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Open quantum theory of magnetoresistance in mesoscopic magnetic materials

Magnetoresistance (MR) in magnetic materials arises from spin-exchange coupling between local moments and itinerant electrons, representing a challenging many-body open-quantum problem. Here we develop a comprehensive microscopic theory of MR within an open-quantum-system framework by solving the Liouville-von Neumann equation for a hybrid system of free electrons and local moments using the time-convolutionless projection operator method. Our approach reveals both ferromagnetic and antiferromagnetic MR as consequences of temperature- and field-dependent spin decoherence, encompassing spin relaxation and dephasing. In particular, the resistance associated with spin decoherence is governed by the order parameters of magnetic materials, such as the magnetization in ferromagnets and the Néel vector in antiferromagnets. This theory deepens the fundamental understanding of MR and offers guidance for interpreting and designing experiments on magnetic materials.