  Computational design of more efficient rare earth/transition metal (RE-TM)
permanent magnets requires accurately calculating the magnetocrystalline
anisotropy (MCA) at finite temperature, since this property places an upper
bound on the coercivity. Here, we present a first-principles methodology to
calculate the MCA of RE-TM magnets which fully accounts for the effects of
temperature on the underlying electrons. The itinerant electron TM magnetism is
described within the disordered local moment picture, and the localized RE-4f
magnetism is described within crystal field theory. We use our model, which is
free of adjustable parameters, to calculate the MCA of the RCo$_5$ (R=Y, La-Gd)
magnet family for temperatures 0--600 K. We correctly find a huge uniaxial
anisotropy for SmCo$_5$ (21.3 MJm$^{-3}$ at 300 K) and two finite temperature
spin reorientation transitions for NdCo$_5$. The calculations also demonstrate
dramatic valency effects in CeCo$_5$ and PrCo$_5$. Our calculations provide
quantitative, first-principles insight into several decades of RE-TM
experimental studies.
