  In this paper, we consider logarithmic and exponential forms of nonlinear
electrodynamics as a source and obtain magnetic brane solutions of the Lovelock
gravity. Although these solutions have no curvature singularity and no horizon,
they have a conic singularity with a deficit angle. We investigate the effects
of nonlinear electrodynamics and the Lovelock gravity on the value of deficit
angle and find that various terms of Lovelock gravity do not affect deficit
angle. Next, we generalize our solutions to spinning cases with maximum
rotating parameters in arbitrary dimensions and calculate the conserved
quantities of the solutions. Finally, we consider nonlinear electrodynamics as
a correction of the Maxwell theory and investigate the properties of the
solutions.
