Topological-Insulator and Spintronic Boundary Electrodynamics for MRI RF Coils: A Theoretical Framework for Loss, Noise, and Reciprocity

MRI radiofrequency (RF) coils are ultimately limited by conductor loss, thermal noise, and reciprocity constraints associated with conventional metallic boundary conditions. These limitations become more severe at higher static fields, where operating frequencies increase and current distributions are governed by surface impedance and electromagnetic coupling in the near field. In this work we develop a theoretical framework that incorporates topological-insulator (TI) surface transport and spintronic interface physics into RF coil electrodynamics. Starting from the Dirac surface Hamiltonian and linear-response (Kubo/Drude) transport, we derive an effective complex surface impedance for TI-coated conductors and establish modified boundary conditions for tangential fields in the presence of spin--momentum locking and spin--charge coupling. We then analyze time-reversal-symmetry-breaking TI/ferromagnet interfaces, where an anomalous Hall surface conductivity produces antisymmetric admittance and enables nonreciprocal RF response. Finally, we connect these results to MRI metrics including coil quality factor, thermal noise, and receive sensitivity through reciprocity-based formulations. The framework identifies parameter regimes in which topological and spintronic surface transport could reduce RF dissipation, modify noise mechanisms, and enable coil-level nonreciprocity without conventional ferrites.