Half-metallicity versus symmetry in half-Heusler alloys based on Pt, Ni, and Co: An ab initio study

Using first-principles calculations based on density functional theory, we study the geometric, electronic, and magnetic properties of Pt-, Ni-, and Co-based half-Heusler alloys, namely, $\mathrm{Pt}BC, \mathrm{Ni}BC$, and $\mathrm{Co}BC$ ($B=\mathrm{Cr}$, Mn, and Fe; $C=\mathrm{Al}$ , Si, P, S, Ga, Ge, As, Se, In, Sn, Sb, and Te). We calculate the formation energy of these alloys in various crystal symmetries, which include the cubic $C{1}_b$ ($F\overline{4}3\mathrm{m}$), orthorhombic ($Pnma$), as well as hexagonal ($P\overline{6}2m$ and $P{6}_3/mmc$) structures. It has been observed that, out of the alloys studied, only 18 are energetically stable in the cubic lowest energy structure. These alloys primarily have either a $C$ atom or an $A$ atom (Pt, Ni, or Co) with a high atomic number. We also observe that, along with the alloys with $C$ atoms from groups IIIA, IVA, and VA, alloys with $C$ atoms from group VIA are also found to be, by and large, energetically stable. Furthermore, among the energetically stable cubic alloys, only CoMnSb, CoMnTe, and NiMnSb show the half-metallic property. Under volume-conserving tetragonal distortion, the half-metallic property is completely destroyed in CoMnSb, whereas CoMnTe and NiMnSb maintain half-metallicity for a $c/a$ value from 0.8 to 1.2 for CoMnTe and from 1.0 to 1.2 for NiMnSb, respectively. From the theoretical calculations, many of the half-Heusler alloys are reported to be half-metals in the cubic phase, but these are synthesized in noncubic structures. We analyze the magnetic moment, the electronic density of states, and the spin polarization at the Fermi level, in detail, to find whether a material in the noncubic lowest energy structure exhibits half-metallicity or not. Based on these analyses, the possibility of existence of any one-to-one relationship between the cubic symmetry and the half-metallicity in these half-Heusler alloys is explored. We predict about the existence of a new noncubic half-Heusler alloy with a substantially low density of states at one of the spin channels and subsequently a reasonably high spin polarization at the Fermi level. However, it is found that for alloys in the lowest energy structure, cubic symmetry is necessary for 100% spin polarization. Furthermore, for Pt-based alloys, the effects of spin-orbit coupling (SOC) have been explored. It is observed that inclusion of SOC in the Pt-based alloys does not play a crucial role in either the geometric or the electronic structure consideration.

Figure 1

The total DOS and partial DOS of $A$ and $B$ atoms, for a few alloys, (a) PtCrIn, (b) PtCrSn, (c) NiMnAs, and (d) CoFeAs, for which two symmetries yield close values of $E_{\mathrm{form}}$ and also geometry. The DOS of the lowest energy phase is plotted with a solid (red) line and the DOS of the other phase is plotted with a (black) dashed line.

Figure 2

The total moment and SP of the $\mathrm{Co}BC, \mathrm{Ni}BC$, and $\mathrm{Pt}BC$ cubic LES as a function of total number of valence electrons per formula unit.

Figure 3

The spin-polarized total DOS and band (plotted with a solid black line) as well as atom projected DOS of $\mathrm{Co}BC$ alloys: (a) CoMnSb, (b) CoMnSe, (c) CoMnTe, (d) CoFeSb, and (e) CoFeTe in the cubic LES. The atom projected DOS of the Co atom is plotted with red color (solid filled pattern for Co $3d_{t_{2g}}$; and hashed pattern for Co $3d_{e_g}$) and that of the $B$ atom is plotted in blue solid ($B 3d_{t_{2g}}$) and dashed lines ($B 3d_{e_g}$). The bands which cross the $E_F$ are plotted in dotted lines (black).

Figure 4

The spin-polarized total DOS and band (plotted with a solid black line) as well as atom projected DOS of $\mathrm{Ni}BC$ alloys: (a) NiCrSb, (b) NiMnSb, (c) NiMnSe, and (d) NiMnTe in the cubic LES. The atom projected DOS of the Ni atom is plotted with red color (solid filled pattern for Ni $3d_{t_{2g}}$; and hashed pattern for Ni $3d_{e_g}$) and that of the $B$ atom is plotted in blue solid ($B 3d_{t_{2g}}$) and dashed lines ($B 3d_{e_g}$). The bands which cross the $E_F$ are plotted in dotted lines (black).

Figure 5

The energy difference between the tetragonal distortion and the cubic structure at its equilibrium lattice parameter as a function of $c/a$ ratio of (a) CoMnSb, (d) CoMnTe, and (g) NiMnSb HHAs. The spin polarization at different $c/a$ ratio of (b) CoMnSb, (e) CoMnTe, and (h) NiMnSb HHAs. The energy gap in the spin-down DOS at different $c/a$ ratio of (c) CoMnSb, (f) CoMnTe, and (i) NiMnSb HHAs. Solid circles and solid squares represent the valence-band maximum and the conduction-band minimum in the spin-down DOS at the same $c/a$ ratio, respectively. $E_F$ is located at 0 eV and indicated by the horizontal solid line.

Figure 6

The spin-polarized total DOS and the atom projected DOS of $\mathrm{Pt}BC$ alloys (a) PtCrSb, (b) PtCrTe, (c) PtMnAs, (d) PtMnSb, (e) PtMnSn, (f) PtMnSe, (g) PtMnTe, and (h) PtFeSb in the cubic LES without including spin-orbit interaction. The total DOS are plotted with a solid line (black). The atom projected DOS of the Pt atom is plotted with red color (solid filled pattern for Pt $4d_{t_{2g}}$; and hashed pattern for Pt $4d_{eg}$) and that of the $B$ atom is plotted in blue solid ($B 3d_{t_{2g}}$) and dashed lines ($B 3d_{e_g}$).

Figure 7

The band structure of $\mathrm{Pt}BC$ HHAs with and without including spin-orbit interaction. The spin-up and spin-down bands without spin-orbit interaction are plotted with a dotted line (blue) and dashed line (black), respectively. The bands with spin-orbit interaction are plotted with a solid line (red).

Figure 8

Flow chart showing the stability of noncubic compounds.

Figure 9

Comparison of the total and partial ($A$ and $B$ atoms) DOS of the cubic as well as the noncubic LES (which show close to integer moment and high SP) of the (a) CoCrP, (b) CoMnP, (c) PtFeIn, and (d) PtCrP HHAs. The cubic DOS are shown in solid filled patterns with a dotted outline and the DOS of noncubic LES are shown in solid lines in black (total DOS), red ($A$ atom), and blue ($A$ atom).