  Kondo effect exemplifies the type of quantum fluctuations driven by strong
correlations, and its cooperation with space group symmetries underlies the
Weyl-Kondo semimetals. Because the Kondo effect of the $f$-electrons is
believed to be suppressed in a magnetic environment, Weyl-Kondo semimetals have
so far been confined to paramagnetic settings. Here we develop the theory of
magnetic Weyl-Kondo semimetal. The key of the proposed mechanism is that the
magnetic order is originated from the conduction $d$ electrons, such that the
local moments can still fluctuate. We illustrate the extreme case where the
magnetic space group symmetries prevent any magnetization on the sites with the
$f$-orbitals. In this case, hourglass Weyl-Kondo nodal lines appear when the
space group symmetry acts on the Kondo-driven low-energy excitations. We
suggest a third-order nonlinear spontaneous Hall response as a means to
diagnose this type of topological crossings. Based on the theoretical
mechanism, we explore the interplay between correlations and symmetries in
magnetic square-net materials, leading to several candidate materials with a
variety of nonlinear Hall responses. Our findings pave the way for future
experimental exploration and theoretical investigations in this new and
promising materials class as a part of an overarching effort to understand and
harness the interplay between strong correlations and topology.
