1. Anisotropy and Dzyaloshinsky- Moriya Interaction in V15 Manabu Machida, Seiji Miyashita, and Toshiaki Iitaka IIS, U. Tokyo Dept. of Physics, U. Tokyo RIKEN

2. V15 Vanadiums provide fifteen 1/2 spins. Recently nano-magnets have attracted a lot of attention. Among them, we study the ESR of V15. [I. Chiorescu et al. (2000)]

3. Hamiltonian J=800K J2 J1

4. Electron Spin Resonance Energy absorptionis calculated by means of the Kubo formula. Double Chebyshev Expansion Method Subspace Iteration Method

5. Double Chebyshev Expansion Method (DCEM) The DCEM makes it possible to obtain the ESR intensity of V15 at arbitrary temperatures. Especially the DCEM has an advantage at high temperatures and strong fields.

6. Kubo Formula Intensity (total absorption): Energy absorption: Dynamical susceptibility:

7. Algorithm Trace Chebyshev polynomial expansion Time evolution Random vectors Leap-frog method ( Boltzmann-weighted time-dependent method ) Chebyshev expansion (Double Chebysev expansion method) Chebyshev expansion method also in time domain

8. Chebyshev vs Leap-frog >> 1000(T)100(T)10(T) Chebyshev 126(min) 187(min) 430(min) Leap-frog 11(min) 165(min)1326(min)

9. Test Parameters for DCEM J=800K, J1=54.4K, J2=160K DM interaction: D=(40K,40K,40K)

10. Temperature Dependence of Intensity [Y.Ajiro et al. (2003)]

11. With and Without DM 32K

12. Subpeak due to DM

13. Subspace Iteration Method (SIM) Much more powerful than the naïve power method. Especially the SIM has an advantage at low temperatures.

14. Method of Diagonalization Combination of (a)Anomalous Quantum Dynamics (Comp.Phys.Comm. Mitsutake et al. 1995) amplifies the eigenstates En Δ ｔ＞１ (b)Subspace Iteration Method (F.Chatelin1988) updates the orthogonal basis sets of low energy subspace S of the total Hilbert space.

15. Subspace and DOS S8 S56 Subspace S152

16. Energy Levels (DM=0,DD=0) (DM=40K,DD=0) (DM=0,DD≠0) (DM=40K,DD≠0) Energy (K)

17. Method of Moments (1) Probability function Moments

18. Total intensity Line width Method of Moments (2)

19. Test Parameters for SIM J1=250K, J2=350K DM interaction: D=(40K,40K,40K)

20. Line Width with DM/DD DM interaction -> Line width diverges!

21. at T=0.5K Larmor precession Peaks due to DM interaction

22. at T=32K Larmor precession Peaks due to DM interaction

23. at T=64K Larmor precession Peaks due to DM interaction

24. at T=128K Larmor precession Peaks due to DM interaction

25. at T=256K Larmor precession Peaks due to DM interaction

26. Summary The DCEM reproduces the experimentally obtained temperature dependence of the intensity. The DM interaction allows a transition between excited states that is otherwise forbidden. Measuring these ESR peaks at higher temperatures may provide a method of estimating the magnitude and direction of the DM interaction.