Spin-polarized energy bands in the Eu chalcogenides have been obtained by the augmented-plane-wave (APW) method. The $4f$ band positions are extremely sensitive to the exchange potential used. A reduced exchange parameter of $\frac{3}{4}$ for the magnetic ${\mathrm{Eu}}^{2+}$ ions has produced proper energy gaps and relative $f$ band positions for EuO, EuS, and EuSe. We have obtained the $f\left(\uparrow \right)$ bandwidth as about 0.5 eV and the up- and down-spin $f$ band separation as about 6 eV. We have also obtained anion $p$ bandwidths of about 2 eV which are almost constant for the Eu chalcogenides. The calculated density of states agrees qualitatively with photoemission data, except for the experimental density of states of the $4f\left(\uparrow \right)$ band which has a large bandwidth of about 1.5 eV. The probable causes of this discrepancy are multiple scattering of the $4f$ electrons with phonons and electrons, or recombinations with ${\mathrm{Eu}}^{3+}$ ions. The observed absorption-edge red shifts are due to the spin-polarized exchange splitting $\Delta E_{\mathrm{ex}}$ of the lowest conduction band $X_3$. Estimated $\Delta E_{\mathrm{ex}}$ values are 0.4-0.5 eV for Gd metal and Eu chalcogenides. The $f\left(\uparrow \right)$ bands in Eu and Gd metals are expected to be located within 3 eV below the Fermi level. The high-energy reflectivity data, effective masses, possible conduction mechanism, and APW charge analysis have been discussed.

• Received 22 October 1969

DOI:https://doi.org/10.1103/PhysRevB.1.4589