Van Hove singularity and ferromagnetic instability in phosphorene

TL;DR

This paper provides numerical evidence of a van Hove singularity in phosphorene that influences its magnetic properties, showing potential for strain-induced ferromagnetism and characteristic temperature-dependent spin susceptibility.

Contribution

It identifies a van Hove singularity in phosphorene and analyzes its impact on magnetic instability and susceptibility behavior under strain.

Findings

Van Hove singularity located at the Γ point near the Fermi energy.

Logarithmic temperature dependence of spin susceptibility near the singularity.

Strain can significantly increase the ferromagnetic transition temperature.

Abstract

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).