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In the zero-field-cooled exchange bias (ZEB) effect the unidirectionalmagnetic anisotropy is set at low temperatures even when the system is cooledin the absence of external magnetic field. La$_{1.5}$Sr$_{0.5}$CoMnO$_{6}$stands out as presenting the largest ZEB reported so far, while forLa$_{1.5}$Ca$_{0.5}$CoMnO$_{6}$ the exchange bias field ($H_{EB}$) is one orderof magnitude smaller. Here we show that La$_{1.5}$Ba$_{0.5}$CoMnO$_{6}$ alsoexhibits a pronounced shift of its magnetic hysteresis loop, with intermediate$H_{EB}$ value in respect to Ca- and Sr-doped samples. In order to figure outthe microscopic mechanisms responsible for this phenomena, these compounds wereinvestigated by means of synchrotron X-ray powder diffraction, Ramanspectroscopy, muon spin rotation and relaxation, AC and DC magnetization, X-rayabsorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD). Theparent compound La$_{2}$CoMnO$_{6}$ was also studied for comparison, as areference of a non-ZEB material. Our results show that the Ba-, Ca- andSr-doped samples present a small amount of phase segregation, and that the ZEBeffect is strongly correlated to the system's structure. We also observed thatmixed valence states Co$^{2+}$/Co$^{3+}$ and Mn$^{4+}$/Mn$^{3+}$ are alreadypresent at the La$_{2}$CoMnO$_{6}$ parent compound, and thatBa$^{2+}$/Ca$^{2+}$/Sr$^{2+}$ partial substitution at La$^{3+}$ site leads to alarge increase of Co average valence, with a subtle augmentation of Mn formalvalence. Estimates of the Co and Mn valences from the $L$-edge XAS indicate thepresence of oxygen vacancies in all samples (0.05$\leq \delta \leq$0.1). OurXMCD results show a great decrease of Co moment for the doped compounds, andindicate that the shift of the hysteresis curves for these samples is relatedto uncompensated antiferromagnetic coupling between Co and Mn.

The zero-field-cooled exchange bias effect in phase-segregated La$_{2-x}$A$_{x}$CoMnO$_{6-\delta}$ (A = Ba, Ca, Sr; x = 0, 0.5)