Physica E 9 (2001) 194201

www.elsevier.nl/locate/physe
Spin coherence in semiconductors: storage, transport
and reduced dimensionality
J.M. Kikkawa, J.A. Gupta, I. Malajovich, D.D. Awschalom

Department of Physics, University of California, Santa Barbara, CA 93106, USA

Abstract
We review the use of femtosecond-resolved optical techniques for the study of electron spin dynamics in semiconduc-
tors and show how these methods are able to address many of the issues that are centrally important to spin polarized
semiconductor-based electronics. Pumpprobe studies can be used to optimize spintronic material parameters, and have led to
the observation of 100 ns spin lifetimes in n-doped bulk GaAs and spin transport across macroscopic length scales (100 m).
We have found that spin coherence is preserved across a semiconductor heterojunction over a broad range of temperatures,
and can be protected by transport to regions of intrinsically lower decoherence. Studies of CdSe quantum dots ranging
from 22 to 80

A in diameter indicate that spin coherence in these structures is thermally robust, with nanosecond-scale spin
lifetimes persisting to room temperature. ? 2001 Elsevier Science B.V. All rights reserved.
Keywords: Spin coherence; Spin transport; Quantum dots; Quantum computation
Whereas conventional electronics rely on the elec-
trons charge for the storage and transport of infor-
mation, interest has emerged in using the electrons
spin degree of freedom for such purposes. Though
spin polarized metallic devices are already in com-
mercial use as read heads in hard disk drives, inte-
gration of magnetic components within computing
elements has remained elusive. For this latter ambi-
tion, semiconductor-based spin devices are favorable,
and could exhibit improved speed and fundamen-
tally dierent functionality [1,2]. Encouraging de-
velopments in this emerging eld of spintronics

Corresponding author.
E-mail address: awsch@physics.ucsb.edu (D.D. Awschalom).
include recent demonstrations of electrical spin injec-
tion in all-semiconductor light-emitting diodes [3,4],
and pulsed emission from spin-polarized solid-state
lasers [5]. Moreover, researchers have envisioned
non-classical devices in which semiconductor spins
are used for quantum information storage and com-
putation [6]. Semiconductors are promising hosts
for quantum computers based on spin because elec-
tronic and magnetic environments may be controlled
through increasingly sophisticated band-gap engineer-
ing and nanofabrication techniques. As an example,
proposals for implementing quantum computation in
semiconductor quantum dots hope to take advantage
of the discrete energy spectrum and potential isola-
tion from environmental decoherence that is expected
1386-9477/01/$ - see front matter ? 2001 Elsevier Science B.V. All rights reserved.
PII: S 1386- 9477( 00) 00194- 6
J.M. Kikkawa et al. / Physica E 9 (2001) 194201 195
when carrier spins are conned to nanometer-sized
regions. This has been suggested for electrostatically
dened quantum dots where entanglement between
qubits is achieved with voltage-tuned gating [7,8], and
self-assembled quantum dots with coupling provided
by modes in an optical cavity [9]. Other proposals
utilize electronnuclear hyperne interactions for the
entanglement of qubits based on nuclear spins in
silicon [10].
A generic requirement for these pursuits is the
ability to store, transport and manipulate spin in
semiconductors. Here, we review an array of optical
techniques that has been developed to address these
issues. Time-resolved Faraday rotation has been used
to establish upper limits on extra-electronic spin deco-
herence in a variety of semiconductors ranging from
bulk systems to quantum dots. We nd that spins
in lightly n-doped semiconductor structures exhibit
a dramatic suppression of such decoherence relative
to insulating controls, and may thereby provide a
foundation for future spintronic devices. A novel res-
onance spectroscopy has been developed to measure
the resulting 100 ns spin lifetimes over a broad
range of magnetic elds and temperatures. Non-local
pumpprobe techniques allow measurements of spin
transport where it is seen that coherently precessing
spin can be transported across macroscopic distances
and heterostructure interfaces. The latter fact allows
the protection of spin by transfer to semiconductors
with intrinsically lower rates of spin decoherence.
Chemically synthesized quantum dot structures ex-
hibit room-temperature nanosecond-scale lifetimes
which appear to be limited by inhomogeneous de-
phasing rather than environmental decoherence.
Remarkably, spin dynamics in such a wide variety
of semiconductor structures can be studied using vari-
ations of the pumpprobe optical technique schemat-
ically illustrated in Fig. 1A. Ti : sapphire-based laser
systems are used to produce 100 fs pump and probe
pulses that are broadly tunable in the near-infrared and
blue regions of the spectrum. By actively synchro-
nizing two such laser systems (with 3 ps resolu-
tion), two-color measurements can be performed, and
spectral coverage from blue to red can be achieved
using a regeneratively pumped optical parametric am-
plier. The pump pulse excites non-equilibrium spin
within the sample, held in a magneto-optical cryostat
typically capable of achieving sample temperatures
Fig. 1. (A) Experimental geometry for time-resolved Faraday
rotation measurements. The angle between the pump and probe
has been exaggerated for clarity and typically does not exceed 3

.
(B) Schematic Faraday rotation versus t in a transverse eld.
The dashed curve represents the intrinsic loss of spin coherence
to the environment, which can be articially increased through
inhomogeneous dephasing (solid curve).
ranging from 1.6 to 300 K and magnetic elds up
to 9 T. The energy of the pump pulse is tuned to a
desired absorption feature within the semiconductor,
and can thereby target particular quantum conned
states in heterostructures or quantum dots. The circu-
lar polarization of the pump pulse then controls the
resulting spin orientation through optical selection
rules. In bulk semiconductors and quantum wells of
zincblende semiconductors such as GaAs and ZnSe,
selection rules are well understood and result in an
electronic magnetization M that initially points paral-
lel or anti-parallel to the laser direction. In such semi-
conductors, the hole spin relaxation is typically quite
fast (picoseconds) so that hole spin dynamics do not
contribute to the long-term spin behavior discussed
here. A time-delayed, linearly polarized probe pulse
then passes through (or is reected o) the sample,
and carries away information about the electronic
196 J.M. Kikkawa et al. / Physica E 9 (2001) 194201
magnetization. In particular, the probe records the
projection of the electron magnetization along the
laser direction as a rotation of its linear polarization,
a process known as Faraday rotation when the probe
is analyzed in transmission and Kerr rotation when it
is analyzed in reection. As with the pump pulse, the
energy of the probe beam can be adjusted to target
particular electronic states and thereby selectively
measures a portion of the total electron spin deposited
in the system by the pump. Often, the objective is to
characterize the spin memory of the electronic states
that are excited by the pump beam, and the probe
beam is energetically degenerate with the pump.
However, non-degenerate studies are also fruitful and
permit one to observe the ow of electronic magneti-
zation as it passes between dierent electronic states
within the system. Typical pump and probe spot di-
ameters are 100 m or less, although expanded pump
spot sizes are occasionally employed to reduce the
eects of spin diusion. Sub-millidegree rotations
can be measured using a balanced photodiode bridge
[11], and alternation of the pump helicity with a pho-
toelastic modulator improves signal-to-noise when
combined with lock-in amplication.
A perpendicular magnetic eld B = B
:
can be
applied to study electron spin coherence. The pump
then excites spins in a coherent superposition of
spin eigenstates quantized along the eld direction.
Because these states exhibit a Zeeman splitting,
E = hv
L
= q
e
j
B
B
:
(where v
L
is the Larmor fre-
quency, q
e
is the electron q-factor, and j
B
is the Bohr
magneton), the temporal evolution of this superposi-
tion results in precession of M about the magnetic
eld at the Larmor frequency. The Faraday}Kerr
rotation imparted to the probe pulse is directly pro-
portional to M
x
and is a function of the pumpprobe
time delay given by
0
F
(t) = Ae
t}1

2
cos(2v
L
t). (1)
Therefore, by tting the frequency and decay rate of
the observed Faraday}Kerr rotation, one obtains the
electron q-factor and transverse spin lifetime, 1

2
, re-
spectively. The quantity 1

2
reects the loss of spin co-
herence to the electronic environment and can contain
contributions from both longitudinal (1
1
) and trans-
verse (1
2
) spin relaxation processes. Measurements of
1

2
cannot probe decoherence from electronelectron
spin interactions of the Heisenberg form, s
i
s
j
, be-
cause these preserve the total electronic magnetiza-
tion [12]. This variety of entanglement cannot be
reversed by a spin echo in systems where the spins
are itinerant, and hence 1

2
is only guaranteed to
probe extra-electronic spin decoherence. Because an
ensemble of spins is probed in these experiments, the
measured decay of spin precession can also contain
dephasing eects reecting inhomogeneities in the
sample that produce articially fast decay times. Fig.
1B shows a schematic Faraday rotation of the data
typically produced by scanning the pumpprobe de-
lay in a degenerate pumpprobe arrangement. The
envelope of the decay is 1

2
, which can be suppressed
by inhomogeneous dephasing as shown.
Fig. 2A shows a typical degenerate Faraday rotation
measurement of silicon doped n-GaAs with n = 1
10
16
dopants cm
3
at 1 = 5 K taken at both B = 0.5 T
and B 0 T. Free carriers with minimal excess en-
ergy are excited by adjusting the pump (and probe)
energy to follow the shift of the absorption edge that
accompanies electrical doping in this range. Note that
the spin polarization exhibits a minimal decay at zero
eld, while at B = 0.5 T one observes the oscillatory
modulation expected from electron Larmor preces-
sion. The tting procedure used to obtain q
e
and 1

2
from Eq. (1) becomes unreliable when 1

2
exceeds
the 3 ns range accessible with a conventional de-
lay line. For samples with high doping concentrations
or undoped samples such complications are not an is-
sue because both exhibit nanosecond or shorter spin
lifetimes. However, we have found that spin lifetimes
increase by more than two orders of magnitude in
moderately doped samples such as in Fig. 2A [13],
so that delay scans are not eective in establishing
the durability of optically excited spin. Additional er-
rors may also arise at low magnetic elds, where slow
Larmor precession can be confused with decay of the
polarization amplitude.
Note the presence of oscillations at negative delay
for data in Fig. 2A taken at 0.5 T. These arise from
the preceding pump pulse, and suggest that the spin
lifetime is suciently long compared to the pump
repetition interval t
rep
(13 ns) to create interference
between spins generated by dierent pump pulses
(Fig. 2B). This eect can be exploited to accurately
measure long transverse spin lifetimes well in excess
of t
rep
. For spin lifetimes comparable to or greater than
t
rep
, contributions from multiple pump pulses must
J.M. Kikkawa et al. / Physica E 9 (2001) 194201 197
Fig. 2. (A) Time-resolved Faraday rotation in n-GaAs at 1 = 5 K [n = 1 10
16
cm
3
in (A), (C), (D)]. (B) Schematic of resonance
condition. In general, spin precession from multiple pump pulses is out of phase (o-resonance, bottom). At resonance values of magnetic
eld, spin precession adds together in phase (top), resulting in spin amplication. (C) Resonance peaks in Faraday rotation appear when the
magnetic eld is scanned at xed delay for the same sample as in (A). 1 = 5 K, t = 10 ps. (D) Spatial map of spin transport compiled by
plotting the amplitude of the zero-eld resonance versus position for bias elds of 16 V}cm. Data are taken at t = 10 ps, 1 = 1.6 K.
(E) Room temperature spin transport across a GaAs}ZnSe heterojunction. Kerr rotation with a probe energy of 2.8 eV detects spins initially
excited in GaAs that cross the interface. Data are plotted for B = 0 T and 0.1 T. (F) Interfacial dephasing associated with the dierence
in q-factors across the heterojunction. Spins crossing the interface at times t
1
and t
2
enter ZnSe with dierent phases.
198 J.M. Kikkawa et al. / Physica E 9 (2001) 194201
be summed to obtain the total spin magnetization,
yielding a Faraday rotation of the form
0
F
(t, B
:
) =

n
O(t + nt
rep
)Ae
(t+nt
rep
)}1

2
cos

q
e
j
B
B
:
(t + nt
rep
)

, (2)
where the step function O(t + nt
rep
) ensures that
only preceding pump pulses (indexed by n) con-
tribute to the signal at any time t [13]. The cosine
term in Eq. (2) indicates that a resonance condition
exists when B
:
= 2m}(q
e
j
B
t
rep
) (m is any inte-
ger); at these values of B
:
the contributions from
pump pulses arrive in phase, producing an additive
amplication of the Faraday rotation signal. This
resonant spin amplication is explored by scanning
the magnetic eld at a xed pumpprobe time delay,
as illustrated in Fig. 2C. The baseline of the data
represents the strength of the spin signal without res-
onance eects, and each resonance produces roughly
a tenfold increase in signal to noise at equally spaced
values of the magnetic eld. Fits to the data using
Eq. (2) enable precise measurements of 1

2
, which
is inversely proportional to the resonance line width
and exceeds 100 ns at zero eld. Comparable spin
lifetimes have also been observed in n-ZnSe [14],
establishing n-doped semiconductors as candidates
for spin storage. We nd that 1

2
decreases sharply
with applied eld, an eect that is not well under-
stood at present. Although inhomogeneous dephasing
(Fig. 1B) can contribute to a reduction in spin life-
time that becomes more severe as the applied eld
increases, the power law associated with this behavior
does not agree with the experimental ndings [13].
The long spin lifetimes present in the regimes
of carrier concentration and magnetic eld identi-
ed above have enabled studies of spin-coherent
transport over macroscopic distances in n-GaAs
(n = 1 10
16
cm
3
) [15]. The results may repre-
sent a step towards spin-coherent analogs of giant
magneto-resistive sensors or spin-valve transistors
[16], because they show that electron spin coherence
is robust during transport over 100 m and across
heterointerfaces. In these experiments, electron trans-
port is achieved by applying a modest electric eld E
:
(of order 100 V}cm) between two electrodes on the
sample surface. A spatial map of electron spin is then
produced by xing the excitation spot at a position
x = 0 and scanning the probe spot along the elec-
tric eld direction to follow the evolution of coherent
electron spins during transport. Fig. 2D shows the
amplitude of the zero eld resonance as a function of
probe position at a xed time delay of t =10 ps
and an applied electric eld of 16 V}cm. The small
negative value of delay indicates that the most recent
pump pulse arrived at the sample t
rep
13 ns prior to
the probe pulse, accounting for the reduced signal at
x = 0 m due to electron transport away from the
pump spot during this time interval. A Faraday rota-
tion signal is observed at distances exceeding 100 m
even for such small electric elds. The resonant spin
amplication technique is particularly powerful in
identifying contributions of individual pump pulses
during transport. This is necessary because the data
in Fig. 2D encompass spins created by many distinct
pump pulses. The resonance behavior seen in Fig.
2C can be viewed as arising from distinct Fourier
components corresponding to spins with dierent
ages, t + n

t
rep
(see Eq. (2)). A Fourier transform
of the observed resonance structure along the mag-
netic eld axis allows one to extract the amplitude of
spins arising from distinct pump pulses. Using this
method, individual spin packets can be monitored
during transport, and the contrast between spin and
charge diusion can be studied [15].
As discussed above, non-degenerate pumpprobe
measurements can be used to follow the ow of
spin information throughout a system. Fig. 2E shows
two-color Kerr rotation demonstrating the preserva-
tion of spin coherence as spins cross a GaAs}ZnSe
heterojunction at room temperature and zero electri-
cal bias [17]. The sample is a 300 nm thick Cl-doped
n-ZnSe epilayer (n 5 10
17
cm
3
) grown by
molecular beam epitaxy on a semi-insulating GaAs
substrate. The pump energy is tuned to excite electron
spins in the GaAs substrate (1.5 eV), while the probe
energy is tuned to the ZnSe absorption threshold
(2.8 eV). The data shows that a fraction of spins (2.5
10%) excited in the GaAs substrate transfer to the
ZnSe epilayer on a timescale of 200 ps. Subsequent
electron spin precession occurs over 10 ns time
scales and reects the ZnSe q-factor of 1.1. Be-
cause spin lifetimes in semi-insulating GaAs are con-
siderably less than a nanosecond, coherent transfer to
a region of intrinsically lower decoherence (n-ZnSe)
has resulted in the extension of spin lifetimes by more
J.M. Kikkawa et al. / Physica E 9 (2001) 194201 199
than one order of magnitude. Moreover, spin that is
excited at 1.5 eV appears when the system is probed
at a higher energy, an eect that is possible because
the spin transfer between materials involves only spin
motion in the conduction band. The relative contri-
butions of charge-assisted and pure spin diusion in
this process remains to be determined. In contrast to
homogeneous systems, the initial amplitude of the
transferred spin decreases with increasing eld, and
the spin precession experiences a magnetic eld de-
pendent shift in phase [17]. Both the appearance of
a phase shift and the eld dependence of the initial
amplitude are predicted to arise from the dierence
in q-factors between the two materials and their mea-
sured distribution of spin transfer times [17]. Fig. 2F
illustrates this process, wherein two spins simultane-
ously excited in GaAs will acquire a phase dierence
if they cross the interface at dierent times.
These spin transport experiments indicate that spin
coherence is surprisingly robust during transport in
semiconductors. It is also interesting to study the ef-
fects of extreme connement on spin coherence, which
could potentially lead to spin-memory devices where
spin information is stored in the atomic-like states
of nanometer-sized quantum dots (QDs). For these ex-
periments, chemical synthetic methods have been used
to fabricate CdSe quantum dots ranging from 2280

A in diameter with relatively good size distributions

(10%) and high crystallinity [18,19]. Because of
the large surface-to-volume ratio of these small dots,
passivation of surface trap states is important. In ad-
dition to the organic passivating layer on as-grown
quantum dots, additional passivation can be achieved
through epitaxial overgrowth of a higher band-gap
CdS shell [20]. Faraday rotation measurements have
been performed by tuning the pump and probe energy
to inhomogeneously broadened, hydrogen-like exci-
ton transitions in the quantum dots [21]. Decays of
the Faraday rotation at zero eld are characterized
by two lifetimes that may reect electron and hole
spin relaxation. In contrast to the n-doped semicon-
ductors discussed elsewhere in this paper, it is di-
cult to denitively ascertain the species responsible
for spin dynamics in these insulating QDs. Here the
strongly size-dependent exchange interaction between
electrons and holes in nanometer-sized clusters might
be expected to couple their spin dynamics, an eect
warranting further investigation [21]. In order to study
quantum connement eects on spin dynamics, the
two extracted spin lifetimes at B = 0 T are plotted in
Fig. 3A versus quantum dot diameter for samples with
and without CdS passivation (solid and open sym-
bols). We observe little systematic size dependence,
with the two lifetimes ranging from 100 50 ps
and 3 0.5 ns for 2257

AQDs and somewhat shorter
lifetimes of 50 ps and 1 ns in 80

A QDs. In compar-
ing the larger of these components for CdS-passivated
and as-grown samples, we see that the addition of a
CdS shell decreases the spin lifetime by 0.5 ns, per-
haps reecting additional interfacial spin scattering in
the core}shell samples.
Fig. 3Bindicates that spin coherence in these QDs is
thermally robust, with nanosecond-scale spin lifetimes
persisting to room temperature. In measurements from
1 = 6290 K we observe no change in signal mag-
nitude or decay up to 1 = 100 K, and little change
in precession frequency over the entire temperature
range studied. Fig. 3C compares the Faraday rotation
for 80

A QDs with B = 0, 0.25 and 1.0 T revealing a
ten-fold decrease in spin lifetime over this range of
magnetic eld. These data are accurately t with the
sum of two exponentially decaying cosinusoids with
distinct lifetimes and Larmor frequencies. By plotting
(1

2
)
1
versus magnetic eld for the two lifetime
components, we obtain linear relationships that are a
signature of inhomogeneous dephasing within the en-
semble of QDs ( 10
10
) probed in the experiment. As
depicted in the inset to Fig. 3C, spins that are initially
excited with nominally zero angular spread at t = 0
experience an explicitly eld-dependent angular
spreading [(t, B) due to precession at a distribu-
tion of Larmor frequencies around the two peak val-
ues extracted from the tting procedure. A Gaussian
variance in q-factors, q, results in eld-dependent
dephasing given by (1

2
)
1
= qj
B
B}(

2) +
(1

2
|
B=0
)
1
for each component. The slopes in
Fig. 3D allow us to estimate the variance in q-factors
to be 10% and 20% for the two components. While
the exact source of this dephasing is not well under-
stood, comparisons of dephasing in 80 and 57

A QDs
suggest an association with the size distribution [21].
In Fig. 3E the Larmor frequencies extracted from the
tting procedure are plotted versus magnetic eld for
80

A QDs, giving spin q-factors of 1.6 and 1.0 from
the slopes of linear ts to the data. Similar frequen-
cies have also been observed in 40

A and 57

A QDs,
200 J.M. Kikkawa et al. / Physica E 9 (2001) 194201
Fig. 3. (A) Spin lifetimes versus quantum dot diameter at 1 = 6 K, B = 0 T. Open and solid symbols represent core and core}shell
quantum dots, respectively. Squares and circles are the two lifetime components as described in the text. The vertical axis is broken
for clarity, and the dotted line is a guide to the eye. (B) Faraday rotation from 40

A quantum dots at 1 = 280 K and B = 1 T. (C)
Field-dependence of Faraday rotation from B = 01 T for 80

A quantum dots at 1 = 6 K. Inset: Illustration of eld-dependent angular
spreading due to inhomogeneous dephasing. (D) Dephasing rates (1}1

2
) and (E) Larmor frequencies extracted from curve tting for 80

A
quantum dots at 1 = 6 K. Solid lines are linear ts to the data.
again showing little size dependence over this range.
The relatively long spin lifetimes established in these
insulating QDs lead us to expect even longer times
if methods can be developed to introduce n-type
dopants into these structures.
In summary, recent experiments have utilized
time-resolved Faraday rotation as a sensitive probe
of spin dynamics in a wide variety of semiconduc-
tors ranging from bulk systems to quantum dots.
The identication of regimes with extended elec-
tron spin lifetimes has enabled demonstrations of
coherent spin transport in bulk crystals and across
heterointerfaces. The persistence at room temperature
of coherent transport across interfaces and storage in
quantum dots is promising for future spin-coherent
device applications. These results, combined with re-
cent innovations in using electron spin to resonantly
manipulate nuclear spins [22], represent signicant
advances toward next generation technologies such
as quantum computation and spintronics.
Acknowledgements
This work was supported by ARO DAAG55-98-1-
0366, NSF DMR 9871849, ONR N00014-98-1-0077,
and DARPA}ONR N00014-99-1-1096.
References
[1] G.A. Prinz, Science 282 (1998) 1660.
[2] D.D. Awschalom, J.M. Kikkawa, Physics Today 52 (1999)
33.
[3] Y. Ohno et al., Nature 402 (1999) 790.
[4] R. Fiederling et al., Nature 402 (1999) 787.
J.M. Kikkawa et al. / Physica E 9 (2001) 194201 201
[5] S. Hallstein et al., Phys. Rev. B 56 (1997) R7076.
[6] D.P. DiVincenzo, Science 270 (1995) 255.
[7] G. Burkard, D. Loss, D.P. DiVincenzo, Phys. Rev. B 59
(1999) 2070.
[8] D. Loss, D.P. DiVincenzo, Phys. Rev. A 57 (1998) 120.
[9] A. Imamoglu et al., Phys. Rev. Lett. 83 (1999) 4204.
[10] B.E. Kane, Nature 393 (1998) 133.
[11] S.A. Crooker et al., Phys. Rev. B 56 (1997) 7574.
[12] J.M. Kikkawa, I.P. Smorchkova, N. Samarth,
D.D. Awschalom, Science 277 (1997) 1284.
[13] J.M. Kikkawa, D.D. Awschalom, Phys. Rev. Lett. 80 (1998)
4313.
[14] I. Malajovich et al., J. Appl. Phys. 87 (2000) 5073.
[15] J.M. Kikkawa, D.D. Awschalom, Nature 397 (1999) 139.
[16] G. Prinz, Phys. Today 48 (4) (1995) 58.
[17] I. Malajovich et al., Phys. Rev. Lett. 84 (2000) 1015.
[18] J.E. Bowen Katari, V.L. Colvin, A.P. Alivisatos, J. Phys.
Chem. 98 (1994) 4109.
[19] C.B. Murray, D.J. Norris, M.G. Bawendi, J. Am. Chem. Soc.
115 (1993) 8706.
[20] X. Peng, M.C. Schlamp, A.V. Kadavanich, A.P. Alivisatos,
J. Am. Chem. Soc. 119 (1997) 7019.
[21] J.A. Gupta, D.D. Awschalom, X. Peng, A.P. Alivisatos, Phys.
Rev. B 59 (1999) 10 421.
[22] J.M. Kikkawa, D.D. Awschalom, Science 287 (2000)
473.