From one to three, exploring the rungs of Jacob’s ladder in magnetic alloys

Magnetic systems represent an important challenge for electronic structure methods, in particular Density Functional Theory (DFT), which uses a single determinant wavefunction. To assess the predictions obtained by DFT in this type of materials, we benchmark different exchange correlation functionals with respect to each other, and with respect to available experimental data, on two families of binary iron alloys which are metallic and magnetic. We climb three rungs in Jacob’s ladder of DFT (i) the local density approximation, (ii) the industry standard approximation due to Perdew, Burke and Ernzerhof, and the revised version for solids, PBEsol (iii) and finally a very accurate meta-GGA functional SCAN, which corresponds to the third rung. More than 350 structures in ferromagnetic and antiferromagnetic configurations were considered. We compare the Convex Hull, the calculated magnetic moment, crystal structure, formation energy and electronic gap if present. We conclude that none of the functionals work in all conditions: whereas PBE and PBEsol can give a fair description of the crystal structure and the energetics, SCAN strongly overestimates the formation energy – giving values which are at least twice as large as PBE (and experiment). Magnetic moments are better predicted by PBE as well. Our results show that magnetic and strongly correlated materials are a tough litmus test for DFT, and that they represent the next frontier in the development of a truly universal exchange correlation functionals.