  The universal oscillation of the tunnel magnetoresistance (TMR) ratio as a
function of the insulating barrier thickness in crystalline magnetic tunnel
junctions (MTJs) is a long-standing unsolved problem in condensed matter
physics. To explain this, we here introduce a superposition of wave functions
with opposite spins and different Fermi momenta, based on the fact that
spin-flip scattering near the interface provides a hybridization between
majority- and minority-spin states. In a typical Fe/MgO/Fe MTJ, we solve the
tunneling problem and show that the TMR ratio oscillates with a period of
$\sim3\,$\r{A} by varying the MgO thickness, consistent with previous and
present experimental observations.
