Asymptotic behavior of tunneling magnetoresistance in epitaxial MgO tunnel junctions

Almost a decade after the theoretical prediction of large tunneling magnetoresistance ratio (TMR) in epitaxial Fe/MgO/Fe tunneling junctions, there is still debate on how the TMR should behave as a function of MgO thickness for thick MgO. In this Brief Report we prove that the optimistic TMR grows indefinitely with MgO thickness, and in particular, that for large MgO thicknesses it must grow linearly. This rather surprising result is obtained using straightforward and completely general asymptotic analysis and is applicable to other tunneling junctions with MgO barrier. We give a simple formula for the growth of TMR and show that it is in excellent agreement with computational studies on realistic epitaxial systems. The formula also provides a valuable test to check that numerical studies are converging to the correct answer.