Weak ferromagnetism and spiral spin structures in honeycomb Hubbard planes

TL;DR

This paper analyzes the spin wave spectrum of weak ferromagnetic phases in the honeycomb Hubbard model, revealing instabilities towards spiral spin structures and discussing disorder effects relevant to ferromagnetism in irradiated graphite.

Contribution

It derives the spin wave spectrum using Hartree Fock-RPA and uncovers a transition to spiral spin structures influenced by lattice geometry and electron density.

Findings

Identification of spin wave branches in the honeycomb lattice.

Discovery of an instability towards spiral spin structures at high electron densities.

Discussion of disorder effects on ferromagnetism in related materials.

Abstract

Within the Hartree Fock- RPA analysis, we derive the spin wave spectrum for the weak ferromagnetic phase of the Hubbard model on the honeycomb lattice. Assuming a uniform magnetization, the polar (optical) and acoustic branches of the spin wave excitations are determined. The bipartite lattice geometry produces a q-dependent phase difference between the spin wave amplitudes on the two sub-lattices. We also find an instability of the uniform weakly magnetized configuration to a weak antiferromagnetic spiraling spin structure, in the lattice plane, with wave vector Q along the Gamma-K direction, for electron densities n>0.6. We discuss the effect of diagonal disorder on both the creation of electron bound states, enhancement of the density of states, and the possible relevance of these effects to disorder induced ferromagnetism, as observed in proton irradiated graphite.