  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 (SCAN) exchange correlation
functional in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ 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.
