# Analysis of over-magnetization of elemental transition metal solids from the SCAN Density Functional

## TL;DR

This paper investigates why the SCAN density functional over-magnetizes elemental transition metals like Fe, Co, and Ni, identifying the source as the functional’s insensitivity to certain iso-orbital indicator values.

## Contribution

It reveals that the over-magnetization issue stems from the SCAN switching function's insensitivity to the iso-orbital indicator alpha in specific ranges, clarifying the functional's limitations.

## Key findings

- SCAN over-magnetizes Fe, Co, Ni by over 20% compared to experiments.
- The discrepancy is linked to the alpha indicator's dispersion and the switching function's sensitivity.
- The source of error is the insensitivity of the SCAN switching function to alpha values between 0.5 and 0.8.

## Abstract

Recent investigations have found that the strongly constrained and appropriately normed (SCAN) meta-GGA exchange-correlation functional significantly over-magnetizes elemental Fe, Co, and Ni solids. For the paradigmatic case, bcc Fe, the error relative to experiment is $\gtrsim 20 \%$. Comparative analysis of magnetization results from SCAN and its \textit{deorbitalized} counterpart, SCAN-L, leads to identification of the source of the discrepancy. It is not from the difference between Kohn-Sham (SCAN-L) and generalized Kohn-Sham (SCAN) procedures. The key is the iso-orbital indicator $\alpha$ (the ratio of the local Pauli and Thomas-Fermi kinetic energy densities). Its \textit{deorbitalized} counterpart, $\alpha_L$, has more dispersion in both spin channels with respect to magnetization in an approximate region between 0.6 Bohr and 1.2 Bohr around an Fe nucleus. The overall effect is that the SCAN switching function evaluated with $\alpha_L$ reduces the energetic disadvantage of the down channel with respect to up compared to the original $\alpha$, which in turn reduces the magnetization. This identifies the cause of the SCAN magnetization error as insensitivity of the SCAN switching function to $\alpha$ values in the approximate range $0.5 \lesssim \alpha \lesssim 0.8$ and oversensitivity for $\alpha \gtrsim 0.8$.