<i>Ab initio</i> description of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Bi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>CaCu</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mrow><mml:mn>8</mml:mn><mml:mo>+</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> electronic structure

Bi-based cuprate superconductors are important materials for both fundamental research and applications. As in other cuprates, the superconducting phase in the Bi compounds lies close to an antiferromagnetic phase. Our density functional theory calculations based on the strongly-constrained-and-appropriately-normed exchange correlation functional in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ reveal the persistence of magnetic moments on the copper ions for oxygen concentrations ranging from the pristine phase to the optimally hole-doped compound. We also find the existence of ferrimagnetic solutions in the heavily doped compounds, which are expected to suppress superconductivity.