A Discussion of the Transition Metals on the Basis of Quantum Mechanics and The Electrical Conductivity of Transition Metals
Mott 1935 Article Link
Mott 1936 Article Link
Mott, N. F., 1935. A Discussion of the Transition Metals on the Basis of Quantum Mechanics. Proc. Phys. Soc. 47, 571 and Mott, N.F., 1936. The Electrical Conductivity of Transition Metals. Proc. Roy. Soc. A153, 699.
Essay about these articles
This story starts shortly, one decade, after the advent of the quantum theory of matter. In a couple of seminal papers, in 1935 and 1936, Sir Neville Mott discussed the magnetic susceptibilities and electrical conductivities of the transition-metals on the basis of this new theory. His discussion of the latter provided a model for understanding the high resistivity of these metals relative to the noble metals [copper, silver, gold], which are the neighboring elements in the periodic table. The distinguishing feature of transition-metals ions is that their electrons start to fill an outer atomic [s] shell before completely filling the inner [d] shells. While the s-electrons in an outer shell move freely throughout the metal, those in an incomplete inner shell tend to hover around the atoms and fell the strong Coulomb forces between atomic-like electrons. The latter has two effects: the inner d-shell electrons develop a magnetic moment, and these electrons are rather localized and are barely moved by electric fields. At the Fermi level, which demarcates empty from filled states in a metal, both types of electrons, s and d, coexist. This has the effect of producing an internal magnetic field in the metal such that the number of localized electrons with their spin parallel [up] to the net magnetization of the metal is different from those with their spin antiparallel [down].
Mott’s model for the itinerant s and localized d electrons has the interesting feature that while the number of itinerant s electrons at the Fermi level is pretty much the same for electrons with spin parallel and opposite to the magnetization of the metal, to create the magnetization in the metal the average energy of the d electrons with spin parallel and antiparallel must be different and their number at the Fermi level must by force of circumstance be different. While the d electrons are rather immobile, the itinerant s electrons can scatter into available states in the atomic d shell; this in turn produces different scattering rates for the spin-up and spin-down itinerant s electrons. It follows in Mott’s picture that while the number of carriers [conducting electrons] is the same for spins parallel and opposite to the magnetization [spin-up and spin-down electrons], their contributions to the electric current are different; electrons which are scattered more often contribute less to the net flow of charge. While some of the details of Mott’s model have been changed by others, e.g., the d electrons do contribute to the current but with a different responses to the electric field than the s electrons, his model in which the spin-up and spin-down electrons carry current in parallel is the basis of what is now called two-current model, or spin-dependent electrical currents in ferromagnetic metals.
a. What are the two electron bands in Mott’s picture of conduction in ferromagnetic metals?
b. Describe the different roles played by these bands in electron conduction.
c. What happens to the spin of electrons undergoing scattering in Mott’s model?
The full text of Mott, 1935 was provided with kind permission of the Institute of Physics and IOP Publishing Limited. The full text of Mott, 1936 was provided with the kind permission of The Proceedings of the Royal Society/The Royal Society.
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