  The Hall effect arises when time reversal symmetry is broken by either
intrinsic magnetism or an external magnetic field. The latter contribution
dominates in non-magnetic materials, in which the angular dependence of the
Hall effect is typically a smooth cosine function because only the out-of-plane
projection of the field generates the in-plane transverse motion of electrons.
Here, we report the observation of an abrupt switching of the Hall effect by
field rotation in a non-magnetic material, ZrTe5. The angular dependence of the
Hall resistivity approaches a signum function, persisting down to an extremely
low field of 0.03 T. By varying the carrier density of ZrTe5 over three orders
of magnitude, we show that this singular behavior is due to the anomalous Hall
effect generated by the ultra-dilute massive Dirac carriers in the quantum
limit of Pauli paramagnetism when the Zeeman energy exceeds the Fermi energy.
Our results elucidate the origin of the anomalous Hall effect in ZrTe5, arising
owing to the spin-polarized massive Dirac electrons rather than the separation
of Weyl nodes.
