Van Hove singularity and ferromagnetic instability in phosphorene

Using Wannier function-based interpolation techniques, we present compelling numerical evidence for the presence of a saddle-point van Hove singularity at the $\Gamma $ point near the phosphorene Fermi energy. We show that in proximity of the van Hove singularity the spin susceptibility presents the logarithmic temperature dependence typical of Liftshitz phase transitions. Furthermore, we demonstrate that the critical temperature for the ferromagnetic transition can be greatly increased (up to 0.05 K) if strain along the zigzag ridges is applied. Although the ferromagnetic state would be very difficult to experimentally reach, the logarithmic temperature behaviour of the spin susceptibility due to the van Hove singularity is found to persist at much higher temperatures (up to $\sim$97 K).