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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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
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)
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)
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)
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
Ardavan, A., et al.: Will spin-relaxation times in molecular magnets permit quantum information processing? Phys. Rev. Lett. 98, 057201 (2007)
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
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)
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)
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)
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
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)
Furukawa, Y., et al.: Evidence of spin singlet ground state in the frustrated antiferromagnetic ring Cr\(_8\)Ni. Phys. Rev. B 79, 134416 (2009)
Gatteschi, D., Sessoli, R., Villain, J.: Molecular Nanomagnets. Oxford University Press, Oxford (2006)
Georgeot, B., Mila, F.: Chirality of triangular antiferromagnetic clusters as qubit. Phys. Rev. Lett. 104, 200502 (2010)
Graham, R.: Bounds of multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)
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)
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)
Kamieniarz, G., et al.: Anisotropy, geometric structure and frustration effects in molecule-based nanomagnets. Acta Phys. Pol. A 121, 992–998 (2012)
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
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
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
Lehmann, J., Gaita-Ariño, A., Coronado, E., Loss, D.: Spin qubits with electrically gated polyoxometalate molecules. Nature Nanotech. 2, 312 (2007)
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
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
Mannini, M., et al.: Magnetic memory of a single-molecule quantum magnet wired to a gold surface. Nature Mat. 8, 194 (2009)
Press, W., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C: The Art of Scintific Computing. Cambridge University Press, Cambridge (1992)
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
Timco, G., et al.: Engineering the coupling between molecular spin qubits by coordination chemistry. Nature Nanotech. 4, 173–178 (2009)
de Velde, E.V.: Concurrent Scientific Computing. Springer, New York (1994). https://doi.org/10.1007/978-1-4612-0849-5
Yao, H., et al.: An iron(III) phosphonate cluster containing a nonanuclear ring. Chem. Commun. 16, 1745–1747 (2006)
LAPACK - Linear Algebra PACKage. http://www.netlib.org/lapack/
ScaLAPACK – Scalable Linear Algebra PACKage. http://www.netlib.org/scalapack/
The Message Passing Interface (MPI) Standard. http://www.mcs.anl.gov/research/projects/mpi/
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
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)