We measured the low temperature specific heat of a sputtered $(Fe_{23AA}/Cr_{12AA})_{33}$ magnetic multilayer, as well as separate $1000AA$ thick Fe and Cr films. Magnetoresistance and magnetization measurements on the multilayer demonstrated antiparallel coupling between the Fe layers. Using microcalorimeters made in our group, we measured the specific heat for $4<T<30 K$ and in magnetic fields up to $8 T$ for the multilayer. The low temperature electronic specific heat coefficient of the multilayer in the temperature range $4<T<14 K$ is $gamma_{ML}=8.4 mJ/K^{2}g-at$. This is significantly larger than that measured for the Fe or Cr films (5.4 and $3.5 mJ/K^{2}mol$ respectively). No magnetic field dependence of $gamma_{ML}$ was observed up to $8 T$. These results can be explained by a softening of the phonon modes observed in the same data and the presence of an Fe-Cr alloy phase at the interfaces.
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