Subtle symmetry breaking in EuB₆ under pressure

Density Functional Theory (DFT) faces challenges in describing strongly correlated systems, known as quantum materials. DFT+U and DFT+DMFT have been developed to address these limitations. Recently, combining functionals with less Self-Interaction Error (SIE), such as meta-GGA’s, with local symmetry breaking has shown promising results. In this work, we compare the r²scan and r²scan+U functionals alongside local spin symmetry breaking to study EuB₆, a rare-earth hexaboride with strongly correlated f electrons. At high pressures (> 25 GPa), experimental data suggest that the ferromagnetic (FM) ground state order vanishes at, and XANES spectra indicate the existence of two distinct Eu atoms. The origin of this feature is still elusive. To model this, we studied several magnetic phases—ferromagnetic, paramagnetic, and antiferromagnetic—as a function of pressure. Our calculations agree with experiment, indicating decreased stability of the FM phase and showing the emergence of two distinct Eu atoms. The key finding is that the polymorphous nature of the Eu spin states induces magnetic clusters, creating a non-uniform exchange field that differentiates each Eu site. These results are subtle but consistent, reflecting the effectiveness of combining functionals with less SIE and symmetry breaking to capture complex behaviors in quantum materials.