Pitfalls of exchange–correlation functionals in description of magnetism: Cautionary tale of the FeRh alloy

The magnetic ground state of FeRh is highly sensitive towards the lattice constant. This, in addition to partially filled $d$-shells of Fe and Rh, posed a significant challenge for Density Functional Theory (DFT) calculations in the past. Here, we have investigated the performance of various exchange–correlation (XC) functionals within the DFT formalism for this challenging binary alloy. We have employed Local Density Approximation (LDA), various Generalized Gradient Approximations (GGAs), and newly developed Strongly Constrained and Appropriately Normed (SCAN) meta-GGA functional. Our results show the limitations of any single functional in capturing the intricate interplay of structural, electronic, and magnetic properties in FeRh. While SCAN can accurately describe some magnetic features and phonon dispersion, it significantly overestimates the Fe-Fe magnetic interactions, leading to an unreasonable magnetic ordering temperature. Conversely, the Perdew–Burke–Ernzerhof (PBE) GGA exhibits the opposite behavior. These findings highlight the challenges in simulating materials with partially filled $d$-shells using DFT, underscoring the crucial need for developing a versatile XC functional that can effectively account for the multifaceted nature of such systems.