  The magnetoresistance (MR) effect, which stems from the spin-exchange
coupling between local moments and itinerant electrons in magnetic materials,
is a challenging many-body and open-quantum problem. Here, we develop a
comprehensive microscopic theory of MR from an open-quantum system perspective.
The theory not only predicts the magnetic field and temperature dependencies of
MR which are related to spin relaxation time and spin-exchange field but also
obtains the universal cosine-square law of anisotropic MR that microscopically
elucidates diverse MR effects from the magnon-induced spin flip, anisotropic
spin relaxation, and Hanle spin precession of itinerant electrons. Moreover, we
reveal fruitful behaviors of the MR effect that enable the simple detection of
the microscopic spin-exchange coupling through an electrical approach. Our
theory contributes to a deeper understanding of the fundamental physics
underlying MR and provides insights for experiments involving magnetic
materials.
