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Systematic derivation of realistic spin models for beyond-Heisenberg solids

Markus Hoffmann and Stefan Blügel
Phys. Rev. B 101, 024418 – Published 21 January 2020

Abstract

We present a systematic derivation of effective lattice spin Hamiltonians derived from a rotationally invariant multiorbital Hubbard model including a term ensuring Hund's rule coupling. The Hamiltonians are derived down-folding the fermionic degrees of freedom of the Hubbard model into the proper low-energy spin sector using Löwdin partitioning, which will be outlined in detail for the case of two sites and two orbitals at each site. Correcting the ground state systematically up to fourth order in the hopping of electrons, we find, for spin S1, the biquadratic, three-spin, and four-spin interactions beyond the conventional Heisenberg term. Comparing the puzzling energy spectrum of the magnetic states for a single Fe monolayer on Ru(0001), obtained from density functional theory, with the spin Hamiltonians taken at the limit of classical spins, we show that the previously ignored three-spin interaction can be comparable in size to the conventional Heisenberg exchange.

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  • Received 27 September 2019

DOI:https://doi.org/10.1103/PhysRevB.101.024418

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Markus Hoffmann* and Stefan Blügel

  • Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany

  • *m.hoffmann@fz-juelich.de

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Issue

Vol. 101, Iss. 2 — 1 January 2020

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