Photon energy and carrier density dependence of spin dynamics in bulk CdTecrystal at room temperatureHong Ma, Zuanming Jin, Guohong Ma, Weiming Liu, and Sing Hai Tang Citation: Applied Physics Letters 94, 241112 (2009); doi: 10.1063/1.3155428 View online: http://dx.doi.org/10.1063/1.3155428 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/94/24?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Long-lived, room-temperature electron spin coherence in colloidal CdS quantum dots Appl. Phys. Lett. 100, 122406 (2012); 10.1063/1.3696069 Transient spectral dependence of photoinduced magneto-optical Faraday effect in CdTe quantum dots AIP Advances 2, 012116 (2012); 10.1063/1.3679403 Carrier dynamics and activation energy of CdTe quantum dots in a CdxZn1−xTe quantum well Appl. Phys. Lett. 99, 231908 (2011); 10.1063/1.3669412 Response to “Comment on ‘Photon energy and carrier density dependence of spin dynamics in bulk CdTecrystal at room temperature’ ” [Appl. Phys. Lett.96, 136101 (2010)] Appl. Phys. Lett. 96, 136102 (2010); 10.1063/1.3371819 Comment on “Photon energy and carrier density dependence of spin dynamics in bulk CdTe crystal at roomtemperature” [Appl. Phys. Lett.94, 241112 (2009)] Appl. Phys. Lett. 96, 136101 (2010); 10.1063/1.3371817

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Photon energy and carrier density dependence of spin dynamics in bulkCdTe crystal at room temperature

Hong Ma,1 Zuanming Jin,1 Guohong Ma,1,a� Weiming Liu,2 and Sing Hai Tang2

1Department of Physics, Shanghai University, 99 Shangda Road, Shanghai 200444,People’s Republic of China2Department of Physics, National University of Singapore, Singapore 117542, Singapore

�Received 16 March 2009; accepted 27 May 2009; published online 17 June 2009�

Excitation photon energy and carrier density dependence of spin dynamics in bulk CdTe crystalwas studied by time resolved pump-probe reflectivity technique at room temperature. The resultsshow that spin relaxation time decreases monotonously. While with increasing excitation carrierdensity, the time constants increases initially then decreases after reaching a maximum value.Our experimental results reveal that both D’yakonov–Perel’ �M. I. D’yakonov and V. I. Perel’,Sov. Phys. JETP 38, 177 �1974�� and Elliot–Yafet �R. J. Elliott, Phys. Rev. 96, 266 �1954�; Y. Yafet,Solid State Phys. 14, 1 �1963�� mechanisms dominate the spin relaxation process in CdTecrystal. © 2009 American Institute of Physics. �DOI: 10.1063/1.3155428�

In the past few decades, spin dynamics down to subpi-cosecond time domain in semiconductors and semiconductornanostructures have attracted intense interest because of thepotential applications in emerging areas such as “spintron-ics” and quantum information processing. The popularmethod studying spin dynamics is the time resolved pump-probe reflectivity �TRPPR� technique,1–3 which has proved tobe one of the simple and powerful means to study the dy-namical behavior of carriers in semiconductor, especially inthick and nontransparent samples such as GaAs, CdTe.

At present, most studies of spin dynamics have beencarried out in III-V compound materials at lowtemperatures,3–7 where the behavior of the carriers is simpleto describe. However, for potential applications, studies ofspin dynamics at room temperature are more important.CdTe is also an interesting candidate because it has the simi-lar structure to GaAs and larger ratio of split-off band energyto band-gap energy. Under high magnetic field �up to 10 T�and low temperature �10 K�, Chen et al.8 studied the mag-netic field-induced suppression of spin relaxation in CdTequantum dots with time-resolved photoluminescence. Withpolarimetric technique, Kimel et al.9 studied the dynamics ofKerr rotation and Kerr ellipticity in bulk CdTe at room tem-perature, a particular relaxation with time constant of 2.5 pswas obtained, which was attributed to electron spin relax-ation. Whereas little work was done about the influence ofthe excitation photon energy and carrier density on spin re-laxation, which are very important factors to address the spinrelaxation in semiconductor crystal.

In this letter, electron spin dynamics of intrinsic bulkCdTe at room temperature is studied by using TRPPR tech-nique. Similar as GaAs, CdTe has the simple direct band-gapwith zinc blende structure. At room temperature, the bandgap of bulk CdTe is 1.45 eV. Figure 1 shows the band struc-ture of CdTe near the � point �Fig. 1�a�� and the selectionrules and relative transition intensities for left-handed ��−�and right-handed ��+� circularly polarized light �Fig.1�b��.9,10 A laser pulse excites carriers with a preferentialspin orientation because of the selection rules for transitions

induced by circularly polarized photons. For photon energiesequal or slightly superior to the direct band-gap energy Eg,transitions can take place between the top of the degenerateP3/2 valence band at �8 and the bottom of the degenerate S1/2conduction band at �6. In bulk semiconductor, the transitionsexcited by circularly polarized light, e.g., a left-handed cir-cularly polarized �−, involves heavy holes P+3/2 and lightholes P+1/2 �dashed line in Fig. 1�b��. The ratio of the opti-cally generated spin-up n↑ to spin-down n↓ electrons is 3:1,owing to the form of the matrix elements for heavy-hole andlight-hole interband transitions. Therefore, the maximum de-gree of net spin polarization is P= �n↑−n↓� / �n↓+n↑�=0.5.

The CdTe single crystal �purchased from Hefei KejingMaterials Technology co., LTD,� was grown by Bridgmanmethod with crystalline orientation along �111� direction andthe thickness is 450 �m. The sample was not intentionallydoped with the background doping level of 9�1014 cm−3.Optical measurements of the electron spin dynamics werecarried out using the TRPPR. Both pump and probe pulseswere generated by a tunable mode-locked Ti: Sapphire laserwith a pulse width of 100 fs and a repetition rate of 80 MHz�Mai Tai HP 1020�. The two beams with the intensity ratio ofmore than 10:1 were focused on the same spot of the samplewith a spot size of 160 �m. The pump beam reflected by thesample was blocked with a nontransparent aperture, while

a�Author to whom correspondence should be addressed. FAX: 86-21-66134208. Electronic mail: ghma@staff.shu.edu.cn.

FIG. 1. �a� Band structure of CdTe near the � point �b� selection rules andrelative transition intensities for right-handed �+ �solid arrow� and left-handed �− �dashed arrow� circularly polarized light.

APPLIED PHYSICS LETTERS 94, 241112 �2009�

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the probe beam was guided into a photodiode connected witha lock-in amplifier. The polarizations of both beams werechanged by two achromatic quarter wave plates. The photonenergy range used in the present study is from 1.476–1.512eV, which makes it impossible to reach the transition be-tween the split-off band �7 and the conduction band �6. Acontinuous variable attenuator was used to control input laserpower so that the carrier densities were kept the same in allphoton energy range. All experiments were conducted atroom temperature.

The typical time dependence spectroscopy of differentpolarized pump and probe pulse with photon energy of 1.494eV at room temperature is shown in Fig. 2. It is seen that adramatic increase in reflectivity change occurs due to bandbleaching and followed by a long bleaching recovery pro-cess. The curves labeled as ��+ ,�+� and ��+ ,�−� are ob-tained from cocircularly, counter-circularly polarized pumpand probe beams, respectively, whereas the one labeled ��,�� stands for pump and probe pulses with linear polariza-tion, which reflects the carriers relaxation and recombination,and is insensitive to electron spin. The difference of the threecurves is still distinct though it is not as pronounced as thatmeasured typically in quantum well structures. It is also seenthat the curve ��+ ,�+� is the strongest, while the ��+ ,�−� isthe weakest among the three curves. But finally, both��+ ,�+� and ��+ ,�−� curves tend to completely coincidewith ��, �� curve, which indicates spin polarization relax-ation between �+1 /2� and �−1 /2� spin states in conductionband. The ��+ ,�+� curve reflects the decay of majority spinpopulation after photoexcitation with �+ pump pulses, whilethe curve changes between ��+ ,�−� and ��, �� reflectspopulation increase in minority spin state induced by spinflip from the majority spin state.11 The spin relaxation life-time can be obtained by taking the difference between twocurves of ��+ ,�+� and ��+ ,�−�.2,12 As shown in the inset ofthe Fig. 2, the curve can be well fitted using a single-

exponential decay. Recalling that �s /2=�fit, the spin relax-ation with time constant of 5.88�0.02 ps is obtained forCdTe crystal according to our experimental data.

The D’yakonov–Perel’ �DP� mechanism13 is thought asthe dominant mechanism in zinc-blende semiconductorswithout inversion symmetry at room temperature. The en-ergy dependent spin relaxation rate is followed by10

1

�s�Ek�=

32

105�3

−1�pc2 Ek

3

2Eg, �1�

where �3 is a parameter with relation to scattering process. �pis momentum relaxation time, which is independent of theexcess energy at lower excitation density in bulksemiconductor.14 c is determined by c=4me��1−1 /3��−1/2 / �3mc�� and �= / � +Eg�, Ek is the excess elec-tron energy. Assuming optical phonon scattering mechanismplays dominant role for spin relaxation, the calculated non-degenerate electron spin lifetime is about 20 ps. Although thetheoretical prediction shows the same order of magnitude asthe previously reported results,15,16 it is about fourfold largerthan our experimental measurement.

In order to completely understand the mechanisms ofelectron spin relaxation, the carrier density and photon en-ergy dependences of spin relaxation were studied systemati-cally. Figure 3�a� shows time dependence of reflectivitychanges of probe beam with three selected photon energy atthe excitation carrier density of about 2.53�1011 cm−2. Themeasured photon energy dependence of spin relaxation timeis presented in Fig. 3�c� �open square�, �s shows continu-ously decreases with photon energy in the investigated rangeof 1.476 to 1.512 eV. However, the electron spin relaxationtime described by DP mechanism is related with the excesselectron energy Ek by �s

−1�Ek3.10 The discrepancy between

the experimental value and theoretical prediction indicatesthat the spin relaxation cannot be described by DP mecha-nism only. Carrier density dependence of spin relaxationtime at fixed photon energy of 1.485 eV is plotted in Figs.3�b� and 3�c� �filled squares�, the most interesting feature isthat the spin relaxation time shows complex density depen-dence: At carrier density below 2.86�1011 cm−2, �s in-creases with carrier density, when density is higher than2.86�1011 cm−2, �s shows a decrease with excitation den-sity. This experimental finding is different from the previousreport in an intrinsic GaAs, in which at low densities, �sincreases linearly with the carrier density due to DP mecha-nism dominating the spin relaxation process.17 The experi-mental results reveal that other mechanisms may also con-tribute to the spin relaxation in our case.

The candidate spin relaxation mechanisms in semicon-ductor are Elliot–Yafet �EY� process18,19 and Bir–Aronov–Pikus �BAP� process20 besides the DP process. The BAPprocess, which originates from the exchange interaction be-tween electrons and holes, plays an important role at highp-type doped level. In our work, the BAP process is re-frained due to the lower holes density of 1011 cm−2. Theexact Bloch state is not a spin eigen state but a superpositionof them owing to the presence of spin orbit coupling. Thisinduces a chance for spin flip during the scattering processes,which is the EY process.

Just like DP mechanism, EY mechanism becomes impor-tant for semiconductors with great ratio of split-off band en-ergy to band-gap energy by the relation of �= / � +Eg�.

FIG. 2. Time dependence spectroscopy of different polarized pump andprobe pulses at room temperature. The curves labeled as ��+ ,�+� and��+ ,�−� were obtained from co-circularly and counter-circularly polarizedpump and probe beams respectively, whereas the one labeled ��, �� was thelinearly polarized pump and probe pulse. The inset was the time dependenceof the difference between the reflection signals for ��+ ,�+� and ��+ ,�−�curve. The spin-relaxation time constant is 5.88�0.02 ps by fitting theexperimental data using a single-exponential decay. The photon energy andphoto-excited carrier density are 1.494 eV and 2.53�1011 cm−2,respectively.

241112-2 Ma et al. Appl. Phys. Lett. 94, 241112 �2009�

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The value of �=0.383 in CdTe can be expected from the dataEg=1.45 eV and =0.9 eV, which is much larger than thatin GaAs of �=0.193. Therefore, it is possible that both EYand DP mechanisms take effect in electron spin relaxation inCdTe. In fact, the momentum relaxation time �p is given by�p�N−1/3,21 where N is the carrier density. The EY and DPmechanisms principally differ by their opposite dependences

on �p: for the former mechanism �sEY−1

��p−1, whereas for the

latter one �sDP−1

��p. Therefore, the contribution from EYmechanism increases and that from DP mechanism decreaseswith increasing the carrier density. It is seen that discrepancyof theoretical prediction based on Eq. �1� originates fromneglecting the contribution from EY mechanism at highercarrier density.

In conclusion, carrier density and photon energy depen-dence of electron spin relaxation in CdTe crystal were inves-tigated by TRPPR technique at room temperature. With pho-ton energy increasing from 1.476 to 1.512 eV, the spinrelaxation time continuously decrease from 7.78 to 3.08 ps.By varying carrier density, it is found that the spin relaxationtime increases initially, reaching a maximum value of �7 psat carrier density of 2.86�1011 cm−2, then it shows continu-ously decrease with carrier density. These results reveal thatboth DP and EY mechanisms take equal important role forspin relaxation in CdTe crystal at room temperature. Theopposite dependences on momentum relaxation time �p ofEY and DP mechanism makes the spin relaxation tendencyof theory coincide with that of the experimental data.

The research is supported by National Natural ScienceFoundation of China �Grant No. 10774099�, the Program forProfessor of a Special Appointment �Eastern Scholar� atShanghai Institutions of Higher Learning, Science and Tech-nology Commission of Shanghai Municipal �Grant No.06PJ14042�, and the National University of Singapore underGrant No. R144000176112. Part of the work was also sup-ported by Shanghai Leading Academic Discipline Project�Grant No. S30105�.

1A. J. Sabbah and D. M. Riffe, Phys. Rev. B 66, 165217 �2002�.2K. C. Hall, S. W. Leonard, H. M. van Driel, A. R. Kost, E. Selvig, and D.H. Chow, Appl. Phys. Lett. 75, 3665 �1999�.

3A. Tackeuchi, H. Otake, Y. Ogawa, T. Ushiyama, T. Fujita, F. Takano, andH. Akinaga, Appl. Phys. Lett. 88, 162114 �2006�.

4J. M. Kikkawa and D. D. Awschalom, Phys. Rev. Lett. 80, 4313 �1998�.5T. S. Lai, X. D. Liu, H. H. Xu, Zh. X. Jiao, J. H. Wen, and W. Zh. Lin,Appl. Phys. Lett. 88, 192106 �2006�.

6P. E. Hohage, G. Bacher, D. Reuter, and A. D. Wieck, Appl. Phys. Lett.89, 231101 �2006�.

7Yu. D. Glinka, T. V. Shahbazyan, I. E. Perakis, N. H. Tolk, X. Liu, Y.Sasaki, and J. K. Furdyna, Appl. Phys. Lett. 81, 220 �2002�.

8Y. Chen, T. Okuno, Y. Masumoto, Y. Terai, S. Kuroda, and K. Takita,Phys. Rev. B 71, 033314 �2005�.

9A. V. Kimel, V. V. Pavlov, R. V. Pisarev, V. N. Gridnev, F. Bentivegna,and Th. Rasing, Phys. Rev. B 62, R10610 �2000�.

10Optical Orientation, edited by F. Meier and B. P. Zakharchenya �Elsevier,Amsterdam, 1984�.

11L. H. Teng, P. Zhang, T. S. Lai, and M. W. Wu, Europhys. Lett. 84, 27006�2008�.

12T. F. Boggess, J. T. Olesberg, C. Yu, M. E. Flatté, and W. H. Lau, Appl.Phys. Lett. 77, 1333 �2000�.

13M. I. D’yakonov and V. I. Perel’, Sov. Phys. JETP 38, 177 �1974�.14S. Arlt, U. Siegner, J. Kunde, F. Morier-Genoud, and U. Keller, Phys. Rev.

B 59, 14860 �1999�.15P. Nahálková, P. Němec, D. Sprinzl, E. Belas, P. Horodyský, J. Franc, P.

Hlídek, and P. Malý, Mater. Sci. Eng., B 126, 143 �2006�.16T. Ito, W. Shichi, Y. Okami, M. Ichida, H. Gotoh, H. Kamada, and H.

Ando, Phys. Status Solidi C 6, 319 �2009�.17S. Oertel, J. Hübner, and M. Oestreich, Appl. Phys. Lett. 93, 132112

�2008�.18R. J. Elliott, Phys. Rev. 96, 266 �1954�.19Y. Yafet, Solid State Phys. 14, 1 �1963�.20G. L. Bir, A. G. Aronov, and G. E. Pikus, Sov. Phys. JETP 42, 705

�1976�.21P. C. Becker, H. L. Fragnito, C. H. Brito Cruz, R. L. Fork, J. E. Cunning-

ham, J. E. Henry, and C. V. Shank, Phys. Rev. Lett. 61, 1647 �1988�.

FIG. 3. �a� Time dependence of spin relaxation with different photon energyat the density of 2.53�1011 cm−2 and �b� different excited carrier density atfixed photon energy of 1.485 eV. In order to easily compare the distinctionof different polarized pump and probe beams ��, �� were not shown. �c�the spin relaxation time constant as a function of electron density and pho-ton energy.

241112-3 Ma et al. Appl. Phys. Lett. 94, 241112 �2009�

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