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Anisotropy and Dzyaloshinsky-Moriya Interaction in V15

Manabu Machida, Seiji Miyashita, and Toshiaki Iitaka. Anisotropy and Dzyaloshinsky-Moriya Interaction in V15. IIS, U. Tokyo Dept. of Physics, U. Tokyo RIKEN. V15. Recently nano-magnets have attracted a lot of attention. Among them, we study the ESR of V15. . V15. Vanadiums provide

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Anisotropy and Dzyaloshinsky-Moriya Interaction in V15

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

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

  3. Hamiltonian J=800K J2 J1

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

  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 Dynamical susceptibility: Energy absorption: Intensity (total absorption):

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

  8. Chebyshev vs Leap-frog >>

  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 Δｔ＞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 Subspace S152 S56 S8

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

  17. Method of Moments (1) • Probability function • Moments

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

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

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

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

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

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

  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.

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