  Considering the nonlinear electromagnetic field coupled to Einstein gravity
in the presence of cosmological constant, we obtain a new class of
$d$-dimensional magnetic brane solutions. This class of solutions yields a
spacetime with a longitudinal nonlinear magnetic field generated by a static
source. These solutions have no curvature singularity and no horizons but have
a conic geometry with a deficit angle $\delta \phi$. We investigate the effects
of nonlinearity on the metric function and deficit angle and also find that for
the special range of the nonlinear parameter, the solutions are not asymptotic
AdS. We generalize this class of solutions to the case of spinning magnetic
solutions, and find that when one or more rotation parameters are nonzero, the
brane has a net electric charge which is proportional to the magnitude of the
rotation parameters. Then, we use the counterterm method and compute the
conserved quantities of these spacetimes. Finally, we obtain a constrain on the
nonlinear parameter, such that the nonlinear electromagnetic field is
conformally invariant.
