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

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. 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.