Anisotropy and DzyaloshinskyMoriya Interaction in V15

1
Anisotropy and Dzyaloshinsky-Moriya Interaction
in V15

• Manabu Machida, Seiji Miyashita, and Toshiaki
  Iitaka

IIS, U. Tokyo Dept. of Physics, U. Tokyo RIKEN
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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)
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Hamiltonian
J800K
J2
J1
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Electron Spin Resonance
Energy absorption
is calculated
by means of the Kubo formula.

• Double Chebyshev Expansion Method
• Subspace Iteration Method

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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.

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Kubo Formula
Dynamical susceptibility
Energy absorption
Intensity (total absorption)
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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)
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Chebyshev vs Leap-frog
gtgt
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Test Parameters for DCEM

• J800K, J154.4K, J2160K
• DM interaction D(40K,40K,40K)

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Temperature Dependence of Intensity
Y.Ajiro et al. (2003)
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With and Without DM
32K
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Subpeak due to DM
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Subspace Iteration Method(SIM)

• Much more powerful than the naïve power method.
• Especially the SIM has an advantage at low
  temperatures.

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Method of Diagonalization

• Combination of
• (a)Anomalous Quantum Dynamics (Comp.Phys.Comm.
  Mitsutake et al. 1995)amplifies the eigenstates
  En ?tgt1
• (b)Subspace Iteration Method (F.Chatelin1988)upda
  tes the orthogonal basis sets of low energy
  subspace S of the total Hilbert space.

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Subspace and DOS
Subspace
S152
S56
S8
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Energy Levels
(DM40K,DD0)
(DM0,DD0)
Energy (K)
Energy (K)
(DM0,DD?0)
(DM40K,DD?0)
Energy (K)
Energy (K)
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Method of Moments (1)

• Probability function
• Moments

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Method of Moments (2)

• Total intensity
• Line width

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Test Parameters for SIM

• J1250K, J2350K
• DM interaction D(40K,40K,40K)

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Line Width with DM/DD
DM interaction -gt Line width diverges!
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at T0.5K
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at T32K
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at T64K
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at T128K
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at T256K
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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.