A theory for magnetic-field effects of nonmagnetic organic semiconducting materials X. R. Wang Physics Department, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China S. J. Xie School of Physics, National Key Laboratory of Crystal Materials, Shandong University, Jinan, P. R. China (Dated: November 21, 2018) A universal mechanism for strong magnetic-field effects of nonmagnetic organic semiconductors is presented. A weak magnetic field (less than hundreds mT) can substantially change the charge carrier hopping coefficient between two neighboring organic molecules when the magnetic length is not too much longer than the molecule-molecule separation and localization length of electronic states involved. Under the illumination of lights or under a high electric field, the change of hopping coefficients leads also to the change of polaron density so that photocurrent, photoluminescence, electroluminescence, magnetoresistance and electrical-injection current become sensitive to a weak magnetic field. The present theory can not only explain all observed features, but also provide a solid theoretical basis for the widely used empirical fitting formulas. One of the long-term[1–4] unsolved fundamental issues in organic physics is the mechanism behind the strong (a few per cent) responses of electrical and optical properties of nonmagnetic organic semiconductors to a weak mag- netic field (less than hundreds mT), known as organic magnetic-field effect (OMFE). The recent revival inter- est in OMFE on the magnetoresistance, photolumines- cence, photocurrent, electroluminescence, and electrical- injection current in nonmagnetic organic semiconductors is largely due to its importance in fundamental science and technology applications[5]. Firstly, there is a belief that the OMFE can be used as a powerful experimen- tal tool to probe useful and non-useful excited processes of organic materials. Secondly, the OMFE can be used to develop new multifunctional organic devices for infor- mation, sensing and energy technologies[6]. Experiments showed that OMFE has following surprising yet universal features. 1) The OMFE appears in vast different organic semiconductors without any magnetic elements at room temperature although the possible energy level shifts due to the presence of a magnetic field are orders magnitude smaller than the thermal energy and other energy scales. 2) The electroluminescence, photocurrent, photolumines- cence, and electrical-injection current are very sensitive to weak magnetic field with both positive and negative OMFE though positive OMFE (or negative magnetore- sistance (MR) in the convention terminology) at very weak field is typically observed. 3) The OMFE can of- ten be fitted by two empirical formulas: [ B/ ( B + B$_{0}$ )] 2 and B $^{2}$/ ( B 2 + B 2 $_{0}$)[4], where B is the applied magnetic field. In the theoretical side, it is known[3, 4] that famil- iar MR mechanisms such as Lorentz force, conventional hopping MR, electron-electron interaction and weak lo- calization are highly unlikely to be the cause behind the OMFE. The current belief in the community is that the MEFS is intimately tied to spin physics involving spin configuration, spin correlation, and spin flip[5]. How- ever, there is no convincing arguments why an extremely small Zeeman energy can beat other much larger energy scales in controlling electron spin dynamics to generate this OMFE. Debate on whether excitons, biexcitons, po- larons, or bipolarons are the cause of the OMFE has been going on for many years with more confusions than any conclusion[7–11]. Even the studies on the possible roles of the hyperfine and spin-orbital interactions in the OMFE can hardly provide any clue to the answer to this standing puzzle why a field of less than hundreds mT (including contributions from hyperfine and spin-orbital interactions) can produce such big magnetic-field effects at room temperature. Both extensive experimental and theoretical studies so far are suggesting a novel explana- tion is needed. This new MR mechanism should explain not only all OMFE features, but also why the similar ef- fects does not appear in the usual inorganic nonmagnetic semiconductors. In this report, we present such a theory that does not explicitly rely on the electron spin degrees of freedom. It is showed that the OMFE originates from the substantial change of electron hopping coefficient in a magnetic field because of narrow bandwidth of nonmag- netic organic semiconductors and large (comparable to the magnetic length) molecule-molecule separation and localization length. Nonmagnetic organic semiconductors have a few dis- tinct properties that their inorganic counterparts do not have. Instead of covalent chemical bonding, organic molecules in nonmagnetic organic semiconductors are bonded by the Van der Waals force so that the electron hopping coefficient between nearby molecules is small at tenths eV, resulting in very narrow band instead of order of 10eV bandwidth for their inorganic counterparts [12]. The intramolecular excitons have strong binding energies of order of eV[5]. On the other hand, the electron and hole become polaron pair when they are located on differ- ent molecules because the intermolecular exciton binding energy is smaller than the thermal energy[5]. The elec- trical properties of an organic semiconductor are mainly arXiv:1001.1796v1 [cond-mat.mes-hall] 12 Jan 2010