Theory of tunneling magnetoresistance

Abstract This review is an account of theory of spin-dependent tunneling and magnetoresistive transport in magnetic tunnel junctions, covering coherent and incoherent tunneling processes, first-principles theory, and device-level phenomena. We begin with early theories predating the Fe-MgO-Fe era, then proceed to the symmetry-filtered tunneling through crystalline MgO barriers, where the Δ 1 band of bcc ferromagnets enables nearly perfect spin selectivity. The dependence of tunneling magnetoresistance (TMR) on interfacial chemistry, atomic order, and electrode symmetry is discussed in connection with both experimental observations and electronic structure calculations. Alternative barriers, including spinel oxides, ferroelectric oxides, and two-dimensional materials, are surveyed with attention to their spin-filtering efficiency, electronic compatibility, and structural tunability. Beyond coherent tunneling, we also cover theoretical models for nonspecular and inelastic scattering inside the barrier. We explain several persistent discrepancies between theory and experiment—such as the reduced antiparallel resistance and oscillatory TMR by showing how diffuse scattering equalizes the decay of all evanescent states. Inelastic effects from magnons and magnetic impurities offer additional spin–flip channels that degrade TMR with increasing bias or temperature, providing a microscopic interpretation of zero-bias anomalies and magnon-assisted tunneling. First-principles modeling, particularly density functional theory combined with nonequilibrium Green’s functions, enables quantitative simulation of spin-dependent transport under finite bias. The emerging steady-state density functional framework further generalizes this to strongly nonequilibrium conditions. Finally, the review connects microscopic tunneling physics with the macroscopic behavior of spin-transfer torque and spin–orbit torque magnetic random-access memories. Through this synthesis, we highlight the underlying principles: symmetry, scattering, and spin–orbit coupling that unify diverse material systems and device concepts. The goal is to provide both a coherent conceptual framework and a roadmap linking fundamental spin-dependent tunneling mechanisms to practical spintronic technologies.