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Proposed mechanisms for large intrinsic anomalous Hall effect (AHE) in magnetic topological semimetals include diverging Berry curvatures of Weyl nodes, anticrossing nodal rings or points of non-trivial bands. Here we demonstrate that a half-topological semimetal (HTS) state near a topological critical point can provide an alternative mechanism for a large AHE via systematic studies on an antiferromagnetic (AFM) half-Heusler compound TbPdBi. We not only observe a large AHE with tanΘ^H≈ 2 in its field-driven ferromagnetic (FM) phase, but also find a distinct Hall resistivity peak in its canted AFM phase. Moreover, we observe a large negative magnetoresistance with a value of ~98%. Our in-depth theoretical modelling indicates that these exotic transport properties originate from the HTS state which exhibits Berry curvature cancellation between the trivial spin-up and nontrivial spin-down bands. Our study offers alternative strategies for improved materials design for spintronics and other applications.

The family of transition-metal dipnictides has been of theoretical and experimental interest because this family hosts topological states and extremely large magnetoresistance (MR). Recently,${\mathrm{T}\mathrm{a}\mathrm{A}\mathrm{s}}_2$, a member of this family, has been predicted to support a topological crystalline insulating state. Here, by using high-resolution angle-resolved photoemission spectroscopy (ARPES), we reveal both closed and open pockets in the metallic Fermi surface (FS) and linearly dispersive bands on the ($\bar{2}01$) surface, along with the presence of extreme MR observed from magneto-transport measurements. A comparison of the ARPES results with first-principles computations shows that the linearly dispersive bands on the measured surface of${\mathrm{T}\mathrm{a}\mathrm{A}\mathrm{s}}_2$are trivial bulk bands. The absence of symmetry-protected surface state on the ($\bar{2}01$) surface indicates its topologically dark nature. The presence of open FS features suggests that the open-orbit fermiology could contribute to the extremely large MR of${\mathrm{T}\mathrm{a}\mathrm{A}\mathrm{s}}_2$.

Quantum geometry in condensed-matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in two-dimensional electron gases and the anomalous Hall effect (AHE) in ferromagnets, the quantum metric has rarely been explored. Here, we report a nonlinear Hall effect induced by the quantum metric dipole by interfacing even-layered MnBi₂Te₄with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the antiferromagnetic (AFM) spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.