Berlin 2015 – scientific programme

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MA: Fachverband Magnetismus

MA 14: Electronic Structure of Magnetism, Computational Magnetism

MA 14.2: Talk

Tuesday, March 17, 2015, 09:45–10:00, H 0112

Systematic derivation of an effective spin-Hamiltonian based on a modified multi-orbital Hubbard model — •Markus Hoffmann and Stefan Blügel — Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany

Theoretical descriptions of magnetic ground states, dynamical or thermodynamical properties of magnetic systems are often achieved through a multi-scale approach: DFT calculations are mapped onto a lattice spin-Hamiltonian whose properties are then evaluated carrying out Monte-Carlo or spin-dynamic simulations. For many bulk materials, the well-known Heisenberg exchange provides a sufficient description of the properties, whereas at surfaces or thin films occasionally so-called higher-order exchange interactions play a significant role. Those interactions are motivated from a single-band Hubbard model of a spin S=1/2 system. However, typical magnetic moments at surfaces are in the order of 2 or 3 µ_B equivalent to S=1 or S=3/2. In this contribution, we present a systematic derivation of effective lattice spin-Hamiltonians based on a rotational invariant multi-orbital Hubbard model including a term ensuring Hund’s rule coupling. The model is derived down-folding the degree of freedom into the proper low-energy spin sector using Löwdin’s partitioning. Up to fourth order perturbation we found for S≥1 beyond the conventional Heisenberg term a biquadratic, 3-spin and 4-spin interaction. We show that the so-far not considered 3-spin interaction explains the puzzling energy spectrum of the magnetic states for a single Fe monolayer on Rh(111).