Velocity of the electron in the metal is ~ 10^6 m/S which is 1/300 the speed of light. So, If the electron's velocity is not relativistic, then how a moving electron in a material can experience an electric field as magnetic field in its rest frame and hence exhibits Spin-Orbit coupling. How can I understand this.
What you're talking about is the group velocity of electrons in a metal as a whole when exposed to an external electric filed. Electrons individually perform an orbital motion around the background nuclei which can reach to a relativistic limit especially when the nuclei are heavy with large number of protons. The result of this orbital motion is an internal magnetic field felt by electrons in their rest framework through a Zeeman-like coupling to their spins that is commonly known as the spin-orbit coupling.
What you're talking about is the group velocity of electrons in a metal as a whole when exposed to an external electric filed. Electrons individually perform an orbital motion around the background nuclei which can reach to a relativistic limit especially when the nuclei are heavy with large number of protons. The result of this orbital motion is an internal magnetic field felt by electrons in their rest framework through a Zeeman-like coupling to their spins that is commonly known as the spin-orbit coupling.
Indeed, the velocity of an electron in solid is interesting. When we talk about the relativistic effect of an electron in solid, we talk more about the movements of the electron around its nuclear, rather than the movements as a charge carrier or so. Therefore, the relativistic effect, specially the spin-orbital coupling is more atomically localised. In this case the velocity of the electron depends on the number of positive electrons in the nuclei or Z-value as mentioned by Mohammad. The (averaged) velocity of the valence electrons of heavy metal should be higher than that of the light metals based ab initio molecular dynamics simulations which employ pseudo-potentials. However, probably we need more accurate approaches to obtain the velocity of the valence electrons around the nuclei for heavy metals, Pb, as an example.
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