Two-orbital spin-fermion model study of ferromagnetism in honeycomb lattice

The spin-fermion model was previously successful to describe the complex phase diagrams of colossal magnetoresistive manganites and iron-based superconductors. In recent years, two-dimensional magnets have rapidly raised up as a new attractive branch of quantum materials, which are theoretically described based on classical spin models in most studies. Alternatively, here the two-orbital spin-fermion model is established as a uniform scenario to describe the ferromagnetism in a two-dimensional honeycomb lattice. This model connects the magnetic interactions with the electronic structures. Then the continuous tuning of magnetism in these honeycomb lattices can be predicted, based on a general phase diagram. The electron/hole doping, from the empty $e_{g}$ to half-filled $e_{g}$ limit, is studied as a benchmark. Our Monte Carlo result finds that the ferromagnetic $T_{C}$ reaches the maximum at the quarter-filled case. In other regions, the linear relationship between $T_{C}$ and doping concentration provides a theoretical guideline for the experimental modulations of two-dimensional ferromagnetism tuned by ionic liquid or electrical gating.