Competing exchange bias and field-induced ferromagnetism in La-doped BaFeO3

An exchange bias (EB) effect was observed in mixed valent $\mathrm{L}{\mathrm{a}}_x\mathrm{B}{\mathrm{a}}_{1\ensuremath{-}x}\mathrm{Fe}{\mathrm{O}}₃$ ($x=0.125$, 0.25, 0.33) perovskites exhibiting the antiferromagnetic (AFM) helical order among $\mathrm{F}{\mathrm{e}}⁴⁺$ ions coexisting with the ferromagnetic (FM) cluster phase in the ground state. The $\mathrm{L}{\mathrm{a}}³⁺$ ions for $\mathrm{B}{\mathrm{a}}²⁺$ site substitution, associated with increase in number of the AFM coupled $\mathrm{F}{\mathrm{e}}³⁺$ - $\mathrm{F}{\mathrm{e}}⁴⁺$ pairs as well as some $\mathrm{F}{\mathrm{e}}³⁺$ - $\mathrm{F}{\mathrm{e}}³⁺$ pairs, leads to strengthening of the AFM phase and consequently to the alteration of the EB characteristics, which depend on level of the La doping $x$. At low doping $x\ensuremath{\le}0.25$, an abnormal dependence of the EB field, ${H}_{\mathrm{EB}}$, on the cooling field, ${H}_{\mathrm{cool}}$, was found. The ${H}_{\mathrm{EB}}$ increases rapidly with increasing cooling field at low ${H}_{\mathrm{cool}}$, but it falls suddenly at cooling fields higher than 20 kOe, reducing by an order of magnitude at 90 kOe. The suppression of EB is caused by the field-induced increased volume of the FM phase, due to the transformation of the AFM helical spin structure into the FM one. Thus, low-doped $\mathrm{L}{\mathrm{a}}_x\mathrm{B}{\mathrm{a}}_{1\ensuremath{-}x}\mathrm{Fe}{\mathrm{O}}₃$ demonstrates a competition of two alternate cooling-field-induced effects, one of which leads to the EB anisotropy and another one to the enhanced ferromagnetism. In contrast, the $x=0.33$ sample, having a strong AFM constituent, shows no field-induced FM and no drop in the EB field. Accordingly, the ${H}_{\mathrm{EB}}$ vs ${H}_{\mathrm{cool}}$ dependence was found to be well explained in the framework of a model describing phase-separated AFM-FM systems, namely, the model assuming isolated FM clusters of size \ensuremath{\sim}4 nm embedded in the AFM matrix.