Augmented-plane-wave calculation of indirect-exchange matrix elements for gadolinium

The exchange matrix elements between a local $4f$ moment and the conduction electrons (Ruderman-Kittel-Kasuya-Yosida exchange) have been calculated for paramagnetic gadolinium metal using nonrelativistic augmented-plane-wave wave functions. The magnitude of the matrix elements is found to be largest for $d$-like conduction electrons and is quite sensitive to their angular distribution. Because of band crossings, which cause rapid changes in wave-function character, the matrix elements cannot be well described as slowly varying functions of $\overrightarrow{\mathrm{q}}={\overrightarrow{\mathrm{k}}}^{\prime }-\overrightarrow{\mathrm{k}}$.