  The phenomena of odd-parity magnetoresistance and the planar Hall effect are
deeply entwined with ferromagnetism. The intrinsic magnetization of the ordered
state permits these unusual and rarely observed manifestations of Onsager's
theorem when time reversal symmetry is broken at zero applied field. Here we
study two classes of ferromagnetic materials, rare-earth magnets with high
intrinsic coercivity and antiferromagnetic pyrochlores with strongly-pinned
ferromagnetic layers at domain walls, which both exhibit odd-parity
magnetoresistive behavior. The peculiar angular variation of the response with
respect to the relative alignments of the magnetization, magnetic field, and
current reveal the two underlying microscopic mechanisms:
spin-polarization-dependent scattering of a Zeeman-shifted Fermi surface and
magnetoresistance driven by the anomalous velocity physics usually associated
with the anomalous Hall effect.
