Structural and magnetic properties of epitaxially-strained Pb₂CoTeO₆ from first-principles

B-site ordered double perovskites exhibit a range of structural, electronic, and magnetic orders that can coexist within one material. For example, Pb₂CoTeO₆ has been discussed as a multiferroic candidate due to the presence of lone pair-active Pb on the A-site and magnetic Co on the B-site. However, so far no polar phase has been identified in this compound, although a sequence of phase transitions between non-polar structures with different octahedral rotation patterns has been observed as a function of temperature and pressure. In this work, we combine group theoretic analysis with density functional theory calculations to investigate the energy landscape of bulk Pb₂CoTeO₆. We find that a P2₁/c phase (a^-a^-c⁺ octahedral rotations) with A-type antiferromagnetic order is the ground state, in agreement with the experiment, and identify a competing R-3 phase (a^-a^-a^- octahedral rotations) that is slightly higher in energy. We explore the impact of epitaxial biaxial strain on the structural and magnetic phases of Pb₂CoTeO₆ and investigate whether any polar instabilities arise under strain. Our results provide new insight into strain control of the structural and magnetic properties of Pb₂CoTeO₆.