Including fringe fields from a nearby ferromagnet in a percolation theory of organic magnetoresistance

Abstract

Random hyperfine fields are essential to mechanisms of low-field magnetoresistance in organic semiconductors. Recent experiments have shown that another type of random field -fringe fields due to a nearby ferromagnet -can also dramatically affect the magnetoresistance. A theoretical analysis of the effect of these fringe fields is challenging, as the fringe field magnitudes and their correlation lengths are orders of magnitude larger than that of the hyperfine couplings. We extend a recent theory of organic magnetoresistance to calculate the magnetoresistance with both hyperfine and fringe fields present. This theory describes several key features of the experimental fringe-field magnetoresistance, including the applied fields where the magnetoresistance reaches extrema, the applied field range of large magnetoresistance effects from the fringe fields, and the sign of the effect.

Spin relaxation in materials lacking coherent charge transport

“…In this article we generalize our previous work 15 with organic semiconductors to describe spin relaxation in a broader range of regimes of incoherent charge transport, focusing on amorphous semiconductors such as silicon (a-Si) and germanium (a-Ge) to showcase our results. This is done by explicit calculations of spin lifetimes and coherence times using continuous-time random walk (CTRW) theory 31,32 as well as with Monte-Carlo simulations.…”

“…15 Some physical intuition regarding this result can be obtained by noting that P(t) = Φ(t)/γ 2 . By recalling that Φ(t) is the probability that a hop has not taken place up to time t, we see that the polarization decays as carriers hop in agreement with what is true from low disorder case.…”

“…which shows that spin polarization is characterized by algebraic decay. 15 Figure 5 displays the results of our CTRW theory (black solid line from numerical Laplace inversion) and analytic asymptotic expression (dotted line). A large discrepancy appears between the Multiple Trapping and Hopping models, though the qualitative features (algebraic decay) are identical.…”

“…Considerably less attention has been directed towards spin relaxation in systems where charge transport occurs through incoherent motion. These largely focused on organic (non-crystalline) semiconductors [8][9][10][12][13][14][15] , due to their small spin-orbit interaction, affordability, and large room temperature spin-dependent effects 16 . Spin transport in disordered crystalline semiconductors has been used as a diagnostic tool for very small numbers of defects in semiconductor junctions using electrically-detected magnetic resonance 17 , but has not drawn the same attention to fundamental mechanisms in macroscopic materials as these other systems.…”

ΔBmechanism for fringe-field organic magnetoresistance

“…An explanation based on mixing of spin states of a spin pair on adjacent sites prior to their reaction ("two-site model") by differently oriented magnetic fields at these sites was dismissed by the authors because of the large correlation length of the fringe fields, resulting in almost completely aligned fields at adjacent sites. On the other hand, Harmon et al recently suggested the fringefield gradients might cause additional spin mixing [13]. These gradients are on the order of a few millitesla per nanometer.…”