Skip to main content

clique: A Parallel Tool for the Molecular Nanomagnets Simulation and Modelling

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12044))

Abstract

A powerful program for modelling the molecular nanomagnets is presented. The exact diagonalization method is used, which gives numerically accurate results. Its main bottleneck is the diagonalization time of large matrices, however it is removed by exploiting the symmetry of the compounds and implementing the method in the parallel computing environment. The diagonalization scheduling algorithm is implemented to increase the balance of the parallel processes workload. The running times of two different diagonalization procedures are compared.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Adelnia, F., et al.: Low temperature magnetic properties and spin dynamics in single crystals of Cr8Zn antiferromagnetic molecular rings. J. Chem. Phys. 143(24), 244321 (2015). https://doi.org/10.1063/1.4938086

    Article  Google Scholar 

  2. Antkowiak, M., Florek, W., Kamieniarz, G.: Universal sequence of the ground states and energy level ordering in frustrated antiferromagnetic rings with a single bond defect. Acta Phys. Pol. A 131, 890 (2017)

    Article  Google Scholar 

  3. Antkowiak, M., Kozłowski, P., Kamieniarz, G.: Zero temperature magnetic frustration in nona-membered s=3/2 spin rings with bond defect. Acta Phys. Pol. A 121, 1102–1104 (2012)

    Article  Google Scholar 

  4. Antkowiak, M., Kozłowski, P., Kamieniarz, G., Timco, G., Tuna, F., Winpenny, R.: Detection of ground states in frustrated molecular rings by in-field local magnetization profiles. Phys. Rev. B 87, 184430 (2013)

    Article  Google Scholar 

  5. Antkowiak, M., Kucharski, Ł., Kamieniarz, G.: Genetic algorithm and exact diagonalization approach for molecular nanomagnets modelling. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds.) PPAM 2015. LNCS, vol. 9574, pp. 312–320. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-32152-3_29

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  7. Atzori, M., et al.: Quantum coherence times enhancement in vanadium(IV)-based potential molecular qubits: the key role of the vanadyl moiety. J. Am. Chem. Soc. 138(35), 11234–11244 (2016). https://doi.org/10.1021/jacs.6b05574. pMID:27517709

    Article  Google Scholar 

  8. Baker, M., et al.: A classification of spin frustration in molecular magnets from a physical study of large odd-numbered-metal, odd electron rings. Proc. Natl. Acad. Sci. USA 109(47), 19113–19118 (2012)

    Article  Google Scholar 

  9. Cador, O., Gatteschi, D., Sessoli, R., Barra, A.L., Timco, G., Winpenny, R.: Spin frustration effects in an oddmembered antiferromagnetic ring and the magnetic Möbius strip. J. Magn. Magn. Mater. 290–291, 55 (2005)

    Article  Google Scholar 

  10. Florek, W., Antkowiak, M., Kamieniarz, G., Jaśniewicz-Pacer, K.: Highly degenerated ground states in some rings modeled by the ising spins with competing interactions. Acta Phys. Pol. A 133, 411 (2018)

    Article  Google Scholar 

  11. Florek, W., Antkowiak, M., Kamieniarz, G.: Sequences of ground states and classification of frustration in odd-numbered antiferromagnetic rings. Phys. Rev. B 94, 224421 (2016). https://doi.org/10.1103/PhysRevB.94.224421

    Article  Google Scholar 

  12. Florek, W., Kaliszan, L.A., Jaśniewicz-Pacer, K., Antkowiak, M.: Numerical analysis of magnetic states mixing in the Heisenberg model with the dihedral symmetry. In: EPJ Web of Conferences, vol. 40, p. 14003 (2013)

    Google Scholar 

  13. Furukawa, Y., et al.: Evidence of spin singlet ground state in the frustrated antiferromagnetic ring Cr\(_8\)Ni. Phys. Rev. B 79, 134416 (2009)

    Article  Google Scholar 

  14. Gatteschi, D., Sessoli, R., Villain, J.: Molecular Nanomagnets. Oxford University Press, Oxford (2006)

    Book  Google Scholar 

  15. Georgeot, B., Mila, F.: Chirality of triangular antiferromagnetic clusters as qubit. Phys. Rev. Lett. 104, 200502 (2010)

    Article  Google Scholar 

  16. Graham, R.: Bounds of multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)

    Article  MathSciNet  Google Scholar 

  17. Hoshino, N., Nakano, M., Nojiri, H., Wernsdorfer, W., Oshio, H.: Templating odd numbered magnetic rings: oxovanadium heptagons sandwiched by \(\beta \)-cyclodextrins. J. Am. Chem. Soc. 131, 15100 (2009)

    Article  Google Scholar 

  18. Kamieniarz, G., Florek, W., Antkowiak, M.: Universal sequence of ground states validating the classification of frustration in antiferromagnetic rings with a single bond defect. Phys. Rev. B 92, 140411(R) (2015)

    Article  Google Scholar 

  19. Kamieniarz, G., et al.: Anisotropy, geometric structure and frustration effects in molecule-based nanomagnets. Acta Phys. Pol. A 121, 992–998 (2012)

    Article  Google Scholar 

  20. Kamieniarz, G., et al.: Phenomenological modeling of molecular-based rings beyond the strong exchange limit: bond alternation and single-ion anisotropy effects. Inorg. Chim. Acta 361, 3690–3696 (2008). https://doi.org/10.1016/j.ica.2008.03.106

    Article  Google Scholar 

  21. Kozłowski, P., Antkowiak, M., Kamieniarz, G.: Frustration signatures in the anisotropic model of a nine-spin \(s=3/2\) ring with bond defect. J. Nanopart. Res. (2011). https://doi.org/10.1007/s11051-011-0337-8

    Article  Google Scholar 

  22. Kozłowski, P., Musiał, G., Antkowiak, M., Gatteschi, D.: Effective parallelization of quantum simulations: nanomagnetic molecular rings. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds.) PPAM 2013. LNCS, vol. 8385, pp. 418–427. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55195-6_39

    Chapter  Google Scholar 

  23. Lehmann, J., Gaita-Ariño, A., Coronado, E., Loss, D.: Spin qubits with electrically gated polyoxometalate molecules. Nature Nanotech. 2, 312 (2007)

    Article  Google Scholar 

  24. Luis, F., et al.: Molecular prototypes for spin-based CNOT and SWAP quantum gates. Phys. Rev. Lett. 107, 117203 (2011). https://doi.org/10.1103/PhysRevLett.107.117203

    Article  Google Scholar 

  25. Majee, M.C., et al.: Synthesis and magneto-structural studies on a new family of carbonato bridged 3d–4f complexes featuring a [CoII3LnIII3(CO3)] (Ln = La, Gd, Tb, Dy and Ho) core: slow magnetic relaxation displayed by the cobalt(II)-dysprosium(III) analogue. Dalton Trans. 47, 3425–3439 (2018). https://doi.org/10.1039/C7DT04389A

    Article  Google Scholar 

  26. Mannini, M., et al.: Magnetic memory of a single-molecule quantum magnet wired to a gold surface. Nature Mat. 8, 194 (2009)

    Article  Google Scholar 

  27. Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C: The Art of Scintific Computing. Cambridge University Press, Cambridge (1992)

    MATH  Google Scholar 

  28. Sobocińska, M., Antkowiak, M., Wojciechowski, M., Kamieniarz, G., Utko, J., Lis, T.: New tetranuclear manganese clusters with [MnII3MnIII] and[MnII2MnIII2] metallic cores exhibiting low and high spin ground state. Dalton Trans. 45, 7303–7311 (2016). https://doi.org/10.1039/C5DT04869A

    Article  Google Scholar 

  29. Timco, G., et al.: Engineering the coupling between molecular spin qubits by coordination chemistry. Nature Nanotech. 4, 173–178 (2009)

    Article  Google Scholar 

  30. de Velde, E.V.: Concurrent Scientific Computing. Springer, New York (1994). https://doi.org/10.1007/978-1-4612-0849-5

    Book  MATH  Google Scholar 

  31. Yao, H., et al.: An iron(III) phosphonate cluster containing a nonanuclear ring. Chem. Commun. 16, 1745–1747 (2006)

    Article  Google Scholar 

  32. LAPACK - Linear Algebra PACKage. http://www.netlib.org/lapack/

  33. ScaLAPACK – Scalable Linear Algebra PACKage. http://www.netlib.org/scalapack/

  34. The Message Passing Interface (MPI) Standard. http://www.mcs.anl.gov/research/projects/mpi/

  35. Zadrozny, J.M., Niklas, J., Poluektov, O.G., Freedman, D.E.: Millisecond coherence time in a tunable molecular electronic spin qubit. ACS Cent. Sci. 1(9), 488–492 (2015). https://doi.org/10.1021/acscentsci.5b00338. pMID: 27163013

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michał Antkowiak .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Antkowiak, M., Kucharski, Ł., Haglauer, M. (2020). clique: A Parallel Tool for the Molecular Nanomagnets Simulation and Modelling. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12044. Springer, Cham. https://doi.org/10.1007/978-3-030-43222-5_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-43222-5_27

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43221-8

  • Online ISBN: 978-3-030-43222-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics