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Atomic-scale computational modeling of technologically relevant permanentmagnetic materials faces two key challenges. First, a material's magneticproperties depend sensitively on temperature, so the calculations must accountfor thermally induced magnetic disorder. Second, the most widely-used permanentmagnets are based on rare-earth elements, whose highly localized 4$f$ electronsare poorly described by standard electronic structure methods. Here, we taketwo established theories, the disordered local moment picture of thermallyinduced magnetic disorder and self-interaction-corrected density functionaltheory, and devise a computational framework to overcome these challenges.Using the new approach, we calculate magnetic moments and Curie temperatures ofthe rare-earth cobalt (RECo$_5$) family for RE=Y--Lu. The calculationscorrectly reproduce the experimentally measured trends across the series andconfirm that, apart from the hypothetical compound EuCo$_5$, SmCo$_5$ has thestrongest magnetic properties at high temperature. An order-parameter analysisdemonstrates that varying the RE has a surprisingly strong effect on the Co--Comagnetic interactions determining the Curie temperature, even when the latticeparameters are kept fixed. We propose the origin of this behavior is a smallcontribution to the density from $f$-character electrons located close to theFermi level.

physical review. b./physical review. b

Rare-earth/transition-metal magnets at finite temperature:  Self-interaction-corrected relativistic density functional theory in the  disordered local moment picture