Abstract
IN order to find whether spin-orbit interaction gives an adequate explanation of the extraordinary Hall effect in ferromagnetics, in particular in its dependence on temperature, we have treated this problem quantum-mechanically. An elementary classical calculation using as Hamiltonian shows that, to the first order in the spin orbit coupling constant, the motion of an electron with spin along the z-axis is the same as that in a fictitious magnetic field of components (s/2emc) (—∂2V/∂x∂z, —∂2V/∂2V/∂y∂z, ∂2V/∂y2. In a lattice where, on the average, the first two components are zero, and, with certain types of symmetry, in which ∂2V/∂x2 + ∂2V/∂y2 might be replaced by –(8π/3)ρ where ρ is the mean charge density met by the electron, the equivalent ‘magnetic field’ would be of the order of magnitude 4πsρ/3emc = 4πρM/3e2 where M is the probable z-component of magnetic moment per electron. This is numerically quite sufficient for the purpose, but of course the magnitude depends very strongly on the path of the electron which governs the values of ρ which it meets.
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References
Kikuchi, S., and Nordheim, L., Z. Phys., 60, 652 (1930).
Karplus, R., and Luttinger, J. M., Phys. Rev., 95, 1154 (1954).
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STRACHAN, C., MURRAY, A. Spin-Orbit Coupling and the Extraordinary Hall Effect. Nature 181, 1260 (1958). https://doi.org/10.1038/1811260a0
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DOI: https://doi.org/10.1038/1811260a0
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