Spin-polarized transport in dilute magnetic semiconductors (DMS) is a fundamental phenomenon arising from the exchange interaction between localized magnetic moments and charge carriers. These materials, typically semiconductors doped with transition metal ions such as Mn, Fe, or Co, exhibit unique spin-dependent transport properties due to the strong spin-orbit coupling and exchange interactions. Key effects include the anomalous Hall effect, tunneling magnetoresistance, and spin injection efficiency, each governed by material-specific mechanisms.

The anomalous Hall effect (AHE) in DMS originates from spin-polarized carriers experiencing a transverse voltage under an applied magnetic field, distinct from the ordinary Hall effect due to Lorentz force. In DMS like GaMnAs, the AHE is primarily driven by intrinsic mechanisms related to Berry phase curvature in momentum space, as well as extrinsic skew scattering and side-jump contributions. The intrinsic contribution dominates in high-quality epitaxial GaMnAs films, where the Berry phase effect arises from spin-orbit coupling modified by the ferromagnetic order. The Hall resistivity scales with the magnetization, providing a direct probe of spin polarization. In contrast, materials like ZnMnO exhibit weaker AHE due to lower carrier mobility and localized magnetic moments, leading to extrinsic skew scattering as the dominant mechanism. The temperature dependence of AHE in DMS reflects the interplay between carrier spin polarization and magnetic order, often showing a peak near the Curie temperature where spin fluctuations maximize.

Tunneling magnetoresistance (TMR) in DMS-based heterostructures arises from spin-dependent tunneling across barriers such as AlOx or MgO. In junctions with GaMnAs electrodes, TMR ratios exceeding 100% have been observed at low temperatures, attributed to coherent tunneling of spin-polarized carriers. The TMR effect depends critically on the spin polarization at the Fermi level, which in GaMnAs can exceed 80% due to the half-metallic nature of the density of states. The tunneling process is sensitive to interfacial disorder and oxide barrier quality, with defects acting as spin-scattering centers. In II-VI DMS like ZnCoO, TMR effects are weaker due to lower spin polarization and higher defect densities, but resonant tunneling through impurity states can enhance spin selectivity. The bias dependence of TMR reveals inelastic tunneling channels at higher voltages, where magnon or phonon excitations reduce spin polarization.

Spin injection efficiency quantifies the transfer of spin-polarized carriers from a DMS into a non-magnetic semiconductor. In GaMnAs/AlGaAs heterostructures, electrical spin injection efficiencies above 90% have been achieved at cryogenic temperatures, facilitated by the closely matched conductivities and Fermi level alignment. The efficiency drops at higher temperatures due to increased spin-flip scattering and thermal depolarization. Optical pump-probe measurements in ZnMnSe/ZnSe quantum wells demonstrate spin injection efficiencies sensitive to the Schottky barrier height, with optimal values near 50% for barrier widths below 5 nm. The role of interfacial defects is critical; for example, Mn segregation at GaMnAs/GaAs interfaces creates spin-blocking layers that reduce efficiency. In oxide DMS like TiO2:Co, spin injection is hampered by low carrier concentrations, though doping strategies can improve efficiency to around 30% at room temperature.

Material-specific transport mechanisms govern these phenomena. In III-V DMS like GaMnAs, the p-d hybridization between Mn dopants and host valence bands creates spin-polarized hole carriers, leading to high conductivity and strong exchange interactions. The carrier-mediated ferromagnetism results in a strong coupling between transport and magnetic properties, with resistivity showing a peak at the Curie temperature due to critical scattering. II-VI DMS such as CdMnTe exhibit paramagnetic behavior with giant Zeeman splitting under external fields, enabling tunable spin polarization but limiting spontaneous spin order. The transport is dominated by hopping conduction between localized states at low doping levels. Oxide DMS like ZnO:Co display n-type conductivity with localized moments weakly coupled to conduction electrons, leading to low spin polarization at room temperature. The presence of oxygen vacancies further complicates transport by introducing defect states that scatter spins.

The temperature dependence of spin-polarized transport reveals distinct regimes. Below the Curie temperature, DMS like GaMnAs show metallic behavior with resistivity decreasing as T^2 due to electron-magnon scattering. In the paramagnetic phase, resistivity follows an Arrhenius law indicative of thermally activated transport. Magnetic fields can suppress spin disorder, leading to negative magnetoresistance proportional to the square of the magnetization. In contrast, insulating DMS such as ZnMnO exhibit variable range hopping conduction with a characteristic T^-1/4 dependence, where spin polarization is maintained only at very low temperatures.

Interfaces play a crucial role in spin-dependent transport. In GaMnAs/GaAs heterojunctions, the mismatch in lattice constants and work functions creates interfacial dipoles that modify band alignment and spin injection properties. Atomic-scale control during growth is essential to minimize intermixing and defect formation. For tunneling structures, the symmetry of the wavefunction matching between electrodes and barrier determines spin selectivity; MgO barriers preferentially transmit Delta1 symmetry states in Fe-based junctions, but this filtering is less effective in DMS due to complex band structures.

External perturbations such as strain, electric fields, and light can dynamically modulate spin transport. Piezoelectric strain in GaMnAs shifts the heavy-hole light-hole splitting, altering the spin-orbit coupling and AHE magnitude. Electric fields in gated structures modify carrier densities and exchange interactions, enabling non-volatile control of spin polarization. Optical excitation can generate non-equilibrium spin populations through the inverse Faraday effect or spin-dependent recombination, with relaxation times extending into nanoseconds at cryogenic temperatures.

Challenges remain in achieving high-temperature operation and integration with conventional semiconductors. The Curie temperature of most DMS is below 200 K, though advances in co-doping and heterostructure design have pushed this limit in selected materials. Contact resistance and impedance mismatch at interfaces continue to limit device performance, requiring innovative solutions such as spin filters or resonant tunneling structures. Future progress hinges on understanding and controlling defect complexes, interfacial diffusion, and strain effects at the atomic scale.