Gauge concepts in theoretical applied physics

Gauge concept evolves in the course of nearly one century from Faraday's rather obscure electrotonic state of matter to the physically significant Yang-Mills that underpin today's standard model. As gauge theories improve, links are established with modern observations, e.g. in the Aharonov-Bohm effect, the Pancharatnam-Berry's phase, superconductivity, and quantum Hall effects. In this century, emergent gauge theory is formulated in numerous fields of applied physics like topological insulators, spintronics, and graphene. We will show in this paper the application of gauge theory in two particularly useful spin-based phenomena, namely the spin orbit spin torque and the spin Hall effect. These are important fields of study in the engineering community due to great commercial interest in the technology of magnetic memory (MRAM), and magnetic field sensors. Both spin orbit torque and spin Hall perform magnetic switching at low power and high speed. Furthermore, spin Hall is also a promising source of pure spin current, as well as a reliable form of detection mechanism for the magnetic state of a material.