Effects of Magnetic Fields on the Mutual Annihilation of Triplet Excitons in Anthracene Crystals

Detailed measurements of the magnetic field dependence of the rate of mutual annihilation of triplet excitons in anthracene crystals at room temperature are presented. The field dependence consists of an increase at low fields, with a maximum at ca. 350 Oe, followed by a decrease at higher fields to less than the zero-field annihilation rate. For most field directions, a second maximum occurs at ca. 600 Oe. The amplitude of the field dependence is highly anisotropic. For fields >2000 Oe, resonances in the annihilation rate are found at +76° and -17° with respect to the $a$ axis for fields in the $\mathrm{ac}$ plane and at ±23.5° with respect to the $b$ axis in the $\mathrm{ab}$ plane. For fields <500 Oe, a second set of resonances occurs at directions bisecting the high-field resonances and at intermediate fields the two sets coexist. These results are discussed in terms of a density-matrix description of the spin states of the interacting triplet pair and of the annihilation process. The field dependence is accounted for on the basis of the field dependence of the pair spin states together with the postulate that annihilation is spin-allowed. The observed resonances result from level crossings among the pair spin states. All of the structure in the field dependence and anisotropy data is satisfactorily reproduced by calculations based on the model, although complete quantitative agreement is not achieved.