arXiv:1008.0157v1 [cond-mat.mtrl-sci] 1 Aug 2010
V1 – August 3, 2010
Two-dimensional optical control of electron spin orientation by
linearly polarized light in InGaAs
K. Schmalbuch,1, 2S. G¨ obbels,1,2Ph. Sch¨ afers,1, 2Ch. Rodenb¨ ucher,1, 2P.
Schlammes,1, 2Th. Sch¨ apers,3, 2M. Lepsa,3, 2G. G¨ untherodt,1,2and B. Beschoten1, 2, ∗
1II. Institute of Physics, RWTH Aachen University,
Otto-Blumenthal-Straße, 52074 Aachen, Germany
2JARA: Fundamentals of Future Information Technology,
J¨ ulich-Aachen Research Alliance, Aachen, Germany
3Institute of Bio- and Nanosystems,
Forschungszentrum J¨ ulich, 52428 J¨ ulich, Germany
(Dated: August 3, 2010)
Optical absorption of circularly polarized light is well known to yield an electron spin polarization
in direct band gap semiconductors. We demonstrate that electron spins can even be generated with
high efficiency by absorption of linearly polarized light in InxGa1−xAs. By changing the incident
linear polarization direction we can selectively excite spins both in polar and transverse directions.
These directions can be identified by the phase during spin precession using time-resolved Faraday
rotation. We show that the spin orientations do not depend on the crystal axes suggesting an
extrinsic excitation mechanism.
The generation of spin-polarized charge carriers by optical orientation in non-magnetic
semiconductors is well-established. In optical orientation the angular momentum of circu-
larly polarized photons will be transferred to electrons and holes during absorption [1, 2].
This can result in a large spin polarization of 50% in bulk III-V semiconductors. Besides
static imaging and probing of the spin polarization [3, 4], optical pump probe measure-
ments using time-resolved Faraday rotation (TRFR) has become a standard method both
for triggering and probing of spin coherence in semiconductors [5–12]. In contrast, optical
absorption of linearly polarized photons should not result in net spin polarization as an equal
number of spin-up and spin-down electrons and holes will be generated. Yet it is known that
illumination of III-V-semiconductor quantum wells with linearly polarized light can yield a
spin-dependent photo-voltage response originating from spin photo-galvanic effects [13, 14].
However, those spin currents have not been probed by magneto-optical methods.
In this Letter we report on measurements of electron spin coherence in InGaAs by TRFR
after optical orientation by linearly polarized laser pulses.We observe both polar and
transverse initial spin orientations, which can be controlled independently as a function of
the incident linear polarization direction. The number of transverse spins increases linearly
with the magnitude of a perpendicular external magnetic field and vanishes at zero field,
while the number of polar spins is unaffected by the external magnetic field. We demonstrate
that the optical orientation by linearly polarized light has a comparable efficiency as that by
circularly polarized light. The generated respective spin orientations are furthermore found
to be independent of the crystal axes orientation of the InGaAs layer indicating an extrinsic
We have studied several InxGa1−xAs samples with In-contents 0 ≤ x ≤ 0.1 and
thicknesses between 300 nm and 1 µm, which are grown by molecular beam epitaxy on
semi-insulating (001)GaAs substrates. The room temperature carrier density was set to
n ∼ 3 × 1016cm−3by Si co-doping to allow for long spin dephasing times at low tempera-
tures [4, 5]. Note that all presented results have been observed in all samples independent of
In content and thickness. In the following, we show representative data, which were taken
on a 500 nm epilayer of InxGa1−xAs with x = 4.9 %. The sample was mounted strain-free
in an optical He-flow cryostat. Phase triggering of electron spin coherence is achieved either
by circularly or linearly polarized ps pump pulses. The incident polarization direction of the
latter can be changed continuously by an angle ϕ as defined in Fig.1a. Spin precession is
probed in a transverse external magnetic field B (oriented along the y-direction) by a sec-
ond time-delayed linearly polarized probe pulse using standard measurements of the TRFR
angle θF, which is a measure of the polar spin component. Its time dependent evolution can
be described by an exponentially damped cosine function
θF(∆t) = θ0· exp
· cos(ωL∆t + δ), (1)
with amplitude θ0, transverse spin dephasing time T∗
2, Larmor frequency ωL = gµBB/¯ h,
time delay ∆t between the pump and probe beam and phase factor δ. g is the effective
electron g-factor, µBthe Bohr magneton, and ¯ h the Planck constant. The sample plane can
furthermore be rotated by an angle α about the x-axis.
Fig.1b depicts TRFR measurements after optical excitation with both circularly and
linearly polarized pump pulses using a laser energy near the fundamental band gap of the
InGaAs layer. Data were taken at T = 30 K and B = 0.5 T. When using circularly
ϕ = 225°
ϕ = 135°
Figure 1: (Color). (a) Setup for all-optical measurements of TRFR using linearly polarized pump
pulses. The incident linear polarization direction can continuously be adjusted by the angle ϕ.
(b) Comparison of TRFR after excitation by circularly (red) and linearly (blue) polarized pump
pulses. Data are taken at T = 30 K in a transverse magnetic field of 0.5 T. The dashed vertical
lines indicate a phase shift in the precession between circular and linear excitation. A vertical
offset is added for clarity.
delay ∆t (ns)
ϕ = 276.6°
delay ∆t (ns)
ϕ = 0°
Figure 2: (Color). TRFR for optical excitation with linearly polarized laser pulses measured in
n-InGaAs at T = 30 K and B = 0.5 T for (a) ϕ = 0...360◦(the vertical dotted line helps to see
the sign reversal every 90◦). The sign reversal is accompanied by a continuous phase shift of the
precessing spins, which can be seen in (b) and (c).
polarized light the angular momentum of the photon will be absorbed during interband
absorption resulting in spin-polarized electrons and holes. The holes will be ignored in the
following discussion. By changing the light helicity from σ+to σ−, we can control the
initial spin orientation between parallel and antiparallel alignment relative to the incident
light propagation direction. The resulting TRFR measurements are depicted in Fig.1b (red
curves) for σ+/σ−laser excitation under nearly normal incidence. The change of the initial
spin orientation is easily seen by a sign change of θF right after excitation (∆t = 0 ns).
Note that we measure θF in the polar geometry for all presented experiments. We are thus
only sensitive to spin components, which are pointing in the ±z-direction. When using
linearly polarized pump pulses, we would not expect to excite a net spin polarization as
the linearly polarized light is a superposition of σ+and σ−photons, which results into
an equal number of spin-up and spin-down electrons after absorption. In Fig.1b we show
TRFR data taken for normal incidence α = 0◦at two distinct polarization angles of linearly
polarized pump pulses, which differ by 90◦(blue curves). We, however, clearly observe spin
precession. Surprisingly, the amplitude is only slightly reduced compared to the curves taken
under σ+/σ−excitation demonstrating that optical orientation of electron spins by linearly
polar δ = 0°transverse δ = - 90°
phase δ (°)
Figure 3: (Color). (a) Phase of precessing spins after optical excitation with linearly polarized
light at different incident polarization angles ϕ near the sign reversal in Fig.2b, c. (b) Illustration
of spins oriented in polar and transverse direction and respective TRFR curve as expected in the
polar observation direction. According to the measured phase, θF will be decomposed into polar
and transverse amplitudes plotted as a function of (c) incident linear polarization direction and
(d) external magnetic field.
polarized light is strikingly efficient.
We note that spins of opposite directions can be excited when changing the polarization
by 90◦from 135◦to 225◦. While the precession frequency is identical for all excitations, we
observe a phase shift in the precession for linear polarized excitation as indicated by the
vertical dashed lines in σ+/σ−in Fig.1b. Such a phase shift indicates a change of the initial
To further explore the polarization dependence of θF, we plot a series of TRFR measure-
ments with ϕ varying between 0◦and 360◦in Fig.2a. The most striking observation is the
sign reversal of θFevery 90◦(see also Fig.4a), which is further investigated in Figs.2b and c,
where the polarization angle resolution is enhanced in a regime of sign reversal. It is clearly
seen that spin precession is observed at all angles. The sign reversal of θF between point A
(ϕ = 280.2◦, red color code θF > 0◦) and point B (ϕ = 275.8◦, blue color code θF< 0◦) in
Fig. 2c is accompanied by a continuous change of the phase δ of the precessing spins (see
also dotted line in Fig.2b). The phase can be extracted from fitting all TRFR traces in
Fig.2c by Eq.1. As seen in Fig.3a, the phase continuously changes from −180◦to almost
0◦within a small range of linear polarization angles. We want to emphasize that in our
polar configuration we only probe spins, which have a finite projection along the ±z-axis.
For δ = 0◦, spins are oriented in the polar +z direction at ∆t = 0, which results in a TRFR
curve starting in a positive maximum (see also Fig.3b). On the other hand, spins are ori-
ented in the −z direction for δ = −180◦. This explains the sign reversal between points A
and B in Fig.2c. In contrast, for a phase of δ = −90◦spin precession starts with θF= 0◦at
∆t = 0 ns, which is illustrated in Fig.3b. This unambiguously demonstrates that spins will
be oriented along the x-axis (transverse to both incident light direction and magnetic field
direction) at the respective linear polarization angle. It is important to note that the exci-
tation of transverse spins is unique to the optical orientation with linearly polarized light.
It has not been observed for excitation with circularly polarized light. Knowing that we can
excite both polar and transverse spins with linearly polarized light, we can now decompose
the projections for any polarization angle along the polar and the transverse direction using
θp= θ0· cosδ and θt= θ0· sinδ, respectively. As shown in Fig.3c, polar and transverse
spin signals change sign at different pump polarization angles. By carefully adjusting the
polarization angle ϕ we achieve a full 2-dimensional control over the initial spin orientation,
which cannot be realized by any other electrical or optical technique.
To further explore the origin of these unexpected findings, we plot the magnetic field de-
pendence of both polar and transverse spin components in Fig.3d. Note that the amplitude
is a measure of the number of electron spins initially oriented in the respective direction. The
amplitude of the polar spins (black squares) is almost independent of magnetic field, while
the amplitude of the transverse spins (red squares) depends linearly on the magnetic field
and vanishes at B = 0 T. This shows that transverse spins can only be excited at non-zero
magnetic fields. We note that the transverse spin orientation switches sign from +x to −x
direction for negative B values. Such a linear B dependence has previously been reported
in photocurrent measurements where spins are optically generated by infrared absorption.
The underlying intrinsic theory of the so-called magnetogyrotropic photogalvanic effect 
relates the spin orientation directly to the underlying crystal structure. We can easily test
whether the observed effect is related to the crystal axis by comparing the linear polarization
dependence of θ0for different sample orientations. In Fig.4a we compare the dependence of
the Faraday amplitudes θpand θton ϕ with the [1¯10] crystal axis either oriented parallel
(left panel) or under 26◦(right panel) with respect to the external magnetic field direction
θ [100 µrad]
Figure 4: (Color). (a) Polar diagrams of θp (black/grey) and θt (red/orange) as a function of
incident polarization direction for two different crystal orientations. (b) θpvs. ϕ at various angles
of incidence α. A vertical offset is added for clarity. (c) Linear dependence of θpplotted at ϕ = 40◦.
The sign reversal at α = −3◦shows a change in spin orientation of the polar spins near normal
(see also Fig.1a) using polar plots. The amplitudes have been extracted from the TRFR
data using the above analysis . It is obvious that the observed symmetry is independent
of the crystal orientation. The same behavior was also observed for other angles at 45 and
90◦(not shown) suggesting that our effect is of extrinsic origin. This excludes various intrin-
sic effects as a source for the observed spin polarization, such as spin polarization induced
by the Dresselhaus fields , intrinsic spin Hall effect , intrinsic double refraction and
dichroism [18, 19], inverse Faraday and Cotton-Mouton effect [20, 21] or piezo-optical effects
We note that the observed spin polarization becomes largest for both polar and transverse
spin components at an incident polarization direction of 45◦(see Fig.4a), while it vanishes
for s and p polarized light at ϕ = 0◦and 90◦, respectively. Away from normal incidence,
it is well-known, that the linear polarization state is conserved only for s and p polarized
light. For other polarization angles, there will be an additional birefringence, which becomes
largest for ϕ = 45◦. At this angle, the light is elliptically polarized, which would result in spin
orientation by the circular polarization component along the laser propagation direction. As
the birefringence is negligible near normal incidence, it will be instructive to study the spin
polarization away from normal incidence. We therefore rotated the sample about the x-axis
by an angle α as defined in Fig.1a. In Figs.4b and c, we focus on the polar spin amplitude
θp. The data in Fig.4b were taken at a fixed pump-probe delay of ∆t = 1 ns with B = 0 T
for different values of α. As expected, the sign of θposcillates as a function of ϕ. Surprisingly,
there is a sign reversal of θpat α = −3◦, which is not seen for excitation with circularly
polarized light (not shown), showing that the polar spin orientation can be switched into
opposite orientations when rotating the sample from α < −3◦to α > −3◦(Fig. 4c). This
furthermore explains why we observe spins at normal incidence, i.e. at α = 0◦. Note that
there is a remarkable increase of θpslightly away from α = −3◦. At α =< −7.5◦we find a
value of θp, which is 85% of the corresponding amplitude obtained for σ+excitation. Such
a large number of spins cannot be explained by the above birefringence effect, which is
estimated to be on the order of a few percent at α = −7.5◦. We should emphasize that the
birefringence in our optical setup is less than 1% and thus can also not explain the observed
Another possible source of spin polarization are local electric fields induced by the laser
pulse. It was shown previously that static electric fields can indeed induce a spin polarization
as demonstrated, e.g., in experiments on current-induced spin polarization  or extrinsic
spin Hall effect . In our ultrafast optical experiments, the ps laser pulse generates a
non-equilibrium electron-hole population. As the mobility of holes is much lower than for
electrons, there will be a fast built-up of local electric fields. In fact, Nuss et al.  showed
that electron diffusion in GaAs starts on timescales much shorter than a ps. Although
we currently do not understand the complex linear light polarization dependence of the
spin population, it is, however, likely that these local electric fields resulting from the non-
equilibrium carrier distribution are relevant for the observed effect.
In conclusion, we have demonstrated that optical orientation of electron spins by linearly
polarized light is very effective. From the phase during spin precession we can unambigu-
ously prove that spins can be generated in both polar and transverse directions. This is in
contrast to optical orientation by circularly polarized light for which spins are aligned in
polar directions only. Surprisingly, the spin orientation is independent of the in-plane crys-
tallographic directions of the sample, pointing to an extrinsic origin of the spin polarization.
The full two-dimensional control over the initial spin direction offers to study anisotropies
in spin relaxation. This might give decisive clues about the dominating spin generation and
This work was supported by DFG through FOR 912.
∗Electronic address: firstname.lastname@example.org
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