  The optimal Co concentration in Fe$_{1-x}$Co$_{x}$/MgO magnetic tunnel
junctions (MTJs) that maximizes tunneling magnetoresistance (TMR) is still
under investigation. We perform a first-principles transport study on MTJs
using disordered electrodes modeled using the virtual crystal approximation
(VCA) and ordered alloys with various MgO barrier thicknesses. We find that
10-20$%$ Co concentration maximizes TMR using VCA to represent disorder in the
electrodes. This TMR peak arises due to a minority d-type interfacial resonance
state (IRS) that becomes filled with small Co doping, leading to a decrease in
antiparallel conductance. Calculations with ordered Fe$_{1-x}$Co$_{x}$
electrodes confirm the filling of this minority d-type IRS for small Co
concentrations. In addition, we construct a 10x10 supercell without VCA to
explicitly represent disorder at the Fe$_{1-x}$Co$_x$/MgO interface, which
demonstrates a quenching of the minority-d IRS and significant reduction in
available states at the Fermi level that agrees with VCA calculations. These
results explain recent experimental findings and provide implications for the
impact of IRS on conductance and TMR in Fe$_{1-x}$Co$_x$/MgO tunnel junctions.
