LaBella et al. (1) claimed
92% spin polarization for electrons injected into gallium arsenide
[GaAs(110)] from a Ni scanning tunneling microscope (STM) tip, which,
they asserted, emitted 100% spin-polarized electrons. Such a claim, if
substantiated, would constitute a development of great importance for
the emerging field of spintronics: It would suggest that the field is
rapidly closing in on the goal of injecting electrons with 100% spin
polarization, a key to device applications. For reasons discussed
below, however, we believe that the actual injected electrons had a
spin polarization of much less than 92% and that emission of 100%
spin-polarized electrons from the Ni tip would not be expected.
The measured polarization of the emitted light in the LaBella
et al. study, 11.5%, is connected to the spin polarization
of the injected electrons by three conversion factors: (i) the ratio of
the detected light polarization to the emitted light polarization; (ii)
the ratio of the emitted light polarization to the polarization of the
electron spin density; and (iii) the ratio of the polarization of the
electron spin density to the polarization of the injected current. By
ignoring the refraction of the light when it leaves the GaAs, LaBella
et al. (1) both missed the first correction factor and overestimated the second. The final conversion factor depends strongly on material parameters that LaBella et al.
did not determine and that vary quite strongly in existing
measurements.
Because the index of refraction for GaAs is 3.4, light that was
collected at an angle of 60° in these experiments was emitted at
angle of 14.8°. From the Fresnel formulae, the circular polarization decreases slightly on refraction, so the polarization of the emitted light would have been a factor of 1.06 greater than the measured light
polarization. The circular polarization of the emitted light is related
to the spin polarization of the electron density through matrix
elements that give a factor of two divided by the cosine of the
emission angle; this results in a conversion factor of 2/cos(14.8°) = 2.07. The total conversion factor between the
measured light polarization and the spin polarization of the electrons at recombination is thus 2.07 × 1.06 = 2.19. Ignoring
refraction led LaBella et al. to use a factor of
2/cos(60°) = 4.0. Thus, the measured electron spin polarization
at recombination was 25.2%, rather than the 46% that they claimed.
The polarization of the electron spin density at recombination
would have been less than the polarization of the injected current because of spin-flip scattering. The authors used values for
the recombination and spin-relaxation lifetimes based on published results, which, through equation 1 in (1), gave an injected electron spin polarization a factor of two larger than the
recombination polarization. However, the lifetimes depend on doping,
temperature, and sample quality. Consequently, different groups using
different samples will obtain different values. Without reliable spin
and electron lifetime values that pertain to the sample investigated, we do not believe that the factor-of-two-larger value for the injected
electron polarization claimed by LaBella et al. is
justified. Rather, we believe it would be more appropriate for them to
claim a measured spin polarization of 25.2% and to point out that the injection polarization is likely to be larger, possibly by a factor even greater than two, but also possibly by a factor much closer to
one.
It is not surprising that the injected electron spin polarization that
can be inferred from the measured circular polarization of the emitted
light is not close to 100%. The authors assert that the Ni(110) STM
tip emits 100% spin polarized electrons because along the 
direction in Ni, the density of spin-up states at the Fermi level is
zero. Indeed, both the spin-up and spin-down 
1 bands
cross the Fermi level in mid-zone. In the photoemission measurements
referenced by LaBella et al., selection rules suppressed photoemission from the 1 states and hence achieved 100%
spin polarization. These selection rules do not apply to tunneling; furthermore, at the tunneling voltages used in the experiment, both the
spin-up and spin-down states below the Fermi level are accessible for
tunneling. As a consequence, it was incorrect to assert that the
tunneling current from the Ni(110) tip was 100% polarized.
In summary, we believe that an electron spin polarization at
recombination of 25.2% can be inferred from these experiments and that
it is difficult to say definitively by how much the actual electron
polarization upon injection exceeded that number.
W. F. Egelhoff, Jr.
M. D. Stiles
D. P. Pappas
D. T. Pierce
National Institute of Standards and Technology
Gaithersburg, MD
20899, USA
and Boulder, CO 80305, USA
J. M. Byers
M. B. Johnson
B. T. Jonker
Naval Research
Laboratory
Washington, DC 20375, USA
S. F. Alvarado
IBM Zurich Research Laboratory
CH-8803 Rueschlikon, Switzerland
J. F. Gregg
University of Oxford
Oxford OV1 3PU, UK
J. A. C. Bland
University of Cambridge
Cambridge CB3 0HE, UK
R. A. Buhrman
Cornell University
Ithaca, NY 14853, USA
REFERENCES
2 January 2002; accepted 12 April 2002
Response: We thank Egelhoff et al.
for carefully scrutinizing our recent study (1). We agree
with their comment that light emitted from the GaAs sample refracts and
that we overlooked this in our conversion factors. Refraction affects
the polarization of the light in two ways. First, using the index of
refraction of GaAs at 100 K (3.27), a detector oriented at 60° to the
surface normal actually measures emissions coming from an angle of
15.4° to the surface normal. Including the selection rules, this
results in a conversion factor between the optical polarization and
electron polarization at the time of recombination of 2.07, as Egelhoff et al. assert. Second, because of the Fresnel effect (a 1.06 conversion factor), the measured polarization is reduced from the true
value. These combined results yield a conversion factor of 2.19 between the measured optical polarization and the electron spin polarization at
the time of recombination, not a factor of 4.0 as originally published,
as Egelhoff et al. correctly point out. Thus, the measured optical polarization of 11.5% results in an electron spin polarization at the time of recombination of 25.2%, not 46%.
Egelhoff et al. further comment that we should be
concerned about the accuracy of the spin-relaxation lifetime. It is
true that we did not measure the spin-relaxation lifetime for the
sample studied in (1). As we noted there, however, a
published value for spin-relaxation lifetime of 2.5 × 10
10 s exists for GaAs at a temperature of 77 K and an
acceptor doping concentration of 1019 (2). If
that result also applied to our sample, then the polarization at the
time of injection was 50.4% (not the 92% reported). Of course, if
that result were not applicable to our sample, then the polarization at
the time of recombination may have been as low as 25.2%.
Finally, we agree with the observation by Egelhoff et al.
that the polarization state of tunneling electrons may be different from that of photoemitted electrons.
V. P. LaBella
D. W. Bullock
Z. Ding
C. Emery
A. Venkatesan
W. F. Oliver
G. J. Salamo
P. M. Thibado
Department of Physics
University of Arkansas
Fayetville, AR 72701, USA
M. Mortazavi
Department of Physics
University of Arkansas
Pine Bluff, AR 71601, USA
REFERENCES
| 1. |
V. P. LaBella,
et al.,
Science
292,
1518
(2001)
. |
| 2. |
L. G. E. Pikus, A. N. Titkov, in Optical Orientation, F. Meier, B. P. Zakharchenya, Eds. (Elsevier, New York, 1984), p. 121. |
29 January 2002; accepted 12 April 2002
