  Motivated by the very recent fabrication of sub-10-nm-wide semiconducting
graphene nanoribbons [X. Li et al., Science 319, 1229 (2008)], whose band gaps
extracted from transport measurements were fitted to density functional theory
predictions for magnetic ordering along zigzag edges that is responsible for
the insulating ground state, we compute current-voltage (I-V) characteristics
of finite-length zigzag graphene nanoribbons (ZGNR) attached to metallic
contacts. The transport properties of such devices, at source-drain bias
voltages beyond the linear response regime, are obtained using the
nonequilibrium Green function formalism combined with the mean-field version of
the Hubbard model fitted to reproduce the local spin density approximation
description of magnetic ordering. Our results indicate that magnetic ordering
and the corresponding band gap in ZGNR can be completely eliminated by passing
large enough DC current through it. The threshold voltage increases with the
ZGNR length (e.g., reaching $\approx 0.8$ V for $\simeq 13$ nm long ZGNR) which
provides possible explanation of why the recent experiments [Wang et al., Phys.
Rev. Lett. 100, 206803 (2008)] on $\sim 100$ nm long GNR field-effect
transistors with bias voltage less than 1 V did not detect the I-V curve
signatures of the band gap collapse. Thus, observation of predicted abrupt jump
in the I-V curve of two-terminal devices with short ZGNR channel and
transparent contacts will confirm its zigzag edge magnetic ordering via
all-electrical measurements, as well as a current-flow-driven
magnetic-insulator--nonmagnetic-metal nonequilibrium phase transition.
