Numerical study on ESR of V15

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Numerical study on ESR of V15
June 27- July 1, 2005 Trieste, Italy

• IIS, U. Tokyo, Manabu Machida
• RIKEN, Toshiaki Iitaka
• Dept. of Phys., Seiji Miyashita

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Nanoscale molecular magnet V15
A. Mueller and J. Doering (1988)
Vanadiums provide fifteen 1/2 spins.
(http//lab-neel.grenoble.cnrs.fr/)
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Hamiltonian and Intensity
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The parameter set
H. De Raedt, et al., PRB 70 (2004) 064401
M. Machida, et al., JPSJ (2005) suppl.
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Difficulty
difficult!
Direct diagonalization requires memory of
Its computation time is of (e.g. S. Miyashita
et al. (1999))
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Two numerical methods

• The double Chebyshev expansion method (DCEM)
• - speed and memory of O(N)
• - all states and all temperatures
• The subspace iteration method (SIM)
• - ESR at low temperatures.

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DCEM
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ESR absorption curves
DCEM
Typical calculation time for one absorption curve
is about half a day.
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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
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DCEM (1)
Random phase vector
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DCEM (2)
Chebyshev expansions of the thermal and
time-evolution operators.
small w
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Temperature dependence of intensity
Our calculation
Experiment
Y.Ajiro et al. (2003)
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SIM
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ESR at low temperatures by SIM
Intensity ratio
We consider the lowest eight levels.
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Temperature dependence of R(T)
With DM
Without DM
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Triangle model analysis
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Energy levels with weak DM








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Intensity ratio of triangle model
At zero temperature
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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)