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We have studied the electronic, magnetic and linear phonon dispersionbehavior of Phosphorene monolayer using rst principle based ab initio method.Phosphorene monolayer is a semiconducting system with a dimensional dependentvariable range of band gap. Vacancy has been done to study the geometry andphysical behavior of the monolayer system. Pristine, vacancy induced monolayerand vacancy induced doped monolayer are included in the calculation. Dopantconcentration has been well checked via optimization algorithm to maintain thedilute magnetic semiconducting behavior of the monolayer system. Density ofstates and partial density of state indicates the contribution of individualorbitals in the system. Band closing nature in observed in vacancy and dopedvacancy states indicating closed dense states and metallic behavior of theperturbed phases. Both antiferromagnetic and ferromagnetic ordering is includedin our calculation to get a charm of both ordering in the physical propertiesof the system. Landau energy level distribution is mapped via Fermi surfacewith linear dispersion relation in terms of phonon vibrational density ofstates and linear dispersion relations. The results of linear phonon density ofstates corroborating with electronic density of states.

Non collinear Magnetism and Phonon Dispersion Relation in Vacancy Induced Phosphorene Monolayer