Temperature dependence of the first-and second-order cubic anisotropy constants in EuO

The temperature dependence of the first-and second-order cubic anisotropy constants in EuO has been determined from ferromagnetic-resonance measurements on spherical singledomain, single-crystal samples. The observed dependence of $K_1$ is largely explained by a single-ion interaction. The constant $K_2$ is observed to change sign at $\sim \frac{1}{2}{T}_C$ and its temperature dependence cannot be explained by just a single-ion interaction. The data have been analyzed by including the dipolar and pseudodipolar terms obtained by Kasuya and Tachiki in extending Van Vleck's calculation to third order. Very good agreement is obtained. The crystal-field parameters determined are $b_4=2.3\mathrm{}\times {10}^{-3\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ /ion and $b_6=0.2\mathrm{}\times {10}^{-3\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ /ion. It is found that pseudodipolar contributions are important with nearest-and next-nearest-neighbor contributions of 1.35 and 2.5 respectively, expressed in units of the corresponding pure magnetic dipolar term. The measured angular dependence of the resonance field has been analyzed including terms to second order in the ratio of the anisotropy to Zeeman energies. The values of $\frac{K_1}{M}$ and $\frac{K_2}{M}$ at 4.2 K are -247.5 ± 2.5 and 82 ± 10 Oe, respectively.