Counterion-Controlled Magnetization from Polaron–Bipolaron Crossover at Elevated Carrier Densities

Abstract

The optoelectronic and thermoelectric properties of organic semiconductors at ultrahigh charge densities critically depend on the relative abundance of paramagnetic polarons and magnetically silent singlet bipolarons. In this study, we employ a modified Hubbard–Ising framework that incorporates the key physical interactions governing polarons, bipolarons, and counterions in the presence of an external magnetic field to uncover the microscopic origin of spin-density evolution across different doping regimes. Our results reveal that counterion-induced electrostatics play a dominant role in driving spin pairing and the polaron-to-bipolaron crossover, outweighing the effects of electron–phonon coupling. By systematically exploring the interplay between polymer electronic structure, counterion size, counterion proximity to the backbone, spatial distribution, and intercounterion spacing, we identify key design principles governing the nonmonotonic evolution of spin density in highly doped organic semiconductors. The theory rationalizes recent experimental measurements of unpaired spin concentrations and, in doing so, establishes predictive guidelines for controlling magnetic response in purely π-conjugated carbon-based materials. More broadly, a fundamental understanding of the quantum-mechanical and structural factors governing the crossover from polarons to bipolarons provides a blueprint for the rational design of organic spintronic devices, metal-free magnets, and molecular quantum sensing technologies.