Oscillatory exchange coupling between iron layers separated by chromium

The exchange coupling J between Fe layers separated by nonmagnetic Cr is calculated for Fe/Cr/Fe (001) trilayer structures as a function of the spacer thickness N for several temperatures $T$. It is shown that for perfectly sharp interfaces $J(N,T)\mathrm{}$ is entirely dominated by short period oscillations for $0\hspace{0.5em}\mathrm{K}<~T<~500\hspace{0.5em}\mathrm{K}$ and N varying from $5$ to $50$ atomic planes. At zero temperature the amplitude of J decays as $N^{-3/2}$ for large values of $N.\mathrm{}$ This behavior is caused by the particular type of singularity in the nesting of the Cr Fermi which is responsible for one of the dominant short-period oscillations of $J\left(N\right)\mathrm{}$. A strong temperature dependence of the coupling strength is obtained for some values of $N,$ in excellent agreement with experiments. The effect of interface mixing on $J\left(N\right)\mathrm{}$ reduces the overall coupling strength, as well as the relative importance of the short period oscillatory components, and causes a phase shift in the oscillations of $J\left(N\right).$