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Quantum interference of tunnel trajectories between states of different spin length in a dimeric molecular nanomagnet

Abstract

Tunable electron spins in solid media are among the most promising candidates for qubits1. In this context, molecular nanomagnets have been proposed as hardware for quantum computation2. The flexibility in their synthesis represents a distinct advantage over other spin systems, enabling the systematic production of samples with desirable properties, for example, with a view to implementing quantum logic gates3,4. Here, we report the observation of quantum interference associated with tunnelling trajectories between states of different total spin length in a dimeric molecular nanomagnet. We argue that the interference is a consequence of the unique characteristics of a molecular Mn12 wheel, which behaves as a molecular dimer with weak ferromagnetic exchange coupling: each half of the molecule acts as a single-molecule magnet, whereas the weak coupling between the two halves gives rise to an extra internal spin degree of freedom within the molecule—that is, its total spin may fluctuate. More importantly, the observation of quantum interference provides clear evidence for quantum-mechanical superpositions involving entangled states shared between both halves of the wheel.

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Figure 1: Structure and magnetism of the Mn12 wheel.
Figure 2: Energy of the exchange-coupled wheel halves.
Figure 3: Quantum interference effects on the tunnel splittings.

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References

  1. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).

    Article  ADS  Google Scholar 

  2. Leuenberger, M. & Loss, D. Quantum computing in molecular magnets. Nature 410, 789–793 (2001).

    Article  ADS  Google Scholar 

  3. Wernsdorfer, W., Aliaga-Alcade, N., Hendrickson, D. N. & Christou, G. Exchange-biased quantum tunneling in a supramolecular dimer of single-molecule magnets. Nature 416, 406–409 (2002).

    Article  ADS  Google Scholar 

  4. Hill, S., Edwards, R. S., Aliaga-Alcade, N. & Christou, G. Quantum coherence in an exchange-coupled dimer of single-molecule magnets. Science 302, 1015–1018 (2003).

    Article  ADS  Google Scholar 

  5. Prokof ’ev, N. V. & Stamp, P. C. E. Theory of the spin bath. Rep. Prog. Phys. 63, 669–726 (2000).

    Article  ADS  Google Scholar 

  6. Chudnovsky, E. M. Universal decoherence in solids. Phys. Rev. Lett. 92, 120405 (2004).

    Article  ADS  Google Scholar 

  7. del Barco, E., Kent, A. D., Yang, E. C. & Hendrickson, D. N. Quantum superposition of high spin states in the single molecule magnet Ni4 . Phys. Rev. Lett. 93, 157202 (2004).

    Article  ADS  Google Scholar 

  8. Wernsdorfer, W., Mailly, D., Timco, G. A. & Winpenny, R. E. P. Resonant photon absorption and hole burning in Cr7Ni antiferromagnetic rings. Phys. Rev. B 72, 060409 (2005).

    Article  ADS  Google Scholar 

  9. Waldmann, O., Dobe, C., Mutka, H., Furrer, A. & Güdel, H. U. Neel-vector tunneling in antiferromagnetic molecular clusters. Phys. Rev. Lett. 95, 057202 (2005).

    Article  ADS  Google Scholar 

  10. Bal, M. et al. Non-equilibrium magnetization dynamics in the Fe8 single-molecule magnet induced by high-intensity microwave radiation. Europhys. Lett. 71, 110–116 (2005).

    Article  ADS  Google Scholar 

  11. Ardavan, A. et al. Will spin-relaxation times in molecular magnets permit quantum information processing? Phys. Rev. Lett. 98, 057201 (2007).

    Article  ADS  Google Scholar 

  12. Friedman, J. R., Sarachik, M. P., Tejada, J. & Ziolo, R. Macroscopic measurements of resonant magnetization tunneling in high-spin molecules. Phys. Rev. Lett. 76, 3830–3833 (1996).

    Article  ADS  Google Scholar 

  13. Thomas, L. et al. Macroscopic quantum tunneling of magnetization in a single crystal of nanomagnets. Nature 383, 145–147 (1996).

    Article  ADS  Google Scholar 

  14. Bokacheva, L., Kent, A. D. & Walters, M. A. Crossover between thermally assisted and pure quantum tunneling in molecular magnet Mn12-acetate. Phys. Rev. Lett. 85, 4803–4806 (2000).

    Article  ADS  Google Scholar 

  15. Wernsdorfer, W. & Sessoli, R. Quantum phase interference and parity effects in magnetic molecular clusters. Science 284, 133–135 (1999).

    Article  ADS  Google Scholar 

  16. del Barco, E., Kent, A. D., Rumberger, E. M., Hendrickson, D. N. & Christou, G. Symmetry of magnetic quantum tunneling in single molecule magnet Mn12-acetate. Phys. Rev. Lett. 91, 047203 (2003).

    Article  ADS  Google Scholar 

  17. del Barco, E. et al. Magnetic quantum tunneling in the single-molecule magnet Mn12-acetate. J. Low. Temp. Phys. 140, 119–174 (2005).

    Article  ADS  Google Scholar 

  18. Chudnovsky, E. M. & Tejada, J. Quantum Tunneling of the Magnetization (Oxford Univ. Press, New York, 1983).

    Google Scholar 

  19. Carretta, S. et al. Quantum oscillations of the total spin in a heterometallic antiferromagnetic ring: Evidence from neutron spectroscopy. Phys. Rev. Lett. 98, 167401 (2007).

    Article  ADS  Google Scholar 

  20. Chiolero, A. & Loss, D. Macroscopic quantum coherence in ferrimagnets. Phys. Rev. B 56, 738–746 (1997).

    Article  ADS  Google Scholar 

  21. Meier, F. & Loss, D. Electron and nuclear spin dynamics in antiferromagnetic molecular rings. Phys. Rev. Lett. 86, 5373–5376 (2001).

    Article  ADS  Google Scholar 

  22. Loss, D., DiVincenzo, D. P. & Grinstein, G. Suppression of tunneling by interference in half-integer-spin particles. Phys. Rev. Lett. 69, 3232–3235 (1992).

    Article  ADS  Google Scholar 

  23. von Delft, J. & Henley, C. L. Destructive quantum interference in spin tunneling problems. Phys. Rev. Lett. 69, 3236–3239 (1992).

    Article  ADS  Google Scholar 

  24. Garg, A. Topologically quenched tunnel splitting in spin systems without Kramers’ degeneracy. Europhys. Lett. 22, 205–210 (1993).

    Article  ADS  Google Scholar 

  25. Leuenberger, M. N. & Loss, D. Spin tunneling and topological selection rules for integer spins. Phys. Rev. B 63, 054414 (2001).

    Article  ADS  Google Scholar 

  26. Sjöqvist, E. Geometric phase for entangled spin pairs. Phys. Rev. A 62, 022109 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  27. Rumberger, E., Zakharov, L., Rheingold, A. & Hendrickson, D. N. Synthesis and magnetic properties of wheel shaped [Mn12] and [Fe6] complexes. Inorg. Chem. 43, 6531–6533 (2004).

    Article  Google Scholar 

  28. Rumberger, E. et al. Wheel shaped [Mn12] single molecule magnets. Inorg. Chem. 44, 2742–2752 (2005).

    Article  Google Scholar 

  29. Foguet-Albiol, D. et al. DFT computational rationalization of an unusual spin ground state in an Mn-12 single-molecule magnet with a low-symmetry loop structure. Angew. Chem. Int. Edn 44, 897–901 (2005).

    Article  Google Scholar 

  30. Dugan, D. M. & Hendrickson, D. N. Magnetic exchange interactions in transition-metal dimers 3: Nickel (II) di-μ-cyanato, di-μ-thiocyanato, and di-μ-selenocyanato complexes and related outer-sphere copper (II) complexes. Inorg. Chem. 13, 2929–2940 (1974).

    Article  Google Scholar 

  31. Bonesteel, N. E. Theory of anisotropic superexchange in insulating cuprates. Phys. Rev. B 47, 11302–11313 (1993).

    Article  ADS  Google Scholar 

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Acknowledgements

We gratefully acknowledge fruitful discussions with Eduardo Mucciolo and Michael Leuenberger. E.d.B., S.H. and D.N.H. acknowledge support from the US National Science Foundation (DMR0706183 and DMR0747587), (DMR0506946 and DMR0239481) and (CHE0350615), respectively.

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Contributions

C.M.R. and E.d.B. planned and carried out the experiments. S.H. helped in the interpretation of the results. S.J.S., C.C.B. and D.N.H. synthesized the compound. All authors discussed the results and contributed to their interpretation.

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Correspondence to Enrique del Barco.

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Ramsey, C., del Barco, E., Hill, S. et al. Quantum interference of tunnel trajectories between states of different spin length in a dimeric molecular nanomagnet. Nature Phys 4, 277–281 (2008). https://doi.org/10.1038/nphys886

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