Magnetic phase diagram of single-layer CrBr3 *

We theoretically provide a magnetic phase diagram for the single-layer (SL) CrBr3, which could be effectively tuned by both strain engineering and charge doping in SL-CrBr3. Through systematical first-principles calculations and Heisenberg model Hamiltonian simulations, three different magnetic phases in SL-CrBr3, which are off-plane ferromagnetic, in-plane ferromagnetic and in-plane Neel-antiferromagnetic phases, are found in the strain and charge doping regimes we studied. Furthermore, our results show that higher order Heisenberg exchange parameters and anisotropy exchange parameters should be taken into account for accurately illustrating the magnetic phase transition in SL-CrBr3. As a result, we find from the SpinW simulation that the Curie temperature is about T (c) = 38.4 K, which is well consistent with the experimental result 34 K [Nano Lett. 19 3138 (2019)]. The findings here may be confirmed in future experiments, and may be useful for the potential applications of SL-CrBr3 in spintronics field.