Control of Polarity in Kagome-NiAs Bismuthides

Abstract

A 2×2×1 superstructure of the P6₃/mmc NiAs structure is reported in which kagome nets are stabilized in the octahedral transition metal layers of the compounds Ni_0.7Pd_0.2Bi, Ni_0.6Pt_0.4Bi, and Mn_0.99Pd_0.01Bi. The ordered vacancies that yield the true hexagonal kagome motif lead to filling of trigonal bipyramidal interstitial sites with the transition metal in this family of "kagome-NiAs" type materials. Further ordering of vacancies within these interstitial layers can be compositionally driven to simultaneously yield kagome-connected layers and a net polarization along the c axes in Ni_0.9Bi and Ni_0.79Pd_0.08Bi, which adopt Fmm2 symmetry. The polar and non-polar materials exhibit different electronic transport behaviour, reflecting the tuneability of both structure and properties within the NiAs-type bismuthide materials family.

Keywords: Intermetallic; Kagome; NiAs; Polar metal.

Figure 1

a) NiAs structure formed from layers of transition metal (grey) octahedrally coordinated by a main group element (green) forming a hexagonal lattice. Possible defects in the NiAs structure include transition metal occupancy of interstitial sites in trigonal bipyramidal voids (blue), or vacancies within the octahedral transition metal layer (dashed grey circle). b) Structural evolution of the NiAs structure type (middle). The structure is Ni₂In‐type (left) when the trigonal bipyramidal interstitial sites are fully occupied (represented by solid black outlines). The structure is CdI₂‐type (right) when every other layer of octahedral sites is removed through ordering of transition metal vacancies (empty sites represented by dashed outlines). A range of transition metal to main group metal ratios are possible, and can lead to diverse superstructures. Atom colours: transition metal—grey, main group element—green.

Figure 2

a) Crystal structure of “kagome‐NiAs” Ni_0.6Pt_0.4Bi. This 2×2×1 superstructure of NiAs arises from ordered removal of 25 % of the octahedrally coordinated metal, and ordered filling of 25 % of the trigonal bipyramidal sites with Ni. b) The ordering of vacancies within the octahedral layer (dashed circles) yields a true hexagonal kagome net of transition metal sites. The octahedral layer consists of mixed Pt/Ni sites (Pt occupancy: 0.530(9); Ni occupancy: 0.470(9)), and trigonal bipyramidal voids are filled with Ni (Ni occupancy: 1). Atom colours: Ni—grey, Pt—orange, Bi—purple.

Figure 3

a) Structural relationship between NiAs with P6₃/mmc symmetry (left), kagome NiAs‐type represented by Ni_0.6Pt_0.4Bi which has a 2×2×1 expansion of the P6₃/mmc unit cell (middle), and polar kagome NiAs‐type represented by Ni_0.9Bi which has Fmm2 symmetry (right). The structure of the polar kagome NiAs‐type material, Ni_0.9Bi, is obtained when every fourth trigonal bipyramidal interstitial layer is empty and interstitial Ni is arranged into partially occupied layers (Layer A) and fully occupied layers (Layer B). The combination of two A and one B layers in an A‐B‐A‐empty‐A′‐B′‐A′‐empty stacking sequence along the a direction leads to a net polarization along the c axis, where the A′‐B′‐A′ set of interstitial layers is translated by half a unit cell length along the c axis relative to the A‐B‐A set. b) Orthogonal view of the two distinct pseudo‐hcp Bi layers (A and B) with occupied trigonal interstitial sites, each with a net polarization generated by the Ni site occupied away from the centre of the Bi rhombus. c) Pseudo‐hexagonal Ni2 layer kagome net from Ni_0.9Bi with in‐plane distances labelled. The unit cell is shown by the black outline. The ordered Ni vacancies in the octahedral layer (dashed circles) generate the kagome net. Atom colours: Ni—grey, Pt—orange, Bi—purple.

Figure 4

a) Crystal structure of polar kagome‐NiAs Ni_0.79Pd_0.08Bi with Fmm2 symmetry and ordering of kagome and interstitial layers along the stacking axis (a direction). The occupied interstitial Ni sites are arranged into partially occupied layers (Layer A) and fully occupied layers (Layer B); the absence of interstitials in half of what were originally B layers leads to a net polarization along the c axis. b) pseudo‐hexagonal Ni2 kagome net from Ni_0.79Pd_0.08Bi with fully occupied Ni and partially occupied Pd (Pd occupancy: 0.645(7)) sites occupied within the layer. The net is orthorhombically distorted and in‐plane distances are labelled. The unit cell is shown by the black outline. Atom colours: Ni—grey, Pd—blue, Bi—purple.

Figure 5

Formation energies of the Ni−Bi binary system. The black line indicates the convex hull representing phases that are thermodynamically stable at 0 K. The polar kagome‐NiAs structure in Fmm2 symmetry is computed to be 1 meV/atom above the convex hull at the composition Ni_0.9375Bi. The full convex hull is provided in Figure S11 and Table S17 in the Supporting Information.

Figure 6

Resistivity of Ni_0.9Bi (blue squares) and Ni_0.7Pd_0.2Bi (cyan circles). For Ni_0.7Pd_0.2Bi, the modified Bloch‐Gruneisen fit to the resistivity from 5 K to 100 K is shown in the red line. For both materials, the current was applied along the c‐axis.