Measurement of the cubic anisotropy constant K3 of Fe films on GaN{0001}

The magnetocrystalline anisotropy of a ferromagnet is determined by its crystal structure and is thus an inherent source of magnetic anisotropy.[1,2] It is the key to an understanding of ferromag-netism itself and is still actively investigated even for apparently well-understood materials such as Fe.[3-5] The magnetocrystalline anisotropy energy of bcc Fe can be expressed in terms of the direction cosines α₁, α² and α₃ of the magnetization vector with respect to the three cube edges as K₁(α₁² α₂² + α₂² + α₃² α₁²) + K₂α²α₂α₃ + K₃(α₁²α₂² + α₂² α₃² + α₃² α₁²)², where K₁, K₂ and K₃ are the cubic anisotropy constants. Experimentally, it is rather straightforward to determine the leading term of the expansion and reliable values of about 4.7×10⁵ erg/cm³ for K ₁ of Fe have been measured already in early studies. The determination of the higher-order anisotropy constants K₂ and K₃ is far more difficult, since their prefactors are of 6th and 8th order, respectively, and decrease correspondingly in magnitude. Recently, researchers using the unique configuration encountered for Fe(111) films have been able to improve accuracy by orders of magnitude, resulting in a value of K₂ = (2.2 ± 0.1) × 10⁴ erg/cm³.[3,4] There is no analogous situation for the determination of K₃, i.e., no crystal orientation exists for which this term would be the only one being anisotropic.