Three previously considered relations for the dependence of the activation energy $\Delta$ on magnetic order, in "activated" EuO samples, are tested. These relations are: (i) $\Delta ={\Delta }_0-(1+\alpha ){\delta }_R$, where ${\Delta }_0\equiv \Delta (T\gg T_C,H=0)$, ${\delta }_R$ is the red shift of the optical obsorption edge due to magnetic order, and $\alpha$ is a constant; (ii) $\Delta ={\Delta }_0(1-a\sigma )$, where $\sigma$ is the reduced magnetization and $a$ is a constant; (iii) $\Delta ={\Delta }_0(1-b\eta )$, where $\eta$ is the nearest-neighbor two-spin correlation function and $b$ is a constant. The resistivity and Hall data in the preceding paper, and additional Hall data, are analyzed in detail and compared with these relations. New high-field magnetization and optical red-shift data are presented and used in this comparison. The analysis includes the $H$ dependence of the Hall coefficient at $T\gg T_C$, which is sensitive to the dependence of $\Delta$ on magnetic order. It is shown that neither relation (ii) nor relation (iii) represents the data accurately. Penney, Shafer, and Torrance proposed relation (ii) on the basis of more limited data. Relation (i) was tested only at 297 K. At this temperature relation (i) agreed with the $H$ dependence of the Hall coefficient. More extensive measurements of ${\delta }_R(H,T)$ and further analysis are necessary to test the validity of relation (i).

• Received 1 March 1973

DOI:https://doi.org/10.1103/PhysRevB.8.2316