Numerical study on esr of v15
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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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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

Nanoscale molecular magnet V15

[A. Mueller and J. Doering (1988)]

Vanadiums provide

fifteen 1/2 spins.

(http://lab-neel.grenoble.cnrs.fr/)


Hamiltonian and intensity

Hamiltonian and Intensity


The parameter set

The parameter set

[H. De Raedt, et al., PRB 70 (2004) 064401]

[M. Machida, et al., JPSJ (2005) suppl.]


Difficulty

Difficulty

difficult!

– Direct diagonalization requires memory of

– Its computation time is of

(e.g. S. Miyashita et al. (1999))


Two numerical methods

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.


Numerical study on esr of v15

DCEM


Esr absorption curves

ESR absorption curves

DCEM

Typical calculation time for one absorption curve is about half a day.


Background of dcem

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


Dcem 1

DCEM (1)

Random phase vector


Dcem 2

>>

DCEM (2)

Chebyshev expansions of

the thermal and time-evolution operators.

small w


Temperature dependence of intensity

Temperature dependence of intensity

Our calculation

Experiment

[Y.Ajiro et al. (2003)]


Numerical study on esr of v15

SIM


Esr at low temperatures by sim

ESR at low temperatures by SIM

Intensity ratio

We consider

the lowest eight levels.


Temperature dependence of r t

Temperature dependence of R(T)

With DM

Without DM


Triangle model analysis

Triangle model analysis


Energy levels with weak dm

Energy levels with weak DM


Intensity ratio of triangle model

Intensity ratio of triangle model

At zero temperature


Summary

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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