  We investigate the nonlinear magneto-optical response in non-centrosymmetric
magnetic Weyl semimetals featuring a quadratic tilt, focusing particularly on
the influence of the van Hove singularity (VHS). In the absence of a magnetic
field, the second-order nonlinear Drude conductivity components exhibit
inflection or dip behavior across the VHS. In contrast, the second-order
nonlinear anomalous Hall conductivity, primarily governed by the Berry
curvature dipole, manifests a subtle plateau-like structure. As the tilt
strength increases, the VHS energy escalates, thereby amplifying the
VHS-induced characteristics within these second-order conductivity components.
However, in the presence of a magnetic field, we show that the resultant
magnetic moment suppresses nonlinear electron transport while enhancing
nonlinear hole transport. %both suppresses and notably enhances nonlinear
magnetic-optical transport in the electron and hole regions, respectively. This
effect serves to mitigate the impact of the VHS, resulting specifically in an
asymmetric peak or a kinked-like structure in the magnetic field-induced
contribution to the second-order nonlinear conductivity near the Weyl nodes.
These findings provide new insights into the intricate interplay among the VHS,
Berry curvature, and magnetic moment in nonlinear magneto-optical transport
through non-centrosymmetric magnetic Weyl semimetals.
