The honeycomb quantum Heisenberg ferromagnet model with anisotropic exchange interactions*

Since the discovery of magnetism in single-layered CrI₃ about two years ago [1], research into the magnetic properties of this type of monolayer materials has ever been growing. However, a fundamental theory describing the origin of two-dimensional ferromagnetism, which is key in understanding its properties, is still missing.

We modelled these two-dimensional materials using a honeycomb quantum Heisenberg ferromagnet, accounting not only for the exchange interactions up to third nearest neighbours, but also allowing an overal exchange anisotropy. The latter turns out to be key for the ferromagnetic ordering. Here, we present analytical results that were obtained using double-time temperature-dependent Green's functions [2]. We furthermore discuss the influence of temperature, anisotropies and exchange constants on the resulting magnetization.

[1] Huang, B., et al. "Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit." Nature 546.7657 (2017): 270.
[2] Vanherck, J., Sorée, B., and Magnus, W. "Anisotropic bulk and planar Heisenberg ferromagnets in uniform, arbitrarily oriented magnetic fields." Journal of Physics: Condensed Matter 30.27 (2018): 275801.