Calculations have been performed

in the framework of Spin Density Functional Theory as implemented in quantum

espresso package using the

generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE)

exchange-correlation functional. Plane wave

cutoff is 45 RY, ultrasoft pseudopotentials have been used throughout the

study. Brillouin zone has been integrated with Gaussian smearing of 0.04Ry. Convergence

energy is 0.005 Ry for a 10*10*10 Monkhorst–Pack K point grid. The local magnetic moment (that is, net spin polarization on an

atom) was obtained by integrating the local density of states up to the Fermi

level for spin-up and spin-down states separately and then taking the

difference between the two.

Car-Parrinello molecular dynamics have

been used to the difference in the total

energy (etot) between relaxed and randomized positions can be used to estimate

the temperature that will be reached by the system. Usibng nose thermostat

temperature chanves have been done.

kinetic

energy cutoff 450 eV Full relaxation of magnetization was performed for

spin-polarized calculations. we used all-electron broken symmetry DFT with an

atom-centered basis 6-311G**1 and hybrid exchange-correlation

functionals B3LYP1 Ref. 481 and PBE0 Ref. 491 to verify the energetics

and existence of the magnetic phases. The main reason for these calculations

was to check if there were any strong electron correlation effects by adding

exact exchange to help reduce the self-interaction error1

the

finite-temperature magnetic properties of Co we performed standard Monte Carlo

calculations of a Heisenberg Hamiltonian with fixed-size magnetic moments by

means of the Metropolis algorithm36. We applied the magnetic force theorem44

and the Liechtenstein-Katsnelson-Antropov-Gubanov (LKAG) formalism45, 46 as

implemented in the self-consistent field multiple-scattering

Korringa-Kohn-Rostoker (KKR) Green’s function approach47, 48 to calculate the

exchange coupling constants.

A

periodic saw-toothtype potential perpendicular to the direction of the ribbon

edge is used to simulate the external electric fields (Eext) in a supercell