Optical Pumping in Solid State Nuclear Magnetic Resonance

in physical chemistry, condensed matter physics, and biomedical sciences, is reviewed. ... usefulness of solid state NMR has become widely recognized...
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13240

J. Phys. Chem. 1996, 100, 13240-13250

Optical Pumping in Solid State Nuclear Magnetic Resonance Robert Tycko* Laboratory of Chemical Physics, National Institute of Diabetes and DigestiVe and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520

Jeffrey A. Reimer Center for AdVanced Materials, Lawrence Berkeley Laboratory, and Department of Chemical Engineering, UniVersity of California, Berkeley, California 94720-1462 ReceiVed: December 8, 1995; In Final Form: February 1, 1996X

An important current trend in solid state nuclear magnetic resonance (NMR) is the growing exploitation of optical pumping of nuclear spin polarizations as a means of enhancing and localizing NMR signals. Recent work has been concentrated in two areas, namely optically pumped NMR in semiconductors and optical pumping of noble gases. Progress in these two areas, including technical developments and new applications in physical chemistry, condensed matter physics, and biomedical sciences, is reviewed. Likely directions for future developments are suggested.

I. Introduction Solid state nuclear magnetic resonance (NMR), by which one generally means the application of NMR spectroscopy to chemical systems that are not isotropic liquids or solutions, is a powerful probe of chemical structures, molecular conformations, molecular dynamics, electronic properties, magnetic properties, and phase transitions. In the past decade, the usefulness of solid state NMR has become widely recognized in the fields of physical chemistry, chemical engineering, geochemistry, materials science, condensed matter physics, and biophysical chemistry. Two factors have contributed to the growing interest in solid state NMR. First, technological advances, in particular the development of affordable high-field, high-homogeneity superconducting magnets and powerful laboratory computers, and advances in techniques, such as multidimensional spectroscopy and techniques for line narrowing and spectral simplification that depend on complex radio-frequency (rf) pulse sequences and rapid sample rotations, have expanded the range of chemical systems and phenomena that can be studied by solid state NMR. Second, successful NMR studies of specific systems that are of widespread interest have been carried out in the past decade, thereby providing dramatic evidence of the utility of solid state NMR. For example, our current understanding of the properties of high-Tc ceramic superconductors1 and of fullerene-based materials2 has been influenced strongly by NMR measurements. The principal limitation of solid state NMR, and NMR in general, is its relatively low sensitivity. Nuclear magnetic moments are small (µ ≈ 10-23 erg/G), NMR frequencies are low (typically 10-500 MHz), and nuclear spin polarizations at thermal equilibrium are tiny (typically 1000 s in the dark in undoped materials). Therefore, the nuclear spin polarization can build up over many optical excitation cycles. The electron spin-lattice relaxation time T1e is much shorter (less than 10-6 s); however, as long as T1e is comparable to or greater than the lifetime of the optically excited electronic state, the net electron spin polarization will have a nonequilibrium value, and optical pumping of the nuclei may result. 2. Optical Detection. The large nuclear spin polarizations generated by optical pumping result in proportionately large NMR signals when the signals are detected by direct rf induction (as in conventional NMR spectroscopy). Direct detection of NMR signals from optically pumped nuclei was in fact the method used in the first OPNMR experiments, as well as in more recent experiments described below. However, many other OPNMR experiments on semiconductors have made use of optical methods to detect the NMR signals indirectly. Such optically detected NMR (ODNMR) measurements can be extremely sensitive, in principle requiring considerably fewer than 1011 nuclei. Therefore, ODNMR ultimately may prove useful for characterizing defects and impurities at low concentration in bulk semiconductors, as well as thin films with small surface areas. In direct-gap semiconductors such as GaAs, the selection rules for optical excitation described above also apply to luminescence; e.g., an mS ) -1/2 conduction electron can recombine with a hole in the mJ ) -3/2 heavy hole band only by emitting a σ+ photon. The degree of spin polarization of the conduction electrons is therefore reflected in the degree of circular polarization of the photoluminescence. ODNMR is possible in directgap semiconductors because the spin polarization of the conduction electrons can be affected by the spin polarization of the nuclei. When the nuclei become strongly polarized by optical pumping, they exert a magnetic field (called the nuclear hyperfine field) on the electron spins which is proportional to the nuclear spin polarization; this field adds vectorially to the externally applied magnetic field. In GaAs, the total nuclear hyperfine field due to 69 Ga, 71 Ga, and 75 As can be as large as 5.3 T. Radio-frequency irradiation near an NMR transition can change the direction of the nuclear hyperfine field and hence the direction of the net magnetic field felt by the electron spins. The electron spins then precess and dephase in the tilted field, and the degree of circular polarization of the photoluminescence diminishes. Thus, by monitoring the polarization of the photoluminescence while sweeping the rf frequency or the external field strength (or by applying rf pulse sequences), one can detect the NMR transitions. This phenomenon is sometimes called the “nuclear Hanle effect” because of its similarity to the Hanle effect, in which the application of a purely external magnetic field perpendicular to the direction of propagation of the light reduces the polarization of the photoluminescence from semiconductors and gases. The mechanisms of optical pumping and optical detection in bulk semiconductors are discussed in much greater detail in ref 4. This reference presents most of the relevant experimental and theoretical results prior to 1984. B. Early Work. The first demonstration of the optical pumping effect on nuclear spin polarizations in a semiconductor

13242 J. Phys. Chem., Vol. 100, No. 31, 1996 was reported by Lampel in 1968.5 In these experiments, a weakly n-doped Si sample (donor concentration ≈1013 cm-3 ), in the form of a disk with a 16 mm diameter and a 1 mm thickness, was irradiated with approximately 1 W of light from a xenon lamp at approximately 1.2 eV at a sample temperature of 77 K. After 37 h of irradiation with unpolarized light in a magnetic field of 0.16 T, the 29 Si NMR signal amplitude was observed to be enhanced by a factor of 5.6 and inverted in sign relative to the thermal equilibrium signal amplitude in the same field. After 21 h of irradiation with circularly polarized light in a field of only 0.1 mT, the NMR signal amplitude was equivalent to the signal amplitude arising from a thermal equilibrium nuclear spin polarization in a field of 1.5 T. Lampel’s experiments showed that nuclear spin polarizations could be driven away from equilibrium by simple optical irradiation. The magnitude of the nuclear spin polarizations generated in these initial experiments was not great, however, primarily because T1e was much less than the lifetime of the optical excitations so that the net electron spin polarization was only slightly different from its equilibrium value. Further work by Bagraev et al. showed that larger nuclear spin polarizations could be produced by optical pumping in Si samples with deep donor impurities.6 The increased polarizations were attributed to increases in T1e and in the degree of localization of the photoexcited electrons. Following Lampel’s work, the emphasis of optical pumping in semiconductors shifted to GaAs. Unlike Si, GaAs is a directgap semiconductor, meaning that the minimum energy in the conduction band and the maximum energy in the valence band occur at the same value of k (specifically, k ) 0). As a result, GaAs is strongly photoluminescent. The photoluminescence excited with circularly polarized light can be strongly circularly polarized at low temperatures, at least in undoped and p-doped samples. Very large nuclear spin polarizations, in excess of 10%, can be generated by optical pumping. The nuclear hyperfine fields are correspondingly large, on the order of 1 T. Thus, optically detected NMR measurements are possible in GaAs, as first shown by Ekimov and Safarov.7 An important series of optically detected NMR experiments was carried out by Paget and co-workers.8 These experiments served to characterize many of the important physical and photophysical parameters and phenomena that enter into the optical pumping and optical detection processes, including hyperfine fields, spin relaxation rates, nuclear spin diffusion, and electron spin exchange. C. Recent Work. 1. Optically Detected NMR. Much of the recent work on OPNMR and ODNMR in semiconductors has focused on quantum wells and heterojunctions, in particular GaAs/AlGaAs structures. GaAs/AlGaAs quantum wells consist of thin GaAs layers embedded in thicker AlxGa1-x As layers. Because the band gap in GaAs is less than that in AlxGa1-x As, the GaAs layers serve as potential energy wells and the AlxGa1-x As layers serve as potential energy barriers in the direction normal to the layers for electrons in the conduction band and for holes in the valence band. GaAs/AlGaAs heterojunctions consist of an interface between a GaAs layer and an AlxGa1-x As layer. Because of the band gap differences and because of band-bending effects, a potential energy well for conduction electrons (or holes) is created on the GaAs side of the interface. Quantum wells and heterojunctions are of interest because of their technological importance and because of the unusual properties of two-dimensionally confined electrons and holes.9 Because of the relatively small number of nuclei in a quantum well or in the region of a heterojunction (roughly 1016 71Ga nuclei per cm2 in a 10 nm thick GaAs layer), conventional NMR

Tycko and Reimer measurements on such structures are not possible. Optical pumping is essential because of the enhanced sensitivity it produces. It is also advantageous because it allows the NMR signals to be localized spatially to the optically absorptive region of the sample, which can be made to coincide with the structurally or electronically interesting region by tuning the wavelength of the pumping light. Three independent groups reported ODNMR measurements on quantum wells and heterojunctions in 1990 and 1991. Kalevich et al. carried out experiments in which they measured optically pumped nuclear spin polarizations and ODNMR spectra of a 100 nm wide GaAs/Al0.3Ga0.7As quantum well.10 They observed 75As, 69Ga, and 71Ga resonances in spectra obtained in a 75.3 mT field. On the basis of measurements of photoluminescence polarization in a field that was tilted away from the direction of propagation of the incident laser light, they estimated the nuclear spin polarizations to be roughly 7% at 2 K in a 0.25 T field. In addition, they estimated the time constant for the buildup of the nuclear spin polarization to be less than 1 s under their experimental conditions. Flinn et al. carried out similar experiments on a GaAs/Al0.3Ga0.7As quantum well structure.11 In these experiments, ODNMR spectra were recorded at a fixed rf frequency of 2.4 MHz with a swept magnetic field. They observed 75As, 69Ga, and 71Ga resonances, but at fields of roughly 0.34, 0.24, and 0.19 T, respectively. They also reported splittings of the resonance lines, by approximately 70 kHz in the case of 75As, due to nuclear quadrupole couplings. They attributed these splittings to strains in their sample that were the result of differential thermal contraction of the sample and of the sample mount. In the absence of strain, in pure bulk GaAs, nuclear quadrupole couplings would necessarily vanish because of the cubic symmetry of the crystal lattice. Although the quadrupole splittings in the experiments of Flinn et al. were due to strains of extrinsic origin, these observations suggested that NMR measurements could be used to measure intrinsic strains in quantum wells and heterojunctions that arise from the slight mismatch of the GaAs and AlGaAs lattice constants. The feasibility of such measurements remains unproven but warrants further investigation. Nonzero quadrupole couplings could also result from internal electric fields associated with the separation of charges in doped quantum wells and heterojunctions. Again, the feasibility of using quadrupole splittings in ODNMR and OPNMR spectra to characterize these internal fields remains unproven. Finally, Krapf et al. reported ODNMR experiments on a p-doped Al0.36Ga0.64As/GaAs heterojunction.12 In addition to observing 75As, 69Ga, and 71 Ga resonances in a 0.172 T field, they observed small shifts of the resonant frequencies when the exciting light was switched from σ+ polarization to σ- polarization. They attributed these shifts to changes in the net conduction electron spin polarization produced by the changes in the polarization of the light. Electron-nucleus hyperfine couplings produce Knight shifts of the NMR frequencies that are proportional to the conduction electron spin polarization (see below) and to the electron probability densities at the nuclei. From the observed frequency shifts, Krapf et al. estimated the ratio of the probability density at an As nucleus to the probability density at a Ga nucleus to be 1.4 for the optically excited conduction electrons. The ODNMR experiments described above used continuous optical excitation, both to pump the nuclear spin polarization and to excite photoluminescence for optical detection, and continuous rf excitation, either at a constant frequency with a swept magnetic field or at a swept frequency with a constant magnetic field, to excite NMR transitions. In a recent series of

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experiments, Weitekamp and co-workers have developed more sophisticated ODNMR techniques, called time-sequenced optical NMR (TSONMR), in which the optical pumping process, the NMR excitation process, and the optical detection process occur in separate time periods.13,14 The separation of the three stages of the ODNMR measurement permits each process to be optimized and leads to improved resolution and sensitivity. In particular, TSONMR techniques readily allow NMR spectra of semiconductor samples in their thermal equilibrium electronic states to be detected optically and allow pulsed NMR methods such as spin echoes, transient nutations, and multidimensional spectroscopy to be incorporated into ODNMR. Initial demonstrations of TSONMR were carried out on p-type GaAs films. 69Ga resonances as narrow as 2 kHz in width were recorded, roughly an order of magnitude narrower than in previous ODNMR spectra. Spectra were obtained with both frequencydomain13 and time-domain14 excitation of the NMR transitions. Interestingly, the time-domain spectra showed broader lines, suggesting a greater sensitivity to nuclei near optically relevant defect sites, where nonvanishing quadrupole couplings are to be expected. Nutation spectra showed evidence for nuclei with quadrupole splittings greater than 20 kHz. Very recent experiments were carried out on a p-type AlGaAs/GaAs heterojunction, using a new double-resonance method called Larmor beat detection.5 This method allows the free induction decay (FID) signals of one type of nucleus (e.g., 71Ga) to be observed in real time while another type of nucleus (e.g., 75As) is irradiated continuously near resonance. 71 Ga spectra obtained with Larmor beat detection in a 0.24 T field at 2 K showed quadrupole splittings on the order of 10 kHz. The origin of these splittings was again uncertain, but may be differential thermal contractions as observed by Flinn et al.11 Many additional variants and applications of TSONMR are conceivable, including measurements of electron probability distributions at defect sites and in quantum wells.16 2. Directly Detected NMR. Interest in directly detected OPNMR of semiconductors has been revived by recent experiments at AT&T Bell Laboratories by Tycko and co-workers.17-19 These experiments demonstrated both the feasibility of directly detected OPNMR measurements on GaAs/AlGaAs quantum well structures and the importance of such measurements as probes of the properties of two-dimensional electron systems (2DES) confined in quantum wells in high magnetic fields. The samples examined by Tycko and co-workers were n-type delta-doped quantum well structures, meaning that the GaAs wells contained conduction electrons contributed by Si donor atoms that were deposited in a thin layer in the center of the AlxGa1-xAs barriers. In such samples, the density of electrons in the wells at low temperatures is determined primarily by the value of x and by the dimensions of the barriers and wells. For example, a delta-doped multiple quantum well structure with 180 nm thick Al0.1Ga0.9As barriers and 300 nm thick GaAs wells has an areal electron density nS ≈ 1.5 × 1011 cm-2. These electrons occupy the lowest quantum-confined conduction subband in the wells. In zero field (and in an ideal quantum well), the conduction electrons are fully delocalized in the plane of the wells (the xy plane) and can therefore be represented by two-dimensional Bloch states with well-defined wavevectors kx and ky. The conduction electron wave functions have envelopes in the direction normal to the plane of the wells (the z direction) that are approximately particle-in-a-box wave functions. Thus, to a good approximation, electrons in the lowest subband have probability density distributions with an envelope of the form sin2(z/d), where d is the well thickness. At low temperatures, there are essentially no free conduction electrons in the barriers.

In a strong magnetic field Bz perpendicular to the plane of the wells (parallel to the growth axis), the translational motion of the quantum-confined electrons in the xy plane becomes quantized as well.9 In the absence of electron-electron interactions, the translational motion is quantized in units of the cyclotron energy Ez ) peBz/m*c, where e and m* are the electronic charge and effective mass, corresponding to the classical motion of charged particles in cyclotron orbits perpendicular to an applied magnetic field. The resulting electronic energy levels, called Landau levels, are further split by the electron spin Zeeman energy Ez ) g*µBB, where g* is the effective g factor (-0.44 in bulk GaAs), µB is the Bohr magneton, and B is the total magnetic field. Each spin-split Landau level has a degeneracy nL ) eBz/hc. One then defines a quantity called the “filling factor” ν to be nS/nL. ν represents the fractional number of spin-split Landau levels that would be occupied by electrons at T) 0 in a perfect noninteracting 2DES. Current interest in the properties of electrons confined in quantum wells at low temperatures and in strong magnetic fields derives from the discovery of the quantum Hall effect (QHE) in such systems.20 The QHE refers to the observation of characteristic plateaus in the transverse resistivity, i.e., the Hall resistivity, and zeroes in the longitudinal resistivity of twodimensional electron systems (2DES) at both integral and certain fractional values of ν (the integer and fractional quantum Hall effects, IQHE and FQHE). Remarkably, the values of the Hall resistivity in these plateaus are completely independent of physical properties of the 2DES such as the electron effective mass, the electron mobility, the temperature, the chemical composition of the quantum wells, and the thickness of the wells. The QHE is a signature of the existence of particular correlated, low-energy states of the 2DES at these particular values of ν. The problem of characterizing and understanding the nature of the low-energy states of a real 2DES, including the effects of electron-electron interactions, has therefore become an extremely active area of research in condensed matter physics. Initial OPNMR studies of a GaAs/Al0.1Ga0.9As quantum well structure with 40 identical wells, each with nS ≈ 6.3 × 1010 cm-2, indicated that enhancements of 69Ga, 71Ga, and 75As NMR signals from the GaAs wells by roughly 2 orders of magnitude over the corresponding thermal equilibrium signals were possible at 5 K in a 7.05 T field.17 Figure 2 shows examples of the 71Ga NMR and OPNMR spectra. The OPNMR signals were found to exhibit a strong dependence on the laser wavelength and polarization, as shown in Figure 3. This behavior arises from the quantization of valence and conduction band states into subbands and Landau levels. At a fixed wavelength, the OPNMR signals do not simply change sign when the sense of circular polarization of the light is reversed, as seen in bulk semiconductors at low fields. The dependence of the OPNMR signal amplitudes on the laser power was found to saturate at surprisingly low levels, roughly 100 mW/cm2. The photoluminescence intensity does not saturate at these levels. The saturation of the OPNMR signal amplitudes suggests that the optical pumping effect in GaAs quantum wells arises from specific trapped excitations associated with structural features that are present at low concentration. Thus, the initial studies raised a number of interesting questions about the photophysics and spin physics of the optical pumping process in n-doped quantum wells in high magnetic fields. These questions have not yet been answered. More importantly from the standpoint of applications, however, the initial measurements showed that OPNMR signals from quantum wellsseven a single quantum wellscould be detected easily with a simple experimental apparatus. Moreover, these measurements showed that nuclei

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Figure 2. 71Ga NMR spectra of a GaAs/AlGaAs multiple quantum well structure with electron densities of 6.3 × 1010 cm-2 in each well, obtained at 5.1 K in a 7.05 T field. The top spectrum represents the thermal equilibrium NMR signal from both GaAs well and AlGaAs barrier layers (2.7 × 1018 nuclei), obtained by allowing 5400 s for nuclear spin-lattice relaxation of the entire sample in the dark. The bottom spectrum represents optically pumped NMR signals from the GaAs wells alone (2.1 × 1017 nuclei), obtained after irradiation with σ+ light at 815 nm and 120 mW/cm2 for only 30 s. The middle spectrum represents signal obtained after allowing 30 s for nuclear spin-lattice relaxation in the dark. All spectra have the same vertical scale. The splitting of the optically pumped NMR signal is due to electric quadrupole couplings of the nuclei in the wells, indicating the presence of electric field gradients of uncertain origin. Reproduced with permission from ref 17. Copyright 1994 American Institute of Physics.

Figure 3. Dependence of the OPNMR signal amplitude on optical pumping wavelength, for the same sample as in Figure 2, at 5.7 K and 7.05 T. Measurements were carried out with 30 s of pumping, 30 mW/ cm2 light power density, and either σ+ (a) or σ- (b) light polarization. The oscillatory behavior reflects qualitatively the discrete energy spectrum of valence band and conduction band electronic states due to confinement in the GaAs quantum wells and due to Landau quantization in the strong magnetic field. The quantitative details are not well understood. Reproduced with permission from ref 17. Copyright 1994 American Institute of Physics.

in the GaAs wells differ from nuclei in the Al0.1Ga0.9As barriers in both their NMR frequencies and their T1n values.17 These differences arise from the presence of conduction electrons in the wells. The observation that the NMR properties were sensitive to the presence of electrons suggested that directly detected OPNMR measurements could probe the properties of the 2DES in the wells. Subsequent measurements18,19 were performed on a multiple quantum well sample with nS ) 1.5 × 1011 cm-2, for which ν ) 0.66 at 9.39 T and 0.88 at 7.05 T. A series of 71Ga OPNMR spectra obtained from this sample are shown in Figure 4. Spectra in this series were obtained with the timing sequence

Tycko and Reimer

Figure 4. 71Ga spectra of a GaAs/AlGaAs multiple quantum well structure with electron densities of 1.5 × 1011 in each well, obtained at 1.9 K in a 7.05 T field, with optical pumping times τL ) 2 s (top), 200 s (middle), and 1000 s (bottom). Vertical scales are not equal for the three spectra. The broad, asymmetric peak at the lower frequency arises from the GaAs wells. The peak at the higher frequency arises from the AlGaAs barrier layers. The frequency shift between wells and barriers is due to hyperfine couplings of nuclei in the wells to electrons in the wells and is proportional to the electron spin polarization of the two-dimensional electron system. Differences between these spectra and the spectra in Figure 2 are primarily due to the lower temperature and higher electron density. Reproduced with permission from ref 19. Copyright 1995 American Association for the Advancement of Science.

SAT-τL-τD-DET, where SAT represents a train of resonant rf pulses that saturates the nuclear spin transitions (i.e., destroys the nuclear spin polarization), τL is the period of laser irradiation during which nuclear spin polarization builds up, τD is a dark period during which the electron system returns to thermal equilibrium (but the nuclei remain polarized), and DET represents the detection of the NMR FID signals after a single rf pulse. If there is no laser irradiation during DET, as is the case in Figure 4, the NMR signals reflect the thermal equilibrium properties of the sample. In Figure 4, τD is held constant at 1 s. At small values of τL, a single resonance line arising from 71Ga nuclei in the wells is observed. At larger values of τ , an L additional line arising from nuclei in the barriers appears. The appearance of the barrier resonance results from the transport of nuclear spin polarization from the wells to the barriers by nuclear spin-spin couplings. The frequency shift ∆f between the well and barrier lines is a Knight shift, i.e., a shift due to the contact (isotropic) hyperfine coupling of nuclear spins in the wells to the 2DES. The Knight shift is therefore ∆f ) b) is the AN(r b)〈Sz〉, where A is a hyperfine coupling constant, N(r average three-dimensional electron density in a primitive cell containing the nucleus at position b, r and 〈Sz〉 is the average spin polarization of the conduction electrons. Thus, the observed frequency shift is a measure of the spin polarization of the 2DES in the GaAs quantum wells. Based on the work of Paget et al.,8 A is estimated to be 5.2 × 10-13 cm3 s-1. Assuming nS ) 1.5 × 1011 cm-2 and a probability density envelope of the form sin2(z/d), the maximum value ∆f ) 26 kHz is obtained when 〈Sz〉 ) 1/2. Barrett et al.18 used OPNMR to measure the dependence of ∆f on ν. Since to an excellent approximation ν depends only the component of the applied magnetic field perpendicular to the quantum well layers, ν was varied in a constant applied field by varying the angle θ between the perpendicular direction and the applied field direction. The results of measurements at 1.6 K and in fields of 9.39 and 7.05 T are shown in Figure 5. Several features of these data are significant. First, maxima in ∆f occur at ν ≈ 1 in both fields, with values that imply 〈Sz〉 ≈ 1/2. The fact that these maxima occur at the same value of ν in both fields, corresponding to quite different values of θ (28° at 7.05 T; 49° at 9.39 T), indicates that the variations in ∆f indeed arise from the electronic properties of the sample,

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Figure 5. Dependence of the 71Ga NMR frequency shift between well and barrier nuclei, as in Figure 4, on the Landau level filling factor ν. Data obtained at 1.55 K and in fields of 7.05 T (triangles) and 9.39 T (circles). ν was varied by varying the angle between the field and the plane of the GaAs quantum wells. The sharp maximum at ν) 1 is evidence for the existence of electronic quasi-particle states with spins greater than 1/2, called skyrmions, immediately above or below ν) 1. The local maximum at ν ) 2/3 is a signature of a spin-polarized fractional quantum Hall state. Reproduced with permission from ref 18. Copyright 1995 American Institute of Physics.

Figure 6. Dependence of the 71Ga nuclear spin-lattice relaxation rate on the Landau level filling factor ν, obtained from measurements of the rate of decay of OPNMR signals from GaAs quantum wells in the dark after optical pumping. Data obtained at 2.1 K and in fields of 7.05 T (triangles) and 9.39 T (circles). Minima in the relaxation rate at ν ) 1 and ν ) 2/3 reflect the absence of low-energy electronic excitations at these filling factors. Reproduced with permission from ref 19. Copyright 1995 American Association for the Advancement of Science.

rather than from a possible anisotropy of the hyperfine couplings. Second, ∆f decreases rapidly as ν either increases or decreases from ν ) 1. The rapid decrease of ∆f with decreasing ν is particularly surprising, since a 2DES should be fully spin polarized at low temperatures for ν e 1 in the absence of electron-electron interactions. The rate at which ∆f decreases with increasing ν above ν ) 1 is also much greater than expected for a noninteracting 2DES. Third, a local maximum in ∆f also occurs at ν ≈ 2/3, one of the FQHE values. The value of ∆f at ν ) 2/3 is less than the maximum possible value, implying that 〈Sz〉 < 1/2, but measurements of the temperature dependence of ∆f suggest that 〈Sz〉 at ν ) 2/3 may reach 1/2 at temperatures below 1.6 K. The results in Figure 5 demonstrate that the spin polarization of a real 2DES can be strongly reduced by electron-electron interactions when ν * 1. This experimental observation coincides with recent theoretical work.21 According to theory, an interacting 2DES should be fully spin polarized at ν ) 1, regardless of the strength of the applied magnetic field. However, calculations indicate that 〈Sz〉 decreases substantially at ν ) 1 (  ( , 1) when the electron-electron Coulomb energy Eee is comparable to or greater than the Zeeman energy Ez. In effect, an extra electron added into or subtracted from a 2DES at ν ) 1 carries with it a spin that can be much greater than 1/2 and that depends on Ez/Eee. In the language of condensed matter physics, the charged excitations of a 2DES at ν ) 1 are quasi-particles, called “skyrmions”, that possess spins greater than 1/2. The spin of such a skyrmion can be estimated from the slope of the ∆f data on either side of ν ) 1 to be 1.8 at 7.05 T.18 The OPNMR data in Figure 5 represent the first experimental evidence for the existence of skyrmions in a real 2DES. These data have stimulated a series of measurements by other techniques that support the OPNMR results,22 as well as additional theoretical work on skyrmions in 2DES.23 Nuclear spin-lattice relaxation rates in GaAs quantum wells can also be determined from OPNMR measurements. At low temperatures, nuclear spin-lattice relaxation is driven by fluctuations in the electron-nucleus hyperfine couplings. The relaxation rates therefore reflect the electronic excitation spectrum and spin states. Relaxation measurements on the same sample are presented in Figure 6. The QHE states at ν ) 1 and ν ) 2/3 produce minima in the 71Ga spin-lattice relaxation rate measured at 2.2 K. These minima indicate that the manyparticle ground state of the 2DES is separated from all excited

Figure 7. Hypothetical optical pumping scheme for a nuclear spinless isotope of an alkali metal atom. σ+ refers to right circularly polarized light.

states by a nonzero energy gap. The relatively rapid relaxation on either side of ν ) 1 indicates that there is a manifold of low-energy electronic states at these values of ν. From the experimental standpoint, the relaxation measurements are quite striking, in that a rotation of the sample by merely 3° can produce a change in T1n by a factor greater than 20. The OPNMR measurements described above show that OPNMR is a powerful probe of the properties of quantumconfined electrons. Future experiments on GaAs quantum wells and other quantum semiconductor structures are expected to yield a wealth of detailed information about their electronic energies, spin states, and probability density distributions. III. Noble Gas Pumping A. Overview. The conservation of angular momentum in atomic systems in the presence of electromagnetic radiation was the subject of the 1966 Nobel Prize in physics, awarded to Alfred Kastler. In brief, specification of the angular momentum of incoming electromagnetic radiation (such as choosing right circularly polarized light) results in selective excitation within the atomic Zeeman-perturbed energy levels via the selection rules for electric dipole transitions. Fluorescence repopulates the ground states, but subsequent selective excitation ultimately builds a steady-state, non-Boltzmann population of the other metal atom ground state magnetic sublevels, at least as long as the excitation rate exceeds the rate at which ground state electron spins thermalize. An example based upon a generic (and nonexistent) alkali metal atom is detailed in Figure 7; obviously, significant non-Boltzmann populations of the 2S1/2 can accrue. Simultaneous with the optical pumping of an atomic Zeeman state can be the formation of a long-lived complex with an inert

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Tycko and Reimer

Figure 8. Schematic representation of a Rb-Xe van der Waals molecule in the presence of N2 buffer gas. Adapted from ref 53, with permission. Figure 10. Schematic representation of the energy levels associated with the Breit-Rabi formula. Note that the energy levels as drawn are not solution to the equation. Energy splittings are given by the numbers in the figure in units of gigahertz. Low-field pumping is shown by the broken lines and high-field pumping by the thick gray line.

angular momenta B. I In the case of zero applied magnetic field the total angular momentum B F is given by

B F ) BI + JB ) BI + B L+B S

Figure 9. Typical apparatus used for optical pumping of xenon nuclei via rubidium polarization. Note that the magnetic field may come from laboratory sources, such as Helmholtz coils, the fringe field of a superconducting solenoid, or the high field present in the bore of an NMR superconducting magnet. In the latter case Xe NMR may occur in the active cell; for other configurations the pumped xenon gas is transported to a storage vessel or introduced into the sample area of the NMR superconducting magnet.

gas atom, such as xenon. Such complexes owe their long lifetime to the presence of significant van der Waals forces and energy-mediating (via collisions) buffer gases. Figure 8 depicts this process. During the lifetime of the van der Waals complex the nuclear spin of the inert gas atom experiences a Fermi contact interaction with the (polarized) alkali atom electron; this interaction results in spin exchange between the electron and rare gas nuclei and, after dissociation of the complex, produces highly nuclear Zeeman-polarized rare gas atoms. A schematic of an experimental apparatus for the production of polarized rare gas atoms is shown in Figure 9. Polarized xenon gas, for example, has been exploited for many NMR studies24 of solids, thin films, and surfaces. The description given above and depictions in Figures 7-9 suggest that preparation of polarized rare gases is accomplished in a straightforward manner with relative ease. As anyone who has attempted such experiments knows, however, both the implementation of such experiments and their underlying physics are fraught with subtleties, ranging from appropriate atomic energy eigenstates for a given applied magnetic field to proper coating and pretreatment of glass vessels. The pertinent theoretical issues and experimental results are described in more detail below. B. Theory. The quantum mechanical fundamentals of the alkali metal atom pumping process is described well in textbooks on atomic spectroscopy (see ref 25, for example.) The metal atom is described by orbital B L, electron spin B S, and nuclear

(1)

Using eigenstates labeled by these quantum numbers, quantitative agreement between observed and calculated energy levels has been achieved for the J ) 1/2 states of the alkali atoms. The pumping process is in fact achieved in the presence of a static magnetic field; this ensures that the Zeeman quantum number of the (ultimately) polarized inert gas is a good one; it is also convenient if the net polarization of the metal atoms is long-lived enough for subsequent use in spin exchange with rare gas atoms. Thus, we must consider the role of a static magnetic field on the energy levels of an alkali metal atom, such as rubidium, and the processes that induce relaxation of non-Boltzmann populations. The addition of a magnetic field lifts the degeneracy of the atomic F levels; further increases in magnetic field strength cause the nuclear spin angular momentum BI to completely uncouple from B J)B L +B S. The Breit-Rabi formula,26 derived from perturbation theory,25 describes the energy eigenvalues of alkali atoms in a magnetic field B:

EMJMI ) -

hνfs 2(2I + I)

- gIµnBMq (

[

hνfs 4Mqx 1+ + x2 2 2I + I

]

1/2

(2) where hνfs ) AJ(I + 1/2) is the energy separation between levels F + I ( 1/2 in zero field, Mq ) MI ( 1/2, and the dimensionless parameter x is

m g + g )µ B ( M x) J

I

hνfs

B

(3)

Figure 10 (adapted from refs 25 and 33) shows the relevant energy levels for the case of J ) 1/2 and I ) 5/2, i.e, 85 Rb. The choice of magnetic field strength for the pumping process depends on a variety of factors, such as the end use of the polarized (inert) gas, the availability of apparatus, and limitations on the ultimate polarization of the inert gas. In general, application of optical pumping toward study of the spin

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dynamics of the metal atoms and/or the inert gas atoms has used very low fields;27-29 production of polarized inert gas for use in high-resolution NMR experiments uses either the fringe fields of superconducting solenoids30 or the static fields of the NMR magnet itself31-33 to produce polarized inert gases. The eigenstates labeled in Figure 10, for example, may be used as a guide for the choice of the “good” quantum numbers for analysis of the pumping process. The optical pumping process uses the appropriate energy levels and the dipole selection rules from a general timedependent perturbation expansion for an electromagnetic wave.34 The spin ) 1 photons of incoming laser light may be selected to have m ) 1 using a linear polarizer followed by a quarterwave plate. The “right circularly” polarized light will follow the usual electric dipole selection rules, namely, that the orbital angular momentum will change by plus or minus one and the quantum number specifying the Zeeman sublevel will also change by plus one. For alkali metal atoms in low fields we may use Figure 10 as a guide (see dashed vertical line); we see that the ∆mF ) +1 selection rule affords excitation directly from the F ) 2 singlet ground state into the F ) 3 2P1/2 state; at low fields the magnetic F-state sublevels (labeled by mF) are not typically resolvable given the bandwidth of current laser sources. In the case of very high magnetic fields, in excess of about 1 T, the nuclear Zeeman interaction uncouples from the J(L + S) angular momenta, and the product representation |mJ,mI〉 best describes the system.31-33 Returning to the right-hand (high field) side of Figure 10, we see that the eigenstates split into bands labeled by L ) 0 or L ) 1 and mJ equal to +1/2 and -1/2; each of these bands contains all the possible values of mI. Irradiation with σ+ light of bandwidth exceeding the breadth of the mI sublevels results in transitions shown by the filled arrow in Figure 10; note that in this product representation the magnetic quantum number mI is conserved in the electronic transition. The absorption process alone, however, does not produce spin-polarized metal atoms. Once in their excited state, the metal atoms fluoresce back into their ground states by emitting either a σ+ or π photon within approximately 30 ns; the branching ratios for these emissions are given by ClebschGordon coefficients. At the pressures typically used for preparation of polarized rare gas atoms, however, metal atom collisions lead to mixing of the excited states and subsequent equalization of the branching ratios. (Note that the reabsorption by ground state metal atoms of the emitted π photons from neighboring metal atom excited states could lead to selfdepolarization, i.e., a significant loss of net polarization.) Since the laser is tuned, however, to only one ground state level, significant populations of the other ground state should accrue. The angular momentum from the radiation field has been transferred, then, to the atomic sample by adsorption of σ+polarized light. Obviously, if one changes the pumping light polarization to σ-, the atomic polarization will reVerse direction. Aside from depolarization by radiation trapping, it would seem that high metal atom spin polarizations are possible when one pumps faster than ground state electron spin-lattice relaxation. The spin exchange that occurs in the rare gas-alkali metal atom complex is necessary for the production of polarized rare gas atoms.28 The angular momentum in the van der Waals complex is usually described with the Hamiltonian

the molecular rotation angular momentum, and rare gas nuclear spin angular momentum, respectively. A is the metal atom hyperfine interaction, γ is the spin-rotation constant for the van der Waals complex, and R is the isotropic hyperfine interaction between the metal atom electron spin and the rare gas nuclear spin angular momenta. The “flip-flop” terms on the right-hand side of this equation describe the essential physics of polarization transfer from the non-Boltzmann populated electron spin states of the optically pumped metal atom to the nuclear spin states of the rare gas atom. Besides the isotopes of xenon, 3He, 21Ne, and 83Kr have been prepared in highly polarized states (refs 55, 37, and 38, respectively). The overall efficiency for production of polarized rare gases depends on the population of polarized metal atoms and the spin-exchange rates between the polarized metal atom and the rare gas in the van der Waals complex. Both of these quantities are sensitive to the details of the experimental apparatus. For example, unpaired electron spins from impurities on the walls of optical cells can significantly reduce net metal atom polarizations; choice of applied magnetic field strength, or buffer gas pressures, significantly affects the resonance conditions necessary for depolarization by self-trapping. Finally, nuclear spinlattice relaxation39 of the polarized rare gas atoms must be quenched for production of large quantities of polarized gas.40 Indeed, it appears certain41 that the protons in the silicone-coated optical pumping cell provide the dominate relaxation mechanism for rare gases in pumping cells. The influence of surface relaxation on overall pumping efficiencies is described in refs 31-33. C. Applications. The preparation of highly polarized rare gas atoms has been exploited for studies involving solid state NMR of systems where signal-to-noise is a critical factor. Xenon chemical shifts have been exploited for years in studies of chemical environments, especially surfaces;24 it comes as no surprise that polarized xenon has become the workhorse of optically polarized rare gas atoms. In addition to exploitation of polarized gases for chemical or materials studies, polarized gases have been used in several studies of intrinsic interest to chemical physicists. These studies include optically detected multiple quantum coherences and multipole polarizations42 (and references therein), observation of Berry’s dephasing due to diffusion,43 and multiple-pulse coherent averaging methods.29 1. Thin Films and Surfaces. Xenon NMR has been shown to be a powerful probe of chemical environment since its chemical shift is so strongly dependent upon collisions with neighbors. In this regard temperature-, pressure-, and coveragedependent 129Xe NMR signals have been interpreted in terms of structure and dynamics of organic and inorganic surfaces, as well as microporous solids.24 There are many systems, however, for which the signal-to-noise from conventional xenon NMR would be unacceptable; these systems, it would seem, form ideal choices for study with polarized xenon gas. In analogy with xenon NMR studies of high surface area materials, optically polarized 129Xe gas was used to study the interaction of xenon gas with relatively low surface area materials,44 such as powdered benzanthracene (≈0.5 m2/g). In a full study of xenon over poly(acrylic acid)45 (≈15 m2/g), the xenon chemical shifts were obtained as a function of sample temperature and pressure and interpreted in terms of rapid exchange between gas phase xenon atoms, surface diffusing xenon atoms, and an average sticking time for xenon on the polymer surface. Using a virial-type expansion for the xenon shifts, the data were analyzed ultimately so as to yield a surface diffusion coefficient, determined to be 3.3 × 10-9 m2/s.

H ) AB‚S I B + γN B‚S B + R[KzSz + 1/2(K+S- + K-S+)] (4) where B, I B S, N B, and K B are the alkali metal nuclear spin angular momentum, the metal atom electron spin angular momentum,

13248 J. Phys. Chem., Vol. 100, No. 31, 1996

Figure 11. Pulse sequence and schematic representation of goals for polarization transfer experiments utilizing adsorbed, optically pumped xenon gas. Given the typical proton spin diffusion coefficient in polymers, depth profiling with a resolution of a few angstroms is possible.

Similar methods were used in studies of xenon adsorbed to the surfaces of porous silicon46 and semiconducting nanocrystals.47 In the both cases it was the extraordinarily long xenon relaxation times that precluded studies with unpolarized xenon. By measuring xenon shifts over porous silicon as a function of temperature,46 the authors were able to show that various adsorbents and surface treatments were able to affect the adsorption energy for the xenon gas. In the case of CdS nanocrystals,47 multiple xenon peaks were observed, and their line widths as a function of coverage were found to be different. The authors interpreted these two peaks in terms of a domain model for the distribution of organic capping ligands. Polarized xenon gas is also useful for measurement of chemical environments where extended signal averaging is not possible due to kinetic effects. In the formation of ice particles around xenon molecules, for example, the initial clathrate hydrates form in just a few minutes; observation of the xenon NMR parameters in these systems is not possible with the usual NMR signal-averaging methodologies. With polarized xenon, however, sufficient signal-to-noise is available on a single acquisition to afford such studies.48 In this case, the authors observed multiple xenon NMR peaks whose relative intensities varied as a function of time; the multiple peaks corresponded to xenon in large and small cages. The interpretation of the data resulted in expressions for the equilibria of xenon onto ice surfaces and the kinetics of subsequent formation of the clathrate formation. 2. Polarization Transfer. The production of large quantities of polarized rare gases, especially xenon, raises the possibility of signal enhancement of other nuclei via polarization transfer methods. Figure 11 details one scheme whereby the NMR signals from surface nuclei could be obtained via crosspolarization from surface-adsorbed xenon; if highly abundant nuclei such as protons are used as an intermediate (or final) spin system for cross-polarization, then spin diffusion may be exploited for depth profiling of NMR information. Initial demonstrations of polarization transfer from optically pumped rare gas nuclei and other spins utilized low- or zerofield mixing methods.49,50 The first demonstration of crosspolarization from polarized xenon to another nucleus utilized a low-field thermal mixing method whereby a molecular mixture

Tycko and Reimer

Figure 12. Depth profiling of proton broad line signals from optically pumped xenon adsorbed on poly(triarylcarbinol). Full width at halfmaximum of Gaussian lines fit to the spectra are also shown. Adapted from ref 53, with permission.

Figure 13. Proton multiple contact interferograms and broad line signal obtained via cross-polarization from optically pumped xenon adsorbed on 30 m2 of Aerosil R812. Adapted from ref 53, with permission.

of xenon and carbon dioxide (13 C enriched) was allowed to cross-relax in a low magnetic field.50 Of particular importance in this work was the demonstration that changing the helicity of the optical pumping light results in an inversion of the carbon13 NMR signal, thus providing clear evidence for the persistence of the pumping process from metal atom to rare gas atom and from rare gas atom to cross-polarized NMR nucleus. True high-field cross-polarization from xenon to surface nuclei was achieved by monitoring the proton NMR signals of a high surface area polymer51 after cross-polarization from adsorbed, optically pumped xenon gas. The pulse sequence (Figure 11) and representative data, shown in Figure 12, show that protons may be used as a “spin-diffusion” conduit for depth profiling. In this study, long contact times resulted in proton NMR signals that were consistent with bulk measurements; surface protons, however, exhibited broader proton NMR signals for reasons which are not yet clear. Figure 13 shows the proton NMR signal obtained via crosspolarization from optically pumped, adsorbed xenon gas for the hydroxyl protons on a sample containing only 30 cm2 of surface.

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Clearly, even without combining data from multiple contacts, there is sufficient signal-to-noise in only one acquisition to perform useful chemical or materials studies. High-field cross-polarization from optically pumped xenon is subject, however, to a number of limitations.52,53 Mobility of the adsorbed xenon atoms can significantly reduce the effectiveness of cross-polarization (because of reduced dipolar couplings), although very effective CP contact can be performed multiple times when bulk diffusion brings “fresh” xenon in contact with the surface nuclei. Perhaps the most difficult issue is the dispersion of xenon itself on the surface of the sample. Xenon aggregation on the surface, or xenon “snow” forming prior to adsorption, severely limits the amount of surface in contact with the polarized xenon. Furthermore, one must be very careful about introduction of paramagnetic species on the surface; rapid spin-lattice relaxation of polarized xenon would preclude multiple contact cross-polarization methods and perhaps the single contact CP studies as well. Further polarization transfer studies of surface nuclei will clearly depend upon a deeper understanding and appreciation of the subtleties of rare gas adsorption and diffusion on surfaces. 3. Imaging. Polarized rare gases have also been used for NMR imaging studies, both directly via modern MRI techniques and indirectly through the sensitivity of xenon NMR to chemical environment. Again, it is the sensitivity advantage afforded by optical pumping that is exploited. The bulk diamagnetic susceptibility of solid xenon is quite large compared to that of most nuclei. Thin films of xenon on macroscopic surfaces of varying shape will therefore exhibit NMR line shapes that can be deconvoluted in terms of the geometry of the sample container.54 In this study the authors found quantitative agreement between observed “powder patterns” and calculation for thin films coating the surfaces of cylinders, spheres, and flat plates. The possible use of polarized rare gases in clinical MRI applications has also been demonstrated recently.55,56 In these studies the gas space of animal lungs was probed by addition of polarized helium-3 and 129xenon gases. The optical pumping process afforded sufficient signal-to-noise so as to allow for modest-resolution MR images to be obtained as a function of time after introduction into the animal. The authors predict that polarized rare gases may be used to selectively monitor the chemical environment or any portion of a liVing mammal. Gas phase imaging of materials has had limited application owing to the poor inherent sensitivity of NMR to low spin densities. A recent publication57 has demonstrated that optically pumped xenon gas may also be used in MRI studies of void spaces in phantom as well as aerogel materials. In this case the authors show 0.1 mm resolution studies are possible; rapid diffusion of freshly polarized gas through materials allows for repolarization, leading to the use of signal averaging methods. D. Future Outlook. Future exploitation of optically polarized gases will depend upon solution to a number of technological and scientific issues. Routine preparation and long-term storage of polarized rare gas atoms will surely improve accessibility to the scientific community. In this regard stable, low-cost laser sources of polarized light would be helpful, as well as a thorough understanding of the dominant relaxation mechanisms (and their field dependances) for a variety of optical cell surface coatings. It would be extremely interesting if vendors were to make available rapid delivery of “bottles” of polarized gases; in this context a number of researchers would exploit the high polarizations for solution, solids, and imaging studies. Gas phase NMR studies of reactive systems, such as flames and gas discharges, may be realized, as well as dilute

solution studies in system of biological and/or medical interest. Finally, we note that many atoms, or even molecules, may be prepared with non-Boltzmann populations of nuclear spin states; the criterion outlined in Figure 7 need not be restricted to atomic systems. IV. Summary and Conclusions The work cited above demonstrates that optical pumping of nuclear spin polarizations, originally a subject of interest primarily from the standpoint of photophysics and spin physics, has progressed in recent years to the point of being a useful tool in NMR investigations of structures, dynamics, and electronic properties of a wide variety of systems. OPNMR studies of GaAs/AlGaAs quantum wells have had a real impact on our understanding of the properties of quantum-confined twodimensional electron systems. These studies have stimulated a great deal of subsequent experimental and theoretical work by condensed matter physicists, who are by no means magnetic resonance specialists. Future OPNMR and ODNMR studies of semiconductors and semiconductor heterostructures are likely to produce additional information about defect structures, strains, and internal electric fields. Optical pumping of noble gases has provided a means of applying NMR in studies of the surface properties of low-surface-area materials, including synthetic organic polymers and semiconductor nanocrystals. The use of optically pumped 3 He and 129 Xe is currently one of the most active areas for research in medical magnetic resonance imaging. The growth of interest and activity in optical pumping of nuclear spin polarizations will undoubtedly continue for at least the next several years. The existing techniques and level of understanding are sufficient to be the basis for many new applications. However, activity in optical pumping could conceivably accelerate substantially if there is progress in either of two fundamental areas. The first is the development of new processes by which optically pumped nuclear spin polarization can be transferred from an initially polarized medium to an initially unpolarized system of interest. One conceivable example of this might be the transfer of polarization from an optically pumped semiconductor substrate to an organic overlayer, such as a biological membrane. The second area is the identification of new materials, compounds, or systems in which significant optical pumping effects can be generated.3 An intriguing series of experiments in which highly selective optical pumping effects are observed in photosynthetic bacterial reaction centers has been reported recently.58 Since many details of the mechanism of optical pumping in these experiments, as well as in the OPNMR studies of semiconductor heterostructures described above, remain mysterious, and since systematic searches for optical pumping effects in other systems have not been carried out, it seems possible that new classes of organic and inorganic systems that exhibit large optical pumping effects may exist but remain undiscovered. Acknowledgment. J.A.R. wishes to thank Drs. Holly Gaede and Henry Long for the opportunity to serve on their thesis committees; Figures 8, 12, and 13 are taken from Dr. Gaede’s thesis. J.A.R. also wishes to thank Matt Augustine and Kurt Zilm for preprints of their work and Dr. Augustine for pointing out ref 3. J.A.R. is Camille and Henry Dreyfus TeacherScholar. R.T. wishes to thank S. E. Barrett, G. Dabbagh, L. N. Pfeiffer, and K. W. West for their many contributions to the OPNMR studies of GaAs/AlGaAs quantum wells. R.T. also wishes to acknowledge the support of this work by AT&T Bell Laboratories.

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