Scaling of the Hall effects beyond the quantum resistance threshold in oxidized CoFeB

Abstract

The ordinary and the extraordinary Hall effects were studied in gradually oxidized amorphous CoFeB ferromagnets over six orders of resistivity from the metallic to the strongly insulating regime. Polarity of the extraordinary Hall effect reverses, and the amplitude of both the ordinary and the extraordinary Hall effects increases quadratically with resistivity when resistance exceeds the quantum resistance threshold ℎ 2 2 ⁄ . The absolute value of the extraordinary Hall effect scales linearly with the ordinary one in the entire range over eight orders of magnitude between the metallic and the insulating states. The behavior differs qualitatively and quantitatively from theoretically predicted and experimentally known in other materials. PACS: 73.50.-h; 75.76.+j; 75.50.Kj 2 Introduction.Hall effect is the major source of information on a type and density of charge carriers.Regretfully, our knowledge of the phenomenon in strongly disordered conductors is quite poor as experimental data are scarce and sometimes controversial. The reason is essentially technical: for any practical arrangement of electric contacts, there is an unavoidable geometrical mismatch in positioning of transverse to current (Hall) probes.Since longitudinal electric field is usually much larger than the transverse one, a relatively small Hall signal is hidden on a background of the longitudinal resistance noise. Thus, practically no data are available on the insulating side of the metalinsulator transition for resistivity exceeding 0.1 -1 Ωcm. Absence of data does not reflect an absence of interest, as a number of puzzling phenomena, like an existence of the Hall insulator state [1-3], double reversal of Hall effect polarity [4, 5] and the giant Hall effect [6] were pointed out but remained unresolved. Availability of the extraordinary Hall effect (EHE) data in ferromagnetic systems is somewhat better, sincethe effect is usually much larger than the ordinary Hall effect and is easier to measure.An impression has been created that recent theoretical models [7 -10] provide