Study of a cobalt nanocontact

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Presentation transcript:

Study of a cobalt nanocontact László Balogh, Krisztián Palotás, Bence Lazarovits, László Udvardi, László Szunyogh Budapest, November 11―12, 2010.

Review: last slide from Uppsala

Physical system: Co[001] + 3 x 3 + 2 x 2 + 1 + 1 + 1 + 2 x 2 + 3 x 3 + Co[001]

Questions What is the (magnetic) ground state? Bloch ↔ Néel wall versus x What spin model describes the system? Isotropic Heisenberg Ab initio energy function Anisotropy

Methods Infinitesimal rotations method: 2 Screened Korringa–Kohn–Rostoker / embedded cluster method 1 1 B. Lazarovits, et. al. PRB 65, 104441 (2002) Infinitesimal rotations method: 2 ► parameters of isotropic Heisenberg model 2 A.I. Liechtenstein et al. JMMM 67, 65 (1987) 2 L. Udvardi et al. PRB 68, 104436 (2003) Monte Carlo: simulated annealing / Metropolis algorithm ► ≈ ground state Minimization of the band energy by Newton− Raphson method frozen potential approximation ► ground state ► local quantities Self-consistent energy calculation 1 ► GS energy, local quantities

Domain wall: Néel- or Bloch

Self-consistent energies Etot( Bloch ) – Etot( Néel ) > 0

Local quantities Spin momentum vs. layer (x = 1.00) Spin-, orbital momentum vs. x (cental atom)

Effect of the vacuum “envelop” Néel-wall; x = 1.00; central atom

Effect of the vacuum “envelop” Bloch-wall; x = 1.00; central atom

Model of the energy function

Mollweide-projection How to plot an function?

Mollweide-projection C. M. Quinn et al., J. Chem. Edu., 61, 569, (1984) http://en.wikipedia.org/wiki/Mollweide_projection

Energy function (mRyd) Néel (x = 1.00) Bloch (x = 1.00) (1 mRyd = 13.6 meV)

Components of the energy function Néel (x = 1.00) Bloch (x = 1.00) E – dipole – uniaxial anis. E – dipole higher order terms Rest:

Anisotropy vs. deformation Néel Bloch

Summary Infinitesimal rotations method: Screened Korringa–Kohn–Rostoker / embedded cluster method Infinitesimal rotations method: ► parameters of isotropic Heisenberg model Monte Carlo: simulated annealing / Metropolis algorithm ► ≈ ground state Minimization of the band energy by Newton− Raphson method frozen potential approximation ► ground state ► local quantities Self-consistent energy calculation ► GS energy, local quantities

Thank you for your attention László Balogh, Krisztián Palotás, Bence Lazarovits, László Udvardi, László Szunyogh

Bonus slide: quantize the spin model ► Eigenenergies (x) ? ► Degenerations (x) ?