Crystal-field magnetic anisotropy of dilute dysprosium or erbium in yttrium single crystals

Magnetization measurements have been performed between 1.3 and 300 K in fields up to 50 × ${10}^5$ A/m in the $a$, $b$, and $c$ directions of hcp crystals of pure Y and Y doped with 0.14-at.% Dy or 0.14-at.% Er, using the Faraday method and a vibrating-sample method. The characteristic behavior of both the isothermal and isofield susceptibility curves could be interpreted in terms of a general single-ion anisotropy Hamiltonian and a molecular-field exchange model. In this way the following anisotropy parameters $A_{\mathrm{nm}}〈r^n〉$, with $(n,m)=(2,0), (4,0) (6,0), \mathrm{and} (6,6)$ respectively, were obtained (in units of K): Er, -122±12, +18.3±1.8, +11.7±1.2, -135±13; Dy, -50.5±5, +49.5±5, +40.4±4, -321±32. The higher-order anisotropy parameters play an important part in determining the crystal-field-level scheme and they are incompatible with a model assuming that the charges giving rise to the crystal field are solely external to the magnetic ion. The exchange interactions differ by up to a factor of 15 for $c$ and basal-plane directions.