APPLIED PHYSICS LETTERS 86, 162107 共2005兲

Electron spin interferometry using a semiconductor ring structure
Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschaloma兲
Center for Spintronics and Quantum Computation, University of California,
Santa Barbara, California 93106

共Received 12 January 2005; accepted 7 March 2005; published online 13 April 2005兲
A ring structure fabricated from GaAs is used to achieve interference of the net spin polarization ofconduction band electrons. Optically polarized spins are split into two packets by passing throughtwo arms of the ring in the diffusive transport regime. Optical pumping with circularly polarized
light on one arm establishes dynamic nuclear polarization which acts as a local effective magnetic
field on electron spins due to the hyperfine interaction. This local field causes one spin packet toprecess faster than the other, thereby controlling the spin interference when the two packets arecombined. © 2005 American Institute of Physics. 关DOI: 10.1063/1.1906301兴
Recent progress in electron spin manipulation using nonmagnetic semiconductors includes the ultrafast all-opticalscheme,1 electrical control using g-factor engineering inparabolic2,3 and coupled quantum wells,4 the strain induced
spin-orbit interaction,5,6 and the spin Hall effect,7 demonstrating the broad scope of techniques that can be achieved
using state-of-the-art semiconductor engineering. The flexibility offered by semiconductor spintronics8–10 is anticipatedto lead to devices and may eventually become useful for
quantum information processing. Another advantage offeredby spin systems in semiconductors is their long coherence
times. For example, conduction electron spins in n-type
GaAs can have a coherence time exceeding 100 ns and canbe transported over distances exceeding 100 ␮m.11,12 In contrast, the coherence time of the orbital part of the electron
wave function is at most a few picoseconds even in highmobility two-dimensional systems. Here, we demonstrate adevice which takes advantage of the long coherence time of
the carrier spin system. A ring structure is fabricated fromn-GaAs in which electron spins are optically initialized, split
into two different paths, and recombined on the opposite
side. Local nuclear polarization gives rise to an additional
spin precession phase in one path, causing constructive anddestructive interference between the two spin packets.
On a semi-insulating 共001兲 GaAs substrate, 2 ␮m of undoped Al0.4Ga0.6As and 2 ␮m of n-GaAs 共Si doped for n= 3 ⫻ 1016 cm−3兲 are grown by molecular beam epitaxy. Theinterferometer is fabricated from the n-GaAs film, while theAlGaAs film underneath acts as an etch stop layer. The substrate is polished to ⬃200 ␮m prior to processing, and thering structure 关Fig. 1共a兲兴 is defined by standard photolithography techniques. The mesa is formed by selective sprayetching13 with a mixture of one part NH4OH 共30%兲 to 30parts H2O2 共35%兲, and a second photolithography step isperformed to define the contact areas. The metal layers forthe contacts are deposited by electron beam evaporation in
the following order: Ni 共5 nm兲 / Ge 共25 nm兲 / Au 共65 nm兲 /Ni 共20 nm兲 / Au 共200 nm兲. The sample is annealed at 420 °C
for one minute to form ohmic contacts, and a third photolithography step defines a square window on the back side of
the substrate. Selective spray etching is used again to etchthe substrate from the back, forming a membrane to allowa兲

Electronic mail: awsch@physics.ucsb.edu

optical transmission experiments. The device has a twocontact resistance of 6.2 k⍀ at a temperature T = 5 K.
To monitor the electron spin dynamics in the device, weemploy time-resolved Faraday rotation14,15 in the Voigt geometry with the sample growth axis parallel to the opticalaxis. A mode-locked titanium sapphire laser produces⬃150 fs pulses at a repetition frequency of 76 MHz and its
wavelength is tuned to 818 nm to address the band gap ofGaAs. A circularly polarized pump pulse injects spin polarized electrons, and the Faraday rotation of a linearly polarized probe pulse measures the electron spin component along
the laser propagation direction at a time delay ⌬t. The laser
beams are focused to a spot size of ⬃30 ␮m, and the averagelaser powers are 500 and 60 ␮W for the pump beam and theprobe beam, respectively. The circular polarization of thepump beam is modulated with a photoelastic modulator at 50
kHz for lock-in detection and ⌬t is controlled with a mechanical delay line. Measurements are conducted at T = 5 K
where the longest electron spin lifetimes have beenobserved.11
We focus the pump beam to the right side of the ring togenerate electron spin polarization, while the probe beam
detects the spins at the left side of the ring 关Fig. 1共b兲兴. A
positive voltage is applied to the contact on the left while theright contact is grounded, establishing an electric field which

FIG. 1. 共a兲 Device schematic. Dark areas are contacts and light gray area isthe GaAs spin interferometer. 共b兲 Schematic of experimental geometry. 共c兲
Faraday rotation as a function of B at ⌬t = −10 ps and an applied voltage of3.5 V. 共d兲 Faraday rotation as a function of ⌬t at B = 1 T and an applied
voltage of 3.5 V.

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Kato et al.

causes the spins to drift across the structure and into theprobe spot. In general, the Faraday rotation signal can be
described as⬁

S0e−共⌬t+nt 兲/␶cos关␻L共⌬t + ntrep兲兴,兺n=0rep

共1兲

where S0 is the amplitude, n is an integer specifying successive pulses, trep = 13.15 ns is the repetition time of the laser, ␶is the spin lifetime, and ␻L = g␮BB / ប is the electron Larmor
frequency, g is the effective electron g factor, ␮B is the Bohrmagneton, B is the applied magnetic field, and ប is thePlanck constant.11 In order to simplify the data analysis, thevoltage is chosen such that only the n = 1 pulse contributes tothe signal. This is possible as the spin packets from successive pulses are spatially well separated after trep if a large
enough electric field is applied.12 In Fig. 1共c兲, the magnetic
field dependence of the Faraday rotation around B = 1 T witha bias voltage of 3.5 V is shown. The absence of other harmonic components indicates that pulses with n ⬎ 1 are notcontributing to the signal since the spins generated from earlier pulses have drifted past the probe spot. In Fig. 1共d兲,Faraday rotation is plotted as a function of ⌬t. We see noabrupt jump at ⌬t = 0 ns, showing that there is no contribution from the n = 0 pulse. This is expected as the pump andthe probe spots are spatially separated. The frequency of thespin precession signal is used to extract the electron g factor,and gives 兩g兩 = 0.42. We also note that the voltage has been
tuned such that the spin precession signal has uniform amplitude throughout the available range of ⌬t, meaning thatthe center of the spin packet goes through the center of theprobe spot at around ⌬t = 1.5 ns. The strain-induced effective
magnetic field5 plays a negligible role at these large appliedmagnetic fields.
In order to establish a phase difference between the twopaths, optically pumped dynamic nuclear polarization 共DNP兲
is utilized. A circularly polarized third beam with an average
power of 5 mW is derived from the same laser and is focusedon the lower arm 关Fig. 1共b兲兴. A slight tilt of the sample
causes refraction of the DNP beam and results in some electron spin polarization along B. A part of the electron spin
angular momentum is transferred to nuclear spins, establishing DNP along the applied magnetic field which acts as anadditional effective magnetic field for the electron spinsthrough the contact hyperfine interaction.16,17 In this manner,the electrons traveling through the lower arm gain an additional phase to their spin precession. After the two packets
have recombined, the expected time-resolved Faraday rotation isAucos共␻L⌬t兲 + Alcos共␻L⌬t + ⌽兲 = A cos共␻L⌬t + ␾兲, 共2兲
whereA = 共A2u + 2AuAlcos ⌽ + A2l 兲1/2and␾ = tan−1冋册Alsin ⌽.
Au + Alcos ⌽共3兲

共4兲

Here, Au and Al are the amplitudes of the spin packets in theupper and the lower arms, respectively, ⌽ is the phase difference between the two packets, and lastly, A and ␾ are theamplitude and the phase, respectively, of the combinedpacket. As ⌽ is varied, a change in the amplitude of the spin

FIG. 2. 共a兲 Series of time-resolved Faraday rotation data as a function of lab
time with an applied voltage of 3.5 V at T = 5 K and B = 1 T. 共b兲 Amplitudeof the spin precession signal obtained from fits to data in 共a兲, normalized tothe value at t = 1500 s. 共c兲 Amplitude of the expected spin precession signal
from the simulation. 共d兲 Phase of the spin precession signal from fits to data
共filled circles兲 and exponentially decaying background 共line兲. 共e兲 The data in共d兲 with the background subtracted. 共f兲 Phase of the expected spin precession signal from the simulation.

precession signal should occur as a result of the interferenceterm AuAlcos ⌽.
We initialize the device by waiting for 30 mins at B
= 1 T with the DNP beam on the sample and the bias voltage
set to 0 V. The voltage is turned off in an effort to localize thenuclear polarization, while the magnetic field is needed toestablish the nuclear polarization.16–18 After the nuclear polarization has built up, the DNP beam is blocked, the voltage
is set to 3.5 V, and measurements of Faraday rotation as afunction of ⌬t are made repeatedly 关Fig. 2共a兲兴. Since theDNP beam is turned off, the nuclear spins begin to relax overa time scale of ⬃30 mins and reduce the phase difference
between the two paths. As a consequence, the recombined
electron spin polarization at the left side of the ring cycles
through constructive and destructive interferences, which
manifests as an oscillation in the amplitude of the spin precession signal. Two and a half oscillations are observed in1500 s, corresponding to a difference in an average effective
magnetic field of 28 mT between the two arms.
In order to quantitatively characterize the interference,
we fit individual time-resolved Faraday rotation data withA cos共␻L⌬t + ␾兲. The parameters A and ␾ obtained from thefits are plotted as a function of lab time in Figs. 2共b兲 and2共d兲, respectively. The amplitude does not dip down to zero,
which is expected if the spin packets from the two arms do
not have equal amplitudes. Additionally, the oscillation amplitude increases with lab time, which we attribute to thedecrease in signal at early times due to inhomogeneous
nuclear polarization that extends to both arms. Diffusion ofspin polarized electrons generated by the DNP beam canresult in such nuclear polarization, which in turn causes theelectron spins used for the interference to dephase. The
dephasing will diminish as the nuclear spins depolarize, andthis will increase the amplitude of the spin precession signal.
This is consistent with the behavior of the phase, whichshows an exponential decay with small oscillations superim-Downloaded 18 Apr 2005 to 128.111.16.138. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

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Kato et al.

posed. This decay can be explained by changes in ␻L as aresult of nuclear polarization in both arms.
Assuming that both the amplitude and the phase difference recover with the nuclear spin relaxation time ␶n, theamplitude of each packet and the phase difference are modeled asAu = Pu共1 − pue−t/␶n兲,

共5兲

Al = Pl共1 − ple−t/␶n兲,

共6兲⌽ = ⌽0e−t/␶n .

共7兲

andHere, Pu and Pl = 1 − Pu are the fractions of upper and lower
arms contributing to signal, respectively, pu and pl represent
the portions of the signal which have been reduced due toinhomogeneous nuclear polarization, and ⌽0 is the phase difference due to the nuclear polarization between the two paths
at time t = 0 s. The lab-time dependence of the amplitude andphase of the combined spin packet are simulated from Eqs.
共3兲 and 共4兲. The model gives good agreement to data with
Pu = 0.57, pu = 0.45, pl = 0.70, ⌽0 = 4.5␲, and ␶n = 400 s 关Fig.
2共c兲兴. For the analysis of the phase, we have subtracted anexponentially decaying component and an offset given by⌽1exp共−t / ␶n兲 + 0.75␲ with ⌽1 = 2.86␲ and ␶n = 400 s, whichis shown as a solid line in Fig. 2共d兲, and the data after subtraction is shown in Fig. 2共e兲. The simulation of the lab-timedependence of the phase is obtained from the same set ofparameters used in Fig. 2共c兲, and is shown in Fig. 2共f兲. A
good agreement is seen between the data and the model forthe phase as well.
The parameters obtained in the analysis allow us to infer
the spatial extent of the nuclear spin polarization. ⌽1 gives ameasure of the nuclear polarization in the upper arm, while⌽0 + ⌽1 gives a measure of that in the lower arm. The ratio ofthese two values is ⬃2.5, indicative of significant nuclear
polarization in the upper arm. This can be explained by electron spin diffusion, which has been seen to extend to⬃15 ␮m in a similar system.19 In addition, suppression of
nuclear spin polarization at the center of a laser spot has also
been observed previously,20 and this may be playing a role in
keeping this ratio to a relatively small value. There may also
be nuclear polarization arising from electron spins excited in
the upper arm by tails of the DNP beam.
We note that the interference we observed is of net spinpolarization of the electrons, and is not orbital quantum
interference21–23 since the orbital part of the electron wave
function does not stay coherent. We also note that theAharonov–Bohm effect24–26 is not expected here as the magnetic field is applied in the plane of the sample.
In summary, we have demonstrated electron spin interferometry using a semiconductor ring structure. It takes ad-vantage of the long lifetime of spin polarization relative tocharge coherence, and may find applications in detectingmagnetic field gradients. The measurements also provide insights into the effect of nuclear polarization on electron spindephasing. Although DNP is only efficient at lowtemperatures,18 it may be possible to use the spin-orbit
effects5,21–23 or ac Stark effect1 for manipulating the local
magnetic field at higher temperatures.
The authors thank G. Salis and acknowledge support
from the DARPA and the DMEA.
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