  Iron tungstate (FeWO$_4$) and manganese tungstate (MnWO$_4$) belong to a
family of wolframite-type materials that has applications in various areas,
including supercapacitors, batteries, and multiferroics. A detailed
understanding of bulk properties and defect physics in these transition-metal
tungstates has been lacking, however, impeding possible improvement of their
functional properties. Here, we report a first-principles study of FeWO$_4$ and
MnWO$_4$ using screened hybrid density-functional calculations. We find that in
both compounds the electronic structure near the band edges are predominantly
the highly localized transition-metal $d$ states, which allows for the
formation of both hole polarons at the Fe (Mn) sites and electron polarons at
the W sites. The dominant native point defects in FeWO$_4$ (MnWO$_4$) under
realistic synthesis conditions are, however, the hole polarons at the Fe (Mn)
sites and negatively charged Fe (Mn) vacancies. The presence of low-energy and
highly mobile polarons provides explanation for the good p-type conductivity
observed in experiments and the ability of the materials to store energy via a
pseudocapacitive mechanism.
