First-principles analysis of the effect of magnetic states on the oxygen vacancy formation energy in doped  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>La</mml:mi> <mml:mrow> <mml:mn>0.5</mml:mn> </mml:mrow

Oxygen vacancies are critical for determining the electrochemical performance of fast oxygen ion conductors. The perovskite <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>La</a:mi> <a:mrow> <a:mn>0.5</a:mn> </a:mrow> </a:msub> <a:msub> <a:mi>Sr</a:mi> <a:mrow> <a:mn>0.5</a:mn> </a:mrow> </a:msub> <a:msub> <a:mi>CoO</a:mi> <a:mn>3</a:mn> </a:msub> </a:mrow> </a:math> , known for its excellent mixed ionic-electronic conduction, has attracted significant attention due to its favorable vacancy characteristics. In this study, we employ first-principles calculations to systematically investigate the impact of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>3</b:mn> <b:mi>d</b:mi> </b:mrow> </b:math> transition-metal doping on the oxygen vacancy formation energies in the perovskite. Two magnetic states, namely the ferromagnetic and paramagnetic states, are considered in our models to capture the influence of magnetic effects on oxygen vacancy energetics. Our results reveal that the oxygen vacancy formation energies are strongly dependent on both the dopant species and the magnetic state. Notably, the magnetic states alter the vacancy formation energy in a dopant-specific manner due to double exchange interactions, indicating that relying solely on the ferromagnetic ground state may result in misleading trends in doping behavior. These findings emphasize the importance of accounting for magnetic effects when investigating oxygen vacancy properties in perovskite oxides.