Contrasted Sn substitution effects on Dirac line node semimetals SrIrO₃ and CaIrO₃

Recently, 5d iridium oxides with perovskite-related structures have been explored extensively as a mine for exotic quantum phases, partly because of an interplay of strong spin-orbit interaction and electron correlation of the 5d electrons.¹ The strong spin-orbit coupling of ∼0.4 eV for 5d electrons, which is larger than the typical crystal field splitting of ≲0.1 eV within t_2g,² splits the t_2g bands with five d electrons into the upper half-filled J_eff = 1/2 band and lower completely filled J_eff = 3/2 bands. In the two-dimensional layered perovskite Sr₂IrO₄, a modest on-site Coulomb U of ∼2 eV³ brings the system to a spin-orbital Mott state with the J_eff = 1/2 moments.^4,5 Such a spin-orbital Mott state has been identified in many two-dimensional layered iridium oxides, where an exotic magnetism of J_eff = 1/2, particularly the Kitaev spin liquid state, has been explored.⁶ In the three-dimensional perovskites SrIrO₃ and CaIrO₃, in contrast, the J_eff = 1/2 band remains metallic marginally due to the increased bandwidth³ and forms a “correlated” topological semimetal.

SrIrO₃ and CaIrO₃ have a GdFeO₃-type distorted perovskite structure where the rotation and the buckling of IrO₆ octahedra give rise to a unit cell with the size of $2ac×2ac×2ac$ (a_c is the lattice constant of the original cubic lattice), as shown in Fig. 1(a).^7,8 The results of band calculations indicate that SrIrO₃ and CaIrO₃ have Dirac electron bands with a line of nodes and heavy hole bands at the Fermi level.⁹ The line nodes of Dirac bands are protected by the time-reversal symmetry and the gliding symmetry of the GdFeO₃-type perovskite structure.¹⁰ The existence of Dirac electrons has been supported by experiments, for example, by ARPES^11,12 and transport measurements.^13,14 Their proximity to the spin-orbital Mott state and moderately strong electron correlations are evident, for example, from the observation of a transition from a Dirac semimetal to a magnetic insulator by decreasing the number of SrIrO₃ layers in $(SrIrO3)n,(SrTiO3)1$ superlattice structures.¹⁵ The presence of an apparent correlation effect is a prominent feature of the two Ir perovskites when compared with many other topological semimetals which are only weakly correlated and makes them an interesting arena to explore the effect of electron correlation in topological semimetals. As the ionic radius of Ca²⁺(1.34 Å) is smaller than that of Sr²⁺(1.44 Å),¹⁶ the lattice is more distorted in CaIrO₃ than in SrIrO₃, which reduces the bandwidth of CaIrO₃ appreciably as compared with that of SrIrO₃. The effect of electron correlation should be larger in CaIrO₃ than SrIrO₃. Recently, it was shown that the strong electron correlation modifies the semimetallic band structures appreciably in the two three-dimensional iridium perovskites. The stronger electron correlation effects of CaIrO₃ bring its Fermi level closer to the Dirac node and therefore further reduces its density of electrons and holes when compared to SrIrO₃.¹⁴ 

A transition from the Dirac semimetal to a magnetic insulator was also discovered in bulk polycrystalline SrIrO₃ by substituting Ir with Sn.¹⁷ As Sn ions are tetravalent like Ir ions in SrIrO₃, Sn doping does not change the valence of Ir ions and therefore reduces the hopping path of the Ir 5d electrons in real space and, hence, the effective width of the J_eff = 1/2 band, as in the case of the superlattice structure. We note here that Sn doping should modify not only the effective bandwidth but also the degree of disorder. With this unique opportunity of controlling the electron correlations and disorder in mind, we synthesized epitaxial thin films of SrIr_1−xSn_xO₃ and CaIr_1−xSn_xO₃ and measured their resistivity to probe the effects of Sn doping. A transition from a semimetal to a (magnetic) insulator is observed in both SrIr_1−xSn_xO₃ and CaIr_1−xSn_xO₃ thin films, as in the bulk SrIr_1−xSn_xO₃. We discovered a sharp contrast in the transition behavior between the Sr and Ca iridium perovskites: the appearance of well-defined transition from the Dirac semimetal to a magnetic insulator as a function of temperature above a critical Sn concentration of x_c ∼0.1 for SrIrO₃ and the continuous increase in resistivity without a clear signature of the semimetal-insulator transition for CaIrO₃, which we ascribe to the interplay of the electron correlation and the disorder effect.

SrIr_1−xSn_xO₃ and CaIr_1−xSn_xO₃ thin films were epitaxially grown in the range of 0 ≤ x ≤ 0.2 on SrTiO₃(001) substrates by the pulsed laser deposition technique using polycrystalline targets with 5% excess B (Ir/Sn) cations. The film deposition of SrIr_1−xSn_xO₃ (CaIr_1−xSn_xO₃) was conducted at 650 °C (750 °C) in a 100 mTorr O₂ atmosphere. The typical thickness of our samples estimated from the X-ray reflectivity measurement is ∼15 nm (10 nm). Magnetization and transport measurements were conducted using a commercial SQUID magnetometer (MPMS, Quantum Design) and in a physical property measurement system (PPMS, Quantum Design). The X-ray diffraction (XRD) measurements were performed using SmartLab, Rigaku.

The results of 2θ-θ scans of XRD indicate that all the grown SrIr_1−xSn_xO₃ and CaIr_1−xSn_xO₃ films crystallize in the perovskite structure without any trace of impurity phase within the given resolution [Fig. 1(b)]. The full width at half maximum of the rocking curve is typically as narrow as 0.1° at the pseudocubic (001) peak, and the Laue oscillations around the Bragg peaks are clearly observed. Reciprocal space mapping (RSM) measurements reveal that the in-plane lattice of the films is locked to that of the SrTiO₃ substrate [Figs. 1(c) and 1(d)]. Those observations clearly demonstrate the epitaxial growth and high crystallinity of the grown films. The out-of-plane lattice constant of the CaIr_1−xSn_xO₃ films as a function of Sn content x, as an average, increases almost 0.7% from x = 0 to x = 0.2 which should reflect the larger ionic radius of Sn⁴⁺ (0.690 Å) than that of Ir⁴⁺ (0.625 Å)¹⁶ [Fig. 1(e)].

The film orientation was identified by RSM measurements of XRD and transition electron microscopy [Figs. 2(a)–2(c)]. We will describe the lattice orientation of films by the pseudocubic unit cell in this paper using lattice parameters $apc=a2+b2/2$ and c_pc = c/2, where a, b, and c denote the orthorhombic unit cell parameters of the distorted GdFeO₃ structure.¹⁹ In the case of SrIr_1−xSn_xO₃, the c_pc axis (∥ orthorhombic c) lies within the substrate plane independent of Sn doping [Fig. 2(d)]. This is natural because c_pc is closer to that of the SrTiO₃ substrate than a_pc (see Table I). In contrast, a_pc is closer to that of SrTiO₃ in CaIrO₃. The c_pc axis (∥ orthorhombic c) therefore aligns perpendicular to the substrate plane in the CaIrO₃ case [Fig. 2(f)].²⁰ The inclusion of minority domains with the c_pc axis lying within the substrate plane as in SrIr_1−xSn_xO₃ is observed for the high Sn content films (x ≥ 0.1) [Fig. 2(g)], which very likely reflects the expansion of c_pc due to Sn doping and the resultant proximity to the lattice constant of SrTiO₃.

As a_pc is larger than c_pc, the orientation of c_pc within the substrate plane can be controlled by introducing additional epitaxial strain using step edges of the vicinal substrate.^21,22 We used a vicinal SrTiO₃(δ01) substrate with the substrate plane 0.4° rotated from (001) toward the [100] direction for the growth of SrIr_1−xSn_xO₃. Because of the epitaxial strain from the side (100) plane at the step edges, the c_pc (∥ orthorhombic c) axis prefers to align along the edge, namely, [010]_STO direction [Fig. 2(e)]. The RSM measurements clearly indicate that more than 95% of domains have the c_pc axis parallel to the substrate [010] direction for the films on the vicinal substrates. Consistent with the in-plane preferred orientation, a clear anisotropy of magnetization within the substrate plane was observed for the x = 0.2 sample on the vicinal substrate as we describe below. Pronounced anisotropy in the magnetization was not observed in the resistivity ρ(T).

The resistivity ρ(T) measurements on the SrIr_1−xSn_xO₃ films indicate the presence of a metal-insulator transition accompanied by a weak ferromagnetism as in the bulk.¹⁷ The SrIrO₃ (x = 0) film shows only weakly temperature-dependent behavior of ρ(T), where a gradual increase followed by the temperature-independent behavior is observed with decreasing temperature [Fig. 3(a)]. This agrees well with previous reports on SrIrO₃ thin films^15,23 and can be understood as a typical behavior of semimetals with extra conductivity at a high temperature from thermally excited electrons and holes. With Sn doping [Fig. 3(b)], we do not observe an appreciable change in ρ(T) up to the critical concentration x_c = 0.1. Above x_c = 0.1, however, the resistivity shows a transition from the semimetal to a weak insulator at a transition temperature T_c where we observe a kink in ρ(T) and a well-defined peak of the second derivative d²ρ(T)/dT² [Fig. 3(c)]. T_c increases rapidly with increasing x. The metal-insulator transition below T_c is accompanied by a weak ferromagnetism with the easy axis parallel to the pseudocubic c_pc axis (∥ orthorhombic c), as seen in Fig. 3(d). This behavior, the emergence of the magnetic insulator out of the Dirac node semimetal with Sn doping, can be summarized as a Sn content x-T phase diagram on top of the contour map of the magnitude of ρ(T) [Fig. 3(e)]. The stabilization of the magnetic insulator phase at low temperatures above x_c = 0.1 highly likely originates from the increase in the effective electron correlation. We argue that this is because of the reduced hopping of J_eff = 1/2 electrons by the introduction of Sn⁴⁺ without conduction electrons.

We find contrasting behavior in the Sn doping effect on ρ(T) in CaIr_1−xSn_xO₃ compared to SrIr_1−xSn_xO₃. For CaIrO₃ (x = 0) films [Fig. 3(a)], the overall behavior of ρ(T) is similar to that observed in SrIrO₃. The magnitude of resistivity is, however, appreciably larger than that of SrIrO₃. A weak increase in ρ(T), reminiscent of a weak localization and not observed in SrIrO₃, is seen below 20 K, which is suggestive of the presence of an appreciable disorder effect. It was discussed in the recent transport study on single crystal CaIrO₃ that the Fermi level is much closer to the Dirac nodes, and hence, the electron and the hole densities are lower in CaIrO₃ than in SrIrO₃ due to the enhanced correlation effect originating from the narrow band in CaIrO₃.¹⁴ The effect of disorder should be enhanced in CaIrO₃ because of the reduced carrier density, which may account for the larger resistivity and the weakly localized behavior.

With Sn substitution, ρ(T) gradually increases and shows a poorly insulating behavior with a power-law divergence [Figs. 4(a) and 4(b)]. We do not see a well-defined semimetal-insulator transition as a function of T and x in contrast to the case for SrIrO₃. We argue that the gradual transition from the Dirac node semimetal to a weak insulator is driven by the disorder and perhaps the inhomogeneity and that the nature of semimetal-insulator transition is distinct from that of SrIrO₃. It is natural that the effect of disorder associated with Sn-doping is much more profound in CaIrO₃ than in SrIrO₃ because of the lower carrier density and Fermi energy of CaIrO₃. For CaIr_0.8Sn_0.2O₃, a very weak ferromagnetic moment appears to emerge below T_mag ∼ 100 K with B perpendicular to the film plane, smaller in magnitude and lower in temperature than SrIr_0.8Sn_0.2O₃, as shown in Fig. 4(c). No clear anomaly can be identified in ρ(T) at T_mag, and ρ(T) shows an insulating behavior above T_mag, implying that the magnetic ordering is not a trigger of the semimetal-insulator transition in CaIr_1−xSn_xO₃ in contrast to that in SrIr_1−xSn_xO₃. The emergence of magnetism in the disordered insulator may suggest a Mott insulator character and therefore a Mott-Anderson type metal-insulator transition in CaIr_1−xSn_xO₃.

In summary, we have successfully grown thin films of Dirac semimetals SrIr_1−xSn_xO₃ and CaIr_1−xSn_xO₃ epitaxially on SrTiO₃(001), with their orthorhombic c axis parallel and perpendicular to the substrate plane, respectively. In the case of SrIr_1−xSn_xO₃, the c axis can be aligned within the substrate plane using a vicinal substrate. While a well-defined Dirac node semimetal to a magnetic insulator transition with Sn doping is observed at a critical Sn concentration of x_c ∼ 0.1 in SrIr_1−xSn_xO₃, we observe in CaIr_1−xSn_xO₃ that the Dirac node semimetal changes only gradually to a poor insulator without any well-defined semimetal-insulator transition. We argue that the contrast between SrIr_1−xSn_xO₃ and CaIr_1−xSn_xO₃ is a consequence of the interplay between the enhanced effective electron correlation and the disorder effect by Sn doping. While the correlation effect dominates in the case of SrIr_1−xSn_xO₃, the disorder effect and the carrier localization dominate in CaIr_1−xSn_xO₃ due to the proximity of the Fermi level to the Dirac nodes and the resultant low carrier concentration. These results clearly indicate that Sn-doped iridium perovskite oxides are an interesting playground to study the effect of electron correlations and disorders in a topological semimetal.

This work was supported by JSPS KAKENHI, Grant Nos. JP24224010, JP17H01140, JP15H06092, JP17K14335, and JP18J21922.