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Unified theory of anomalous Hall effect, anomalous Nernst-Ettingshausen effect, and anomalous thermal Hall effect in ferromagnets

 

― intrinsic Berry-phase mechanism versus extrinsic mechanisms ―

 

 

Novel crossovers found in the quantum (T=0) anomalous Hall transport by means of the gauge-covariant Keldysh formalism

 

 

I.              Extrinsic regime in the superclean metal, where the skew-scattering (Mott-scattering) dominates over the intrinsic contribution:

 

II.         Intrinsic regime in the moderately dirty metal:

Berry-phase contribution resonantly enhanced by the avoided-crossing of band dispersions across the Fermi level.

 

III.     Dephased intrinsic regime in the dirty metal:

It is important that the behavior requires a dephasing of the Berry phase, but not necessarily the Anderson localization in 3D or the weak localization in 2D which lead to rather different behaviors [5,6].

 

 

Summary of experimental results on the scaling in the electric conductivity tensor

 

References:

1.         For the first report on the two crossovers and the associated scaling behaviors, see Shigeki Onoda, Naoyuki Sugimoto, and Naoto Nagaosa, “Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets”: Physical Review Letters 97, 126602 (2006).

2.         For the self-contained and comprehensive report on the unified theory of anomalous Hall effect as well as its application to the anomalous Nernst-Ettingshausen and Leduc-Rhigi effects, see Shigeki Onoda, Naoyuki Sugimoto, and Naoto Nagaosa, “Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets”:
Physical Review B 77, 165103 (2008). Selected as an Editors’ suggestion. The above summary of experimental data and the relevant references also included.

3.        For the gauge-covariant reformulation of the nonequilibrium Keldysh Green’s function in multi-band systems and its application to linear transport coefficients, see Shigeki Onoda, Naoyuki Sugimoto, and Naoto Nagaosa, “Theoy of Non-Equilibirum States Driven by Constant Electromagnetic Fields: Non-Commutative Quantum Mechanics in the Keldysh Formalism”: Progress of Theoretical Physics 116, 61 (2006).

4.        The first experimental verification of the crossovers and the scaling behaviors has been reported by T. Miyasato, N. Abe, T. Fujii, A. Asamitsu, S. Onoda, Y. Onose, N. Nagaosa, and Y. Tokura, “Universal scaling behavior of anomalous Hall effect and anomalous Nernst effect in itinerant ferromagnets”: Physical Review Letters 99, 086602 (2007).

5.        Weak-localization corrections to the anomalous Hall conductivity have been calculated by, for instance, V.K. Dugaev, P. Bruno, and J. Barnas, Physical Review B 64, 144423 (2001) and P. Mitra, R. Misra, A.F. Hebard, K.A. Muttalib, and P. Wölfle, Physical Review Letters 99, 046804 (2007).

6.        The phonon-assisted anomalous Hall conductivity in the localized regime has been calculated by A. A. Burkov and L. Balents, Physical Review Letters 91, 057202 (2003).

 

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Last updated: April 14, 2008.