  Titanates with the perovskite structure, including ferroelectrics (e.g.,
BaTiO$_3$) and ferromagnetic ones (e.g., YTiO$_3$), are important functional
materials. Recent theoretical studies predicted multiferroic states in strained
EuTiO$_3$ and titanate superlattices, the former of which has already been
experimental confirmed. Here, a first-principles calculation is performed to
investigate the structural, magnetic, and electronic properties of Y
half-substituted LaTiO3. Our results reveal that the magnetism of
Y$_{0.5}$La$_{0.5}$TiO$_3$ sensitively depends on its structural details
because of the inherent phase competition. The lowest energy state is the
ferromagnetic state, resulting in 0.25 $\mu_{\rm B}$/Ti. Furthermore, some
configurations of Y$_{0.5}$La$_{0.5}$TiO$_3$ exhibit hybrid improper
polarizations, which can be significantly affected by magnetism, resulting in
the 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 exhibit
interesting relaxor behaviors.
