Where is magnetic anisotropy field pointing to?

The desired result of magnetic anisotropy investigations is the determination of value(s) of various anisotropy constant(s). This is sometimes difficult, especially when the precise knowledge of saturation magnetization is required, as it happens in ferromagnetic resonance (FMR) studies. In such cases we usually resort to `trick' and fit our experimental data to the quantity called \emph{anisotropy field}, which is strictly proportional to the ratio of the searched anisotropy constant and saturation magnetization. Yet, this quantity is scalar, simply a number, and is therefore of little value for modeling or simulations of the magnetostatic or micromagnetic structures. Here we show how to `translate' the values of magnetic anisotropy constants into the complete vector of magnetic anisotropy field. Our derivation is rigorous and covers the most often encountered cases, from uniaxial to cubic anisotropy.