Determination of exchange integralsJ1andJ2and magnetic surface-anisotropy energy in EuS from standing-spin-wave resonance

Abstract

The standing-spin-wave absorption spectrum in this EuS films has been measured in the temperature interval 1.3-4.2 K. The dependence of the magnetization on temperature has been determined from the ferromagnetic-resonance field and compared with spin-wave theory. The results are well described by the exchange-parameter combination $\frac{(J_1+J_2)}{k_B}=(0.096\mathrm{}\pm 0.003)$ K. The temperature dependence of the exchange stiffness parameter $D\mathrm{}\left(T\right)\mathrm{}$ has been calculated including the contribution of a nonzero internal field. The experimental results have been analyzed taking the surface boundary conditions into account and correcting for the temperature and field dependence of $H_i$. The results show that the apparent temperature dependence of $D\mathrm{}\left(T\right)\mathrm{}$ arises almost entirely from the surface-anisotropy energy. The small observed variation $\frac{\Delta D\mathrm{}\left(T\right)\mathrm{}}{D_0}$ has been analyzed yielding $\frac{J_2}{J_1}=-0.57\mathrm{}\pm 0.05$. The results, expressed as $\frac{J_1}{k_B}=(0.214\mathrm{}\pm 0.026)$ K, $\frac{J_2}{k_B}=-(0.122\mathrm{}\pm 0.025)$ K are in essential agreement with the inelastic-neutron-scattering determination of Passel et al. but in marked disagreement with Swendsen's Green's-function theory and its application to the calculation of the ferromagnetic and paramagnetic Curie temperature. A comparison with other experimental determinations of $J_1$ and $J_2$ is made.