Magnetic string coupled to nonlinear electromagnetic field

We introduce a class of rotating magnetically charged string solutions of the Einstein gravity with a nonlinear electrodynamics source in four dimensions. The present solutions has no curvature singularity and no horizons but has a conic singularity and yields a spacetime with a longitudinal magnetic field. Also, we investigate the effects of nonlinearity on the properties of the solutions and find that for the special range of the nonlinear parameter, the solutions are not asymptotic AdS. We show that when the rotation parameter is nonzero, the spinning string has a net electric charge that is proportional to the magnitude of the rotation parameter. Finally, we use the counterterm method inspired by AdS/CFT correspondence and calculate the conserved quantities of the solutions.