Suppression of D'yakonov-Perel spin relaxation in InAs and InSb by n

Suppression of D'yakonov-Perel spin relaxation in InAs and InSb by n

Suppression of D'yakonov-Perel spin relaxation in InAs and InSb by n-

type doping at 300K

P. Murzyn 1 , C. R. Pidgeon 1 and P. J. Phillips 1

1 Department of Physics, Heriot-Watt University, Edinburgh EH14 4AS, UK.

M. Merrick 2 , K. L. Litvinenko 2 J. Allam and B. N. Murdin 2

2 Advanced Technology Institute, University of Surrey, Guildford GU2 7XH, UK.

T Ashley 3 and J H Jefferson 3

3 QinetiQ, St Andrews Road, Malvern, Worcs WR14 3PS, UK.

L F Cohen 4

4 Blackett Laboratory, Imperial College, London SW7 2BW, UK.

We have made direct pump-probe measurements of spin lifetimes in intrinsic and

degenerate n-InAs at 300K. In particular, we measure remarkably long spin lifetimes, τ s ~

1ns, for near-degenerate epilayers of InAs. For intrinsic material we determine τ s ~ 20ps in

agreement with other workers. There are two main models that have been invoked for

describing spin relaxation in narrow gap semiconductors: the D'yakonov-Perel (DP) model

and the Elliott-Yafet (EY) model. For intrinsic material the DP model is believed to dominate

in III-V materials above 77K, in agreement with our results. We show that in the presence of

strong n-type doping, the DP relaxation is suppressed both by the degeneracy condition and

by electron-electron scattering, and that the EY model then dominates for the n-type material.

We show that this same process is also responsible for a hitherto unexplained lengthening of

τ s with n-type doping in our earlier measurements of n-InSb.

PACS: 72.25.Fe, 72.25.Rb

Utilisation of the electron spin has become a focus of interest in semiconductor

electronics, or spintronics, in recent years, and it is important to realise a sufficiently long spin

lifetime, τ s , to process information stored in the form of the polarisation of spin ensembles.

To find a way to control τ s it is necessary to understand the spin relaxation mechanisms in

both bulk and low dimensional semiconductor structures which are designed so that spins can

be appropriately confined and/or transferred. In contrast to GaAs-based systems, relatively

little attention has been paid to InAs, even although it may be important in future spintronics

applications. We previously measured spin lifetimes in narrow gap semiconductors (NGS),

Hg 1-x Cd x Te and InSb, at wavelengths between 4 and 10µm and from 4 - 300K 8 . We have

now extended those measurements to include bulk epilayers of InAs as a function of doping at


The InAs samples were grown at Imperial College by MBE on GaAs substrates with

the following 300K Hall effect characteristics. IC313: n = 3.8x10 16 cm -3 , mobility µ =

3x10 4 cm 2 V -1 s -1 ; IC311: n = 1x10 17 cm -3 , µ = 2.5x10 4 cm 2 V -1 s -1 . The InSb samples used in

our previous work 8 were as follows: ME1654: n = 1.5x10 16 , µ = 6.9x10 4 cm 2 V -1 s -1 ;

ME1629: n = 2.3x10 17 cm -3 , µ = 4.5x10 4 cm 2 V -1 s -1 . To measure the spin lifetimes, we used

the standard polarization pump-probe method 7,8,14 , which excites spins in the semiconductor

with above-bandgap, circularly polarized light, and probes the induced bleaching with either

the same or the opposite circularly polarized light (SCP or OCP respectively). The pump and

probe beams are pulsed, and by changing the time delay between the pump and probe and

comparing the SCP and OCP results we measure the spin decay lifetime. The optical pulses

for the experiment, carried out at the University of Surrey, were generated with a solid-state

laser system (DFG 9850, Coherent Inc., Santa Clara CA, USA) that produces ~40 fs pulses

from 2.5 to 11 µm wavelength, with a repetition rate of 250kHz and typical average power of

5mW. The beams were focused on to the sample with spot sizes of approximately 100µm,

and the transmitted probe light was detected with a liquid nitrogen cooled InSb photodiode.

Results for the transmission change in the probe due to the pump are shown for

sample IC313 in Fig. 1 for SCP and OCP configurations. The data are characterised by three

features and are in extremely good agreement with the results of other workers 7 . In both

cases there is a transient increase in transmission that is initiated and decays in less than 2ps.

We attribute this to thermalisation of the optically injected carriers, hole spin relaxation and

coherent artifacts of the system 7 . The second feature is a clear distinction between the SCP

and OCP data that occurs during the first 40ps and is caused by the spin polarisation

relaxation. Finally, there is a long decay of both SCP and OCP that occurs on a longer,

nanosecond scale. Following ref 7, we plot the fractional difference in transmission between

SCP and OCP, P opt = (∆T SCP - ∆T OCP )/( ∆T SCP + ∆T OCP ) shown in the inset. This, when fitted

with a monoexponential decay, yields a time constant of τ = 20ps. The error in the fitting due

to noise in the data is estimated to be ±10 ps.

Because of the different transition strengths associated with heavy hole and light hole

to conduction band transitions from a complex (spin-orbit mixed) valence band, a partially

spin-polarised distribution is created by pumping with circularly polarised radiation. If we

take the case of (e.g.) a left circularly polarised pump pulse (σ-), the relative concentration of

optically generated spin up (n ↑ ) to spin down (n ↓ ) electrons is 3:1, leading to a maximum spin

polarisation of P s = 0.5, where P s = (n ↑ - n ↓ )/( n ↑ + n ↓ ) 7,8,14 . The actually measured probe

transmission is proportional to the absorption change, ∆α. A σ - probe will experience ∆α - ∝

3n opt↑ + n opt↓ , while a σ + probe will experience ∆α + ∝ 3n opt↓ + n opt↑ . Thus the optical

polarisation signal becomes: P opt = (∆α - - ∆α + )/(∆α - + ∆α + ) = 0.5 P s , which has a maximum

value 0.25. In practice our polarisers were not fully optimised for these long wavelengths, so

the maximum polarisation we achieve is somewhat less than 25%.

In order to test the effect of n-type doping the measurements were repeated for the

near degenerate sample, IC311, and the results are shown in Fig. 2. Although the change in

polarization P opt from SCP to OCP is quite large, the decay times of each are similar to each

other and also to the electron-hole recombination rate. We therefore show in this figure the

SCP and OCP data normalized to the peak so that the difference in slope is more apparent.

Clearly the decay of the spin polarisation is substantially lengthened, and the decay time of

P opt , plotted in the inset, is now τ = 1.6±0.5 ns. Similar, and hitherto uninterpreted, results

were obtained for InSb in our earlier work 8 : ME1654 (τ = 16ps) and ME1629 (τ = 300ps).

In bulk semiconductors three main spin relaxation processes have been found to be

important in optical orientation experiments: the Elliott-Yafet (EY) 1,4,5,6 , D'yakonov-Perel

(DP) 2,5,6 and the Bir-Aronov-Pikus (BAP) 3 mechanisms. The BAP mechanism is thought to

be particularly important in p-type wide gap materials and is based on the electron-hole

exchange interaction. By contrast with the other two processes, it depends directly on the

concentration of holes, and is not thought to be important in n-type NGS.

The EY mechanism results from the fact that in real crystals Bloch states are not spin

eigenstates because of the strong spin-orbit coupling induced by the lattice ions. In the

presence of strong spin-orbit coupling, the valence band states have mixed spin character. In

NGS the conduction electron states, in turn, are strongly mixed with the valence states

through the k.p interaction across a narrow energy gap. In this case spin-independent

interactions with impurities, boundaries, phonons etc., can connect spin up and down

electrons, leading to spin flip transitions whose rate 1/τ s is proportional to 1/τ p where τ p is the

orbital momentum (mobility) scattering time. This process has been shown to be important at

low temperatures in NGS 4,5,6 . The EY spin relaxation rate for ionised impurity scattering and

degenerate statistics is:




32 ⎛ γE


⎝ E




⎞ ⎛1− γ / 2 ⎞

⎟ ⎜ ⎟

⎠ ⎝1− γ / 3 ⎠





, (1)

where γ = ∆/(E G +∆), and ∆ is the spin-orbit splitting of the valence band. In the other limit of

lattice scattering and non-degenerate statistics the EY expression becomes:




⎛ γkT

≈ 2


⎝ G ⎠


⎛1− γ / 2 ⎞

⎜ ⎟

⎝1− γ / 3 ⎠





. (2)

The DP mechanism has been shown to dominate at temperatures above 77K in

intrinsic or lightly n-type NGS 6,7 , where the lack of inversion symmetry in the presence of a

k-dependent spin-orbit interaction lifts the spin degeneracy even in the absence of a magnetic

field 2 . Somewhat counter-intuitively, and in contrast with EY, the spin relaxation rate 1/τ s is

subject to motional narrowing, and is therefore directly proportional to the orbital (mobility)

scattering time, τ p . In NGS both the EY and the DP mechanisms may be important, as shown

by reports of spin relaxation in InSb at helium temperature 4,5 and InAs at room temperature 7 -

the former being interpreted in terms of EY and the latter of DP. Typically spin lifetimes in

the range 1-10ns were obtained from spin resonance in degenerate n-type InSb at helium

temperatures, whereas a spin lifetime of 20ps was reported for lightly n-type InAs at 300K.

The DP relaxation rate for lattice scattering and non-degenerate statistics:




≈ 0.8β




h E





. (3)

For the case of degenerate statistics the DP expression becomes:


















, (4)

where 6 4γ



: β ≈ .




We note that the spin relaxation in interband optical orientation experiments such as

this will be dominated by electrons, as the fourfold degeneracy of the valence band at k = 0

and the large spin-orbit coupling are expected to result in extremely rapid decay of the hole

spin polarisation.

In our previous work 8 we demonstrated that the temperature dependence of the results

for n-type Hg 0.78 Cd 0.22 Te could be explained in terms of the EY model. We also showed a

remarkable lengthening of the spin lifetime in InSb from ~16ps for intrinsic material to 300ps

for the degenerate case. The reason for lengthening was not explained in detail, but we

showed that the longer spin lifetime of the degenerate case was consistent with the EY

process dominating as with the HgCdTe.

For intrinsic and lightly doped samples the DP process (equation (3)) dominates for both

InAs and InSb [theoretical/experimental values for τ DP are obtained as follows: IC313

(20ps/20ps), and ME1654 (10ps/16ps)]. The EY process (equation (2)) gives τ EY ~ 530ps

and τ EY ~ 350ps respectively, so that clearly it is not important for this case.

In the presence of significant n-doping two points become extremely important with

regard to the DP process. In the first instance it is obvious from the pre-factor in equation (4)

that the onset of degeneracy considerably suppresses the DP process. Thus, for the more

heavily doped samples in this limit we obtain theoretical values from equations (1) and (4) as

follows: IC311 (τ EY ~ 500ps, τ DP ~ 800ps) and ME1629 (τ EY ~ 100ps, τ DP ~ 100ps).

However, in addition to this it has been convincingly demonstrated recently 9 that for the DP

process the precession of an electron spin can be as effectively randomised by scattering from

another electron (i.e. electron-electron scattering) via the Coulomb interaction as by scattering

from thermal vibrations or defects, and yet this process can affect the mobility only weakly.

These authors have found in the case of GaAs that for a degeneracy temperature given by

kT/E F ~ 1.0 (approximately our case for the InAs, IC311) the actual time between momentum

scattering events, τ p *, is an order of magnitude shorter than the mobility time τ p , thereby

lengthening the value of τ DP obtained by a further factor of 10. Thus, for both these reasons

we expect the spin relaxation for samples IC311 and ME1629 to be dominated by the EY

process, and in fact this gives reasonable agreement with our measured values of τ given the

simplifications of the model (equation (1)) [experiment/theory(τ EY ): IC311, 1.0ns/500ps;

ME1619, 300ps/100ps].

In summary, we have measured remarkably long spin lifetimes (~ 1.6 ns) in neardegenerate

n-InAs at 300K. This, together with our earlier results for degenerate n-InSb (τ ~

300 ps) 8 , is explained in terms of the suppression of the DP spin relaxation process by the

degeneracy condition and by electron-electron scattering. We here present new results for

both intrinsic and near-degenerate InAs at 300K, and show that both the InAs results and the

earlier InSb results give direct evidence of the suppression of the DP process by the

degeneracy condition and by electron-electron scattering 9,10 , in the presence of strong n-type

doping. The EY process then dominates for the n-type material. The long spin lifetimes are

clearly important from the point of view of devices of the spin transistor type 11,12,13 .

We gratefully acknowledge the support by EPSRC and the Stichting voor Fundamenteel

Onderzoek der Materie (FOM), as part of the UK programme at FELIX. We are also grateful

for partial support from the FENIKS project (EC: G5RD-CT-2001-00535).


[1] R J Elliott, Phys. Rev. 96, 266 (1954); Y Yafet, "Solid State Physics" 14 (ed. F Seitz

and D Turnbull, Ac. Press, NY, 1963).

[2] M I D'yakonov and V I Perel, Sov. Phys. JETP 33, 1053 (1971); Sov. Phys. Solid

State 13, 3023 (1972).

[3] G L Bir, A G Aronov and G E Pikus, Sov. Phys. JETP 42, 705 (1976).

[4] J N Chazalviel, Phys. Rev. B11, 1555 (1975).

[5] R Bichard, P Lavallard and C Benoit a la Guillaume, Inst. Phys. Conf. Ser. No 43,

1047 (1979). See also: Optical Orientation, edited by F Meier and B Zakharchenya

(North Holland, New York, 1984), Chapter by G E Pikus and A N Titkov, p. 84.

[6] P H Song and K W Kim, Phys. Rev. B66, 035207 (2002).

[7] T F Boggess, J T Olesberg, C Yu, M E Flatte and W H Lau, Appl. Phys. Lett. 77,

1333 (2000).

[8] P. Murzyn, C. R. Pidgeon, P. J. Phillips, J-P. Wells, N. T. Gordon, T. Ashley, J. H.

Jefferson, T. M. Burke, J. Giess, M. Merrick, B. N. Murdin, and C. D. Maxey, Phys.

Rev. B 67, 235202 (2003)

[9] M A Brand, A Malinowski, O Z Karimov, P A Marsden, R T Harley, A J Shields, D

Sanvitto, D A Ritchie and M Y Simmons, Phys. Rev. Lett. 89, 236601-1 (2002).

[10] P Boguslawski, Phys. Stat. Sol.(b), 104, 89 (1981).

[11] S Datta and and B Das, Appl. Phys. Lett. 56, 665 (1990).

[12] H Ohno, Science 281, 951 (1998).

[13] J M Kikkawa and D D Awschalom, Phys. Rev. Lett. 80, 4313 (1998); Nature, 397,

139 (1999).

[14] R S Britton, T Grevatt, A Malinowski, R T Harley, P Perozzo, A R Cameron and A

Miller, Appl. Phys. Lett. 73, 2140 (1988).

Figure Captions

1. Pump-probe transmission change as a function of probe delay time for pump and probe

having the same circular polarisation (SCP), and the opposite (OCP), for lightly doped n-

InAs at 300K (sample IC311, n = 3.8x10 16 .cm -3 ). The inset shows the difference of the

SCP and OCP signals divided by their sum. The solid curve is a fit of a monoexponential,

giving a measured decay constant of τ = 20 ps.

2. As Fig 1 for heavily doped n-InAs at 300K (sample IC313, n = 1.0x10 17 .cm -3 ), except that

the SCP and OCP data have been normalized at the peak to make clear the difference in

slope. The inset shows the difference in the un-normalized data, and the decay time of the

fit is τ = 1.0 ns.

Transmission change [a.u]



P [%]





0 50 100

Delay [ps]

0 20 40 60 80 100 120 140

Delay [ps]

Transmission change [a.u]

P [%]



0 500

Delay [ps]




0 200 400 600 800

Delay [ps]

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