Systematic derivation of realistic spin models for beyond-Heisenberg solids

The magnetic properties of many ultrathin films on metal substrates cannot be explained by the Heisenberg exchange interaction. Other known interactions, such as the biquadratic or the four-spin interaction, are also insufficient. This suggests the existence of further multispin interactions. The authors provide a systematic derivation of those interactions based on a multiband Hubbard model combined with a downfolding technique and propose a three-spin interaction. They show that it is strong in the systems with Fe on Ru(0001) and Fe on Rh(111), and even comparable in size to the Heisenberg interaction.