Theory of hyperfine field-induced organic magnetic field effects

In this chapter, we discuss the essence of hyperfine-field induced magnetic field effects in organic semiconductors originating from spindependent reactions between electron and hole polarons. The basic picture we employ is that of two spin-1/2 polarons, each localized on a site in the semiconductor, where one of the polarons incoherently hops to the other site, forming a spin-0 bipolaron or singlet exciton, or a spin-1 triplet exciton. We describe this process within the framework of the stochastic Liouville equation. We introduce the useful simplifications where the hyperfine coupling of the electronic spin with the surrounding nuclear spins is replaced by a classical random hyperfine field (semiclassical approximation) and where the hopping rate is assumed to be much smaller than the hyperfine precession rate (slow-hopping approximation). Within the resulting theoretical framework we discuss the magnetic field effects measured in the conduction and electroluminescence of unipolar and bipolar devices of organic semiconductors at low magnetic field, focusing in particular on the line shapes of the effects. We conclude with a theoretical discussion of a huge organic magnetoresistance that could be realized in donor-acceptor copolymers.