Electronic structure and magnetic properties of CrSb${}_2$ and FeSb${}_2$ investigated via ab initio calculations

The electronic structure and magnetic properties of CrSb${}_2$ have been investigated by ab initio calculations with an emphasis on the role of the magnetic structure for the ground state. The influence of correlation effects has been investigated by performing generalized gradient approximation (GGA) and GGA+U calculations showing their important role for the electronic and magnetic properties. Some details of the electronic structure of CrSb${}_2$ are analyzed by a comparison with those of FeSb${}_2$. The results obtained contribute in particular to the understanding of the temperature dependence of transport and magnetic behavior observed experimentally.

Figure 1

AFM configurations of Cr magnetic moments in CrSb${}_2$ with marcasite structure: AFMe, observed experimentally (a); AFMc, with Cr moments alternation along $c$ axes (b); AFMo, with neighboring Cr atoms creating two sublattices with the opposite magnetic moments (c); AFMb, with Cr moments alternation along the $b$ axes (d).

Figure 2

Total energy of CrSb${}_2$ calculated using the GGA (a) and GGA+U (b, c) for various magnetic phases with marcasite structure and for the FM phase with CuAl${}_2$ structure. The $c/a$ and $c/b$ ratios for all calculations have been kept constant at the experimental value.[23, 30]

Figure 3

Density of states on the transition-metal atoms in FeSb${}_2$ (NM state) at $a=11.08$ a.u. corresponding to the energy minimum (a), and in CrSb${}_2$ ($a=11.62$ a.u.) in NM (GGA results) and weakly magnetic with constrained magnetic moment $m_{\text{Cr}}=0.05{\mu }_B$ (GGA+U results) (b), FM (c), and AFMe (d) states. Solid and thin dashed lines represent the results of GGA+U ($U=2.7$ eV for Cr and $2.6$ eV for Fe) and GGA calculations, respectively.

Figure 4

DOS on Cr sites for the CrSb${}_2$ compound in marcasite phase with various magnetic configurations: AFMe and AFMc within GGA (a) and GGA+U (b) calculations; AFMo and AFMb within GGA (c) and GGA+U (d) calculations.

Figure 5

Electronic band structure for FM CrSb${}_2$ via GGA (a) and GGA+U, $U=2.7$ eV (b).

Figure 6

Density of states on the Cr atoms for CrSb${}_2$ with CuAl${}_2$ structure in the FM state. Solid and dashed lines represent the results of GGA+U ($U=2.7$ eV) and GGA calculations, respectively.

Figure 7

The results of FSM calculations for FeSb${}_2$: Total energy per unit cell vs fixed Fe magnetic moment via GGA (a) and GGA+U ($U=2.6$ eV) (b).

Figure 8

Fe DOS in FeSb${}_2$ obtained via GGA+U: for the NM [(a), $U=0$ eV] and FM [(b), $U=2.6$ eV] states. The solid line corresponds to $3d$ states with $d_{z^2}$ character, the dashed line shows the DOS of states with $d_{x^2-y^2}$ character.

Figure 9

The results of FSM calculations for CrSb${}_2$ with FM order. Total energy per unit cell vs fixed Cr magnetic moment via GGA (a) and GGA+U: $U=2$ eV (b), $U=2.7$ eV (c).

Figure 10

Results of FSM calculations for CrSb${}_2$. Cr $d_{z^2}$ DOS in the FM state for the constrained Cr spin moments: $m=1.8{\mu }_B$ (a) and $m=2.6{\mu }_B$ (b) for $U=0.0$ eV; and $m=1.7{\mu }_B$ (c) for $U=2.0$ eV.

Figure 11

Cr $d_{z^2}$ DOS for CrSb${}_2$ in the AFMe state at $U=0.0$ eV (a) and at $U=2.7$ eV (b).