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The magnetic properties of Fe$_2$Ta and Fe$_2$W in the hexagonal Laves phaseare computed using density functional theory in the generalised gradientapproximation, with the full potential linearised augmented plane wave method.The alloy Fe$_2$Ta$_{1-x}$W$_x$ is studied using the virtual crystalapproximation to treat disorder. Fe$_2$Ta is found to be ferromagnetic with asaturation magnetization of $\mu_0 M_\text{s} = 0.66~\mathrm{T}$ while, incontrast to earlier computational work, Fe$_2$W is found to be ferrimagneticwith $\mu_0 M_\text{s} = 0.35~\mathrm{T}$. The transition from the ferri- tothe ferromagnetic state occurs for $x \leq 0.1$. The magnetocrystallineanisotropy energy (MAE) is calculated to $1.25~\mathrm{MJ/m^3}$ for Fe$_2$Taand $0.87~\mathrm{MJ/m^3}$ for Fe$_2$W. The MAE is found to be smaller for allvalues $x$ in Fe$_2$Ta$_{1-x}$W$_x$ than for the end compounds and it isnegative (in-plane anisotropy) for $0.1 \leq x \leq 0.9$. The MAE is carefullyanalysed in terms of the electronic structure. Even though there are weak 5dcontributions to the density of states at the Fermi energy in both endcompounds, a reciprocal space analysis, using the magnetic force theorem,reveals that the MAE originates mainly from regions of the Brillouin zone withstrong 3d-5d hybridisation near the Fermi energy. Perturbation theory and itsapplicability in relation to the MAE is discussed.

Magnetocrystalline anisotropy of Laves phase Fe$_2$Ta$_{1-x}$W$_x$ from first principles - the effect of 3d-5d hybridisation