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 fifteen 1/2 spins. [I. Chiorescu et al. (2000)]
Hamiltonian J=800K J2 J1
Electron Spin Resonance Energy absorption is calculated • Double Chebyshev Expansion Method • Subspace Iteration Method by means of the Kubo formula.
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.
Kubo Formula Dynamical susceptibility: Energy absorption: Intensity (total absorption):
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)
Test Parameters for DCEM • J=800K, J1=54.4K, J2=160K • DM interaction: D=(40K,40K,40K)
Temperature Dependence of Intensity [Y.Ajiro et al. (2003)]
Subspace Iteration Method(SIM) • Much more powerful than the naïve power method. • Especially the SIM has an advantage at low temperatures.
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.
Subspace and DOS Subspace S152 S56 S8
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)
Method of Moments (1) • Probability function • Moments
Method of Moments (2) • Total intensity • Line width
Test Parameters for SIM • J1=250K, J2=350K • DM interaction: D=(40K,40K,40K)
Line Width with DM/DD DM interaction -> Line width diverges!
Peaks due to DM interaction Larmor precession at T=0.5K
Peaks due to DM interaction Larmor precession at T=32K
Peaks due to DM interaction Larmor precession at T=64K
Peaks due to DM interaction Larmor precession at T=128K
Peaks due to DM interaction Larmor precession at T=256K
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.