Minority-spin conducting states in Fe substituted pyrite CoS$_2$

TL;DR

This study uses first-principles density functional theory with both LDA and GGA to reexamine half-metallicity in CoS$_2$ and its Fe-substituted derivatives Co$_{1-x}$Fe$_x$S$_2$. It identifies two mechanisms—increased dispersion of the minority-spin conduction band due to screening changes of S $3p$ antibonding states, and a decreasing exchange splitting with higher Fe content—that together keep minority-spin states occupied at the Fermi level for all $x$. The work shows that even when band filling is reduced via Fe substitution, minority-spin bands remain near or cross the Fermi level, conflicting with full spin polarization and half-metallicity claims. These findings align with experimental observations (e.g., ARPES) that minority-spin states cross the Fermi level in CoS$_2$, and imply that Co$_{1-x}$Fe$_x$S$_2$ cannot be a robust half-metal across the studied composition range.

Abstract

There has been a longstanding debate whether the pyrite CoS$_2$ or its alloys with FeS$_2$ are half metallic. We argue using first principles calculations that there is a finite occupation of minority-spin states at the Fermi level throughout the series Co$_{1-x}$Fe$_x$S$_2$. Although the exchange-correlation functional influences the specifics of the electronic structure, we observe a similar trend with increasing Fe concentration in both LDA and GGA calculations. Specifically, even as band filling is decreased through Fe substitution, the lowest-lying conduction band in the minority-spin channel broadens such that these states keep getting lowered relative to the Fermi level, which is contrary to the expectations from a rigid band picture. Furthermore, the exchange splitting decreases as more Co atoms are replaced by Fe, and this again brings the minority-spin states closer to the Fermi level. These two mechanisms, in conjunction with the experimental observation that minority-spin bands cross the Fermi level in stoichiometric CoS$_2$, indicate that minority-spin charge carriers will always be present in Co$_{1-x}$Fe$_x$S$_2$.

Figures (4)

• Figure 1: Structure of the unit cell of pyrite CoS$_2$ with space group $Pa\overline{3}$. Nearest-neighbor Co-S distances are depicted using solid lines to illustrate the octahedral coordination of Co atoms. There are four formula units in the unit cell. The sites labeled Co1, Co2, Co3, and Co4 are sequentially substituted by Fe to obtain Co$_{1-x}$Fe$_x$S$_2$ for $x$ = 0.25, 0.5, 0.75, and 1.
• Figure 2: LDA band structures of Co$_{1-x}$Fe$_x$S$_2$ for $x = 0, 0.25, 0.5, 0.75,$ and 1. The left and right columns show the majority- and minority-spin channels, respectively. The band structure is not spin polarized for FeS$_2$ ($x = 1$).
• Figure 3: Non-spin-polarized band structures of CoS$_2$ (left) and FeS$_2$ (right). The contribution of Co/Fe $3d$ and S $3p$ characters are depicted by black and red colors, respectively. Both band structures were obtained using the experimental crystal structure of FeS$_2$ to isolate the effect of chemical substitution.
• Figure 4: GGA band structures of Co$_{1-x}$Fe$_x$S$_2$ for $x = 0, 0.25, 0.5, 0.75,$ and 1. The left and right columns show the majority- and minority-spin channels, respectively. The band structure of non-spin-polarized FeS$_2$ ($x = 1$) is shown for comparison.