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Titanates with the perovskite structure, including ferroelectrics (e.g.,BaTiO$_3$) and ferromagnetic ones (e.g., YTiO$_3$), are important functionalmaterials. Recent theoretical studies predicted multiferroic states in strainedEuTiO$_3$ and titanate superlattices, the former of which has already beenexperimental confirmed. Here, a first-principles calculation is performed toinvestigate the structural, magnetic, and electronic properties of Yhalf-substituted LaTiO3. Our results reveal that the magnetism ofY$_{0.5}$La$_{0.5}$TiO$_3$ sensitively depends on its structural detailsbecause of the inherent phase competition. The lowest energy state is theferromagnetic state, resulting in 0.25 $\mu_{\rm B}$/Ti. Furthermore, someconfigurations of Y$_{0.5}$La$_{0.5}$TiO$_3$ exhibit hybrid improperpolarizations, which can be significantly affected by magnetism, resulting inthe multiferroic properties. Because of the quenching disorder of substitution,the real Y$_{0.5}$La$_{0.5}$TiO3 material with random A-site ions may exhibitinteresting relaxor behaviors.

Possible ferrimagnetism and ferroelectricity of half-substituted rare-earth titanate: a first-principles study on Y$_{0.5}$La$_{0.5}$TiO$_3$