  The zero-field-cooled exchange bias (ZEB) effect is a remarkable phenomenon
recently reported for some reentrant spin glass-like compounds. In this work,
the time-evolution of magnetization is thoroughly investigated for two ZEB
materials in order to figure out the role played by the spin glass-like phase
on such effect. La$_{1.5}$Sr$_{0.5}$CoMnO$_{6}$ and
La$_{1.5}$Ca$_{0.5}$CoMnO$_{6}$ were chosen as representative samples of ZEB
systems, since the former compound presents the largest ZEB reported so far,
while the second has a much smaller effect, despite being
structurally/chemically similar. Comprehensive magnetic measurements were
carried on both samples, and the results are discussed in terms of the amount
and time-evolution of the spin glass-like phase under the influence of a
varying field. We also propose a phenomenological model, based on the pinning
of spin glass-like moments and on the dynamics of their magnetic relaxation, to
explain the asymmetry observed in the hysteresis loops. The good agreement
between the simulated and experimental results confirms our hypothesis that the
spin glass-like phase is key to the ZEB effect.
