Multiferroic Two-Dimensional Materials

The relation between unusual Mexican-hat band dispersion, ferromagnetism and ferroelasticity is investigated using a combination of analytical, first-principles and phenomenological methods. The class of material with Mexican-hat band edge is studied using the $\alpha$-SnO monolayer as a prototype. Such band edge causes a van Hove singularity diverging with $\frac{1}{\sqrt{E}}$, and in p-type material leads to spatial and/or time-reversal spontaneous symmetry breaking. We show that an unexpected multiferroic phase is obtained in a range of hole density for which the material presents ferromagnetism and ferroelasticity simultaneously.