Origin of the spin reorientation transitions in (Fe$_{1-x}$Co$_{x}$)$_{2}$B alloys

Low-temperature measurements of the magnetocrystalline anisotropy energy $K$ in (Fe$_{1-x}$Co$_{x}$)$_{2}$B alloys are reported, and the origin of this anisotropy is elucidated using a first-principles electronic structure analysis. The calculated concentration dependence $K(x)$ with a maximum near $x=0.3$ and a minimum near $x=0.8$ is in excellent agreement with experiment. This dependence is traced down to spin-orbital selection rules and the filling of electronic bands with increasing electronic concentration. At the optimal Co concentration, $K$ depends strongly on the tetragonality and doubles under a modest 3% increase of the $c/a$ ratio, suggesting that the magnetocrystalline anisotropy can be further enhanced using epitaxial or chemical strain.