Single-atom vacancy in monolayer phosphorene: A comprehensive study of stability and magnetism under applied strain

Highlights: • Single-atom vacancy induces magnetism in monolayer phosphorene. • Compressive strain reduces the formation energy of single vacancies in phosphorene. • Biaxial compressive strain induces ripple deformation in defective phosphorene. Using first-principles calculations based on density-functional theory we systematically investigate the effect of applied strain on the stability and on the electronic and magnetic properties of monolayer phosphorene with single-atom vacancy. We consider two types of single vacancies: the symmetric SV-$55|66$, which has a metallic and non-magnetic ground state, and the asymmetric SV-$5|9$, which is energetically more favorable and exhibits a semiconducting and magnetic character. Our results show that compressive strain up to 10%, both biaxial and uniaxial along the zigzag direction, reduces the formation energy of both single-atom vacancies with respect to the pristine configuration and can stabilize these defects in phosphorene. We found that the magnetic moment of the SV-$5|9$ system is robust under uniaxial strain in the range of −10 to +10%, and it is only destroyed under biaxial compressive strain larger than 8%, when the system also suffers a semiconductor-to-metal transition. Additionally, we found that magnetism can be induced in the SV-$55|66$ system under uniaxial compressive strain larger than 4% along the zigzag direction and under biaxial tensile strain larger than 6%. Our findings of small formation energies and non-zero magnetic moments for both SV-$5|9$ and SV-$55|66$ systems under zigzag uniaxial compressive strain larger than 4% strongly suggest that a magnetic configuration in monolayer phosphorene can be easily realized by single-vacancy formation under uniaxial compressive strain.