1. ESR Intensity and Anisotropy of Nanoscale Molecular Magnet V15 IIS, U. Tokyo, Manabu Machida RIKEN, Toshiaki Iitaka Dept. of Phys., Seiji Miyashita Fa3-4 (LT1175) August 12, 2005, Florida, USA

2. Nanoscale Molecular Magnet V15 (http://lab-neel.grenoble.cnrs.fr/) Vanadiums provide fifteen 1/2 spins. [A. Mueller and J. Doering (1988)] Dzyaloshinsky- Moriya (DM) interaction?

3. Outline of The Talk ■ A new O(N) algorithm for ESR. ■ Temperature dependence of ESR intensity. ◆ We reproduce the experimental data. ◆ The effect of DM is not clearly seen. ■ESR intensity at very low temperatures. ◆ The intensity is prominently affected by DM. ◆ The deviation due to DM is estimated as Part I Part II

4. Hamiltonian and Intensity

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

6. Our New Method DCEM (The Double Chebyshev Expansion Method) (1) Speed and memory of O(N). (2) Random vector and Chebyshev polynomial. (3) No systematic error. (4) The scheme of time evolution is improved from BWTDM[ T. Iitaka and T. Ebisuzaki, PRL (2003) ].

7. DCEM (1) Random phase vector

8. DCEM (2) Chebyshev polynomial expansions of the thermal and time-evolution operators. >> small 

9. Comparison with Experiment - Temperature Dependence of - [Y.Ajiro et al. (2003)] Our calculation Experiment SIM(8): Intensity by the lowest eight levels.

10. With and Without DM

11. Effect of DM at Low Temperatures With DMWithout DM Intensity ratio Calculated by SIM(8) (the lowest eight levels). : a 1/2 spin

12. Triangle Model and Its Energy Levels Produces energy levels almost equal to those of V15.

13. Intensity Ratio of Triangle Model At zero temperature up to the first order of D

14. Summary Temperature dependence of ESR intensity Intensity ratio at ultra-cold limit ③ Intensity ratio at weak fields (Mz=1/2) deviates from 1 due to DM interaction. ④ The deviation is given by M. M., T. Iitaka, and S. Miyashita, J. Phys. Soc. Jpn. Suppl. 74 (2005) 107 (cond-mat/0501439). M. M., T. Iitaka, and S. Miyashita, in preparation. ① O(N) algorithm both for speed and memory. ② We reproduce the experimental intensity.