The anomalous Hall effect (AHE) in strongly disordered magnetic systems has been buried in persistent confusion despite its long history. We report the AHE in perpendicularly magnetized $L{1}_0\text{−}\mathrm{MnAl}$ epitaxial films with a variable orbital two-channel Kondo (2CK) effect arising from the strong coupling of conduction electrons and the structural disorders of two-level systems. The AHE is observed to excellently scale with ${\rho }_{\mathrm{AH}}/f=a_0{\rho }_{xx0}+b{\rho }_{xx}^2$ at high temperatures where phonon scattering prevails. In contrast, significant deviation occurs at low temperatures where the orbital 2CK effect becomes important, suggesting a negative AHE contribution. The deviation of the scaling agrees with the orbital 2CK effect in the breakdown temperatures and deviation magnitudes.

• Received 19 January 2016
• Revised 14 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.195112