  Large intrinsic anomalous Hall effect (AHE) due to the Berry curvature in
magnetic topological semimetals is attracting enormous interest due to its
fundamental importance and technological relevance. Mechanisms resulting in
large intrinsic AHE include diverging Berry curvature in Weyl semimetals,
anticrossing nodal rings or points of non-trivial bands, and noncollinear spin
structures. Here we show that a half-topological semimetal (HTS) state near a
topological critical point can provide a new mechanism for driving an
exceptionally large AHE. We reveal this through a systematic experimental and
theoretical study of the antiferromagnetic (AFM) half-Heusler compound TbPdBi.
We not only observed an unusual AHE with a surprisingly large anomalous Hall
angle {\Theta}H (tan {\Theta}H ~ 2, the largest among the antiferromagnets) in
its field-driven ferromagnetic (FM) phase, but also found a distinct Hall
resistivity peak in the canted AFM phase within a low field range, where its
isothermal magnetization is nearly linearly dependent on the field. Moreover,
we observed a nearly isotropic, giant negative magnetoresistance with a
magnitude of ~98%. Our in-depth theoretical modelling demonstrates that these
exotic transport properties originate from the HTS state. A minimal Berry
curvature cancellation between the trivial spin-up and nontrivial spin-down
bands results not only in an extremely large AHE, but it also enhances the spin
polarization of the spin-down bands substantially and thus leads to a giant
negative magnetoresistance. Our study advances the understanding of the
interplay between band topology and magnetism and offers new clues for
materials design for spintronics and other applications.
