  Here, we present a review of the phenomenology of the spontaneous exchange
bias effect, a phenomenon in which some materials exhibit unidirectional
magnetic anisotropy even without the assistance of an external magnetic field
applied during its cooling process. We review and discuss the most critical
advances in this field of research that flourished more than a decade ago,
pointing out its main features as well as its similarities and dissimilarities
with the conventional exchange bias effect that has been vastly investigated
since the 1950 decade. Finally, we briefly overview the obstacles to
advancement in the field and discuss what we believe could be promising roads
to overcome them.
