Abstract
We investigate the magnetic anisotropy of epitaxial Fe films on GaN(0001) and $\mathrm{GaN}(000\overline{1})$. Due to the particular orientation relationship between Fe and GaN{0001}, the leading term proportional to ${K}_{1}$ does not contribute to the magnetic anisotropy, allowing us to determine ${K}_{3}$ with unprecedented accuracy. Using two experimental techniques, we obtain values for ${K}_{3}$ of $4.7--9.2\ifmmode\times\else\texttimes\fi{}{10}^{5} \mathrm{erg}/\mathrm{cm}{}^{3}$, i.e., comparable to and even larger than ${K}_{1}$.
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