  We report the discovery of a new mechanism of spontaneous generation of a
magnetic flux in a superconductor cooled through $T_c$. The sign of the
spontaneous flux changes randomly from one cooldown to the next, and follows a
Gaussian distribution. The width of the distribution increases with the size of
the temperature gradient in the sample. Our observations appear inconsistent
with the well known mechanisms of flux generation. The dependence on the
temperature gradient suggests that the flux may be generated through an
instability of the thermoelectric superconducting-normal quasiparticle
counterflow.
