We report the discovery of PSR J0952$-$0607, a 707-Hz binary millisecond pulsar which is now the fastest-spinning neutron star known in the Galactic field (i.e., outside of a globular cluster). PSR J0952$-$0607 was found using LOFAR at a central observing frequency of 135 MHz, well below the 300 MHz to 3 GHz frequencies typically used in pulsar searches. The discovery is part of an ongoing LOFAR survey targeting unassociated Fermi Large Area Telescope $gamma$-ray sources. PSR J0952$-$0607 is in a 6.42-hr orbit around a very low-mass companion ($M_mathrm{c}gtrsim0.02$ M$_odot$) and we identify a strongly variable optical source, modulated at the orbital period of the pulsar, as the binary companion. The light curve of the companion varies by 1.6 mag from $r^prime=22.2$ at maximum to $r^prime>23.8$, indicating that it is irradiated by the pulsar wind. Swift observations place a 3-$sigma$ upper limit on the $0.3-10$ keV X-ray luminosity of $L_X < 1.1 times 10^{31}$ erg s$^{-1}$ (using the 0.97 kpc distance inferred from the dispersion measure). Though no eclipses of the radio pulsar are observed, the properties of the system classify it as a black widow binary. The radio pulsed spectrum of PSR J0952$-$0607, as determined through flux density measurements at 150 and 350 MHz, is extremely steep with $alphasim-3$ (where $S propto u^{alpha}$). We discuss the growing evidence that the fastest-spinning radio pulsars have exceptionally steep radio spectra, as well as the prospects for finding more sources like PSR J0952$-$0607.
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