Fig. 3. LDOS correlation diagram of (A) free CO, (C) Au8/O2/MgO(FC), and (B) after adsorption of a CO molecule, resulting in the complex Au8/O2/CO/MgO(FC). The results correspond to the spin singlet (S = 0) case. The electron populations of the various levels of the free and adsorbed CO molecule are given as 2e, 4e, etc., and isosurface images of the orbitals of the free CO molecules are also shown in (A). Black dashed lines indicate orbital shifts and redistribution caused by the adsorption of the CO molecule.

Fig. 4. LDOS and orbitals of the Au8/O2/CO complex adsorbed on MgO(FC). Results are shown for the spin singlet S = 0 case. The LDOS projected on the CO molecule is shown in black and that projected on the gold cluster is colored orange. EF is indicated by a dashed line. The electronic population of the orbitals of the CO molecule (found to be mainly of 2p* character), with energies in the range that overlaps the gold cluster states, provides an estimate of the back-donated charge (1.27e). Included also are isosurface images of the wave functions of the Au8/O2/CO/MgO(FC) complex, which may be identified with the indicated orbitals of CO (compare to the orbital images of the free CO molecule in Fig. 3A).

Fig. 4. LDOS and orbitals of the Au8/O2/CO complex adsorbed on MgO(FC). Results are shown for the spin singlet S = 0 case. The LDOS projected on the CO molecule is shown in black and that projected on the gold cluster is colored orange. EF is indicated by a dashed line. The electronic population of the orbitals of the CO molecule (found to be mainly of 2p* character), with energies in the range that overlaps the gold cluster states, provides an estimate of the back-donated charge (1.27e). Included also are isosurface images of the wave functions of the Au8/O2/CO/MgO(FC) complex, which may be identified with the indicated orbitals of CO (compare to the orbital images of the free CO molecule in Fig. 3A).

entire energy range of the cluster's electronically occupied spectrum (Fig. 3B, the black-shaded LDOS for energies between about

-10eV and EF). The 2p* orbitals of the CO molecule are pushed below EF, which populates this state via back-donation [that is,

Table 2. Binding energies: BE(O2), binding energy of O2 to Au8/MgO; BE(CO), binding energy of CO to Au8/O2/MgO. Excess electronic charge AQ(Au8/O2/CO) on the complex adsorbed on the (001) surface of magnesia is shown. The C-O bond length d(CO) and the C-O stretch vibrational frequency v(13CO) are shown. Results are given for the gold octamer adsorbed on a MgO(001) surface with (F center), or without (F-center-free), a surface F center, and in each case we give results calculated for two spin states, S. The calculated amount of charge transferred to a bare gold octamer cluster adsorbed on the defect-free surface is AQ(Au8/MgO) = 0.82e, and it is significantly larger for the cluster adsorbed on a surface F center; that is, AQ(Au8/MgO(FC)) = 1.44e. The excess charge AQ is calculated as described in (78).

S BE(O2) (eV) BE(CO) (eV) AQ(Au8/O2/CO) (e) d(CO) (A) v (13CO) (cirj1)

F center 0.79 1.52

F-center-free 0.79 0.87

1.155 1937

1.156 1931

1.152 1965

1.150 1994

hybridization and population of the initially unoccupied antibonding orbitals of the CO molecule through interaction with occupied surface orbitals (30-32)]. All of these features are also present in the correlation diagram of the cluster complex bound to the defect-free MgO surface (not shown here), where back-donation, however, is less pronounced. We can estimate the amount of back-donated electronic charge by integrating over the squared amplitude of the 2p* orbital located below EF. For the Au8/O2/CO bound to the F center of the MgO support, 1.27e are back-donated into the 2p* orbital, whereas a smaller degree of back-donation (1.18e) occurs for the complex bound to the undefective surface.

The above-noted difference in the degree of back-donation is manifested in a variation of the stretch frequencies of the adsorbed CO molecules, and these correlate with the aforementioned variation in the degrees of substrate-induced charging of the gold octa-mer deposited on magnesia surfaces with or without F-center defects (33). Indeed, v(CO) for the complex bound to an F-center-rich surface is measured to be redshifted by 25 to 53 cmj1 with respect to the frequency of a CO molecule bonded to the complex deposited on an F-center-free support (Fig. 1). This compares favorably with the corresponding calculated red shift; for example, from Table 2, a value of 34 cmj1 is estimated when comparing v(CO) for the C(FC-free) and B(FC) states [both corresponding to the complexes exhibiting the largest binding energy of the oxygen molecule (Table 2)].

We conclude that partial electron transfer from the F centers to the adsorbed cluster complex correlates with frequency shifts of the intramolecular vibration of adsorbed CO. In addition, these sites serve to strongly anchor the deposited clusters, thereby inhibiting their coalescence into larger inert ones. Understanding of such issues pertaining to the interactions between deposited clusters and the support surfaces, and in-

vestigations of the dependencies of such interactions on the materials' identity, their size, and their chemical and physical properties, promise to enhance progress toward the design and use of specific nanocatalytic systems.

References and Notes

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5. H. Häkkinen, S. Abbet, A. Sanchez, U. Heiz, U. Landman, Angew. Chem. Int. Ed. Engl. 42, 1297 (2003).

6. M. Mavrikakis, P. Stoltze, J. K. Norskov, Catal. Lett. 64, 101 (2000).

7. N. Lopez, J. K. Norskov, J. Am. Chem. Soc. 124, 11262 (2002).

9. C. Lemire, R. Meyer, S. Shaikhutdinov, H.-J. Freund, Angew. Chem. Int. Ed. Engl. 43, 118 (2004).

10. J. Guzman, B. C. Gates, J. Am. Chem. Soc. 126, 2672 (2004).

11. D. M. Cox, R. Brickman, K. Creegan, A. Kaldor, Z. Phys. D 19, 353 (1991).

12. W. T. Wallace, R. L. Whetten, J. Am. Chem. Soc. 124, 7499 (2002).

13. G. Mills, M. S. Gordon, H. Metiu, Chem. Phys. Lett. 359, 493 (2002).

14. B. Yoon, H. Hakkinen, U. Landman, J. Phys. Chem. A 107, 4066 (2003).

15. L. D. Socaciu et al., J. Am. Chem. Soc. 125, 10437 (2003).

16. D. Stolcic etal.,J. Am. Chem. Soc. 125, 2848 (2003).

17. Y. D. Kim, M. Fischer, G. Gantefor, Chem. Phys. Lett. 377, 170 (2003).

18. Details of the calculation methodology and comments about calculated vibrational frequencies are available on Science Online. The aforementioned theoretical ab initio predictions that charging plays a key role in the catalytic reactivity of gold clusters that are a few atoms in size has been clearly demonstrated recently through gas-phase studies. These investigations showed that only negatively charged even-numbered gold clusters bind a single O2 molecule in a superoxo-like configuration (76, 77) and that negatively charged free gold clusters are cat-alytically active for the CO-combustion reaction (75), whereas positively charged clusters are inert for the reaction, because oxygen cannot be adsorbed (7 7).

19. S. Abbet, K Judai, L Klinger, U. Heiz, Pure Appl. Chem. 74, 1527 (2002).

20. A. S. Worz, K. Judai, S. Abbet, U. Heiz, J. Am. Chem. Soc. 125, 7964 (2003).

21. C. Ruggiero, P. Hollins, J. Chem. Soc. Faraday Trans. 7 92, 4829 (1996).

22. P. Dumas, R. G. Tobin, P. L. Richards, Surf. Sci. 171, 579 (1986).

23. Y. Jugnet, F. J. Cadete Santos Aires, C. Deranlot, L. Piccolo, J. C. Bertolini, Surf. Sci. 521, L639 (2002).

24. D. R. Rainer, C. Xu, P. M. Holmblad, D. W. Goodman, J. Vac. Sci. Technol. A 15, 1653 (1997).

25. C. Winkler, A. J. Carew, S. Haq, R. Raval, Langmuir 19, 717 (2003).

26. U. Heiz, A. Sanchez, S. Abbet, W.-D. Schneider, Chem. Phys. 262, 189 (2000).

27. R. N. Barnett, U. Landman, Phys. Rev. B 48, 2081 (1993).

28. As discussed by us previously (4, 5), for the adsorbed oxygen molecule, the transferred charge partially populates the antibonding orbital of the molecule, resulting for the systems studied here in increased interatomic distance d(O2), exhibiting characteristic superoxo (about 1.35 A for S 0 1; A and C in Table 2) and peroxo (about 1.42 A for S 0 0; B and D in Table 2) O-O distances, compared to a distance of 1.24 A for the free molecule. The calculated stretch frequencies for the adsorbed O2 molecule corresponding to the stronger binding states [B (for the F-center-rich surface) and C (for the F-center-free surface) (Table 2)] are 966 and 1084 cmj1, respectively. For reference, we note that for free O2 we obtained a frequency of 1485 cmj as compared to the experimental value of 1580 cmj1. Because the peripherially adsorbed O2 is oriented parallel to the surface (Fig. 2F), it is IR-inactive. The aforementioned measured IR absorption band (at 1300 cmj1) originates from IR-active configurations of O2 molecules [for example, the ensemble of supported Au8 clusters with the molecule adsorbed on the top facet of the cluster (4)].

29. The consequent depletion of the 5a frontier orbital is often referred to in surface science studies as (forward) donation from CO to the metal (30, 37).

32. L. Lian, P. A. Hackett, D. M. Rainer, J. Chem. Phys. 99, 2583 (1993).

33. The binding energy of the molecule to the gold cluster is the result of several factors that manifest themselves simultaneously (the aforementioned hybridizations of the CO 5a and 1p orbitals with the s-d wavefunctions of the gold cluster, in addition to the contribution to the binding associated with population of the 2p* orbital). Consequently, although the C-O bond length and the CO vibrational frequency are sensitive to and correlate with the degree of back-donation into the hybridized antibonding 2p* orbital, the adsorption energy of CO to the gold cluster may not exhibit such correlation (for example, results in Table 2).

34. U.L., B.Y., and H.H. acknowledge support by the U.S. Air Force Office of Scientific Research and the U.S. Department of Energy (DOE). The computer simulations were performed on U.S. Department of Defense computers supported by the High Performance Computing Modernization Program and at DOE's National Energy Research Scientific Computing Center at the Lawrence Berkeley National Laboratory. The experiments were carried out at the University of Ulm. Support for the experiments was also obtained from the Deutsche Forschungsgemeinschaft, the Sonderforschungsbereich 569, and the Landesstiftung Baden-Württemberg. K.J. thanks the Alexander v. Humboldt foundation and the Japan Society for the Promotion of Science foundation for financial support, J.-M.A. thanks the Swiss National Science foundation, and S.A. thanks the Alexander v. Humboldt foundation for financial support. A.S.W. acknowledges support from the Graduiertenkolleg Molekulare Organisation und Dynamik an Grenz-und Oberflaüchen.

Supporting Online Material



SOM Text


17 August 2004; accepted 30 November 2004


Creating Order from Random Fluctuations in Small Spin Ensembles

We demonstrate the ability to create spin order by using a magnetic resonance force microscope to harness the naturally occurring statistical fluctuations in small ensembles of electron spins. In one method, we hyperpolarized the spin system by selectively capturing the transient spin order created by the statistical fluctuations. In a second method, we took a more active approach and rectified the spin fluctuations by applying real-time feedback to the entire spin ensemble. The created spin order can be stored in the laboratory frame for a period on the order of the longitudinal relaxation time of 30 seconds and then read out.

Creating order from random thermal fluctuations has been of interest to physicists since the development of statistical mechanics in the 19th century (1). In a more modern context, creating order in microscopic physical systems is an essential part of quantum information processing and quantum computation (2-4), where the ability to set the state of a collection of quantum objects to a desired configuration is required. The device used to perform this operation must be capable of controlling the microscopic degrees of freedom of the system while being subjected to environmental fluctuations.

Here, we take advantage of the outstanding sensitivity of magnetic resonance force microscopy (MRFM) to follow statistical Vn fluctuations in small ensembles of electron spins (5, 6) with a real-time sensitivity corresponding to 1.3mB, where mB is the Bohr magneton. The spin manipulation protocols we have developed allow us to monitor and respond to the instantaneous spin imbalance in the rotating frame. By monitoring the spin system and selectively capturing the large positive fluctuations, we have created a mean polarization corresponding to ~6|j.B in an ensemble of N , 70 spins. We also used realtime feedback to effectively cool the spin system and create a mean polarization corresponding to ~7|jb. The spin order was then transferred to the laboratory frame, stored, and later read out.

In MRFM detection, spins are manipulated by using magnetic resonance, and the longitudinal component of the magnetization is detected mechanically by measuring the interaction between the spins and a small permanent magnet attached to the end of a sensitive silicon cantilever. Typically, the

IBM Research Division, Almaden Research Center, 650 Harry Road, San Jose, CA 95120, USA.

*To whom correspondence should be addressed. E-mail: [email protected]

force generated by a spin on the cantilever is quite small. An electron spin will produce a force of only 2 x 10-18 N when subjected to a magnetic field gradient from the tip as large as 2 x 105 T m-1. Sensitivity to such small forces requires the ability to coherently manipulate spins for many cycles of the cantilever. Recently, through the use of specially engineered cantilevers that reduce disturbance to the spins (7-9), we observed longitudinal relaxation times in the rotating frame (i.e., during measurement) of up to several seconds. This has allowed us to realize a single-shot detection sensitivity approaching the single spin level (5) and the detection of an isolated electron spin by signal averaging (6).

In the experimental setup of the MRFM apparatus (Fig. 1A), a custom-fabricated mass-loaded silicon cantilever with a sub-micrometer SmCo magnetic particle attached to the tip is used as the force-sensing element (5, 6). The sample consists of vitreous silica (Suprasil W2, Heraeus Quarzglas GmbH and Company KG, Hanau, Germany) that has been irradiated by gamma rays from a 60Co source to produce spin-1/2 paramagnetic defects or E centers (unpaired electron spins on Si) (10). Experiments were performed with two different cantilever and sample combinations. In setup 1, a cantilever having a fundamental resonance frequency f = 8.7 kHz and stiffness k = 0.6 mN m-1 with a 250-nm-wide SmCo tip was used with a sample that had a spin concentration of ~1015 cm-3. In setup 2, a cantilever with f = 5.5 kHz, k = 0.11 mN m-1, and a 150-nm-wide SmCo tip was used with a ~1014 cm-3 concentration sample. The MRFM apparatus was operated in vacuum and cooled to 300 mK to reduce the thermal vibrations of the cantilever.

Electron spin resonance was excited at wrf/2p = 2.96 GHz with the use of a microwave field with amplitude B1 , 0.3 mT. In the presence of the inhomogeneous field from the tip, only those spins within a thin resonant slice satisfying the resonance condition given by B0(x, y, z) k |Btip (x,y, z) + Bextz| = wrf/f will interact with the microwave field. Here, B0(x, y, z) is the sum of the tip field, Btip(x, y, z), and a uniform external field, Bextz, produced by a superconducting magnet, and g is the gy-romagnetic ratio (g/2p = 2.8 x 1010 Hz T-1). For the vertical orientation of the cantilever shown in Fig. 1A, only those spins that are slightly to the left or right of the tip contribute to the signal. Furthermore, because of symmetry, the cantilever will respond only to the left-right imbalance of spin polarization.

To detect spins, we use the recently developed spin manipulation protocol OSCAR (oscillating cantilever-driven adiabatic reversal), which measures the shift in the fundamental frequency of the cantilever in response to tip-spin interactions (5, 6, 11). The cantilever is self-oscillated at its fundamental resonance frequency by using a piezoelectric transducer that drives the cantilever to a fixed amplitude xpk (11, 12). As the cantilever position oscillates according to xc(t) =

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