Spin polarization of injected electrons.

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°) 5 2.07. The total conversion factor between the measured light polarization and the spin polarization of the electrons at recombination is thus 2.07 3 1.06 5 2.19. Ignoring refraction led LaBella et al. to use a factor of 2/cos(60°) 5 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 j direction in Ni, the density of spin-up states at the Fermi level is zero. Indeed, both the spin-up and spin-down S1 bands cross the Fermi level in mid-zone. In the photoemission measurements referenced by LaBella et al., selection rules suppressed photoemission from the S1 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.