obtained and found different from one in (001) GaAs quantum wells. The difference may be related to different spin relaxation mechanisms in (001) and (110) GaAs quantum wells, and explained qualitatively by a microscopic spin transport theory. The spectroscopy developed has many advantages, such as high detection sensitivity, no requirement of tightly focused pump and probe spots as well as a second pump beam. Its extensive application may be expected in the measurement of spin transport.

Acknowledgments

This work is partially supported by National Natural Science Foundation of China under grant Nos. 10874247, 61078027, National Basic Research under grant Nos. 2010CB923200, and Natural Science Foundation of Guangdong Province under grant No. 9151027501000077 as well as doctoral specialized fund of MOE of China under grant No. 20090171110005.

References and links

1.	I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys. 76(2), 323–410 (2004). [CrossRef]
2.	A. R. Cameron, P. Riblet, and A. Miller, “Spin gratings and the measurement of electron drift mobility in multiple quantum well semiconductors,” Phys. Rev. Lett. 76(25), 4793–4796 (1996). [CrossRef] [PubMed]
3.	K. Jarasiunas, V. Gudelis, R. Aleksiejunas, M. Sudzius, S. Iwamoto, M. Nishioka, T. Shimura, K. Kuroda, and Y. Arakawa, “Picosecond dynamics of spin-related optical nonlinearities in In_xGa_1-xAs multiple quantum wells at 1064 nm,” Appl. Phys. Lett. 84(7), 1043–1045 (2004). [CrossRef]
4.	C. P. Weber, N. Gedik, J. E. Moore, J. Orenstein, J. Stephens, and D. D. Awschalom, “Observation of spin Coulomb drag in a two-dimensional electron gas,” Nature 437(7063), 1330–1333 (2005). [CrossRef] [PubMed]
5.	S. G. Carter, Z. Chen, and S. T. Cundiff, “Optical measurement and control of spin diffusion in n-doped GaAs quantum wells,” Phys. Rev. Lett. 97(13), 136602 (2006). [CrossRef] [PubMed]
6.	H.-L. Yu, X.-M. Zhang, P.-F. Wang, H.-Q. Ni, Z.-C. Niu, and T. S. Lai, “Measuring spin diffusion of electrons in bulk n-GaAs using circularly dichromatic absorption difference spectroscopy of spin gratings,” Appl. Phys. Lett. 94(20), 202109 (2009). [CrossRef]
7.	H. Zhao, M. Mower, and G. Vignale, “Ambipolar spin diffusion and D’yakonov-D’perel’ spin relaxation in GaAs quantum wells,” Phys. Rev. B 79(11), 115321 (2009). [CrossRef]
8.	H.-L. Yu, X.-M. Zhang, and T. S. Lai, “Study of electron spin diffusion transport in intrinsic GaAs quantum wells by time- and space-resolved absorption spectroscopy,” Acta Phys. Sin. 58, 3543–3547 (2009).
9.	D. D. Awschalom and J. M. Kikkawa, “Lateral drag of spin coherence in gallium arsenide,” Nature 397(6715), 139–141 (1999). [CrossRef]
10.	M. Furis, D. L. Smith, S. Kos, E. S. Garlid, K. S. M. Reddy, C. J. Palmstrøm, P. A. Crowell, and S. A. Crooker, “Local Hanle-effect studies of spin drift and diffusion in n:GaAs epilayers and spin transport devices,” New J. Phys. 9(9), 347 (2007). [CrossRef]
11.	K. Chen, W. Wang, J. Chen, J. Wen, and T. Lai, “A transmission-grating-modulated pump-probe absorption spectroscopy and demonstration of diffusion dynamics of photoexcited carriers in bulk intrinsic GaAs film,” Opt. Express 20(4), 3580–3585 (2012). [CrossRef] [PubMed]
12.	A. Miller, R. J. Manning, P. K. Milsom, D. C. Hutchings, D. W. Crust‡, and K. Woodbridge, “Transient grating studies of excitonic optical nonlinearities in GaAs/AlGaAs multiple-quantum-well structures,” J. Opt. Soc. Am. B 6(4), 567–578 (1989). [CrossRef]
13.	T. S. Lai, X. D. Liu, H. H. Xu, Z. X. Jiao, L. Lei, J. H. Wen, and W. Z. Lin, “Elliptically polarized absorption spectroscopy and observation of spin coherence in intrinsic GaAs,” Appl. Phys. Lett. 87(26), 262110 (2005). [CrossRef]
14.	Y. Ohno, R. Terauchi, T. Adachi, F. Matsukura, and H. Ohno, “Spin relaxation in GaAs(110) quantum wells,” Phys. Rev. Lett. 83(20), 4196–4199 (1999). [CrossRef]
15.	S. Döhrmann, D. Hägele, J. Rudolph, M. Bichler, D. Schuh, and M. Oestreich, “Anomalous spin dephasing in (110) GaAs quantum wells: anisotropy and intersubband effects,” Phys. Rev. Lett. 93(14), 147405 (2004). [CrossRef] [PubMed]
16.	R. Völkl, M. Griesbeck, S. A. Tarasenko, D. Schuh, W. Wegscheider, C. Schüller, and T. Korn, “Spin dephasing and photoinduced spin diffusion in a high-mobility two-dimensional electron system embedded in a GaAs-(Al, Ga)As quantum well grown in the [110] direction,” Phys. Rev. B 83(24), 241306 (2011). [CrossRef]
17.	V. V. Bel’kov, P. Olbrich, S. A. Tarasenko, D. Schuh, W. Wegscheider, T. Korn, C. Schüller, D. Weiss, W. Prettl, and S. D. Ganichev, “Symmetry and spin dephasing in (110)-grown quantum wells,” Phys. Rev. Lett. 100(17), 176806 (2008). [CrossRef] [PubMed]
18.	M. Q. Weng and M. W. Wu, “Kinetic theory of spin transport in n-type semiconductor quantum wells,” J. Appl. Phys. 93(1), 410–420 (2003). [CrossRef]
19.	M. Q. Weng, M. W. Wu, and H. L. Cui, “Spin relaxation in n-type GaAs quantum wells with transient spin grating,” J. Appl. Phys. 103(6), 063714 (2008). [CrossRef]

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(300.1030) Spectroscopy : Absorption
(300.6500) Spectroscopy : Spectroscopy, time-resolved
(320.7130) Ultrafast optics : Ultrafast processes in condensed matter, including semiconductors

ToC Category:
Spectroscopy

History
Original Manuscript: February 27, 2012
Manuscript Accepted: March 13, 2012
Published: March 23, 2012

Citation
Ke Chen, Wenfang Wang, Jingda Wu, D. Schuh, W. Wegscheider, T. Korn, and Tianshu Lai, "Transmission-grating-photomasked transient spin grating and its application to measurement of electron-spin ambipolar diffusion in (110) GaAs quantum wells," Opt. Express 20, 8192-8198 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-8192

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References

I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys.76(2), 323–410 (2004). [CrossRef]
A. R. Cameron, P. Riblet, and A. Miller, “Spin gratings and the measurement of electron drift mobility in multiple quantum well semiconductors,” Phys. Rev. Lett.76(25), 4793–4796 (1996). [CrossRef] [PubMed]
K. Jarasiunas, V. Gudelis, R. Aleksiejunas, M. Sudzius, S. Iwamoto, M. Nishioka, T. Shimura, K. Kuroda, and Y. Arakawa, “Picosecond dynamics of spin-related optical nonlinearities in InxGa1-xAs multiple quantum wells at 1064 nm,” Appl. Phys. Lett.84(7), 1043–1045 (2004). [CrossRef]
C. P. Weber, N. Gedik, J. E. Moore, J. Orenstein, J. Stephens, and D. D. Awschalom, “Observation of spin Coulomb drag in a two-dimensional electron gas,” Nature437(7063), 1330–1333 (2005). [CrossRef] [PubMed]
S. G. Carter, Z. Chen, and S. T. Cundiff, “Optical measurement and control of spin diffusion in n-doped GaAs quantum wells,” Phys. Rev. Lett.97(13), 136602 (2006). [CrossRef] [PubMed]
H.-L. Yu, X.-M. Zhang, P.-F. Wang, H.-Q. Ni, Z.-C. Niu, and T. S. Lai, “Measuring spin diffusion of electrons in bulk n-GaAs using circularly dichromatic absorption difference spectroscopy of spin gratings,” Appl. Phys. Lett.94(20), 202109 (2009). [CrossRef]
H. Zhao, M. Mower, and G. Vignale, “Ambipolar spin diffusion and D’yakonov-D’perel’ spin relaxation in GaAs quantum wells,” Phys. Rev. B79(11), 115321 (2009). [CrossRef]
H.-L. Yu, X.-M. Zhang, and T. S. Lai, “Study of electron spin diffusion transport in intrinsic GaAs quantum wells by time- and space-resolved absorption spectroscopy,” Acta Phys. Sin.58, 3543–3547 (2009).
D. D. Awschalom and J. M. Kikkawa, “Lateral drag of spin coherence in gallium arsenide,” Nature397(6715), 139–141 (1999). [CrossRef]
M. Furis, D. L. Smith, S. Kos, E. S. Garlid, K. S. M. Reddy, C. J. Palmstrøm, P. A. Crowell, and S. A. Crooker, “Local Hanle-effect studies of spin drift and diffusion in n:GaAs epilayers and spin transport devices,” New J. Phys.9(9), 347 (2007). [CrossRef]
K. Chen, W. Wang, J. Chen, J. Wen, and T. Lai, “A transmission-grating-modulated pump-probe absorption spectroscopy and demonstration of diffusion dynamics of photoexcited carriers in bulk intrinsic GaAs film,” Opt. Express20(4), 3580–3585 (2012). [CrossRef] [PubMed]
A. Miller, R. J. Manning, P. K. Milsom, D. C. Hutchings, D. W. Crust‡, and K. Woodbridge, “Transient grating studies of excitonic optical nonlinearities in GaAs/AlGaAs multiple-quantum-well structures,” J. Opt. Soc. Am. B6(4), 567–578 (1989). [CrossRef]
T. S. Lai, X. D. Liu, H. H. Xu, Z. X. Jiao, L. Lei, J. H. Wen, and W. Z. Lin, “Elliptically polarized absorption spectroscopy and observation of spin coherence in intrinsic GaAs,” Appl. Phys. Lett.87(26), 262110 (2005). [CrossRef]
Y. Ohno, R. Terauchi, T. Adachi, F. Matsukura, and H. Ohno, “Spin relaxation in GaAs(110) quantum wells,” Phys. Rev. Lett.83(20), 4196–4199 (1999). [CrossRef]
S. Döhrmann, D. Hägele, J. Rudolph, M. Bichler, D. Schuh, and M. Oestreich, “Anomalous spin dephasing in (110) GaAs quantum wells: anisotropy and intersubband effects,” Phys. Rev. Lett.93(14), 147405 (2004). [CrossRef] [PubMed]
R. Völkl, M. Griesbeck, S. A. Tarasenko, D. Schuh, W. Wegscheider, C. Schüller, and T. Korn, “Spin dephasing and photoinduced spin diffusion in a high-mobility two-dimensional electron system embedded in a GaAs-(Al, Ga)As quantum well grown in the [110] direction,” Phys. Rev. B83(24), 241306 (2011). [CrossRef]
V. V. Bel’kov, P. Olbrich, S. A. Tarasenko, D. Schuh, W. Wegscheider, T. Korn, C. Schüller, D. Weiss, W. Prettl, and S. D. Ganichev, “Symmetry and spin dephasing in (110)-grown quantum wells,” Phys. Rev. Lett.100(17), 176806 (2008). [CrossRef] [PubMed]
M. Q. Weng and M. W. Wu, “Kinetic theory of spin transport in n-type semiconductor quantum wells,” J. Appl. Phys.93(1), 410–420 (2003). [CrossRef]
M. Q. Weng, M. W. Wu, and H. L. Cui, “Spin relaxation in n-type GaAs quantum wells with transient spin grating,” J. Appl. Phys.103(6), 063714 (2008). [CrossRef]

Adachi, T.
Aleksiejunas, R.
Arakawa, Y.
Awschalom, D. D.
Bel’kov, V. V.
Bichler, M.
Cameron, A. R.
Carter, S. G.
Chen, J.
Chen, K.
Chen, Z.
Crooker, S. A.
Crowell, P. A.
Crust‡, D. W.
Cui, H. L.
Cundiff, S. T.
Das Sarma, S.
Döhrmann, S.
Fabian, J.
Furis, M.
Ganichev, S. D.
Garlid, E. S.
Gedik, N.
Griesbeck, M.
Gudelis, V.
Hägele, D.
Hutchings, D. C.
Iwamoto, S.
Jarasiunas, K.
Jiao, Z. X.
Kikkawa, J. M.
Korn, T.
Kos, S.
Kuroda, K.
Lai, T.
Lai, T. S.
Lei, L.
Lin, W. Z.
Liu, X. D.
Manning, R. J.
Matsukura, F.
Miller, A.
Milsom, P. K.
Moore, J. E.
Mower, M.
Ni, H.-Q.
Nishioka, M.
Niu, Z.-C.
Oestreich, M.
Ohno, H.
Ohno, Y.
Olbrich, P.
Orenstein, J.
Palmstrøm, C. J.
Prettl, W.
Reddy, K. S. M.
Riblet, P.
Rudolph, J.
Schuh, D.
Schüller, C.
Shimura, T.
Smith, D. L.
Stephens, J.
Sudzius, M.
Tarasenko, S. A.
Terauchi, R.
Vignale, G.
Völkl, R.
Wang, P.-F.
Wang, W.
Weber, C. P.
Wegscheider, W.
Weiss, D.
Wen, J.
Wen, J. H.
Weng, M. Q.
Woodbridge, K.
Wu, M. W.
Xu, H. H.
Yu, H.-L.
Zhang, X.-M.
Zhao, H.
Žutic, I.

Acta Phys. Sin.

H.-L. Yu, X.-M. Zhang, and T. S. Lai, “Study of electron spin diffusion transport in intrinsic GaAs quantum wells by time- and space-resolved absorption spectroscopy,” Acta Phys. Sin.58, 3543–3547 (2009).

Appl. Phys. Lett.

K. Jarasiunas, V. Gudelis, R. Aleksiejunas, M. Sudzius, S. Iwamoto, M. Nishioka, T. Shimura, K. Kuroda, and Y. Arakawa, “Picosecond dynamics of spin-related optical nonlinearities in InxGa1-xAs multiple quantum wells at 1064 nm,” Appl. Phys. Lett.84(7), 1043–1045 (2004). [CrossRef]
H.-L. Yu, X.-M. Zhang, P.-F. Wang, H.-Q. Ni, Z.-C. Niu, and T. S. Lai, “Measuring spin diffusion of electrons in bulk n-GaAs using circularly dichromatic absorption difference spectroscopy of spin gratings,” Appl. Phys. Lett.94(20), 202109 (2009). [CrossRef]
T. S. Lai, X. D. Liu, H. H. Xu, Z. X. Jiao, L. Lei, J. H. Wen, and W. Z. Lin, “Elliptically polarized absorption spectroscopy and observation of spin coherence in intrinsic GaAs,” Appl. Phys. Lett.87(26), 262110 (2005). [CrossRef]

J. Appl. Phys.

M. Q. Weng and M. W. Wu, “Kinetic theory of spin transport in n-type semiconductor quantum wells,” J. Appl. Phys.93(1), 410–420 (2003). [CrossRef]
M. Q. Weng, M. W. Wu, and H. L. Cui, “Spin relaxation in n-type GaAs quantum wells with transient spin grating,” J. Appl. Phys.103(6), 063714 (2008). [CrossRef]

J. Opt. Soc. Am. B

A. Miller, R. J. Manning, P. K. Milsom, D. C. Hutchings, D. W. Crust‡, and K. Woodbridge, “Transient grating studies of excitonic optical nonlinearities in GaAs/AlGaAs multiple-quantum-well structures,” J. Opt. Soc. Am. B6(4), 567–578 (1989). [CrossRef]

Nature

C. P. Weber, N. Gedik, J. E. Moore, J. Orenstein, J. Stephens, and D. D. Awschalom, “Observation of spin Coulomb drag in a two-dimensional electron gas,” Nature437(7063), 1330–1333 (2005). [CrossRef] [PubMed]
D. D. Awschalom and J. M. Kikkawa, “Lateral drag of spin coherence in gallium arsenide,” Nature397(6715), 139–141 (1999). [CrossRef]

New J. Phys.

M. Furis, D. L. Smith, S. Kos, E. S. Garlid, K. S. M. Reddy, C. J. Palmstrøm, P. A. Crowell, and S. A. Crooker, “Local Hanle-effect studies of spin drift and diffusion in n:GaAs epilayers and spin transport devices,” New J. Phys.9(9), 347 (2007). [CrossRef]

Opt. Express

K. Chen, W. Wang, J. Chen, J. Wen, and T. Lai, “A transmission-grating-modulated pump-probe absorption spectroscopy and demonstration of diffusion dynamics of photoexcited carriers in bulk intrinsic GaAs film,” Opt. Express20(4), 3580–3585 (2012). [CrossRef] [PubMed]

Phys. Rev. B

R. Völkl, M. Griesbeck, S. A. Tarasenko, D. Schuh, W. Wegscheider, C. Schüller, and T. Korn, “Spin dephasing and photoinduced spin diffusion in a high-mobility two-dimensional electron system embedded in a GaAs-(Al, Ga)As quantum well grown in the [110] direction,” Phys. Rev. B83(24), 241306 (2011). [CrossRef]
H. Zhao, M. Mower, and G. Vignale, “Ambipolar spin diffusion and D’yakonov-D’perel’ spin relaxation in GaAs quantum wells,” Phys. Rev. B79(11), 115321 (2009). [CrossRef]

Phys. Rev. Lett.

Y. Ohno, R. Terauchi, T. Adachi, F. Matsukura, and H. Ohno, “Spin relaxation in GaAs(110) quantum wells,” Phys. Rev. Lett.83(20), 4196–4199 (1999). [CrossRef]
S. Döhrmann, D. Hägele, J. Rudolph, M. Bichler, D. Schuh, and M. Oestreich, “Anomalous spin dephasing in (110) GaAs quantum wells: anisotropy and intersubband effects,” Phys. Rev. Lett.93(14), 147405 (2004). [CrossRef] [PubMed]
V. V. Bel’kov, P. Olbrich, S. A. Tarasenko, D. Schuh, W. Wegscheider, T. Korn, C. Schüller, D. Weiss, W. Prettl, and S. D. Ganichev, “Symmetry and spin dephasing in (110)-grown quantum wells,” Phys. Rev. Lett.100(17), 176806 (2008). [CrossRef] [PubMed]
S. G. Carter, Z. Chen, and S. T. Cundiff, “Optical measurement and control of spin diffusion in n-doped GaAs quantum wells,” Phys. Rev. Lett.97(13), 136602 (2006). [CrossRef] [PubMed]
A. R. Cameron, P. Riblet, and A. Miller, “Spin gratings and the measurement of electron drift mobility in multiple quantum well semiconductors,” Phys. Rev. Lett.76(25), 4793–4796 (1996). [CrossRef] [PubMed]

Rev. Mod. Phys.

I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys.76(2), 323–410 (2004). [CrossRef]

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