Synthesis, Crystal Structure, and Physical Properties of the Perovskite Iridates

Abstract

Perovskite iridates have emerged as a new paradigm for studying the strongly correlated electron physics with strong spin-orbit coupling. The “113” alkaline-earth iridates AIrO3 (A = Ca, Sr, Ba) display a rich variety of crystallographic and electronic states and are now attracting growing research interest. This chapter aims to provide an overview for these “113” iridates, including the materials’ synthesis, crystal structure, major physical properties, and other interesting results such as the effects of pressure and chemical substitutions, as well as theoretical perspectives.

1. Introduction

The discoveries of high-transition-temperature superconductivity in cuprates and the colossal magnetoresistance in manganites made the first-row (3d) transition-metal oxides (TMOs) with perovskite-related structures the central topics of condensed matter physics over the past four decades. The strong electron–electron correlations intrinsic for these narrow-band 3d-electron systems are believed to be at the heart of rich physics. Following the general wisdom based on the 3d TMOs, the third-row (5d) counterparts having a spatially much extended 5d orbitals were expected to have much reduced electron–electron correlations, U, and broaden bandwidth, W, i.e. U << W, leading to a Pauli paramagnetic metallic ground state, Figure 1(a). Such an expectation, however, was recently found to be violated in many 5d-electron iridium oxides (iridates), such as Sr₂IrO₄ [1], in which an antiferromagnetic insulating ground state was instead observed. Recent studies have revealed that such discrepancy originates from the inherently strong spin-orbit coupling (SOC) for these heavy 5d elements, which have a typical value of SOC, ζ_SO ≈ 0.3–0.5 eV, comparable with the magnitude of U and W, and thus cannot be treated as a negligible perturbation as in the 3d TMOs.

Since an unrealistically large U is required to open a Mott gap in Sr₂IrO₄, Figure 1(b), Kim et al. [2] proposed that the strong SOC splits the otherwise broad t_2g band of the octahedral-site, low-spin Ir⁴⁺(5d ⁵) array into a filled, low-energy J_eff = 3/2 quartet band and a half-filled, high-energy J_eff = 1/2 doublet band, Figure 1(c, e). A moderate Hubbard U can then open a Mott gap, leading to the SOC-driven J_eff = 1/2 Mott insulating state, Figure 1(d). Subsequent experimental [3] and theoretical [4] investigations have confirmed such a novel J_eff = 1/2 state in the strong SOC limit. Since then, the 5d TMOs have emerged as a new paradigm for studying the strongly correlated electron physics with strong SOC. In particular, the iridates have attracted special attention in that the combination of relativistic SOC and electron–electron correlations has been proposed to generate more exotic, unprecedented quantum states of matters, such as the strong topological insulators, Weyl semimetal, quantum spin liquids, and even unconventional superconductors [5].

Figure 1.

Schematic energy diagrams for the 5d⁵ (t_2g⁵) configuration: (a) without SOC and U, (b) with an unrealistically large U but no SOC, (c) with SOC but no U, and (d) with SOC and U, (e) 5d level splitting by the crystal field and SOC. Adapted from Reference [2].

Since the importance of SOC was first recognized in Sr₂IrO₄, which is the n= 1 member of the Ruddlesden–Popper series Sr_n+1Ir_nO_3n+1 (n= 1, 2, ∞), these perovskite (Pv) iridates are currently archetypal systems for studying the interplay of SOC and electron–electron correlations. During the past few years, numerous studies have been performed on the single-layer Sr₂IrO₄ (n= 1) and bilayer Sr₃Ir₂O₇ (n= 2); for a review, see Reference [6]. With increasing the number of Pv layers n, the bandwidth of the J_eff = 1/2 band is expected to increase, and a dimensionality controlled insulator-to-metal transition is eventually realized in the orthorhombic Pv SrIrO₃ (n= ∞) [7]. Recent advances in this emergent field have turned much attention to the “113” alkaline-earth iridates AIrO₃ (A = Ca, Sr, Ba) with the Pv-related structures. However, in-depth investigations on these compounds are hindered to a great extent by the harsh synthesis conditions as well as their complex structural variations. For example, the above-mentioned orthorhombic Pv SrIrO₃ can only be stabilized in the bulk form under high-pressure and high-temperature (HPHT) conditions [8], or in the form of thin films by applying epitaxial strain [9]. Recent theoretical investigations proposed an intriguing topological semimetal state for the orthorhombic Pv phase [10]. When synthesized at ambient pressure, on the other hand, SrIrO₃ adopts a so-called six-layer (6H) polytype [8], which has been characterized as a non-Fermi-liquid metal approaching a ferromagnetic quantum critical point [11]. As the sister compounds of SrIrO₃, both CaIrO₃ and BaIrO₃ also display multiple structural polymorphs with interesting structural–property relationships. Depending on the synthesis conditions, CaIrO₃ can be stabilized in either the Pv or the post-perovskite (pPv) structure, which displays, respectively, a paramagnetic metal and an antiferromagnetic insulator ground states [12, 13]. Although the pPv CaIrO₃ was regarded as the J_eff = 1/2 Mott insulator [14], recent studies revealed a clear deviation from the ideal J_eff = 1/2 state due to the pronounced structural distortions [15]. In addition, in the field of geosciences, CaIrO₃ has been studied extensively as an analogy of MgSiO₃ to elucidate the mechanism of Pv to pPv transition at the boundary of Earth’s lowermost mantle, or the D’’ layer [16]. In the case of BaIrO₃, it also exhibits multiple structural polytypes with interesting structural–property relationship. At ambient pressure, BaIrO₃ adopts a nine-layer structure (9R). It is the first known ferromagnetic insulator among the 5d TMOs and exhibits intriguing charge-density-wave formation accompanying the ferromagnetic order [17, 18]. When treating the 9R phase under different pressures, three more polytypes, i.e. 5H, 6H, and 3C, have been identified [19]. Following the sequence of 9R $\to$5H $\to$6H $\to$3C, their ground states change progressively from a weak ferromagnetic insulator with T_c = 180 K for 9R, through a ferromagnetic metal with T_c = 50 K for 5H, and an exchange enhanced non-Fermi-liquid metal for 6H approaching a ferromagnetic quantum critical point, finally to a Pauli paramagnetic Fermi-liquid metal for 3C [20, 21]. These results demonstrate an intimate structure–property relationship that has been well documented in the 3d TMOs. A brief summary of the structural types and interesting physical properties for these “113” alkaline-earth iridates AIrO₃ (A = Ca, Sr, Ba) is given in Table 1.

Although there are many publications dealing with an individual compound, a monograph that provides a comprehensive overview for these “113” alkaline-earth iridates is still lacking to our knowledge. Taking into account the growing research interests on these iridates, it is imminent to summarize the currently available knowledge in a single chapter. Thus, this chapter aims to bring together the available information in literature for these “113” iridates. In the following, we will give a comprehensive literature survey for each AIrO₃, covering the materials’ synthesis, crystal structure, and major physical properties, as well as other interesting results such as the effects of chemical substitutions and theoretical investigations. Finally, we will give a brief concluding remark on the current research status and provide an outlook on the future research directions on these iridates.

Compound	Structure type	Interesting physical properties
CaIrO3	pPv	AF insulator with TN = 110 K, stripe-type AF order with spin canting;
	Pv	PM semimetal with possible Dirac node protected by reflection symmetry
SrIrO3	6H	Exchange enhanced PM metal with nFL behaviors due to proximity to a FM QCP
	Pv	PM semimetal with possible Dirac node protected by reflection symmetry
BaIrO3	9R	Weak FM insulator with a simultaneous CDW formation below Tc ≈ 180 K
	5H	Weak FM metal with Tc ≈ 50 K
	6H	Exchange enhanced PM metal with nFL behaviors due to proximity to a FM QCP
	3C	FL PM metal

Table 1.

A summary of the “113” Alkaline-earth iridates AIrO₃ (A=Ca, Sr, Ba)

AF: Antiferromagnetic; PM: Paramagnetic; FM: Ferromagnetic; FL: Fermi liquid;

nFL: non Fermi liquid; CDW: Charge density wave; QCP: Quantum critical point

2. CaIrO₃

CaIrO₃ has two different orthorhombic polymorphs, i.e. the layered pPv structure with space group Cmcmand the GdFeO₃-type Pv structure with space group Pbnm. These two compounds have been known since 1960s [22, 23] and received significant attention from geologists since 2004 as an analogy of MgSiO₃, the main constituent mineral of the Earth’s lower mantle [16, 24]. More recently, they have emerged as important correlated 5d-electron systems with strong SOC [14, 25]; the strong local distortion in pPv CaIrO₃ makes it a model system to investigate the interplay of non-cubic crystal field splitting and SOC [15], while the orthorhombic Pv CaIrO₃ might be considered as an intriguing semimetal with symmetry-protected Dirac points [26].

2.1. Synthesis

There are some discrepancies in literature regarding the synthesis of pPv CaIrO₃ at ambient pressure. In the earlier studies [12, 22], it was reported that single-phase pPv phase cannot be obtained at ambient pressure through a solid-state reaction from CaCO₃ and IrO₂ in air. Recently, Harai et al. [27] reported that pure pPv CaIrO₃ can be prepared by heating the stoichiometric mixture of CaO and IrO₂ powders sealed in an evacuated silica tube at 1000°C over 20 h. On the other hand, since the pPv structure is a high-pressure phase, pPv CaIrO₃ can be readily obtained by utilizing HPHT synthesis. For example, Ohgushi et al. [25] reported the synthesis of single-phase pPv CaIrO₃ at 4 GPa and 1150°C.

Needle-shaped pPv CaIrO₃ single crystals have been reported to grow out of the CaCl₂ flux. By adopting a tenfold flux and a relatively low soaking temperature of 836 and 950°C, respectively, Sugahara et al. [28] and Hirai et al. [29] obtained tiny single crystals for the purpose of crystal-structure refinements. On the other hand, Ohgushi et al. [14] seems to grow sizable pPv CaIrO₃ single crystals for anisotropic magnetic property measurements by employing a higher flux molar ratio (16:1) and a higher soaking temperature of 1200°C. However, our attempts by using the latter approach ended up with Ca₂IrO₄ rather than the pPv CaIrO₃.

Because Pv CaIrO₃ is a metastable phase, it cannot be synthesized via a solid-state reaction route at ambient pressure. Alternatively, Sarkozy et al. [12] reported the preparation of pure Pv phase by thermal decomposition at 650–700°C in air of the hydroxide intermediate CaIr(OH)₆, which can be obtained according to the following wet-chemical reaction scheme:

$${\text{K}}_{\text{2}}{\text{IrCl}}_{\text{6}}\stackrel{H_{2}O}{\to }{\text{IrCl}}_{\text{6}}{}^{\text{2–}}\stackrel{KOH,pH10-12}{\to }\text{Ir}{\left(\text{OH}\right)}_{\text{6}}{}^{\text{2–}}\stackrel{C{a}^{2+}}{\to }\text{CaIr}{\left(\text{OH}\right)}_{\text{6}}\downarrow \text{.}$$BB1

By following this approach, we obtained nearly single-phase Pv CaIrO₃ with a trace amount of IrO₂ (0.2 wt.%) and Ca₂IrO₄ (1.3 wt.%) [30]. Recently, Kojitani et al. [31] determined a large positive Clapeyron slope for the pPv/Pv transition of CaIrO₃, i.e. Pv structure is the high-temperature phase of pPv. Thus, Pv CaIrO₃ can be obtained by transforming pPv phase at higher temperature under given pressures. For example, Ohgushi et al. [13] have reported the synthesis of single-phase Pv CaIrO₃ at 1 GPa and 1450°C. In addition, thin films of Pv CaIrO₃ have recently been epitaxially stabilized on various substrates [26, 32].

2.2. Crystal structure

pPv CaIrO₃ As shown in Fig. 2(a), the crystal structure of pPv CaIrO₃ can be described as a pseudo-2D layered structure having IrO₆ octahedral sheets stacked alternatively with the Ca²⁺ ions along the crystallographic baxis. Within the octahedral sheets, IrO₆ octahedra share edges along the aaxis to form rutile-type chains; these chains are then interconnected with each other via apical oxygen atoms along the caxis. Because of the significant interest in geosciences, the crystal structure of pPv CaIrO₃ have been thoroughly studied by several groups [28, 29]. To illustrate the peculiar features of pPv CaIrO₃, here we adopted the results given by Sugahara et al.[28] who refined the crystal structure based on the single-crystal X-ray diffraction (XRD) technique. The crystal structure was refined in an orthorhombic space group Cmcm(No. 63) with Ca at 4c(0, y, 1/4), Ir at 4a(0, 0, 0), O1 at 4c(0, y, 1/4), and O2 at 8f(0, y, z) sites, respectively. The obtained unit cell parameters are a= 3.147 Å, b= 9.866 Å, c= 7.302 Å, and V= 226.7 ų at room temperature. The refined positional parameters and selected bond lengths and bond angles after Reference [28] are listed in Table 2. Within the buckled octahedral layer, the IrO₆ octahedral chains display an alternative rotation about the aaxis, resulting in Ir-O1-Ir bond angles of 134.3°. As a result, for a given octahedron the local zaxis that is along the Ir-O1 bond deviates from the crystallographic caxis by about 23°. In addition, IrO₆ octahedra show a significant tetragonal compression, with two short Ir-O1 (1.978 Å) and four long Ir-O2 (2.066 Å) bonds. Octahedral-site distortions can be generally described by the orthorhombic vibrational modes Q₂ = l_x – l_y and Q₃ = (2l_z–l_x –l_y)/√3, where l_x, l_y, l_z are the bond lengths for bonding along local x, y, zdirections. In pPv CaIrO₃, the octahedral-site distortion corresponds to a negative mode of Q₃ = –0.102. For comparison, the PtO₆ octahedra in the pPv CaPtO₃ with a filled t_2g⁶ manifold show a negligible Q₃ = –0.001. Such a comparison highlights a strong orbital-lattice coupling in pPv CaIrO₃ with low-spin t_2g⁵ configuration for Ir⁴⁺ ions, for which the single hole would be expected to have a dominant yz ± izxorbital character [30], which has been confirmed recently by the resonant inelastic X-ray spectroscopy [15].

Figure 2.

Crystal structure of CaIrO₃ polymorphs: (a) pPv and (b) Pv.

Pv CaIrO₃As shown in Fig. 2(b), the crystal structure of Pv CaIrO₃ is built up from corner-shared IrO₆ octahedra in three dimensions with Ca cations in the interstitial positions. It has been known over 40 years that Pv CaIrO₃ adopts the GdFeO₃-type structure; however, structural refinements have not been performed until recently. We present here our Rietveld refinement results [30] based on the high-resolution synchrotron XRD on polycrystalline Pv CaIrO₃ prepared with the wet-chemical method mentioned above. The crystal structure was refined in space group Pbnm(No. 62) with Ca at4c(x, y, 1/4), Ir at 4b(0.5, 0, 0), O1 at 4c(x, y, 1/4) and O2 at 8d(x, y, z) sites, respectively. The lattice parameters at room temperature are determined as a= 5.35046 Å, b= 5.59291 Å, c= 7.67694 Å, and V= 229.73 ų. The obtained positional parameters and selected bond lengths and bond angles after Reference [30] are listed in Table 3. In comparison with the pPv phase, the IrO₆ octahedra are less distorted with three sets of Ir-O distances of 2.006 Å, 2.020 Å, and 2.038 Å; the average Ir-O distance of 2.021 Å is consistent with the ionic radii sum for Ir⁴⁺ (0.625 Å) and O^2– (1.40 Å). The averaged Ir-O-Ir bond angle is about 145.5° in the Pv phase.

Atom	Site	x	y	z	Biso (Å^2)
Ca	4c	0	0.7492	1/4	0.40
Ir	4a	0	0	0	0.32
O1	4c	0	0.0779	1/4	0.70
O2	8f	0	0.3658	0.4452	0.79
Ir-O1 (×2)	1.978		Ir-O1-Ir	134.3
Ir-O2 (×4)	2.066		O1-Ir-O2	86.3
<Ir-O>	2.037		O1-Ir-O2	93.7
Ir-Ir (×2)	3.1472
Ir-Ir (×2)	3.651

Table 2.

Refined positional parameters and selected bond lengths (Å) and bond angles (°) for pPv CaIrO₃ from single-crystal XRD [28]: space group Cmcm(No. 63), a= 3.1472 Å, b= 9.8655 Å, c= 7.3018 Å, V= 226.71 ų, Z = 4.

Atom	Site	x	y	z	Biso (Å^2)
Ca	4c	-0.01403	0.05962	1/4	0.71
Ir	4b	0.5	0	0	0.27
O1	4c	0.10487	0.47110	1/4	0.92
O2	8d	0.69257	0.30488	0.05602	1.07
Ir-O1 (×2)	2.006		Ir-O1-Ir	146.15
Ir-O2 (×2)	2.020		Ir-O2-Ir	144.95
Ir-O2 (×2)	2.038
<Ir-O>	2.021

Table 3.

Refined positional parameters and selected bond lengths (Å) and bond angles (°) for Pv CaIrO₃ from powder XRD[30]: space group Pbnm(No. 62), a= 5.35046 Å, b= 5.59291 Å, c= 7.67694 Å, V= 229.73 ų, Z = 4.

2.3. Physical properties

pPv CaIrO₃It is an antiferromagnetic insulator with T_N ≈ 110 K. Due to the difficulty in obtaining single-phase samples, the physical properties of pPv CaIrO₃ were not characterized until 2006 by Ohgushi et al. [25], who first reported its electrical transport and magnetic properties on polycrystalline samples synthesized under HPHT conditions. As shown in Figure 3, its resistivity ρ(T) increases quickly upon cooling, following the Arrhenius-type behaviour, i.e. ρ(T) = ρ₀ exp(∆/T), with the activation energy ∆ = 0.17 eV; magnetic susceptibility χ = M/H exhibits a sharp transition at T_N = 115 K, below which a weak ferromagnetic moment of ~ 0.04 μ_B/Ir was observed from the isothermal magnetization curve. In addition, a huge coercive field H_c ≈ 4 T was evidenced at low temperatures. Density functional calculations by Subedi [33] demonstrated that the inclusion of SOC can split the t_2g bands into fully filled J_eff = 3/2 bands and half-filled J_eff = 1/2 bands, as shown schematic in Figure 1(c), and that both SOC and moderate U are required to reconcile the experimentally observed Mott insulating behaviour. By performing the resonant X-ray diffraction at the L absorption edges of pPv CaIrO₃ single crystals, Ohgushi et al. [14] determined its magnetic structure as a stripe-type antiferromagnetic order, i.e. the Ir moments are aligned parallel along the aaxis and antiparallel along the caxis with a canted ferromagnetic component along the baxis. Bogdanov et al. [34] carried out ab initioquantum chemical calculations and reproduced such a striped antiferromagnetic structure. Moreover, their calculations predicted a strong antiferromagnetic exchange interaction of J_c = 121 meV through the corner-shared path along the caxis, and a weak nearest-neighbour ferromagnetic coupling of J_a ≈ -7.3 meV within the edge-shared chains along the aaxis. In this regard, pPv CaIrO₃ can be regarded as a J_eff = 1/2 quasi-1D antiferromagnet. Although the above results suggested that a J_eff = 1/2 ground state is realized in pPv CaIrO₃, first-principles calculations [33, 34] evidenced significant deviations from the ideal J_eff = 1/2 state with highly uneven admixture of the t_2g components due to the pronounced tetragonal distortion. In agreement with these calculations, a very recent resonant inelastic X-ray scattering (RIXS) study by Sala et al. [15] confirmed the departure from the J_eff = 1/2 state. By analyzing the RIXS spectrum, they estimated the effective tetragonal crystal field splitting ∆ = –0.71 eV and the SOC ζ_SO = 0.52 eV, from which a ground state wave function $\left|0,\pm ⟩=\mp 0.32\right|xy, \mp ⟩+0.67\left(\left|yz,\pm ⟩\mp i\right|zx,\pm ⟩\right)$with a dominant yz±izx orbital character was derived.

The Mott insulating nature of quasi-2D pPv CaIrO₃ have motivated Ohgushi et al. [25] to metallize it via the carrier doping. They successfully prepared a series of hole-doped Ca_1–xNa_xIrO₃ (0 ≤ x≤ 0.37) with pPv structure under HPHT conditions and realized a filling-control antiferromagnetic insulator to paramagnetic metal transition around x= 0.3, near which, however, no superconductivity was observed. Nevertheless, anomalous properties such as the non-Fermi-liquid behaviour and positive magnetoresistance violating Kohler’s rule were observed for the metallic samples. In the same report, attempt of electron doping via Y³⁺ substitutions for Ca²⁺ was unsuccessful due to the formation of pyrochlore phase. In a recent work by Gunasekera et al. [35], however, Y-substituted Ca_1–xY_xIrO₃ (0 ≤ x≤ 0.5) samples with pPv structure were successfully fabricated via a conventional solid-state reaction route at ambient pressure. Similar with the Na⁺-doped case, about 30%-Y³⁺ doping can also drive an insulator-to-metal transition; superconductivity was not observed either in this case. In striking contrast with the gradual suppression of T_N by Na doping, surprisingly, T_N remains unchanged upon Y substitutions up to 50%, except that the magnitude of ac susceptibility peak decreases about one order. Further experiments are needed to exclude the possibility that the magnetic order arises from the minor CaIrO₃ phase. Anyhow, metallization of the quasi-2D pPv CaIrO₃ represents an interesting direction to pursue exotic electronic state in the vicinity of metal–insulator transition.

Figure 3.

Temperature dependence of (a) resistivity ρ(T) and (b) magnetic susceptibility M/H for the two polymorphs of CaIrO₃, pPv for post-perovskite and Pv for perovskite. Adapted from Reference [13].

Pv CaIrO₃In sharp contrast with the antiferromagnetic insulating ground state of pPv CaIrO₃, the Pv phase has been reported as a Pauli paramagnetic metal by Sarkozy et al. [12] in 1974. Recent characterizations by Ohgushi et al. [13] on the dense pellets obtained via HPHT synthesis confirmed the paramagnetic nature, but the temperature dependence of resistivity shows bad metal behaviour with a non-diverge upturn at low temperatures, Figure 3. Such a bad metallic behaviour was reproduced on the epitaxially stabilized thin films grown on various substrates [26, 32], and has been ascribed to a semimetallic ground state with the conduction and valence band touching at Fermi level. The observations of a sign change and a nonlinear magnetic-field dependence of the Hall resistance are consistent with the coexistence of electron and hole charge carriers [26]. As discussed below for Pv SrIrO₃, the semimetallic state might originate from the symmetry-protected Dirac nodes around the Fermi level due to a combined effect of SOC and reflection symmetry of the Pbnmorthorhombic lattice. In light of the recent theoretical proposals for the orthorhombic Pv iridates discussed below, further experimental studies on the semimetallic Pv CaIrO₃ are highly desirable.

Figure 4.

Insulator–metal transition in pPv CaIrO₃ induced by hole (Na⁺) and electron (Y³⁺) doping. (a, b) shows the temperature dependence of resistivity and magnetic susceptibility of Ca_1–xNa_xIrO₃. Adapted from Reference [25]; (c, d, e) show the temperature dependence of resistivity and ac magnetic susceptibility of Ca_1–xY_xIrO₃. Adapted from Reference [35].

pPv versus Pv CaMO₃ (M = Ir, Rh, Ru)The distinct ground states of pPv and Pv CaIrO₃ reflect the intimate structural–property relationships. In addition to CaIrO₃, both CaRuO₃ [36] and CaRhO₃ [37] have also been reported to possess quenchable Pv and pPv polymorphs. Besides the importance in geosciences as analogy materials of MgSiO₃, these compounds with partially filled d-electron shells are important correlated electron systems with intriguing physical properties [37, 38]. In a similar manner as CaIrO₃, their ground states differ sharply as the structure changes: Pv CaRuO₃ is a well-known exchanged-enhanced paramagnetic metal on the verge of a ferromagnetic instability, whereas the pPv phase is an antiferromagnetic insulator with T_N = 270 K [38]; Pv CaRhO₃ is a Pauli paramagnetic metal while the pPv phase is insulating and undergoes a canted antiferromagnetic transition below T_N = 90 K [37]. Current first-principles calculations for the pPv compounds failed to capture the correct ground state; it seems that in addition to electron–electron correlations, SOC also plays an essential role in producing the insulating ground state for these 4d and 5d-electron systems [39].

In addition to the interest in fundamental physics, the CaIrO₃ ceramics have also been investigated by Keawprak et al. [40] for the potential thermoelectric applications. They prepared both phases of CaIrO₃ with spark plasma sintering technique and evaluated their thermoelectric properties from room temperature up to 1023 K. The highest dimensionless figure of merit (ZT) reaches 0.02 and 0.003 for Pv and pPv phase, respectively.

3. SrIrO₃

Depending on the synthesis conditions, SrIrO₃ can form in two different structures, i.e. the monoclinically distorted 6H polytype and the orthorhombic GdFeO₃-type Pv structure [8]. The former is a rare stoichiometric oxide exhibiting non-Fermi-liquid behaviours near a ferromagnetic quantum critical point [11]. The latter was recently found to be an exotic narrow-band semimetal that may harvest many topological and magnetic insulating phases [10, 41, 42].

3.1. Synthesis

The 6H phase can be readily prepared in the polycrystalline form at ambient pressure by sintering the stoichiometric mixture of SrCO₃ and IrO₂ (or Ir) at 900–1,100°C in air [8]. Single crystals of 6H phase with dimensions ~0.4 × 0.4 × 0.6 mm³ have been grown in Pt crucibles with the SrCl₂ self-flux techniques [11]. The Pv phase is a HP form of SrIrO₃. Longo et al. [8] performed the first HPHT syntheses and established the temperature–pressure phase diagram for the 6H-Pv transformation of SrIrO₃. It was found that the 6H phase transforms to the Pv structure above 1,650°C at 2 GPa and above 700°C at 5 GPa. Recent HPHT syntheses of Pv SrIrO₃ were usually performed at 1,000–1,100°C and 5–6 GPa [43, 44]. For these samples, Rietveld refinements on the powder XRD patterns evidenced the presence of ~3–4 wt.% IrO₂ impurity. Since the Pv phase is metastable, it remains a challenge to obtain sizable bulk single crystals under HP conditions. However, Pv SrIrO₃ films and superlattices have been stabilized at ambient pressure via applying the epitaxial strain with various techniques, including the metalorganic chemical vapour deposition [9], pulsed laser deposition [45], and reactive oxide molecular-beam expitaxy [42]. As discussed below, given the tolerance factor t< 1, it is unusual for SrIrO₃ to adopt the 6H structure at ambient pressure. It was recently reported [46, 47] that the 6H structure of SrIrO₃ can be destabilized by partial substitution of M = Li, Fe, Co, Ni, Zn for Ir in SrIr_1–xM_xO₃ and converted to the Pv structure within a narrow composition range around x= 0.2. In these cases, it was suggested that the presence of e_g type orbitals on the M ions contributes to the breakdown of face-sharing octahedral dimmers in the 6H structure.

3.2. Crystal structure

6H SrIrO₃The crystal structure of 6H SrIrO₃ was first determined by Longo et al. [8] as a monoclinic distortion of the hexagonal BaTiO₃ structure. The 6H hexagonal structure can be described as close-packed SrO₃ layers stacked perpendicular to the c axis in the sequence hcchcc, where h and c refer to hexagonal (ABAB...) and cubic (ABCABC...) close packing, respectively. The Ir atoms occupy the oxygen octahedra formed by the SrO₃ layers, and the IrO₆ octahedra share common faces across an h layer and common corners across a c layer. As a result, the above hcchcc stacking sequence results in two independent positions for the Ir atoms. As shown in Figure 5(a), two Ir2O₆ octahedra form pairs of face-shared octahedra that are joined by common corners to a plane of corner-sharing Ir1O₆ octahedra. Therefore, the 6H structure can be alternatively depicted as a stacking of layers of corner- (C) and face (F)-sharing IrO₆ octahedra in the sequence FCCFCC along the c axis.

In the original work by Longo et al., the oxygen positional parameters were not refined due to the low scattering of oxygen relative to Ir and Sr. Based on the neutron diffraction data, Qasim et al. [46] recently provided a full refinement on the crystal structure of 6H SrIrO₃ with a= 5.6040 Å, b= 9.6256 Å, c= 14.1834 Å, and β= 93.202° in space group C2/c(No. 15). The refined positional parameters and selected bond lengths and bond angles after Reference [46] are listed in Table 4. In this structure, the Ir1O₆ octahedron has an average Ir-O distance of 2.006 Å typical of Ir⁴⁺ with the individual distances in a narrow range 1.987–2.038 Å. In contrast, the Ir2O₆ octahedra in the Ir₂O₉ dimers are not regular with a longer average Ir-O distance of 2.030 Å. The Ir2–Ir2 distance, 2.770 Å, is relatively short and close to the separation of 2.72 Å found in Ir metal, suggesting a strong Ir–Ir bonding across the common faces. Variable temperature XRD measurements on the 6H phase confirmed that the monoclinic structure is stable without any structural transition up to 1,000°C in air.

Figure 5.

Crystal structure of SrIrO₃ polytypes: (a) 6H and (b) Pv.

Pv SrIrO₃Similar as Pv CaIrO₃, it consists of a 3D network of corner-sharing IrO₆ octahedra that are cooperatively rotated and tilted about the pseudocubic [110] and [001] axes, Figure 5(b). Blanchard et al. [44] recently performed a thorough study on the crystal structure of Pv SrIrO₃ based on the synchrotron and neutron diffraction data. The crystal structure was refined in space group Pbnm(No. 62) with Sr at4c(x, y, 1/4), Ir at 4a(0, 0, 0), O1 at 4c(x, y, 1/4), and O2 at 8d(x, y, z) sites, respectively. The lattice parameters at room temperature are determined as a= 5.60075 Å, b= 5.57115 Å, and c= 7.89601 Å. The obtained positional parameters and selected bond lengths and bond angles after Reference [44] are listed in Table 5. As can be seen, the individual IrO₆ octahedron is relatively rigid with three Ir–O distances being approximately equal. The average Ir–O distance at 300 K of 2.016 Å is consistent with the ionic radii sum for Ir⁴⁺ and O^2–. From the refined atomic coordinates, Blanchard et al. also estimated the two independent octahedral tilt angles, i.e. ψ = 11.5° for out-of-phase tilt about the pseudocubic [110] axis, and φ = 8.7° for in-phase tilt about the pseudocubic [001] axis, respectively. These tilting angles were found to be nearly temperature-independent below room temperature. The orthorhombic Pbnmstructure was shown to persist over the temperature range 3–1,070 K.

6H-Pv transformationAs pointed out by Longo et al. [8], SrIrO₃ and SrMnO₃ are the only SrBO₃ (B = Ti, Zr, Hf, Cr, Mo, Tc, Fe, Ru, Sn, Pb, Ce, Th) compounds that do not adopt the Pv structure at ambient pressure. Given the tolerance factor t≤ 1, the Pv structure would be stabilized for these compounds. However, SrMnO₃ has the 4H polytype structure with a stacking sequence of hchc along the caxis, while SrIrO₃ crystallizes in the 6H polytype as mentioned above. It would appear that the hexagonal polytypes with their face-shared octahedra and trigonal crystal fields are stabilized by the outer electron configurations that allow for metal–metal bonding along the caxis. For example, in the case of low-spin Ir⁴⁺, the trigonal crystal field of the hexagonal polytype should split the t_2g⁵ orbitals to e_gσ⁰e_gπ⁴a_1g¹, which allow for metal–metal bonding along the caxis via the half-filled a_1g orbitals. Thus, the 6H SrIrO₃ and 4H SrMnO₃ can be regarded as a compromise between the continuous face-shared chains of the 2H polytype and the geometrically favoured Pv structure. Since high pressure prefers the cubic close packing with a higher density than the hexagonal close packing, 6H SrIrO₃ transforms to the Pv structure under high-pressure conditions with a ~3% volume reduction.

Atom	Site	x	y	z	Biso (Å^2)
Sr1	4e	0	0.0092	1/4	0.0285
Sr2	8f	0.0122	0.6667	0.0957	0.0482
Ir1	4a	0	0	0	0.0478
Ir2	8f	0.9820	0.6660	0.84698	0.0459
O1	4e	0	0.4981	1/4	0.0584
O2	8f	0.2411	0.2649	0.2603	0.0287
O3	8f	0.8112	0.4077	0.0474	0.0572
O4	8f	0.9407	0.1544	0.4087	0.0535
O5	8f	0.3238	0.4204	0.1058	0.0586
Ir1-O3 (×2)	2.038		Ir1-O3-Ir2	149.6
Ir1-O4 (×2)	1.987		Ir1-O4-Ir2	158.8
Ir1-O5 (×2)	1.994		Ir1-O5-Ir2	149.3
<Ir1-O>	2.006
Ir2-O1	2.100		Ir2-O1-Ir2	82.5
Ir2-O2	2.055		Ir2-O1-Ir2	85.1
Ir2-O2	2.040
Ir2-O3	1.974
Ir2-O4	1.957
Ir2-O5	2.051
<Ir2-O>	2.030
Ir2-Ir2	2.770

Table 4.

Refined positional parameters and selected bond lengths (Å) and bond angles (°) for 6H SrIrO₃ from neutron diffraction [46]: space group C2/c(No. 15), a= 5.60401 Å, b= 9.6256 Å, c= 14.1834 Å, β= 93.202°, V= 763.89 ų, Z = 12.

Atom	Site	x	y	z	Biso (Å^2)
Sr	4c	-0.0068	0.4687	1/4	0.019
Ir	4a	0	0	0	0.017
O1	4c	0.0718	0.0049	1/4	0.019
O2	8d	0.2126	0.2877	-0.0369	0.022
Ir-O1 (×2)	2.015		Ir-O1-Ir	156.92
Ir-O2 (×2)	2.018		Ir-O2-Ir	156.22
Ir-O2 (×2)	2.018
<Ir-O>	2.017

Table 5.

Refined positional parameters and selected bond lengths (Å) and bond angles (°) for Pv SrIrO₃ from neutron diffraction [44]: space group Pbnm(No. 62), a= 5.60075 Å, b= 5.57115 Å, c= 7.89601 Å, V= 246.376 ų, Z = 4.

3.3. Physical properties

6H SrIrO₃Although the 6H SrIrO₃ has been synthesized more than 50 years ago, its physical properties were not characterized in detail until 2007 by Cao et al. [11], who reported the magnetic, electrical transport, and calorimetric properties of 6H SrIrO₃ single crystals grown out of the SrCl₂ flux. The primary results are summarized in Figure 6. Magnetic susceptibility χ(T) measurements evidenced no long-range magnetic order down to 1.7 K, but exhibited at low temperatures strong enhancements that diverge as χ∝ T^γ with 1/2 < γ< 1, suggesting the proximity to a ferromagnetic instability. The isothermal magnetization M(H) at 1.7 K indeed displays a saturation behaviour at H~ 3 T, yet the saturation moment is very small, being less than 0.03 μ_B/Ir. The low-temperature specific heat C(T) exhibits a pronounced –TlogTdependence, which is characteristic of non-Fermi-liquid systems. Such a C/T~ –logTbehaviour can be readily enhanced in low applied fields up to 1.1 T, vanishes for H> 2 T, and eventually changes to a T^3/2 power law expected for a ferromagnetically ordered state at H= 8 T. In accordance with the C(T) results, both the c-axis resistivity, ρ_c, and the ab-plane resistivity, ρ_ab(T), follow a non-Fermi-liquid T^3/2 dependence over a wide temperature range up to 120 K under zero field, while a Fermi-liquid T² behaviour is restored upon applying an external field H≥ 5 T. Taking into account all these observations, 6H SrIrO₃ can be regarded a rare example of stoichiometric oxide that exhibits non-Fermi-liquid behaviours near a ferromagnetic quantum critical point. As will be shown explicitly in BaIrO₃, such a quantum critical point can be realized via subtle structural variations.

Figure 6.

Physical properties of 6H SrIrO₃ single crystal. Adapted from Reference [11]. (a, b) show the temperature dependence of magnetic susceptibility measured along thecaxis andabplane, inset of (a) shows the magnetization curve at 1.7 K. (c) shows the specific heat C(T) data illustrating theC/T~ –logTbehaviour. (d) shows the resistivity following theT^3/2 behaviour.

Pv SrIrO₃In the original work by Longo et al. [8], Pv SrIrO₃ has been described as a Pauli paramagnetic metal. In 2008, Zhao et al. [43] reinvestigated the physical properties of Pv SrIrO₃ bulk sample prepared under 5 GPa and 1,000°C. They observed two characteristic temperatures T^* ≈ 170 K and T_MI ≈ 44 K: at T^*, the paramagnetic susceptibility χ(T) starts to increase with temperature, and the resistivity ρ(T) exhibits a slope change, followed below T^* by the presence of unusual linear field dependence positive magnetoresistance (MR) that reaches about 12% at 5 K and 7 T; a broad metal–insulator transition was observed at T_MI. However, these observations are largely disapproved by the very recent work of Blanchard et al. [44], who studied the bulk samples prepared under 6 GPa and 1,100°C. As shown in Figure 7, it was found in the latter work that ρ(T) exhibits metallic conductivity down to 2 K, following Fermi-liquid T² dependence between 2 and 30 K, without showing an upturn at low temperature. In addition, they observed a smaller positive MR up to 2% at 7 Tand 2–50 K. These discrepancies might originate from the polycrystalline nature of the studied samples, in which the extrinsic effects such as the grain boundary and impurities can largely influence the transport properties. As mentioned above, Pv SrIrO₃ films of single-crystal quality can be stabilized via applying epitaxial strain. The resistivity upturn at low temperatures have been frequently observed in these thin films [9, 48], but the upturn temperature displays a broad distribution, in support of an extrinsic property due to weak Anderson localization. Nevertheless, such sensitivity to defects reflects the bad metal character of semimetallic Pv SrIrO₃ approaching the boundary of metal–insulator transition.

Figure 7.

Temperature dependence of (a) magnetic susceptibility and (b) resistivity of Pv SrIrO₃. Adapted from Reference [44].

As the end member of the Ruddlesden–Popper series Sr_n+1Ir_nO_3n+1 (n= 1, 2, ∞), Pv SrIrO₃ has recently attracted much attention due to the presence of nontrivial features within the J_eff = 1/2 bands. Density-functional theory first-principles calculations by Carter et al. [10] found that in the strong SOC limit the bands near the Fermi energy are mostly composed of J_eff = 1/2 states. Interestingly, they found a node near the U point, Figure 8(a), thus revealing the semimetallic nature of Pv SrIrO₃. By constructing a tight-binding model, they confirmed the presence of a line node near the U point in the Brilloiun zone, and further shown that the line node originates from the reflection symmetry of the crystal structure at the z= 1/4 and 3/4 planes presented in the orthorhombic Pbnmspace group. Since the line node is protected by the underlying lattice symmetry, it has been further proposed that perturbations breaking the sublayer reflection symmetry can lift the line node and convert the system into an insulating phase; the system may become a strong topological insulator at a certain point. In addition, as shown in Figure 8(b), magnetically ordered metallic and insulating phases have also been proposed to arise in the U versus SOC phase diagram of Pv SrIrO₃ [41]. Moreover, Chen et al. [49] further proposed that the presence of reflection symmetry in orthorhombic Pv iridates may realize a novel class of topological crystalline metals with zero-energy surface states at certain planes.

Figure 8.

(a) LDA band structure of Pv SrIrO₃ with Hubbard U = 2 eV and SOC, demonstrating the presence of the node near the U point of J_eff = 1/2 band near the Fermi level; (b) the phase diagram of Pv SrIrO₃ in the U-SOC plane containing three phases: magnetic metal (MM), nonmangetic metal or semimetal (M/SM), and magnetic insulator (MI). Adapted from Reference [41].

Recent angle-resolved photoemission spectroscopy on Pv SrIrO₃ films by Nie et al. [42] has uncovered such an exotic semimetallic state with very narrow bands near the Fermi surface consisting of heavy hole-like pockets around (±π, 0) and (0, 0) and light electron-like pockets at (±π/2, ±π/2). Surprisingly, the bandwidth of Pv SrIrO₃ is found to be narrower than that of Sr₂IrO₄, in contrary to the general expectations of broaden bandwidth with increasing dimensionality [7]. Since the semimetallic ground state has been confirmed experimentally, it is of particular interest to achieve the proposed topological and/or magnetic states via tuning the SOC, U, and/or lattice symmetry. In this regard, Matsuno et al. [45] have made an important step towards these exotic phases; they tailored a spin-orbit magnetic insulator out of the semimetallic state via controlling the dimensionality of [(SrIrO₃)_m, SrTiO₃] superlattices. By utilizing HPHT synthesis, we prepared a series of Sn-doped SrIr_1–xSn_xO₃ orthorhombic perovskites. We found that substitutions of isovalent, nonmagnetic Sn⁴⁺ for Ir⁴⁺ ions lead to a breakdown of the semimetallic state, and convert the paramagnetic, semimetallic ground state of Pv SrIrO₃ to an antiferromagnetic insulator with a concomitant metal–insulator transition at T_N [50]. These recent experimental efforts demonstrated that semimetallic Pv SrIrO₃ is a promising candidate for realizing distinct topological and magnetic insulating states that deserve further investigations in the near future. On the other hand, the Pv SrIrO₃ film has also been regarded as potential electrode material for microelectronic devices [9].

4. BaIrO₃

At ambient pressure, BaIrO₃ crystallizes in the nine-layer (9R) polytype. It is the first known ferromagnetic insulator with T_c ≈ 180 K among the 5d TMOs [17]. Detailed studies on single crystals revealed a charge-density-wave (CDW) formation below the ferromagnetic order [18, 51]. Recent experimental [52] and theoretical [53] investigations further revealed it as an exotic spin-orbit Mott insulator that is of great current research interest. Following the general trend of perovskite hexagonal polytypes, we have explored the high-pressure sequences of BaIrO₃ and found three more polytypes, i.e. 5H, 6H, and 3C [19, 20, 21]. Their ground states exhibit an interesting evolution from a ferromagnetic insulator to a Pauli paramagnetic metal passing through a ferromagnetic quantum critical point tuned by the gradual structural changes as detailed below.

4.1. Synthesis

The ambient-pressure 9R phase can be readily obtained by sintering the stoichiometric mixtures of BaCO₃ and Ir at 1,000°C in air. The sample should be cooled down slowly for the last sintering in order to ensure an oxygen stoichiometry [54]. Single crystals have been reported to grow out of the BaCl₂ flux at a relatively low temperature of 1,000 K [18]. HPHT synthesis is needed for all the other polytypes [19, 21, 55, 56]. For the HP syntheses around 1,000°C, the 9R polytype is stable up to 3 GPa, the 5H phase exists only in a narrow pressure range around 4 GPa, the 6H phase is stabilized in a wide pressure range from 5 to ~20 GPa, and the 3C phase was finally obtained at 25 GPa. We have employed the two-stage (Walker- or Kawai-type) multianvil systems for the HPHT syntheses. During the HPHT experiments, the sample was first compressed to the desired pressure by eight truncated tungsten carbide anvils, and then the temperature was increased to ~1,000°C and kept for 30 min before quenching to room temperature. The resultant samples were recovered after releasing pressure and then subjected to various characterizations at ambient pressure.

4.2. Crystal structure

9R BaIrO₃As shown in Figure 9(a), the crystal structure of the 9R phase consists of Ir₃O₁₂ trimers of face-sharing octahedra that are linked by their vertices to form columns parallel to the c-axis, with a stacking of layers of corner-sharing (C) and face-sharing (F) IrO₆ octahedra in the order FFCFFCFFC along the caxis. Except for the monoclinic distortion, it is isostructural with the 9R BaRuO₃. The monoclinic distortion generates twisting and buckling of the Ir₃O₁₂ trimers that are tilted ~12° relative to each other. Here, we adopted the crystal structure of 9R BaIrO_2.94 obtained by Powell et al. [54] from the NPD data, which were refined in a structural model defined in the C2/mspace group, with three kinds of Ba atoms at 4i(x, 0, z) positions, four types of unequivalent Ir atoms at 4i, 2a(0, 0, 0) and 2d(0.5, 0, 0.5) sites, and six types of oxygen atoms at 4iand 8j(x, y, z) positions. The obtained unit-cell parameters are a= 9.9992 Å, b= 5.7490 Å, c= 15.1707 Å, and β= 103.27°. The final positional parameters and the selected bond lengths and bong angles after Reference [54] are listed in Table 6. Ir1–Ir2 and Ir3–Ir4 distances, of 2.618 Å and 2.627 Å respectively, are even smaller than the separation of 2.72 Å found in Ir metal, which indicates significant interactions between iridium cations at the centre of face-shared pairs of octahedra. It is important to note that, although this polytype has been compared to the ambient 9R BaRuO₃, with rhombohedral (R-3m) symmetry and a stacking sequence (FFC)₃, the monoclinic distortion described for ambient 9R BaIrO₃ actually involves a shorter periodicity, with a stacking sequence (FFC)₂ along the caxis, as shown in Figure 9(a).

Figure 9.

Crystal structure of the BaIrO₃ polytypes: (a) 9R, (b) 5H, (c) 6H, and (d) 3C.

Atom	Site	x	y	z	Biso (Å^2)
Ba1	4i	0.7779	0	0.2501	0.42
Ba2	4i	0.3686	0	0.0720	0.42
Ba3	4i	0.1515	0	0.4224	0.42
Ir1	4i	0.0845	0	0.1766	0.16
Ir2	2a	0	0	0	0.16
Ir3	4i	0.4657	0	0.3230	0.16
Ir4	2d	0.5	0	0.5	0.33
O1	4i	0.2926	0	0.2287	0.33
O2	8j	0.0507	0.2421	0.2617	0.33
O3	4i	0.8931	0	0.0994	0.33
O4	8j	0.1164	0.2362	0.0839	0.33
O5	8j	0.4036	0.2291	0.4040	0.33
O6	4i	0.6427	0	0.4240	0.33
Ir1-O1	2.049		Ir1-Ir2	2.618
Ir1-O2 (×2)	1.979		Ir3-Ir4	2.627
Ir1-O3	2.001
Ir1-O4 (×2)	2.032		Ir1-O1-Ir3	157.3
<Ir1-O>	2.01		Ir1-O2-Ir3	164.0
Ir2-O3 (×2)	2.038		Ir1-O3-Ir2	80.8
Ir2-O4 (×4)	2.034		Ir1-O4-Ir2	80.1
<Ir2-O>	2.04		Ir3-O5-Ir4	81.4
Ir3-O1	1.978		Ir3-O6-Ir4	80.0
Ir3-O2 (×2)	2.037
Ir3-O5 (×2)	1.955
Ir3-O6	2.057
<Ir3-O>	2.02
Ir4-O6 (×2)	2.030
Ir4-O5 (×4)	2.035
<Ir4-O>	2.03

Table 6.

Refined positional parameters and selected bond lengths (Å) and bond angles (°) for 9R BaIrO₃ from neutron diffraction [54]: space group C2/m(No. 12), a= 9.9992 Å, b= 5.7490 Å, c= 15.1707 Å, β= 103.27°, V= 848.81 ų, Z = 12.

5H BaIrO₃The 5H phase was discovered as a new perovskite polytype [19]. As shown in Figure 9(b), its crystal structure contains chains of double dimer units that are corner-connected via oxygen atoms. These clusters of four octahedra are interleaved with single layers of vertex-sharing IrO₆ octahedra, forming infinite chains along the caxis. Adjacent chains are interlinked along the aand bdirections via Ir–O–Ir vertex-sharing bridges. Alternatively, the structure can be described as stacking of layers of corner-sharing (C) and face-sharing (F) IrO₆ octahedra along the sequence FCFCC. The crystal structure was refined in the monoclinic C2/m(No. 12) space group, with three kinds of Ba atoms at 2c(0.5, 0.5, 0.5) and 4i(x, 0, z), three types of Ir atoms at 2a(0, 0, 0) and 4isites, and six unequivalent oxygen atoms at 8j(x, y, z), 4i, 2d(0.5, 0, 0.5), and 4f(0.75, 0.75, 0) positions. The lattice parameters at room temperature are determined as a= 9.9554 Å, b= 5.7434 Å, c= 13.8049 Å, and β= 119.23°. The final positional parameters and the selected bond lengths and bond angles after Reference [19] are listed in Table 7. As can be seen, Ir–O distances vary in the range 1.90 Å for Ir1–O4 to 2.23 Å for Ir2–O3. The average value, of 2.03 Å, is consistent with the ionic radii sum for Ir⁴⁺ and O^2-. It is noteworthy that the structure contains three kinds of octahedra with rather distinct average sizes: <Ir–O> are 1.985 Å, 2.072 Å, and 2.017 Å for Ir1, Ir2, and Ir3 octahedra. The two largest octahedra, Ir2 and Ir3, are those forming dimers, where the Ir–O bonds are weakened by the Ir–Ir bonds. According to these bond distances, the bond valences for the three types of octahedra are 4.26(8)+, 3.35(8)+, and 4.06(9)+, indicating that Ir1 and Ir2 are under certain compressive and tensile stresses, respectively.

6H BaIrO₃Same as the 6H SrIrO₃, the crystal structure of 6H BaIrO₃ consists of dimers of face-sharing octahedra separated by single corner-sharing octahedron, showing the sequence FCCFCC along the caxis. Based on the XRD data, we have refined its crystal structure in the monoclinic C2/cspace group with two kinds of Ba atoms at 4e(0, y, ¼) and 8f(x, y, z) positions, Ir1 at 4a(0, 0, 0) and Ir2 at 8fsites, and four independent oxygen atoms, O1 at 4e, O2, O3, and O4 at 8fpositions. The obtained unit-cell parameters are a= 5.7483 Å, b= 9.9390 Å, c= 14.3582 Å, and β= 91.319°. The final positional parameters and selected bond lengths and bond angles after Reference [19] are listed in Table 8. As can be seen, the Ir2O₆ octahedra within the face-sharing dimmers are considerably more expanded than the Ir1O₆ octahedra, with average Ir–O distances of 2.16 and 1.99 Å, respectively. This is probably a consequence of the metal–metal bond linking the couples of Ir2 atoms in the dimmers, with Ir2–Ir2 distances of 2.710 Å.

Atom	Site	x	y	z	Biso (Å^2)
Ba1	2c	0.5	0.5	0.5	1.2
Ba2	4i	-0.191	0	0.7139	0.1
Ba3	4i	-0.247	0.5	0.8886	0.9
Ir1	2a	0	0	0	3.2
Ir2	4i	-0.4529	0	0.8215	1.0
Ir3	4i	-0.6046	0	0.5920	2.4
O1	8j	0.053	0.72	0.7002	2.3
O2	8j	-0.0093	-0.770	0.1085	1.2
O3	4i	0.703	0	0.303	4.0
O4	4i	0.217	0	0.0607	0.6
O5	2d	0.5	0	0.5	1.5
O6	4f	0.75	0.75	0.5	3.9
Ir1-O2 (×4)	2.029		Ir2-Ir3	2.735
Ir1-O4 (×2)	1.898
<Ir1-O>	1.985		Ir2-O1-Ir3	84.0
Ir2-O1 (×2)	2.12		Ir1-O2-Ir2	165.1
Ir2-O2 (×2)	2.23		Ir2-O3-Ir3	79.1
Ir2-O3	2.038		Ir1-O4-Ir2	160.3
Ir2-O4	2.105		Ir3-O5-Ir3	180
<Ir2-O>	2.072		Ir3-O6-Ir3	180
Ir3-O1 (×2)	2.004
Ir3-O3	2.11
Ir3-O5	1.994
<Ir3-O>	2.017

Table 7.

Refined positional parameters and selected bond lengths (Å) and bond angles (°) for 5H BaIrO₃ from neutron diffraction [19]: space group C2/m(No. 12), a= 9.9554 Å, b= 5.7434 Å, c= 13.8049 Å, β= 119.231°, V= 688.8 ų, Z = 10.

3C BaIrO₃A single-phase Pv BaIrO₃ was finally obtained at 25 GPa [21]. Instead of the simple cubic phase with space groupPm-3m, it was found that the XRD pattern of the Pv phase can be refined excellently in the tetragonal I4/mcm(No. 140) space group with the Ba atom at 4b(0, ½, ¼), the Ir atom at 4c(0, 0, 0), and two kinds of O atoms at 4a(0, 0, ¼) and 8h(x, x+½, 0) sites. The obtained unit-cell parameters are a= b= 5.7044 Å and c= 8.0926 Å. The final positional parameters and the main bond distances and bond angles after Reference [21] are listed in Table 9. It should be noted that we denoted this phase as “3C” in order to follow the conventional notations.

Atom	Site	x	y	z	Biso (Å^2)
Ba1	4e	0	-0.0052	1/4	0.3
Ba2	8f	0.0078	0.3349	0.0912	0.25
Ir1	4a	0	0	0	0.4
Ir2	8f	0.9936	0.3323	0.8442	0.27
O1	4e	0	0.499	1/4	-0.2
O2	8f	0.2180	0.2390	0.2427	-0.2
O3	8f	0.036	0.846	0.0852	-0.2
O4	8f	0.286	0.087	0.049	-0.2
O5	8f	0.809	0.090	0.103	-0.2
Ir1-O3 (×2)	1.93		Ir1-O3-Ir2	164.4
Ir1-O4 (×2)	2.02		Ir1-O4-Ir2	151.4
Ir1-O5 (×2)	2.01		Ir1-O5-Ir2	153.6
<Ir1-O>	1.99
Ir2-O1	2.19		Ir2-O1-Ir2	76.4
Ir2-O2	2.22		Ir2-O1-Ir2	75.1
Ir2-O2	2.23
Ir2-O3	2.10
Ir2-O4	2.09
Ir2-O5	2.11
<Ir2-O>	2.16
Ir2-Ir2	2.710

Table 8.

Refined positional parameters and selected bond lengths (Å) and bond angles (°) for 6H BaIrO₃ from powder XRD [19]: space group C2/c(No. 15), a= 5.7483 Å, b= 9.9390 Å, c= 14.3582 Å, β= 91.319°, V= 820.12 ų, Z = 12.

The small tetragonal distortion of the 3C BaIrO₃ phase is unexpected; we should have a cubic phase as found for BaRuO₃ formed under high pressure. Such a distortion to tetragonal symmetry by cooperative rotations of the IrO_6/2 octahedra about the caxis is typical of an A²⁺ B⁴⁺O₃ perovskite with a tolerance factor t$\equiv$$$\left(\text{A}-\text{O}\right)/\left[\sqrt{2} \left(\text{B}-\text{O}\right)\right]$$a little smaller than unity. However, stabilization of BaIrO₃ in the 9R polytype at ambient pressure is consistent with t> 1 obtained from tabulated equilibrium ionic radii. The larger compressibility of the Ba−O bond makes it possible to stabilize the 3C phase of BaIrO₃ under 25 GPa pressure, but compression of the Ba−O bond by cubic symmetry should not reduce the tolerance factor below t= 1. Retention of the cubic symmetry of the IrO₆ octahedra shows that the threefold degeneracy of the 5d π* bands is not a factor. In fact, the tolerance factor calculated from the measured <Ba−O> and <Ir−O> bond lengths in Table 9 gives a t= 0.998 consistent with the tetragonal structure observed. Therefore, we conclude that at 25 GPa there has been a first-order transition of the Ba−O equilibrium bond length to give a t< 1, which indicates that the 5d π* bands of the IrO₆ array may also have transitioned for J_eff =1/2 and 3/2 bands as a result of a reduction of the orbital angular momentum where the bandwidth is broadened. The high-pressure equilibrium (Ba–O) bond length is retained as a metastable bond length on removal of the pressure, and the Ir–O bonds are not under a tensile stress.

Atom	Site	x	y	z	Biso (Å^2)
Ba	4b	0	0.5	1/4	0.72
Ir	4c	0	0	0	0.49
O1	4a	0	0	1/4	0.8
O2	8h	0.2313	0.7313	0	0.8
Ir-O1 (×2)	2.023		Ir-O1-Ir	180
Ir-O2 (×2)	2.023		Ir-O2-Ir	171.1
<Ir-O>	2.023

Table 9.

Refined positional parameters and selected bond lengths (Å) and bond angles (°) for 3C BaIrO₃ from powder XRD [21]: space group I4/mcm(No. 140), a= b= 5.7044 Å, c= 8.0916 Å, V= 263.30 ų, Z = 4.

Polytype structuresThe polytype structures of the ABO₃ oxides and the phase transformation under high pressure were established during the 1960–1970s, see the Review [57]. As a general trend, the number of the hexagonal close packing along the caxis in a unit cell is reduced as the synthesis pressure increases, which led to a decrease (increase) of face(corner)-sharing octahedra. This is consistent with that fact that pressure stabilizes preferentially the denser phase. The observed crystallographic densities of the 9R, 5H, 6H and 3C phases of BaIrO₃ are 8.84, 9.08, 9.17, and 9.36 g/cm³, respectively. They progressively increase as expected, since these phases have been stabilized at increasing pressures. This sequence corresponds, therefore, to more dense packing of the BaO₃ layers along the caxis, showing an evolution to structures with more corner (C) sharing and fewer face (F) sharing octahedra, i.e. C:F ratios increase in the order 1:2 (9R), 3:2 (5H), 2:1 (6H), and ∞ (3C). As detailed below, the physical properties exhibit interesting evolution in response to these systematic structural variations.

4.3. Physical properties

9R BaIrO₃As mentioned above, 9R BaIrO₃ is the first known ferromagnet among the 5d TMOs [17]. Cao et al. [18] performed the first detailed experimental study on the single-crystal samples and uncovered a CDW formation accompanying the ferromagnetic order at T_c ≈ 180 K. The experimental evidences in support of the CDW formation included [18]: (1) a sudden increase of resistivity at T_c, (2) the presence of non-linear conductivity with negative differential resistivity below T_c, (3) an optical gap formation at ~ 1,200 cm^–1 ≈ 9κ_BT_c in the electron excitation spectrum and a splitting of a phonon mode at 350 cm^–1 for T< T_c, and (4) the emergent X-ray satellite structure below T_c. Besides the transitions at T_c ≈ 180 K, two additional anomalies have also been observed [18] upon cooling on the c-axis resistivity ρ_c, which first changes to a metallic behaviour below T₁ = 80 K and then suddenly enters a Mott-like insulating state below T₂ = 26 K, Figure 10. These two additional transitions are absent for the resistivity within the abplane. The simultaneous occurrence of ferromagnetic order and CDW formation is quite unusual, and 9R BaIrO₃ has thus been the subject of extensive investigations since then. Later on, Nakano and Terasaki [51] carried out similar current-voltage (I-V) measurements on their single crystals by using a pulsed current in order to exclude the self-heating effects. Their observations of the giant nonlinear conduction only appearing below 30 K, well below T_c ≈ 180K, questioned the above scenario of a simultaneous onset of a CDW and a ferromagnetic transition. Instead of the sliding motion of CDW, they proposed an interplay between two different bands is likely the origin of the nonlinear conduction observed in BaIrO₃ [51]. Such discrepancy might arise from the different sample quality. Nevertheless, a clear gap opening is unambiguously evidenced at T_c by other experimental probes, such as the Seebeck coefficient [51, 58] and the high-resolution photoemission spectroscopy [59]. Currently, it remains elusive whether the gap opening is driven by the magnetic order or the Fermi surface nesting.

Figure 10.

(a) Temperature dependence of resistivity for 9R BaIrO₃ for two major crystallographic directions. The first inset shows details of c-axis conductivity and the second the sharp peak in dlnρ/d(1/T) denotes the onset of ferromagnetism. (b) Field-cooled (FC) ad zero field-cooled (ZFC) magnetization showing the ferromagnetic transition atT_c. The inset shows isothermal magnetization at several temperatures, illustrating a large hysteresis. Adapted from Reference [18].

The observation of weak ferromagnetism and insulating ground state in the 9R BaIrO₃ has attracted renewed interest in recent years in light of the SOC-driven Mott insulating state for iridates. As for the nature of the weak ferromagnetism, there also exist long-standing discrepancies. Experimentally, a tiny Ir moment of ~0.03 μ_B/Ir was observed below T_c. In addition, a modified Curie-Weiss fitting to the inverse susceptibility also evidenced a small effective moment of ~ 0.13 μ_B [18]. Originally, a spin canting from a localized full-moment antiferromagnetic configuration had been invoked to explain the tiny ordered moment [17]. In contrast, Cao et al. [18] proposed a model of band magnetism with intrinsically small Ir moment due to d–p hybridization and small exchange splitting. Indeed, the muon-spin relaxation measurements by Brooks et al. [60] provided direct experimental evidences in support of a small Ir moment, i.e. they observed clear oscillations below T_c and found an extremely small internal field at the muon site. Such an itinerant picture of band magnetism, however, is incompatible with the observation of high coercive force and anisotropy in magnetization measurements. By employing the X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) techniques, Laguna-Marco et al. [52] recently elucidated an atomic-like nature of the Ir moment with the orbital moment being ~1.5 times larger than the spin moment, thus highlighting the importance of SOC in addressing the magnetic order of 9R BaIrO₃. After taking into account both SOC and moderate on-site coulomb interactions, first-principles calculations by Ju et al. [53] identified 9R BaIrO₃ as an exotic spin-orbit Mott insulator with multiple J_eff = 1/2 states associated with the unique face-sharing Ir₃O₁₂ octahedral units within the structure.

Although the atomic-like nature of Ir local moment in 9R BaIrO₃ was found to be extremely stable against temperature, pressure, and chemical substitutions [52, 61], these external stimuli can easily lead to a breakdown of the weak ferromagnetism and nonmetallic ground state. For example, Cao et al. [62] grown a series of Sr-doped Ba_1-xSr_xIrO₃ single crystals and found that the chemical pressure applied via Sr doping drastically suppresses T_c and immediately leads to a non-metal to metal transition at high temperatures. On the other hand, although the application of external pressure of ~4.5 GPa can also quench the weak ferromagnetism as Sr doping, BaIrO₃ becomes more insulating under pressure [61]. Such a disparate response of transport and magnetic properties to the chemical and physical pressure has been ascribed to the different compression rates of the lattice parameters aand cupon Sr doping and external pressure. Interestingly, Korneta et al. [63] found that a dilute rare-earth R³⁺ doping (~ 4%) of BaIrO₃ can also suppress the weak ferromagnetism and lead to a metallic state, whereas the application of modest external pressure readily restores the insulating state. Further studies are needed to clarify whether the weak ferromagnetism is also recovered in the pressure-induced insulating state. All these above results demonstrate a delicate interplay between structural and electronic degrees of freedom in 9R BaIrO₃.

Figure 11.

Temperature dependence of magnetic susceptibility χ(T) and its inverse χ^–1(T) for the BaIrO₃ polytypes, illustrating the evolution of the magnetic ground state. Adapted from Reference [21].

5H BaIrO₃The 5H phase is a weak ferromagnetic metal with T_c ≈ 50 K, Figure 11. Cheng et al. [20] and Zhao et al. [56] have characterized this compound through measurements of magnetic susceptibility χ(T), resistivity ρ(T), thermoelectric power S(T), and specific heat C(T). A weak ferromagnetic transition at T_c ≈ 50 K was clearly observed in χ(T), and well reflected as a kink in the plots of ρvs T, S/Tvs lnT, and C/Tvs T. In situhigh-pressure resistivity measurements show that T_c decreases gradually with pressure, and reaches about 40 K under 1.5 GPa.

6H BaIrO₃The 6H phase has been independently identified and characterized by Zhao et al. [55] and Cheng et al. [20]. Similar with the 6H SrIrO₃, it is an exchange-enhanced paramagnetic metal with non-Fermi-liquid behaviours. Zhao et al. [55] reported that its resistivity ρ(T) follows a linear Tdependence below 20 K, whereas a T^5/3 dependence was observed for T< 60 K by Cheng et al. [20]. Such a discrepancy should arise from the polycrystalline nature of the studied samples. As mentioned above, a non-Fermi-liquid ρ~T^3/2 behaviour has also been found in the 6H SrIrO₃ single crystals due to the proximity to a ferromagnetic quantum critical point. In order to verify similar situation taking place in 6H BaIrO₃, we measured the thermopower S(T) that is insensitive to grain boundaries. We indeed found a linear relationship in the plot of S/Tversus –lnTover a wide temperature range, in strong support of the realization of ferromagnetic quantum critical point [20]. Based on the low-temperature specific heat and magnetic susceptibility, the obtained Sommerfeld–Wilson ratio ${\text{R}}_{\text{w}}=\frac{{\text{π}}^2}{3}{\left(\frac{{\text{k}}_{\text{B}}}{{\text{μ}}_{\text{B}}}\right)}^2\frac{{\chi }_0}{\text{γ}}=2.14\left(3\right)$provides further evidence for strong electron-electron correlations.

3C BaIrO₃3C BaIrO₃ is characterized as a Pauli paramagnetic metal with a Fermi-liquid behaviour [21]. Its resistivity ρ(T) displays a metallic behaviour down to at least 1.8 K and follows the Fermi-liquid behaviour, i.e. ρ(T) = ρ₀ + AT² below 6 K with ρ₀ = 0.0584(1) Ω cm and A= 8.1(1) μΩ cm K^–2, respectively. The magnetic susceptibility χ(T) exhibits a nearly temperature-independent Pauli paramagnetism with a shallow minimum around 85 K as observed around T* ≈ 170 K in Pv SrIrO₃. Such an upturn with temperature has been ascribed to the higher-order temperature-dependent term in the Pauli paramagnetism. Low-temperature specific heat C(T) analysis yields an electronic specific-heat coefficient γ = 6.84(6) mJ/mol K² and a Debye temperature Θ_D = 335 K.

Figure 12.

A schematic phase diagram of the BaIrO₃ polytypes showing the evolution of magnetic transition temperautreT_c (left) and the electronic specific-heat coeffcieint γ (right) as a function of the corner-to-face sharing octahedral C:F ratio. Adapted from Reference [21].

Structure–property evolutions in the BaIrO₃ polytypesAs shown in Figure 9, the major change of the crystal structures for these polytypes can be described by the stacking sequence of IrO₆ octahedra that evolves from 9R(CFFCFFCFF) $\to$5H(CFCCF) $\to$6H(CCFCCF) $\to$3C(CCC), where C and F stands for corner- and face-sharing, respectively. Figure 11 displays the temperature dependence of magnetic susceptibility χ(T) and its inverse χ^–1(T) for the BaIrO₃ polytypes, illustrating the evolution of the magnetic ground state. Figure 12 shows a schematic phase diagram of the BaIrO₃ polytypes. With increasing C:F ratio in the sequence 9R(1:2) $\to$5H(3:2) $\to$6H(2:1) $\to$3C(∞), the ground states of BaIrO₃ evolve from a ferromagnetic insulator with T_c = 180 K in the 9R phase to a ferromagnetic metal with T_c = 50 K in the 5H phase, then to an exchange-enhanced paramagnetic metal with non-Fermi-liquid behaviour near a ferromagnetic quantum critical point in the 6H phase, and finally to a Fermi-liquid metal in the 3C phase. Such a structure–physical property evolution has been ascribed to a progressive bandwidth broadening in the sense that the corner-shared arrangement of IrO₆ octahedron can facilitate the Ir overlap integral mediated via O-2p orbitals. Since the electronic specific-heat coefficient γ is proportional to the density of states at the Fermi energy, the gradual enhancement of γ from 9R to 6H phase shown in Figure 12 is in agreement with the bandwidth argument. Both the 6H and 3C phases are metallic. Since the 6H phase is close to a ferromagnetic quantum critical point, the γ is much enhanced due to critical fluctuations relative to that in the 3C phase with an even broader bandwidth. From this systematic study on BaIrO₃ polytypes, we can understand why the 6H SrIrO₃ is a non-Fermi-liquid metal near a ferromagnetic quantum critical point [11]. Moreover, the study on BaIrO₃ demonstrated that HPHT synthesis of structurally closely related perovskite polytypes represents an effective approach to fine tune the physical properties of interest via modifying the octahedral arrangement.

5. Conclusions

We have summarized in this chapter the current knowledge on the materials’ synthesis, crystal structure, and physical properties of the “113” alkaline-earth iridates AIrO₃ (A = Ca, Sr, Ba), which display a rich variety of crystallographic and electronic states that are of great current research interest. For CaIrO₃, it can form in either the layered pPv or the orthorhombic Pv structure, and thus serves as an important analogue of MgSiO₃ to investigate the Pv/pPv transformation in the Earth’s lowermost mantle in geosciences. Corresponding to different crystal structures, their electronic ground states differ sharply: the pPv phase is an antiferromagnetic Mott insulator with T_N = 110 K while the Pv phase is a paramagnetic semimetal with possible Dirac nodes protected by the lattice symmetry. The presence of strong structural distortion in pPv CaIrO₃ makes it a model system to investigate the interplay of non-cubic crystal field and SOC in iridates. On the other hand, metallization of the pPv phase via electron or hole doping represents an important approach to realize the exotic electronic states on the verge of insulator–metal transition. For SrIrO₃, it crystallizes in the 6H polytype at ambient pressure and transforms to the orthorhombic Pv structure under high-pressure conditions. The 6H phase is an exchange enhanced paramagnetic metal with non-Fermi-liquid behaviour due to the proximity of ferromagnetic quantum critical point, while the Pv phase is revealed as an exotic narrow-band semimetal with symmetry-protected Dirac nodes within the J_eff = 1/2 band near the Fermi level. The presence of nontrivial features in the low energy electronic states makes these “113” orthorhombic Pv iridates AIrO₃ (A = Ca, Sr) promising candidates for realizing various topological and magnetic insulating phases via tuning the SOC, Hubbard interactions, and/or lattice symmetry. In this regard, epitaxial growth of superlattices and high-pressure synthesis of bulk materials with proper chemical design are currently important approaches to tailor the proposed quantum phases out of the semimetallic state. For BaIrO₃, it adopts a nine-layer 9R polytype at ambient pressure, and can be transformed to 5H, 6H, and 3C phases under different high pressure conditions. The 9R phase is a weak ferromagnetic insulator with T_c = 180 K, and can be regarded as an exotic SOC Mott insulator with multiple J_eff = 1/2 states associated with the unique Ir₃O₁₂ structural units. An atomic-like nature of the Ir moment driven by strong SOC is rather stable against external perturbations, but the weak ferromagnetism can be easily suppressed by applying chemical and physical pressures or dilute rare-earth substitutions for Ba²⁺. In contrast, the nonmetallic ground state displays distinct response to the chemical and physical pressure, highlighting the delicate interplay of crystal structure and electronic degrees of freedom for this quasi-1D compound. With increasing the ratio of corner-to-face sharing octahedra in the sequence 9R(1:2) $\to$5H(3:2) $\to$6H(2:1) $\to$3C(∞), the ground states of BaIrO₃ evolve from a ferromagnetic insulator with T_c = 180 K in the 9R phase to a ferromagnetic metal with T_c = 50 K in the 5H phase, then to an exchange-enhanced paramagnetic metal with non-Fermi-liquid behaviour near a ferromagnetic quantum critical point in the 6H phase, and finally to a Fermi-liquid metal in the 3C phase. Such a structure–physical property evolution demonstrated that HPHT synthesis of structurally closely related perovskite polytypes represents an effective approach to fine tune the physical properties of interest via modifying the octahedral arrangement.

Acknowledgments

We are grateful to J.-Z. Zhou, J. B. Goodenough, José Alonso, Y. Uwatoko, and M. Akaogi for collaborations on work related to this review. This work is supported by the National Basic Research Program of China (Grant No. 2014CB921500), the National Science Foundation of China (Grant Nos. 11304371, 51402019), and the strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB07020100).