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Numerical study on ESR of V15

June 27- July 1, 2005 Trieste, Italy. Numerical study on ESR of V15. IIS, U. Tokyo, Manabu Machida RIKEN, Toshiaki Iitaka Dept. of Phys., Seiji Miyashita. Nanoscale molecular magnet V15. [A. Mueller and J. Doering (1988)]. Vanadiums provide fifteen 1/2 spins.

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Numerical study on ESR of V15

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  1. June 27- July 1, 2005 Trieste, Italy Numerical study on ESR of V15 IIS, U. Tokyo, Manabu Machida RIKEN, Toshiaki Iitaka Dept. of Phys., Seiji Miyashita

  2. Nanoscale molecular magnet V15 [A. Mueller and J. Doering (1988)] Vanadiums provide fifteen 1/2 spins. (http://lab-neel.grenoble.cnrs.fr/)

  3. Hamiltonian and Intensity

  4. The parameter set [H. De Raedt, et al., PRB 70 (2004) 064401] [M. Machida, et al., JPSJ (2005) suppl.]

  5. Difficulty difficult! – Direct diagonalization requires memory of – Its computation time is of (e.g. S. Miyashita et al. (1999))

  6. Two numerical methods • The double Chebyshev expansion method(DCEM) -speed and memory ofO(N) - all states and all temperatures • The subspace iteration method(SIM) - ESR at low temperatures.

  7. DCEM

  8. ESR absorption curves DCEM Typical calculation time for one absorption curve is about half a day.

  9. Background of DCEM The DCEM = a slight modification of the Boltzmann-weighted time-dependent method (BWTDM). [T. Iitaka and T. Ebisuzaki, PRL (2003)] Making use of the random vector technique and the Chebyshev polynomial expansion

  10. DCEM (1) Random phase vector

  11. >> DCEM (2) Chebyshev expansions of the thermal and time-evolution operators. small w

  12. Temperature dependence of intensity Our calculation Experiment [Y.Ajiro et al. (2003)]

  13. SIM

  14. ESR at low temperatures by SIM Intensity ratio We consider the lowest eight levels.

  15. Temperature dependence of R(T) With DM Without DM

  16. Triangle model analysis

  17. Energy levels with weak DM

  18. Intensity ratio of triangle model At zero temperature

  19. Summary O(N) algorithms for the Kubo formula DCEM ■ Random vector and Chebyshev polynomials ESR of V15 ■ High to low temperatures by DCEM ■Ultra-cold temperature by SIM ■ Triangle model analysis M. Machida, T. Iitaka, and S. Miyashita, JPSJ (2005) suppl. (cond-mat/0501439)

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