# Spin Hall effect

I am trying to understand the paper by Dyakonov and Perel (1971) "Possibility of orienting electron spins with current", but cannot see how they obtain the phenomenological equations for spin density and spin current, neither of which they define. Can anyone help? Was this formulation carried over from a previous effect, and the reader is supposed to already be familiar with it? Are there any books that explain the derivation of these equations in detail?

• Did you read the review of Dyakonov himself? See arxiv.org/pdf/1210.3200.pdf I think he more or less explains where the formulae come from! – Simon Nov 18 '19 at 19:29
• Thanks Simon, that's a very helpful document. Reading through it, I think the first thing that confuses me is what is meant by "spin polarization density" (or "spin density", which is related to the former simply by a factor of 2). How is this vector quantity defined? And what are its units? – dgwp Nov 20 '19 at 20:23
• I think it is well defined in subsection 'Spin currents' of section 'Phenomology'? The units are similar to the units of an electronic current. – Simon Nov 22 '19 at 20:30
• No, this is q_{ij) you are talking about. I'm referring to the vector $\mathbf{P}$ (or $\mathbf{S}=\mathbf{P}/2$) from the section "Coupling of spin and charge currents". – dgwp Nov 23 '19 at 18:00