TY  - JOUR
AU  - Hoffmann, Markus
AU  - Blügel, Stefan
TI  - Systematic derivation of realistic spin models for beyond-Heisenberg solids
JO  - Physical review / B
VL  - 101
IS  - 2
SN  - 2469-9950
CY  - Woodbury, NY
PB  - Inst.
M1  - FZJ-2020-01204
SP  - 024418
PY  - 2020
AB  - 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 S≥1, 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000508449400009
DO  - DOI:10.1103/PhysRevB.101.024418
UR  - https://juser.fz-juelich.de/record/874049
ER  -