  In itinerant magnets, the indirect exchange coupling of
Ruderman-Kittel-Kasuya-Yosida type is known to stabilize incommensurate spin
spiral. Whereas an account of higher order spin interactions favors the
formation of a noncoplanar magnetic texture. This is manifested by the finite
Berry phase the conduction electrons accumulate when their spins follow this
texture, leading thus to the topological Hall effect. We herein utilize the
effective spin model with bilinear-biquadratic exchange interactions for
studying the formation of the magnetic hedgehog lattice, that represents a
periodic array of magnetic anti- and monopoles and has been recently observed
in the B20-type compounds, in a three-dimensional itinerant magnet. As opposed
to widely used Monte Carlo simulations, we employ a neural-network-based
approach for exploring the ground state spin configuration in a
noncentrosymmetric crystal structure. Further, we address the topological Hall
conductivity, associated with nonzero scalar spin chirality, in the itinerant
magnet due to the coupling to the spin hedgehog lattice, and provide the
evidence of magneto-optic Kerr effect.
