Chromium Clusters in an External Magnetic Field: Classical Discrete Models

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Chromium Clusters in an External Magnetic Field
Classical Discrete Models

• Kalin Arsov
• Third Year Undergraduate Student
• University of Sofia, Faculty of Physics
• Adviser Prof. Dr. Ana Proykova
• University of Sofia, Department of Atomic Physics

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Motivation

• Frustrated systems and their degenerated ground
  states
• A frustrated system has one or more rules
  for a given quantity suppressed. An example is a
  non-collinear orientation of half-integer spins
  coupling suppression of the Dirac rule
• Clusters of a specific number of AF
  (anti-ferromagnetic) interacting atoms
  super-paramagnetic states

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Previous Studies in the Field

• Axenovich and Luban, Phys. Rev. B, volume 63,
  2001 - ground state properties of
  - the magnetic moment of this giant icosahedral
  molecule is linear with B until a critical
  saturating field Bsatur.
• Proykova and Stauffer, CEJP, v.3, No.2 , 2005 -
  the magnetic moments of the atoms in the ground
  states of some Cr clusters are planar (no
  magnetic field finite temperatures)

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Studied Configurations of Cr clusters
5-atom Cr configuration
6-atom Cr configuration (a)
6-atom Cr configuration (b)
9-atom Cr configuration
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Studied Configurations of Cr clusters
11-atom Cr configuration
13-atom icosahedral configuration
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Heisenberg Models nn nnn

• Heisenberg Hamiltonian
• B external field
• J1, J2 coupling constants
• Important T0 K

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Goals

• Determine the magnetic field value that restores
  the collinearity of frustrated clusters
• Investigate the dependence of the total
  magnetization as a function of the field B
• Investigate the influence of the next-nearest
  neighbour interactions J2 in the presence of
  magnetic field B

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Results magnetization curves size dependence

• Small B m B
• B 1lt B lt B 2
• Magnetization plateaus
• Vanishing magnetic susceptibility
• Discontinuity of
• Large B saturation
• Size effect

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Results Orientation of the spins with the
increase of the field
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Results Influence of J2/J1 (Cr11)

• Plateaus
• Appearance of a spin gap if J2ltltJ1

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Conclusions

• Classical spin models exhibit magnetization
  plateaus, considered a purely quantum-mechanical
  phenomenon, in finite-size systems
• The plateaus correspond to different spin orders

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Acknowledgements

• The members of the Monte Carlo group
• Prof. Deitrich Stauffer for the code of the
  zero field Ising model