  Despite the rapid progress in the study of planar Hall effect (PHE) in recent
years, all the previous works only showed that the PHE is connected to local
geometric quantities, such as Berry curvature. Here, for the first time, we
point out that the PHE in magnetic Weyl semimetals is directly related to a
global quantity, namely, the Chern number of the Weyl point. This leads to a
remarkable consequence that the PHE observation predicted here is robust
against many system details, including the Fermi energy. The main difference
between non-magnetic and magnetic Weyl points is that the latter breaks
time-reversal symmetry T, thus generally possessing an energy tilt. Via
semiclassical Boltzmann theory, we investigate the PHE in generic magnetic Weyl
models with energy tilt and arbitrary Chern number. We find that by aligning
the magnetic and electric fields in the same direction, the trace of the PHE
conductivity contributed from Berry curvature and orbital moment is
proportional to the Chern number and the energy tilt of the Weyl points,
resulting in previously undiscovered quantized PHE plateau by varying Fermi
energy. We further confirm the existence of PHE plateaus in a more realistic
lattice model without T symmetry. By proposing a new quantized physical
quantity, our work not only provides a new tool for extracting the topological
character of the Weyl points but also suggests that the interplay between
topology and magnetism can give rise to intriguing physics.
