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Monte Carlo study of small deposited clusters from first principle s

Monte Carlo study of small deposited clusters from first principle s. L. Balogh , L. Udvardi, L. Szunyogh Department of Theoretical Physics, Budapest University of Technology and Economics B. Lazarovits Research Institute for Solid State Physics and Optics of the HAS. Outline.

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Monte Carlo study of small deposited clusters from first principle s

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  1. Monte Carlo study of small deposited clusters from first principles L. Balogh, L. Udvardi, L. Szunyogh Department of Theoretical Physics,Budapest University of Technology and Economics B. Lazarovits Research Institute for Solid State Physics and Optics of the HAS

  2. Outline • Motivation: high density magnetic data storage • Simulation possibilities • Solving a model Hamiltonian • MC simulation of a model Hamiltonian • MC simulation from first principles • Investigation of ferromagnetic systems • Antiferromagnetic systems • Outlook

  3. Simulation possibilities Energy as a function ofthe magnetic configuration Electronic structurecalculation Fitting of themodel Hamiltonian Model Hamiltonian Spin dynamics,MC simulation • Ground state • Finite T properties • Ground state • Finite T properties MC simulation

  4. First principles methods to explore magnetic ground state of nanoparticles Fully unconstrained LSDA FLAPWPh. Kurz, G. Bihlmayer, K. Hirai, and S. Blügel, Phys. Rev. Lett. 86, 1106 (2001) PAWD. Hobbs, G. Kresse, and J. Hafner, Phys. Rev. B 62, 11556 (2000) H. J. Gotsis, N. Kioussis, and D. A.Papaconstantopoulos, Phys. Rev. B 73, 014436 (2006) Non-collinear real-space TB-LMTO R. Robles and L. Nordström, Phys. Rev. B 74, 094403 (2006) A. Bergman, L.Nordström, A.B. Klautau, S. Frota-Pessoa and O. Eriksson, J. Phys.: Condens. Matter 19 156226 (2007) A. Bergman, L. Nordström, A.B. Klautau, S. Frota-Pessoa and O. Eriksson, Phys. Rev. B 75, 224425 (2007) Ab initio spin dynamics with constrained LSDA B. Újfalussy, B. Lazarovits, L. Szunyogh, G. M. Stocks, and P. Weinberger, Phys. Rev. B 70, 100404(R) (2004) B. Lazarovits, B. Újfalussy, L. Szunyogh, G. M. Stocks, and P. Weinberger, J. Phys.: Condens. Matter 16, S5833 (2004) G.M. Stocks, M. Eisenbach, B. Újfalussy, B. Lazarovits, L. Szunyogh and P.Weinberger, Prog. Mat. Sci. 52, 371-387 (2007) Multiscale approaches based on a model Hamiltonian mapped from first principles: Spin-cluster expansion& LLG R. Drautz and M. Fähnle, Phys. Rev. B 69, 104404 (2004); Phys. Rev. B 72, 212405 (2005) M. Fähnle, R. Drautz, R. Singer, D. Steiauf, and D. V. Berkov,Comp. Mat. Sci. 32, 118 (2005) Torque method & MC S. Polesya, O. Sipr, S. Bornemann, J. Minár, and H. Ebert,Europhys. Lett. 74, 1074 (2006) O. Sipr, S. Bornemann, J. Minár, S. Polesya, V. Popescu, A. Simunek, and H. Ebert, J. Phys.: Condens. Matter 19, 096203 (2007) O. Sipr, S. Polesya, J. Minár, and H. Ebert, J. Phys.: Condens. Matter 19, 446205 (2007)

  5. Classical Heisenberg model on-site anizotropy Cr3|Au(111) isotropic coupling symmetric antisymmetric(Dzyaloshinsky–Moriya) A. Antal et. al., PRB 77, 174429 (2008)

  6. New approach to finite temperature simulation of magnetic structure Energy as a function ofthe magnetic configuration Fully relativisticscreened KKR Lloyd formula: • Embedded cluster technique • Magnetic force theorem • Frozen potential approx. • 2nd order Taylor approximation: Derivatives: • Ground state • Finite T properties MC simulation

  7. MC simulation The SKKR method provides an approx. of the free energy up to 2nd order Restricted Metropolis algorithm:

  8. MC simulation based on ab initio calculations Initial configuration magneticconfiguration etc… controllingthe temperature MC simulation Ground state,finite temperature properties

  9. Ferromagnetic systems: Con|Au(111) Co36 Co16 Co9 canted states out of plane Orientation of the magnetization depends on the size and the shape of the clusters

  10. Ferromagnetic system: Co36|Au(111) randomconfiguration

  11. Ferromagnetic system: Co36|Au(111)

  12. Ferromagnetic system: Co36|Au(111) Reorientation at about 150 K

  13. Antiferromagnetic system: Cr36|Au(111)

  14. Conclusion, outlook • Ab initiocluster simulations • Larger clusters • Magnetization (thermodynamic average)→ • → Susceptibility (temperature dependence)→ • → Critical temperature (reorientation transition temp.) • Future plan: • Importance sampling → DLM method for layers

  15. Thank you for your attention

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