Evolution of the interfacial perpendicular magnetic anisotropy constant of the Co$_2$FeAl/MgO interface upon annealing

We investigate thickness series of films of the Heusler alloy Co$_2$FeAl in order to study the effect of annealing on the interface with a MgO layer and on the bulk magnetic properties. Our results reveal that while the perpendicular interface anisotropy constant $K^{\perp}_{\rm S}$ is zero for the as-deposited samples, its value increases with annealing up to a value of $1.14\, \pm \,0.07$~mJ/m$^2$ for the series annealed at 320$^{\rm o}$C and of $2.07\, \pm \,0.7$~mJ/m$^2$ for the 450$^{\rm o}$C annealed series owing to a strong modification of the interface during the thermal treatment. This large value ensures a stabilization of a perpendicular magnetization orientation for a thickness below 1.7~nm. The data additionally shows that the in-plane biaxial anisotropy constant has a different evolution with thickness in as-deposited and annealed systems. The Gilbert damping parameter $\alpha$ shows minima for all series for a thickness of 40~nm and an absolute minimum value of $2.8\pm0.1\cdot10^{-3}$. The thickness dependence is explained in terms of an inhomogenous magnetization state generated by the interplay between the different anisotropies of the system and by crystalline disorder.