We present calculations of spin-dependent electron transport through single organic molecules bridging pairs of iron nanocontacts. We predict the magnetoresistance of these systems to switch from positive to negative with increasing applied bias for both conducting and insulating molecules. This novel inverse magnetoresistance phenomenon is robust, does not depend on the presence of impurities, and is unique to molecular and atomic nanoscale magnetic junctions. Its physical origin is identified and its relevance to experiment and to potential technological applications is discussed.

5 pages, 3 figures; published version Phys. Rev. B