In this paper, we report on the interesting phenomenon of magnetic phase transitions (MPTs) observed under the combined influence of an electric field (E) and temperature (T) leading to a thermo-electromagnetic effect on the pristine single-layer zigzag graphene nanoribbon (szGNR). Density functional theory-based first principles calculations have been deployed for this study on the intrinsic magnetic properties of graphene. Interestingly, by tuning electric field (E) and temperature (T), three distinct magnetic phase behaviors, para-, ferro- and antiferromagnetic are exhibited in pristine szGNR. We have investigated the unrivaled positional parameters of these MPTs. MPT occurring in the system also follows a positional trend and the change in these positional parameters with regard to the size of the szGNR along with the varied E and T is studied. We propose a bow-tie schematic to induce the intrinsic magnetism in graphene and present the envisaged model of the processor application with the reported intrinsic MPT in szGNR. This fundamental insight into the intrinsic MPTs in graphene is an essential step towards developing graphene-based spin-transfer torque magnetoresistive random access memory, quantum computing devices, magnonics and spintronic memory application. © 2018 IOP Publishing Ltd.