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

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.

© 2012 OSA

## 1. Introduction

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]

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]

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]

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]

## 2. Principle and model

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]

*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,

^{+}) and left-handed (σ

^{−}) circularly polarized probes, may be expressed under the conditions of

*N*

_{+}<<

*N*

_{−}<<

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]

*I*

_{0}(

*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,where

*L*is the thickness of the sample.

*F*=

*α*

_{0}

*L*exp(-

*α*

_{0}

*L*)/(2

*N*

^{s}) is a scaling constant. Obviously, the transient signal, Δ

*P*(

*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,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

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]

*D*

_{as}is only unknown parameter in this equation, and just what we intend to measure.

## 3. Sample and experiment

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]

_{0.3}Ga

_{0.7}As 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 ~3.5x10

^{11}cm

^{−2}in each quantum well at room temperature. More details on the sample can be found in Ref. 17

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]

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]

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

^{+}pump and probe under a pump-injected spin-polarized electron density of ~1.0 × 10

^{12}

*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

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]

*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).

*E*in Fig. 2 with the optimization fitting program described afore gives

*D*

_{as}= 19.8

*cm*

^{2}/

*s*, and is also plotted in Fig. 2 by a black solid line on trace

*E*. The value of 19.8

*cm*

^{2}/

*s*is slightly larger than the value of ~15

*cm*

^{2}/

*s*[7

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]

*cm*

^{2}/

*s*[8] measured at room temperature of (001) GaAs quantum wells. With consideration of temperature difference and different well width (10 nm [7

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]

*cm*

^{2}/

*s*is much less than the value of ~130 cm

^{2}/s measured by the diffraction of transient spin grating in (001) GaAs quantum wells [2

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]

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]

**79**(11), 115321 (2009). [CrossRef]

*cm*

^{2}/

*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

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]

*D*= <

*k*

^{2}

*τ*

_{1}/2

*m*

^{2}>, where

*k*denotes electron momentum,

*τ*

_{1}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

*τ*

_{1}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

*τ*

_{1}. If the dropping rate of

*τ*

_{1}exceeds the rising rate of

*k*

^{2},

*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

## Acknowledgments

## References and links

1. | I. Žutić, J. Fabian, and S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys. |

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. |

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 |

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 |

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. |

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. |

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 |

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. |

9. | D. D. Awschalom and J. M. Kikkawa, “Lateral drag of spin coherence in gallium arsenide,” Nature |

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. |

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 |

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 |

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. |

14. | Y. Ohno, R. Terauchi, T. Adachi, F. Matsukura, and H. Ohno, “Spin relaxation in GaAs(110) quantum wells,” Phys. Rev. Lett. |

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. |

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 |

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. |

18. | M. Q. Weng and M. W. Wu, “Kinetic theory of spin transport in n-type semiconductor quantum wells,” J. Appl. Phys. |

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. |

**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, S. Das Sarma, “Spintronics: Fundamentals and applications,” Rev. Mod. Phys. 76(2), 323–410 (2004). [CrossRef]
- A. R. Cameron, P. Riblet, 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, 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, D. D. Awschalom, “Observation of spin Coulomb drag in a two-dimensional electron gas,” Nature 437(7063), 1330–1333 (2005). [CrossRef] [PubMed]
- S. G. Carter, Z. Chen, 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, 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, G. Vignale, “Ambipolar spin diffusion and D’yakonov-D’perel’ spin relaxation in GaAs quantum wells,” Phys. Rev. B 79(11), 115321 (2009). [CrossRef]
- H.-L. Yu, X.-M. Zhang, 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, J. M. Kikkawa, “Lateral drag of spin coherence in gallium arsenide,” Nature 397(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, 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, 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]
- A. Miller, R. J. Manning, P. K. Milsom, D. C. Hutchings, D. W. Crust‡, 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]
- T. S. Lai, X. D. Liu, H. H. Xu, Z. X. Jiao, L. Lei, J. H. Wen, 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, 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, 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, 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]
- V. V. Bel’kov, P. Olbrich, S. A. Tarasenko, D. Schuh, W. Wegscheider, T. Korn, C. Schüller, D. Weiss, W. Prettl, S. D. Ganichev, “Symmetry and spin dephasing in (110)-grown quantum wells,” Phys. Rev. Lett. 100(17), 176806 (2008). [CrossRef] [PubMed]
- M. Q. Weng, 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, H. L. Cui, “Spin relaxation in n-type GaAs quantum wells with transient spin grating,” J. Appl. Phys. 103(6), 063714 (2008). [CrossRef]

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