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Chromium Clusters in an External Magnetic Field: Classical Discrete Models

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. Motivation.

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Chromium Clusters in an External Magnetic Field: Classical Discrete Models

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  1. 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

  2. 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

  3. 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)

  4. Studied Configurations of Cr clusters 5-atom Cr configuration 6-atom Cr configuration (a) 6-atom Cr configuration (b) 9-atom Cr configuration

  5. Studied Configurations of Cr clusters 11-atom Cr configuration 13-atom icosahedral configuration

  6. Heisenberg Models: nn & nnn • Heisenberg Hamiltonian • B – external field • J1, J2 – coupling constants • Important – T=0 K

  7. 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

  8. Results: magnetization curves – size dependence • Small B – m~ B • B 1< B < B2 • Magnetization plateaus • Vanishing magnetic susceptibility • Discontinuity of • Large B– saturation • Size effect

  9. Results: Orientation of the spins with the increase of the field

  10. Results: Influence of J2/J1 (Cr11) • Plateaus • Appearance of a spin gap if J2<<J1

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

  12. Acknowledgements • The members of the “Monte Carlo” group • Prof. Deitrich Stauffer – for the code of the zero field Ising model

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