Magnetic freeze-out and anomalous Hall effect in ZrTe\(_5\)

The ultra-quantum limit is achieved when a magnetic field confines an electron gas in its lowest spin-polarised Landau level. Here we show that in this limit, electron doped ZrTe\(_5\) shows a metal-insulator transition followed by a sign change of the Hall and Seebeck effects at low temperature. We attribute this transition to a magnetic freeze-out of charge carriers on the ionised impurities. The reduction of the charge carrier density gives way to an anomalous Hall response of the spin-polarised electrons. This behaviour, at odds with the usual magnetic freeze-out scenario, occurs in this Dirac metal because of its tiny Fermi energy, extremely narrow band gap and a large \(g\)-factor. We discuss the different possible sources (intrinsic or extrinsic) for this anomalous Hall contribution.