Electronic structure and chemical bonding in LaIrSi-type intermetallics

3.1 Crystal chemistry

The LaIrSi type derives from the structure of the Zintl phase SrSi₂ [36], [37], [38] through an ordered substitution of iridium and silicon atoms on the silicon network. This requires a translationengleiche symmetry reduction from P4₁32 (or the enantiomorphic group P4₃32) to P2₁3, along with a splitting of the 8c subcell site into two 4a sites. A view of the LaIrSi structure approximately along the a axis is presented in Fig. 2. The ordered helical chains are readily evident from this drawing. For the present study on the electronic structures and chemical bonding we chose CaPtSi [16], BaIrP [23], BaAuGa [15], LaIrSi [14], CeRhSi [20] and CeIrSi [21] as representatives. The basic crystallographic data of these phases are listed in Table 1.

Fig. 2:

Crystal structure of the LaIrSi-type phases ATX, space group P2₁3. The three-dimensional [TX] network is emphasized.

Before we turn to the crystal chemical description, we need to comment on related compounds. LaIrSi crystallizes with space group P2₁3 (no. 198), the Pearson symbol cP12 and the Wyckoff sequence a³. A search for 198;a³ in the Pearson data base [1] leads to 100 entries. The latter are assigned to the prototypes ZrOS [39] and NiSbS (ullmanite structure; a pyrite superstructure) [40] which show distinctly different features of chemical bonding (dumb-bell formation vs a three-dimensional polyanionic network). Herein we solely focus on the intermetallics which are ascribed to the ZrOS type (Fig. 1).

Each T atom in the LaIrSi-type phases is coordinated by three X atoms and vice versa with T–X distances equal or smaller than the sum of the covalent radii [41] for T+X (see Table 1). Comparison of these distances is already indicative of strong covalent T–X bonding, the main bonding interaction in the LaIrSi-type phases (vide infra). The TX_3/3 units share common corners, leading to a three-dimensional [TX]^δ− polyanionic network in which the alkaline earth and rare earth atoms fill cages. The size of the cages and the coordination of the alkaline earth, respectively rare earth atoms is different within the series of investigated compounds. For CaPtSi, LaIrSi, CeRhSi and CeIrSi both the R–T and the R–X bonds are distinctly longer than the sums of the covalent radii (Table 1), while BaIrP and BaAuGa both have one short R–T contact. This might be a consequence of the large size of barium along with electronegativity differences. These alterations are addressed in more detail below.

3.2 Density of states

For the six ternary representatives discussed above, total spins, non-spin-polarized calculations were carried out with the crystallographic data listed in Table 1. Such calculations can provide the ground state electronic configuration as non-magnetic or not according to the magnitude of the density of states at the Fermi level: n(E_F), i.e. if it is small or too large, respectively. This is described more quantitatively below.

The site-projected densities of states (PDOS) are shown in Fig. 3. The zero energy along the x axis is given with respect to the Fermi level E_F and the six ternary compounds are seen to be metallic. However, the two Ce based compounds present a high density of states due to the Ce 4f states. This could be associated with an instability of the electronic system in such a spin-degenerate configuration and a lowering of the energy (stabilization) should show up upon carrying out spin polarized (SP) magnetic calculations (vide infra). On the contrary the Rh d-DOS are found in the energy window –6; –2 eV well within the valence band (VB), with small PDOS at E_F. Thus the magnetic instability is due to the Ce 4f states which should develop magnetic moments in SP calculations.

Fig. 3:

Site projected density of states PDOS in total spins (NSP) configuration for LaIrSi-type phases ATX: (a) CaPtSi, (b) BaIrP, (c) BaAuGa, (d) LaIrSi, (e) CeRhSi and (f) CeIrSi.

Due to their relatively large filling, the d-like PDOS of Pt, Ir and Au especially with a saturated d subshell are found well within the VB, similarly to Rh. E_F is crossed by itinerant low intensity DOS arising from s,p PDOS of the constituents. The four compounds CaPtSi, BaIrP, BaAuGa and LaIrSi are then qualified as weakly metallic (showing almost a pseudo-gap).

In all compounds the lower part of the VB is dominated by s states of the X atoms and the quantum mixing of the valence states leading to the chemical bonding mainly observed in the energy window ~ –6–E_F. The DOS description should then be complemented with an analysis of the chemical bonding between atoms belonging to the different substructures. This is discussed in the next section.

3.3 Crystal orbital overlap population analyses

The chemical bonding is discussed based on the analysis of the overlap populations S_ij between two chemical species i and j, within the crystal orbitals overlap populations (COOP) scheme of Hoffmann [34]. Figure 4 show the COOPs for the different interactions between the substructures. As described in the crystal chemistry section the major bonding is identified with high intensity T–X COOPs in all panels, in accordance with the above described [TX]^δ− polyanionic network. This is followed by less intense R–X COOPs found closer to the Fermi level due to the positioning of X p states in that energy region. Lastly the R–T interactions are found with least intensity which show mixing at the highest energy part of T d states at –4 eV for CaPtSi and –2 eV for BaIrP. An exception is observed for BaAuGa where the Au d states do not show significant mixing with Ba due to a saturation of the Au d subshell as mentioned above.

Fig. 4:

Chemical bonding from overlap populations with the COOP criterion for interactions between the different substructures of the ATX phases: (a) CaPtSi, (b) BaIrP, (c) BaAuGa, (d) LaIrSi, (e) CeRhSi and (f) CeIrSi. (Positive and negative COOP magnitudes indicate bonding and antibonding interactions; cf. text).

Most COOPs seem to be optimized at E_F. An increase of the valence electron count (within a rigid-band model) would tend towards antibonding states, thus destabilizing the respective phase. This might be a reason for the almost strict occurrence of VEC=16 phases with the LaIrSi type.

3.4 Bader analyses

The analysis of the charge density issued from the self-consistent calculations can be done using the AIM (atoms in molecules) approach [42] developed by Bader who devised an intuitive way of splitting molecules into atoms as based purely on the electronic charge density. Note that such analyses may not be a tool for evaluating absolute ionizations but allows establishing trends between similar compounds.

The charge analyses typically lead to the VEC scheme in Fig. 1: for instance in CaPtSi (VEC=2+10+4) the Bader analysis of the charges provides small magnitude electron transfers between the different chemical species, namely: ∆Q(Ca)=+0.50; ∆Q(Pt)=–0.09 and ∆Q(Si)=–0.41; the sum leading to neutrality as expected. On may not expect full ionization such as Ca²⁺ due to the covalent character within these intermetallic compounds.

On the other hand, for BaIrP and BaPdSi we get

BaIrP: ΔQ(Ba)=+1.22; ΔQ(Ir)=–0.69 and ΔQ(P)=–0.53;

BaPdSi: ΔQ(Ba)=+0.92; ΔQ(Pd)=–1.01 and ΔQ(Si)=0.09;

clearly the larger electronegativity of P: χ=2.19 compared to that of Si: χ=1.80 is responsible of larger charge transfer on the transition metal; knowing that Pd and Ir have similar magnitudes near χ=2.20.

However, greater electron transfer is noted when the transition element is more electronegative as Au with χ=2.54 in the presence of a less electronegative p element as Ga (χ=1.81) in BaAuGa:

ΔQ(Ba)=+1.7; ΔQ(Au)=–1.6 and ΔQ(Ga)=–0.1

The charge transfer clearly classifies BaAuGa as an auride. Nevertheless we keep the chemical formula in its classical form for better comparison with the remaining compounds. Similar Bader charges for the gold atoms were observed for Na₂Au₃Al [43] and EuAu₃Al₂ [44]. Also binary BaAu [45] is a classical auride.

Whereas all studied compounds obey the VEC=16 or 17 electron count, the amount of electron transfer (either way) is dependent of the respective electron affinities of the chemical constituents.

3.5 Magnetic instability

The large Ce PDOS intensity at the Fermi level of both cerium representatives let us suggest a magnetic instability particularly in view of the trivalent character of Ce estimated from the VEC analysis and the experimental magnetic susceptibility data of CeIrSi [21].

Therefore spin-polarized (SP) electronic structure calculations were carried out for CeIrSi and CeRhSi. At self-consistent convergence only CeRhSi presents a stable magnetic solution m_Ce= 0.73 μ_B, m_Rh= –0.14 μ_B and m_Si= –0.003 μ_B. The energy difference with respect to the NSP configuration is ∆E(SP-NSP)=–0.29 eV, showing a stable SP configuration. Figure 5 shows the site and spin projected DOS of SP CeRhSi where the energy shift between the majority (↑) and minority (↓) spin population provides the magnetic moment. This shift is clearly observed for Ce and not for Rh or Si. Thus the moments on Rh and Si are of induced nature (opposite sign) due to the quantum mixing with the Ce valence states.

Fig. 5:

CeRhSi DOS in spin polarized SP configuration; (a) ground state ferromagnetic configuration with majority (↑) and minority (↓) spin populations; (b) antiferromagnetic configuration with full compensation of UP spins half-cell and DOWN spins half-cell (cf. text).

In order to confirm CeRhSi in a SP-feromagnetic ground state, further calculations imposing an antiferromagnetic order were needed. This was done by assuming half of the cell as UP-SPINS (2 formula units FU) and the other half as DOWN-SPINS (the other 2 FU). The self-consistent calculation led to lower magnitude moments with m_Ce=±0.44 μ_B, m_Rh=±0.004 μ_B and m_Si=0.0 μ_B. Also an energy increase with the such imposed AF order was observed with ∆E(SP_ferro–SP_antiferro)=–0.14 eV. Although the energy difference is only half of ∆E(SP-NSP) above, the results let us propose the compound to be in a ferromagnetic ground state.

No stable magnetic model was obtained for CeIrSi. This is in line with the magnetic susceptibility measurements which showed Curie-Weiss paramagnetism and no magnetic ordering down to 2 K [21]. Unfortunately no magnetic data were reported for CeRhSi [20].