solid-state-physics
I need to define electrical conductivity anisotropic tensor in a metal caused by Hall effect. My problem is that i don't know how to define it in case of oscillating magnetic field and static electric field. I'm using the drude model of electrical conduction, and all the books that i found show only in case of oscillating electric field and static magnetic field the opposite of what i need.
P.S. English is not my native language so sorry about my english
Consult [1] and search under Kubo formula(s). If you consider the external electric E and magnetic B field vectors as deriving from an external vector potential A, derivation of the expression for the conductivity tensor comes done to an application of the linear response theory for small variations δA in A. For orientation, you may also consult [2] (see in particular Eq. (2.14) and appendix B herein).
[1] GD Mahan, Many Particle Physics, 3rd edition (Kluwer, New York, 2000).
[2] BI Halperin, PA Lee, and N Read, Phys. Rev. B 47, 7312 (1993). https://doi.org/10.1103/PhysRevB.47.7312
I think the following article may answer your question:
Stricker, S., 1968. The Hall Effect and its Applications. Advances in Electronics and Electron Physics, 25, pp.97-143.
What is the frequency[1,2] of the (your) AC magnetic field ?
1. or, at least, a narrow frequency band of your (experimental ?) interest.
2. The Hall coefficient will become complex in your case and there are no (commercial) experimental set up for this measurement.
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