Recent progress on topological semimetal IrO2: electronic structures, synthesis, and transport properties

5d transition metal oxides, such as iridates, have attracted significant interest in condensed matter physics throughout the past decade owing to their fascinating physical properties that arise from intrinsically strong spin-orbit coupling (SOC) and its interplay with other interactions of comparable energy scales. Among the rich family of iridates, iridium dioxide (IrO2), a simple binary compound long known as a promising catalyst for water splitting, has recently been demonstrated to possess novel topological states and exotic transport properties. The strong SOC and the nonsymmorphic symmetry that IrO2 possesses introduce symmetry-protected Dirac nodal lines (DNLs) within its band structure as well as a large spin Hall effect in the transport. Here, we review recent advances pertaining to the study of this unique SOC oxide, with an emphasis on the understanding of the topological electronic structures, syntheses of high crystalline quality nanostructures, and experimental measurements of its fundamental transport properties. In particular, the theoretical origin of the presence of the fourfold degenerate DNLs in band structure and its implications in the angle-resolved photoemission spectroscopy measurement and in the spin Hall effect are discussed. We further introduce a variety of synthesis techniques to achieve IrO2 nanostructures, such as epitaxial thin films and single crystalline nanowires, with the goal of understanding the roles that each key parameter plays in the growth process. Finally, we review the electrical, spin, and thermal transport studies. The transport properties under variable temperatures and magnetic fields reveal themselves to be uniquely sensitive and modifiable by strain, dimensionality (bulk, thin film, nanowire), quantum confinement, film texture, and disorder. The sensitivity, stemming from the competing energy scales of SOC, disorder, and other interactions, enables the creation of a variety of intriguing quantum states of matter.

The most well-studied 5d TMOs in recent years are the family of iridium oxides (or iridates).In this topic review, we focus on the simplest binary iridate compound, namely iridium dioxide (IrO 2 ), which has been long known as a promising electrocatalyst for oxygen evolution reactions [38][39][40][41].As shown in figure 1(a), IrO 2 has a rutile tetragonal crystal structure with lattice parameters a = b = 4.498 Å, c = 3.154 Å and belongs to the space group P42/mnm [42].Like in many other iridates, each Ir atom in the rutile lattice is coordinated with six oxygen atoms which form a (distorted) IrO 6 octahedron.In a perfect octahedral crystal field (without distortion), the 5d orbitals are split into an e g doublet and a t 2g triplet, and the latter can be regarded effectively as an L = 1 state.The SOC further entangles the orbital and the spin degrees of freedom, forming a doublet J eff = 1/2 and a quartet J eff = 3/2 [25].Since the Ir 4+ ion contains five 5d electrons, the J eff = 3/2 states at a lower energy are completely filled, whereas the J eff = 1/2 states around the Fermi level are partially occupied (figure 1(b)) [25,26].While the J eff = 1/2 state has been demonstrated to be a novel ground state in many insulating iridates (e.g.Sr 2 IrO 4 ), recent hard x-ray photoelectron spectroscopy and x-ray absorption (XAS) spectroscopy studies suggest that this widely accepted model may not be applicable in metallic IrO 2 where the distortion of the octahedron lifts the degeneracy of the t 2g triplet [43,44].
Furthermore, unlike many other iridates (e.g.pyrochlore, Ruddlesden-Popper, and perovskite iridates) where the IrO 6 octahedra are connected in a corner-sharing-only network, the octahedra in the rutile lattice share not only corners but also edges with their neighbors (figure 1(c)) [45].This strong octahedral connectivity facilitates the hopping of electrons (t), yielding a weak effective electron-electron interaction ratio (U/t) and hence a nearly uncorrelated metallic behavior in the system.Despite the relatively weak electron interactions, the nonsymmorphic symmetry in IrO 2 gives rise to a rich band structure which is characterized by several band touching points and lines in the three-dimensional (3D) momentum space [46][47][48][49][50]. Interestingly, the strong SOC can partially lift the band degeneracy, promoting a spin Hall transport associated with the spin-momentum entangled electronic states [48,[51][52][53][54].The exotic topological manifestations and intriguing transport properties have made this simple binary compound one of the most attractive iridates for both fundamental research and technological advances.
In this topic review, we first introduce the topological electronic band structures of IrO 2 , with a focus on the role that the nonsymmorphic symmetry plays on the presence of Dirac nodal lines (DNLs) in the band structure, the gap opening due to SOC, the Fermi surfaces observed in angle-resolved photoemission spectroscopy (ARPES), and a discussion of how this leads to the observed spin Hall effect.We then provide a survey and discussion of various techniques for the synthesis of IrO 2 thin films and nanostructures, and finally a detailed review of their electrical, spin, and thermal transport properties.Since we attempt to focus on the fundamental condensed matter and materials physics, the electrochemical-related properties of IrO 2 and its potential applications in electrocatalysis, electrochromic devices, chemical sensors, etc are not discussed.There are several recent review articles in these areas [55][56][57][58][59] that we encourage the readers to consult.

Electronic structures
In this section, we review the electronic structure of IrO 2 .Specifically, we focus on a discussion of the J eff = 1/2 model, the origin of the DNLs in the presence of strong SOC and nonsymmorphic symmetry, and their relevance to the observed spin Hall effects.

Possible breaking down of the J eff = 1/2 model
In iridates, the iridium ion inside the IrO 6 octahedron has five valence electrons occupying the d-orbitals.A well-accepted picture which considers the effects of the crystal field and SOC is the ground state with a half-filled J eff = 1/2 and a filled J eff = 3/2 [25,26].The J eff = 1/2 picture applies to many of the insulating iridates (e.g.Sr 2 IrO 4 ) [60][61][62] where the valence band width near the Fermi level is reduced by the SOC and a moderate U is sufficient to localize the electron in J eff = 1/2.In IrO 2 , optical conductivity measurements show a Drude-like response, confirming the presence of free electrons [44,63].While earlier resonant x-ray scattering measurements revealed the possible existence of the J eff = 1/2 state in IrO 2 [64], more recent polarization-dependent XAS spectroscopy studies suggest the absence of such ground state [44].An important ingredient for the formation of J eff = 1/2 is the degeneracy among three t 2g orbitals in the presence of crystal field and hybridization with neighboring oxygen orbitals.Density functional theory (DFT) calculations [43,44,65,66] show that while the xz and yz orbitals are still degenerate near the Fermi level, the xy orbital is pushed down by around 2 eV (figure 1(d)).This observation is not compatible with the J eff = 1/2 wave functions in which all three orbitals shall contribute to the density of states equally [43,44].The energy separation between xy and the other two t 2g orbitals is attributed to the different bonding symmetries with the neighboring oxygen orbitals [43,44].This conjecture was supported by the polarization-dependent XAS measurement in which the π -polarization absorption is greatly suppressed in comparison with the σ-polarization one [44].In spite of the debate on J eff = 1/2 states [20,21,43,44,64], it is widely accepted that SOC plays a vital role in the electronic structure of IrO 2 , as discussed below.

Role of electron interaction and SOC
Photoemission spectroscopy studies [45,67,68] in correlation with DFT calculations [69] have suggested that the electron correlation is rather weak in IrO 2 , due to the high connectivity of the IrO 6 octahedra in the rutile structure [45].As a result, the electron-electron interaction is not included in most DFT calculations of the electronic band structure [48,50,70,71].Although the band structure calculations in earlier years did not consider SOC either [70,72,73], recent studies highlight its essential role in determining the electronic properties of IrO 2 [20,63,64,68].A representative band structure along the high symmetry axes is shown in figures 2(a) and (b), where the effect of SOC was studied [71].From X = (π, 0, 0) to M = (π, π, 0), DNLs with four-fold degeneracy appear near the Fermi level (E = 0) regardless of the SOC.Nevertheless, SOC has a strong influence on the bands along A = (π, π, π) to M. Without SOC, the two bands touch at an eight-fold degenerate contact point just below the Fermi level (figure 2(a)).SOC opens a gap at this touching point, leading to two new DNLs from A to M. It is worth mentioning that in the two-dimensional quantum spin Hall insulator model [52], a similar gap opening occurs in the bulk bands due to SOC, leading to robust topological edge states [52,54,74,75].In IrO 2 , the gap opening does not occur at the Fermi level; however, it still contributes to the spin Berry curvature as the SOC-perturbed band (i.e. the upper DNL from A-M in figure 2(a)) passes through the Fermi level [48].As will be discussed in section 2.4, the calculated band structure with SOC shows a good agreement with ARPES studies [50,68,71].In addition, along R-A, the SOC-driven band splitting (about 0.4 eV) near the Femi level allows for an optical transition that is consistent with the measured optical conductivity spectra [44].

Nonsymmorphic symmetry and Kramers' degeneracy
Beyond SOC, crystal symmetry dictates the band dispersion along the high-symmetry axes.Essentially, the fourfold degenerate DNLs are formed by the intersection of two doubly degenerate bands.It is well known from the antiunitary principle in quantum mechanics that a twofold degeneracy must arise in a lattice satisfying time-reversal symmetry T and inversion symmetry P because the antiunitary operator PT leaves the momentum invariant and has (PT ) 2 = −1.Such twofold degeneracy in a band structure is referred to as the Kramers' degeneracy.Furthermore, a generic four-band Hamiltonian producing two doublet bands can be expressed as Pertaining to parameter counting, the spectrum which is impossible without any fine tuning [46,76].Thus, the fourfold degeneracy results from the underlying symmetry.
The rotational and translational symmetries in the tetragonal lattice of IrO 2 belong to the space group P4 2 /mnm (No. 136).The nonsymmorphic symmetry operations, which represent the combined actions of point group symmetry and fractional translation, are included in this space group.The nonsymmorphic symmetries and the time reversal symmetry play a key role in accounting for the origin of DNLs [46,47].In a spin-1/2 electronic system, the Kramers doublet at momentum k is represented as two Bloch states {|Ψ k ⟩ , PT |Ψ k ⟩}.The composite operator PT is also anti-unitary.Along some highly symmetrical path in momentum space, the Bloch states |Ψ k ⟩ are eigenstates of certain nonsymmorphic symmetry operators with complex eigenvalues due to the fractional translation.Therefore, it is possible to form additional anti-unitary operators whose square is equal to minus identity; [49,77] this can result in two inequivalent anti-unitary operators, which leaves momentum invariant and establishes fourfold degeneracy.Such notion is applicable in both spinful and spinless systems.Sun et al [48] introduced two types of DNLs: one in the absence of SOC and the other in the presence of SOC.SU(2) spin rotational symmetry is preserved in the former case where T 2 = 1, whereas in the latter T 2 = −1 scenario, SU(2) symmetry is absent.The former corresponds to a spinless system, whereas the latter is characterized as spinful.
We first focus on the DNLs in the band structure with SOC (figure 2(a)).Sun et al [48] showed the two inequivalent antiunitary operators in the context of the DNL along the path from X to M. The algebraic relations among the nonsymmorphic symmetry operators, time-reversal, and inversion at Brillouin zone (BZ) edges are exploited.The general studies of the nonsymmorphic symmetries on topological aspects of band structures can be found in earlier references [46,[78][79][80][81][82][83][84].The Bloch states |Ψ k ⟩ with k = (π , k y , 0) are invariant under the mirror symmetry M z , the action of which in spatial space is (x, y, z) → (x, y, −z) and in spin space is (σ x , σ y , σ z ) → (−σ x , −σ y , σ z ), and under the nonsymmorphic Mx whose action is (x, y, z) 2 ) together with (σ x , σ y , σ z ) → (σ x , −σ y , -σ z ).It is worthwhile to note the representation in spin space: M z = iσ z as it commutes with T = (iσ y ) K and satisfies the mirror symmetry for spins (e.g.see [85]), (iσ z ) −1 σ x,y (iσ z ) = −σ x,y and σ z is invariant.Similarly, in spin space Mx = iσ x .With these properties, Sun et al [48] showed the invariants, spin and space combined, of the Bloch state along X-M are: is degenerate and orthogonal.Apart from the spin polarization, they can be further labeled by their M z eigenvalues, i, −i, −i, i, respectively.A similar argument can be applied to explain the fourfold degeneracy along A-M.
Next, we consider the band structure without SOC (figure 2(b)) and examine the origins of the DNLs; this helps understand the spin Hall effect that will be discussed in the subsequent subsection [51,53].Without SOC, the Hamiltonian commutes with all spin operators, SU(2) symmetry is restored, and each band is automatically twofold degenerate.Li et al [49] provided examples of deriving Kramersdoublets when T 2 = 1 in other nonsymmorphic materials, such as X 3 SiTe 6 (X = Ta, Nb).One can show that along the path of Z = (0, 0, π) to R = (π, 0, π), for instance, the Bloch states are invariant under the combined Mx T , and the new Kramers doublet {|Ψ k ⟩ , Mx T |Ψ k ⟩} is an orthogonal set as ( Mx T ) 2 = e −iky−ikz = −1.Moreover, the fact that the k x = π plane is a fourfold nodal plane [48] can be explained by the anti-unitary P Mx T .This is consistent with the SOC-free band structure (figure 2(b)), though we note that the degeneracy is indeed split when SOC is present.
It is interesting to note that the fourfold degenerate DNLs also appear in other iridates and nonsymmorphic systems.For example, the effective J eff = 1/2 tight-binding band structure of orthorhombic SrIrO 3 displays fourfold degenerate bands along the paths X-S and Z-T [86].Crystals in space group 135 have similar symmetry with IrO 2 , and the generic and symmetry-preserved tight-binding model [47] also shows the fourfold degenerate bands along X-M and M-A.Along the paths, it can be seen that the original eight-band model reduces to a Hamiltonian consisting of anticommuting matrices only, which leads to two symmetric energy dispersions.

ARPES measurements of DNL semimetal states
The roles of symmetry on the formations of band touchings (points, lines, and planes) in the band structures of various topological materials have been reviewed extensively in [87].For DNL semimetals, the PT-symmetry combining with nonsymmorphic symmetry constitutes a four-fold degeneracy among the Bloch states along some highly symmetric directions (see also section 2.3), with one-dimensional (1D) band touchings between two doubly degenerate bands even in the presence of SOC.The theoretically predicted band touchings in topological materials can be verified by ARPES measurements.Examples include the direct observations of timereversal symmetry protected single Dirac cones on the surface of topological insulators (e.g.Bi 2 Se 3 [88] and Bi 2 Te 3 [89]), mirror-symmetry-protected pairs of Dirac cones on high-symmetry surfaces of topological crystalline insulators [90], as well as rotational-symmetry-protected Dirac points in bulk Na 3 Bi [91,92] along with Fermi arcs on its surfaces.In IrO 2 , DFT calculations reveal the DNLs along A-M and X-M, and the calculated Fermi surface consists of two holelike sheets and one electron-like sheet as shown in figure 3(a) [50].The color-coded band energies along A-M and X-M (figure 3(b)) indicate where the electron-like and hole-like sheets touch at the Fermi energy (E = 0).The Fermi surfaces obtained from the ARPES measurements along various directions match the theoretical predictions and hence verify the presence of DNL in IrO 2 [50].Specifically, the Fermi surfaces projected on the (110) central plane in BZ (figure 3(c)) display the hole-like Fermi surface which has point contacts with two electron-like ones along A-M.Similar arrangement is also seen in the projection onto the (110) boundary plane (figure 3(d)), but an isolated Fermi circle is present around Z due to the SOC (see the band structures in figure 2(a) versus (b)).As for the (001) projection, figure 3(e) shows the Fermi surface with two contact points along X-M on the central plane in the BZ.Besides, the SOC-driven band split along A-R can explain the two disconnected Fermi surfaces projected on the (001) boundary plane in figure 3(f).

Relevance of DNLs to the spin Hall effect
Now we address the point of how the presence of DNLs (with and without SOC) is connected to the experimentally discovered spin Hall conductivity in the 3D IrO 2 [48].The opening of the gap due to the SOC causes nontrivial topology associated with the Bloch wave functions and can lead to robust edge states capable of transporting spin and charge.One can understand this from the two-dimensional example proposed by Haldane in his seminal work of quantum Hall effect without magnetic field [74] where a two-band massive Dirac model H (k x , k y ) = k x τ x ± k y τ y + m ± τ z describes the low-energy continuum in a honeycomb lattice.The Pauli matrices τ x,y,z act in the sublattice space, while the ± sign refers to the two inequivalent K points in momentum space.A nontrivial topological phase arises when the mass terms m ± , due to the imaginary next-nearest neighbor hopping, have opposite signs at ±K.The pseudo-spin associated with τ 's forms a meron texture around ±K and as a whole is equivalent to a skyrmion texture [77,93].The imaginary hopping breaks the time-reversal symmetry, leading to one-way propagating edge states like the quantum Hall effect.The quantum spin Hall model proposed in [52] can be regarded as a direct sum of two Haldane models with each block representing one spin polarization.To restore the time-reversal symmetry, the mass terms in the two blocks must have m ±,↑ = −m ±,↓ (see the corresponding expression equation (3) for SOC in [52]).Counter-propagating edge states carrying opposite spin polarization then appear at the edge.Generalizing the ideas to higher dimensions, 3D topological materials can be constructed by stacking such twodimensional Dirac systems, but the mass term must then be a smooth function of momentum k z .Burkov and Balents [94] proposed alternatively stacking the topological insulator and trivial insulator layers with a periodic width d.When the surface of the topological insulator layers is doped with magnetic impurities, the tight-binding Hamiltonian has the low-energy spectrum of the Weyl Hamiltonian H = k x τ x + k y τ y + m (k z ) τ z around the two Weyl points (0, 0, π /d ± k 0 ) with k 0 determined by the strength of magnetic coupling.Importantly, the Weyl points signify the mass term changing sign (m (k z ) < 0 for k 0 − |k z − π /d| > 0).The segment of momentum along the k z axis corresponding to the negative Dirac mass term contributes to transverse Hall conductivity.
The above examples demonstrate that the SOC-induced gap opening in the region close to DNLs may contribute to a significant spin Berry curvature.Across the DNLs, which can be regarded as a continuum of Dirac points, the Dirac mass terms must change sign.Indeed, Sun et al [48] showed a spin Berry curvature contributed by the SOC-split bands inside the (110) mirror plane.Comparing the band structures with and without SOC, it can be seen that the band touching at points OP and HP (cf figures 4(a) and (b)) are open due to SOC, and the significant spin Berry curvature appears in the narrow stripe perpendicular to the DNL along the path A-M.The resultant spin Hall conductivity not only depends on the strength of SOC but also on the relative location of the split bands, the Fermi level, and the charge conductivity.Sun et al [48] computed the values of spin Hall conductivity for IrO 2 , OsO 2 , and RuO 2 .While OsO 2 does not have the strongest SOC among the three materials, it has the largest spin Hall conductivity as a band gap is opened around the Fermi level [48].

Synthesis
The experimental demonstration of exotic electronic states and other fundamental properties in general requires the controlled synthesis of high-quality materials.Over the past few decades, IrO 2 has been successfully synthesized in various types of forms, including bulk crystals, thin films, nanorods, nanowires, nanotubes, and more.The growth methods are versatile, ranging from chemical vapor transport (CVT), physical vapor deposition (PVD), chemical vapor deposition, to chemical solution methods.In many of these synthetic experiments, the growth parameters can be controllably tuned to achieve the targeted structure, crystalline quality, composition, and size.In this section, we will first introduce the synthesis of bulk single crystals and then focus on the recent progress in the PVD growth of thin films and bottom-up synthesis of quasi-1D nanostructures that serve as a foundation for the study of their topological electronic and transport properties.

Bulk crystal growth by CVT
The CVT synthesis method embodies a series of chemical reactions in which an initial solid or liquid reacts with a transport gas and decomposes into vapor phase reaction products.The latter are transported through a gradient of temperature or pressure and are reformed into desired purified crystalline samples.CVT can be conducted in open or closed systems, in which the glass or ceramic tubes are either open or sealed on both sides [95].During an open growth setup, the transport carrier gas continuously flows through the system and moves the precursors from a location at one temperature to a secondary location in a higher or lower temperature region.Conversely, in a closed system, a sealed tube or ampoule of glass contains generally a small amount of precursor which remains in the system and continuously participates in the reaction.Additionally, it contains as much transport agent as needed to achieve the required pressure [95].
CVT growth in an open system has been widely used to achieve high quality, bulk single crystals of IrO 2 [42,[96][97][98][99].In a typical growth, pure Ir or polycrystalline IrO 2 (or a combination of the two) acts as the precursor, and a pure O 2 gas as the transporting agent [42,96,97,[99][100][101].Various chemical reactions are possible [102]: (1) Ir metal can react with the O 2 around ∼1000 • C and develop solid IrO 2 layers; (2) Ir or (3) IrO 2 can combine with O 2 to form another oxide species, gaseous IrO 3 , at an elevated temperature (T 2 ) of 1150 • C. When the iridium oxide vapors are then carried to a lower-temperature region (T 1 ) across the temperature gradient, a reverse reaction occurs in vapors, where the IrO 3 dissociates back into solid IrO 2 crystals of various sizes in a temperature range between ∼1000-1100 • C [96].Ryden and Lawson observed several different crystal-growth habits based on the temperature distribution and oxygen flow rates, where they achieved [001] and [011] IrO 2 needles and (011) and ( 100) IrO 2 plates [100].Reames reported that the variations in temperature parameters (i.e.oxidation temperature, growth temperature, temperature gradient) and gas flow rates led to a broad growth window for IrO 2 single crystals, within which no significant influence on the crystal quality was observed [96].Both Reames [96] and Butler and Gillson [42] found that the O 2 pressure, on the other hand, did have a substantial impact on the growth results, presumably because it directly influences the formation and dissociation of IrO 3 [96].For instance, crystals exhibited poor quality when O 2 pressures were 1 atm or lower due to excessive intergrowth that hindered the growth of crystals even ∼1 × 1 × 3 mm in size.Conversely, both the size and the shape of the crystals were clearly improved as the pressure was increased [42,96].In growths performed by Reames at higher oxygen pressures of 20 psi and 45 psi, single crystals of 1 × 1 × 5 mm and 3 × 3 × 2 mm, respectively, were obtained [96].
Beyond purely IrO 2 single crystals, mixed/doped single crystals have also been realized through CVT [96,103].Using (Sn,Ir)O 2 as an example [96], SnO 2 and IrO 2 are crystallographically similar as they possess rutile structures with similar lattice parameters but vary in their electrical and optical properties.While IrO 2 is an opaque conductor, SnO 2 is a transparent wide band-gap semiconductor.The mixed SnO 2 :IrO 2 crystals appear transparent as well and are good candidates for optical studies.The growth method was similar to the previously described method used for IrO 2 single crystals, but a mixture of 85% Sn and 15% Ir metal powder was used as the precursor, the transport gas was air at 1/3 atmosphere, and the high temperature T 2 zone was 1475 • C [96].

Pulsed laser deposition (PLD) of IrO 2 thin films.
PLD is one of the most versatile PVD techniques for the growth of TMO thin films and heterostructures.In a PLD process, a pulsed laser strikes the surface of a solid target and ejects a plume of material (with nearly the same stoichiometry as the target) towards a substrate positioned in front, where a film is deposited.Earlier PLD growths of IrO 2 thin films were conducted on silicon or silicon oxide substrates using Ir metal as a target [104][105][106][107][108][109][110][111].Although iridium has a low vapor pressure, laser ablation can readily vaporize the surface of the Ir target and create an iridium plume which reacts with the background O 2 gas to form IrO 2 thin films.The as-grown films are all polycrystalline due to the large lattice mismatch between the film and the Si substrate as well as the formation of amorphous silicon oxide layer at the substrate surface prior to deposition.Textured IrO 2 films were achieved by replacing Si with SrTiO 3 substrates, which have a relatively smaller (yet still large) lattice mismatch with the films [112].Instead of Ir metal, IrO 2 was chosen as the target in this growth, although the precise influence of the target material on the film quality has not been explicitly studied [112].Epitaxial thin films were realized when single-crystalline TiO 2 substrates were used (figures 5(a)-(c)) [44,113].The two binary metal oxides IrO 2 and TiO 2 have the same rutile structure with moderate lattice mismatches of ∼ −2.1% in the a and b-axes and ∼ 6.6% along the c-axis.Consequently, the epitaxial IrO 2 films present different degrees of compressive or tensile strains depending on the substrate orientation and film thickness, as evidenced by x-ray reciprocal space mapping characterizations (figure 5(d)) [44,113].
In the PLD growths, O 2 pressure and substrate temperature are known to play an essential role in the stoichiometry and phase purity of the films.In general, Ir metal clusters can easily form in a low O 2 pressure and at a high temperature, whereas high O 2 pressure favors the volatile IrO 3 phase [115], resulting in significant Ir loss during the growth.It is also worth noting that the Ir metallization and high volatility of IrO 3 have been common challenges in the PLD growth of many other iridates thin films [116][117][118][119][120][121][122], although the extent of the challenges appear dependent on the particular crystal structure and composition of the iridates.As a result, one must cooperatively tailor the O 2 pressure and substrate temperature to achieve stoichiometric films free of Ir metal impurities.Hou et al [114] performed an array of systematic growth experiments and established a phase stability diagram for the IrO 2 films (figure 5(e)), where the optimal O 2 pressure and substrate temperature were found to be 10-100 mTorr and 500 • C, respectively.The epitaxial films grown at the optimal condition, however, were fully strain-relaxed.This was attributed to the nucleation of misfit dislocations at the initial growth stage which eventually led to the formation of columnar grain structures.Each individual grain has atomically flat surfaces, but the height difference between grains was as large as 5 nm for a 15 nm thick film (figure 5(f)).Islands were clearly observed after the deposition of the first couple of atomic layers, suggesting the growth mode is not layer-by-layer.While the O 2 pressure during the deposition strongly affects the phases (Ir vs. IrO 2 ), conditions used in a post-annealing process seem to have negligible influences [123], indicating the stability of the as-grown films.
Beyond single-phase thin films, IrO 2 -based heterostructures have recently been grown by PLD, as well.Heterostructures containing spin-orbit coupled IrO 2 and ferromagnetic γ-Fe 2 O 3 were deposited on Al 2 O 3 (0001) substrates for inverse spin Hall effect studies [124].The IrO 2 layer was deposited on the γ-Fe 2 O 3 film at a relatively low temperature (325 • C) and an optimal O 2 pressure of 50 mTorr.Due to the different crystal structures between rutile IrO 2 and maghemite Fe 2 O 3 , the IrO 2 films were not epitaxially grown; nevertheless, a strong texture along the (100) orientation was observed, which shows a significant influence on the spin Hall transport in the heterostructures.

Molecular beam epitaxy (MBE) growth.
High-quality epitaxial thin films of IrO 2 with large-scale atomically smooth surfaces were realized by the Shen group [45,50,125] and the Kawasaki group [126] using MBE.Unlike in PLD, the Ir flux in MBE was supplied by electron beam evaporation of the elemental Ir source.To maintain a low-pressure MBE condition, distilled pure ozone was used as a highly reactive oxidant at a background pressure of 10 −6 Torr.This contrasts with PLD which typically operates at a much higher O 2 pressure (e.g.10-100 mTorr for IrO 2 ), as the laser ablated species are sufficiently energized to reach the substrate even after colliding with a high density of background gas.The substrates in the MBE growth of IrO 2 were again rutile TiO 2 with varied crystallographic orientations.The optimized substrate temperatures were about 300 • C, lower than the 500 • C in PLD which presumably has a faster deposition rate.Real time monitoring of the growth using reflection high-energy electron diffraction suggested that the IrO 2 films were grown in a layer-by-layer mode in a MBE process [125].X-ray diffraction (XRD) and transmission electron microscopy (TEM) studies confirmed the single crystalline nature of the films (figures 6(a) and (b)).The surfaces of the films were atomically smooth, as evidenced by the sharp Kiessig fringes in the XRD θ − 2θ pattern (figure 6(a)) and the step-and-terrace-like surface morphology (figure 6(c)) which resembles the surfaces of the single-crystalline TiO 2 substrates [45,50,125,126].The atomically smooth films with high-crystalline quality have offered an excellent platform for the in situ ARPES studies of electronic structures [45,50,125].
Furthermore, all-rutile IrO 2 /TiO 2 superlattices were epitaxially grown by MBE on [110]-oriented TiO 2 substrates [127], in spite of the moderate lattice mismatch (6.6% in c-axis and −2.1% in a and b) between the two binary oxides.The superlattices have a periodicity of n = 3, 4, 5 atomic layers, and all the expected superlattice reflections were observed in the XRD.Atomically sharp interfaces were directly visualized by cross-sectional scanning TEM (STEM, figure 6(d)).The STEM intensity line scans indicate a possible interfacial reconstruction in the TiO 2 layer, which partially released the strain at the interface and promoted a growth of superlattices with high structural quality regardless of the lattice mismatch.The success in the superlattice growth is also associated with the low energy of the (110) surfaces of the two rutile oxides, as the growth of [001]-oriented superlattices with high (001) surface energy has turned out to be challenging [127].
In a modified MBE growth, Nair et al [128] replaced the pure elemental Ir source with Ir-organic precursor which has a significantly higher vapor pressure and thus requires a much lower source temperature (<200 • C).Interestingly, their growths produced phase pure Ir or IrO 2 films, which was exclusively dependent on the choice of substrates.To be specific, a (110)-oriented TiO 2 substrate favors the growth of IrO 2 , whereas c-plane sapphire substrates promote the growth of pure Ir metal films.Since those depositions were performed at identical oxidation conditions, the different phases of the asgrown films emphasize the important role of lattice-mismatchinduced-strain in dictating the oxide formation enthalpy.

Sputtering growth.
Sputtering is another common PVD technique for the growth of IrO 2 thin films, particularly owing to its strong capability of sputtering materials with high melting points (e.g.2446 • C for Ir in this case).The sputtering growth of IrO 2 has a longer history than the PLD and MBE growths.In the 1970s and 1980s, the main purpose for the sputtering of IrO 2 was to study its electrochemical properties for potential applications in chemical sensing, electrocatalysis, and electrochromic devices [129][130][131][132][133]. Most of these growths were conducted on Si substrates via reactive sputtering of Ir targets in a mixed O 2 /Ar atmosphere [134].The as-grown IrO 2 films were polycrystalline or partially amorphous, depending on the deposition temperatures.Like in the PLD growth, the O 2 partial pressure and deposition temperatures play a crucial role in determining the phases (i.e.Ir versus iridium oxides) of the films, whereas substrates strongly influence their crystalline quality [135][136][137][138].The recent interest in the sputtering growth has been mainly motivated by the exotic spintronic properties of IrO 2 .Epitaxial thin films were realized on singlecrystalline TiO 2 substrates either in a pure O 2 atmosphere [113] or in an O 2 /Ar gas mixture [139].Heterostructures composed of spin-orbit-coupled IrO 2 and ferromagnetic permalloys, such as Ni 81 Fe 19 and Co 40 Fe 40 B 20 , were deposited in situ in DC or RF sputtering systems for spin transport studies [140][141][142][143][144]. The depositions were conducted either at room temperature followed by a post-annealing process [141] or directly at elevated temperatures [140,142].The substrates were Si/SiO 2 or TiO 2 , which again yields polycrystalline [140,141] or epitaxial IrO 2 layers [142], respectively.Since the layer uniformity impacts the spin transport across the interface, the substrates were typically rotated during the deposition to ensure that each layer has a uniform thickness.Using co-sputtering deposition, various doped IrO 2 films have also been grown recently, including Ir 1−x Sn x O 2 [145], Ir 1−x Co x O 2 [146], and Ir 1−x Cr x O 2 [147], which are either amorphous or polycrystalline depending on the specific growth conditions.

Growth of (quasi-)1D nanostructures 3.3.1. Metal organic chemical vapor deposition (MOCVD).
(Quasi-)1D nanostructures of IrO 2 , with various morphologies including nanorods [148][149][150][151][152], nanotubes [153], and nanowires [154], were first grown by MOCVD, where the precursor was (methylcyclopentadienyl) (1,5-cyclooctadiene) iridium (I).Pure O 2 was introduced as both the carrier gas and reactant [148,154].Chen et al [148] managed to convert the IrO 2 thin film growth into a nanorod growth on Si substrates by increasing the MOCVD chamber pressure from 1 Torr to 30 Torr in a pure O 2 environment at 350 • C. The as-grown nanorods were found to be greater in density and better aligned in the vertical direction when the Si substrate was coated with Ti metal [149].By controlling the precursor temperature T pr and the substrate temperature T s , a series of 1D nanostructures were grown with diverse morphologies such as triangular and square nanorods, incomplete and square nanotubes, as well as scrolled nanotubes (figures 7(a)-(c)) [150].In general, T pr is a direct way to control the supersaturation ∆µ which is a driving force for the growth, whereas T s is critical to the surface kinetics and has significant influence on the surface morphology of the nanostructure.Therefore, different morphologies can be achieved by systematically tuning T pr and T s .From the perspective of surface kinetics, lower ∆µ and higher T s provide more diffusion time and energy for the adhered surface atoms to arrange and diffuse, thus forming structures with a more thermodynamically stable morphology.Solid nanorods with square cross-sections are more energetically favorable compared to other complex 1D structures, thus they were grown at relatively lower supersaturation (T pr ) and higher T s [150].However, at the lowest T pr and highest T s in the studied range, 1D nanostructures no longer exist; instead, a film composed of 3D grains is the most morphologically stable and hence is formed [150].
Although coating the growth substrates with metal nanoparticles increases the density of nanorods/nanowires [154], the 1D nanostructure growth is through a direct vapor-solid (VS) deposition rather than a metal-catalyzed vapor-liquidsolid (VLS) process as typically seen in semiconductor wire growths [156].Indeed, IrO 2 nanowires have been grown on bare Si or SiO 2 substrates without the use of metal particles.The increase in nanowire density by coating metal particles on the substrates was attributed to the enhanced absorption of atoms onto the substrate and the facilitated nucleation for nanowire growth [154].It is not fully understood as to why the VS process gives rise to 1D anisotropic growth of nanowires, but all of the reported IrO 2 nanorods/nanowires were grown along the [001] direction (or the c-axis) of the rutile phase, and the major facets were (110) planes (figure 7(d)).This is consistent with the (110) plane having the lowest surface energy, whereas the (001) plane has the highest surface energy among the low index surfaces [157].As schematically illustrated in figure 7(e), the adatoms deposited on the (110) surfaces tend to diffuse to the (001) surface where they nucleate and grow.This process increases the area of the (110) facets while maintaining that of the (001) surface, which minimizes the total surface energy and leads to a quasi-1D growth along the [001] direction.
The crystal structure and orientation of the substrate has a strong influence on the alignment of the 1D nanostructures that are epitaxially grown on it.For example, nanotubes were vertically aligned on LiNbO 3 (100) substrates [155], but tilted on the LiTaO 3 (012) substrates [153].A fundamental reason is that the formation of the IrO 2 crystal plane on the substrate always tends to minimize its lattice misfit with the substrate and lower the strain energy at the interface.IrO 2 (001) has the best lattice match with the LiNbO 3 (100) plane, whereas IrO 2 (101) matches well with the LiTaO 3 (012).Since the 1D nanostructures grow along the [001] direction, they were perpendicular to the surface of the LiNbO 3 (100) substrate but made an angle of 55 • with the LiTaO 3 (012) surface (figures 7(f) and (g)).

Vapor phase growth.
The 1D nanostructures grown by MOCVD are typically shorter than 2 µm, making it very challenging to fabricate four-terminal devices and limiting their feasibility for advanced transport studies.Singlecrystalline IrO 2 nanostructures with lengths up to tens of micrometers have been grown via a vapor phase transport method in a single-zone tube furnace where IrO 2 powder was used as a precursor.The growth took place either on SiO 2 /Si substrates [158] or on Au [158] and Pt [159] microwires which were positioned downstream from the precursor boat.The nanowires were grown out of plane in random orientations with a non-uniform diameter, resembling a needle-like shape (figure 8(a)).No catalyst particles were observed at the tip of the nanowires, suggesting the growth is through a VS process instead of VLS, like in the case of the MOCVD growth.In the growth process, solid IrO 2 powder placed within the high temperature zone was first oxidized into volatile gaseous IrO 3 species due to the flow of O 2 into the reactor.As such, the vapor phase is essentially created via a chemical process instead of a physical approach like in PLD or sputtering.The IrO 3 vapor was transported by the carrier gas (e.g., a mixture of O 2 and inert gas) onto the substrates located in a low temperature zone where it disassociated into IrO 2 .For this reason, the flow of O 2 is essential to the growth.Indeed, no nanowires were grown without O 2 , as the powder remained as IrO 2 or was reduced to metal Ir, both of which have much lower vapor pressure than IrO 3 .
Single-crystalline IrO 2 nanowires with more uniform diameters and as thin as tens of nanometers were grown through a similar vapor phase transport process in a three-zone tube furnace [160].The nanowire growth was enhanced through the independent control of temperature in different zones as well as the coating of Si substrates with IrO 2 powder prior to the growth.Furthermore, only inert Ar gas was flowed during the ramping up segment to prevent unwanted growth from occurring during this 'unstable' stage.The 'reactive' O 2 gas was introduced only after the growth temperature was stabilized.As shown in figure 8(b), the as-grown nanowires have a uniform diameter along the majority of the wire length with the exception of tapering at the tip.The absence of catalyst particles at the tip again confirms the growth is through VS, instead of VLS.The IrO 2 nanowires achieved in this work have smooth surfaces and well-defined cross-sectional shape (figures 8(c)-(e)), enabling the observation of a pure geometric effect in the electron diffraction measurement for the first time [160].Beyond improving the morphology, the introduction of IrO 2 powder onto the substrate before the growth also tends to increase the nanowire density, similar to the growth of VO 2 nanowires [162].
Chemical doping was realized in the nanowire growth, as well [161,163,164].In particular, single-crystalline Ir 1−x V x O 2 nanowires were achieved on Si substrates using IrO 2 and VO 2 powder as precursors and a mixture of O 2 and Ar as reactive and carrier gas, respectively [161].It is known from the undoped nanowire growth [154,158,162,[165][166][167] that IrO 2 prefers to grow in an O 2 atmosphere, whereas VO 2 prefers Ar.Thus, a mixture of O 2 and Ar is essential for the growth of doped nanowires.In the presence of O 2 , highly volatile IrO 3 and V 2 O 5 phases are expected to form and further react with each other as they dissociate on the substrate to realize V-doped IrO 2 nanowires through a direct VS process.The composition of the nanowires can be tuned not only by the relative temperatures of the two precursors but also by the ratio of O 2 /Ar which directly influences the formation of volatile IrO 3 and V 2 O 5 .The nanowires grown using this approach were smooth and straight and exhibited diameters down to ∼40 nm and lengths up to tens of micrometers long.The density of achieved nanowires was increased by scratching the substrates before the growth to create fresh and rough surfaces, which facilitates the nanowire growth (figures 8(f) and (g)) [161].As illustrated in figure 8(h), the adatoms tend to diffuse towards the edges [168][169][170] in the scratched areas where they interact with multiple surfaces.Such interactions reduce the energy required to form nucleation sites, resulting in an increased number of nucleation sites and hence an enhanced density of nanowire growth [171][172][173].A similar enhancement of nanowire density was realized by using rough substrates in the growth of pure VO 2 wires [174].The high quality and improved density of Ir 1−x V x O 2 nanowires (figures 8(i) and (j)) enabled the fabrication of various nanodevices for electrical and thermal transport studies.

Transport studies
In IrO 2 , the competition between the approximately equal energy scales of SOC and other interactions results in a diverse array of quantum states depending on strain, doping, dimensionality, temperature, magnetic field, and other parameters.The concomitant tunability of IrO 2 as host for quantum states of matter describes one of the attractions of the material, in combination with its relatively high metallic electrical conductivity.This section will describe the richness of the electrical, spin and thermal transport properties of IrO 2 .The dimensionality (bulk form, thin or ultrathin films, or nanowire form) turns out to be a determining factor, not surprisingly, given the common theme of tunable properties.The transport properties illustrate the metallic transport characteristics and the tunability of the properties under external parameters, which include the appearance of a metal-insulator transition due to competition between enhanced U, the bandwidth, and the disorder potential in thin films, a tunability of the carrier type under magnetic fields due to the nonsymmorphic structure of IrO 2 , and an orbital two-channel Kondo effect associated with oxygen vacancies.The strong SOC is of considerable interest in spintronics for spin-to-charge conversion or vice-versa, as it results in a large spin Hall angle.The large atomic mass difference between Ir and O, strong interatomic bonding, and interactions between electrons and phonons give rise to unique thermal transport properties.The influence of chemical doping on transport will also be discussed.In DNL semimetals, such as IrO 2 , the bands may cross along 1D closed loops in the BZ.The nodal loop carries a π Berry phase.Electronic transport properties are affected by the nodal line and by its Berry phase, and of particular note in the materials are Shubnikov-de Haas oscillations, a large positive magnetoresistance, and weak-localization/antilocalization effects [175].Shubnikov-de Haas oscillations (quantum oscillations in resistivity) reflect the extremal cross-sectional areas of the Fermi surface perpendicular to the direction of the magnetic field, and their phases reflect the π Berry phase if the crosssection encloses the nodal line.Given the multiple extremal cross-sections of a toroidal Fermi surface, this set of rules results in a detailed diagnostic allowed by the oscillations but also in a complex set of oscillations requiring careful analysis and defying simple enumeration [175][176][177][178][179]. A large nonsaturating and often anisotropic positive magnetoresistance is often observed [179][180][181][182][183], the origin of which continues to form the topic of discussion [179].Several examples of the Shubnikov-de Haas oscillations and of the positive magnetoresistance are found in the literature [184][185][186].Weaklocalization and antilocalization are quantum corrections to the classical resistivity due to quantum interference on exact time-reversed closed carrier paths created by scattering events, and they result in characteristic magnetoresistances [116,175,187].In DNL materials the toroidal Fermi surface affects the scattering mechanisms while the π Berry phase modifies the quantum interference [187], leading to observations of characteristic quantum corrections in several DNL materials systems [188][189][190][191].
Transport studies of IrO 2 bulk crystals were first conducted back in the 1970s, where a metallic behavior and oscillatory magnetoresistance were observed [100,192,193].Magnetothermal oscillations (oscillations in sample temperature versus magnetic field) in early work on rutile singlecrystal IrO 2 [193] grown by the CVT, showed signatures of a complicated Fermi surface.Earlier related magnetoresistance measurements showed both Shubnikov-de Haas oscillations, and a monotonic positive magnetoresistance [192], anticipating the pronounced positive magnetoresistance described for DNL semimetals.Analysis of the combined works [192,193] was interpreted in terms of a Fermi surface with several pancake-shaped and dumbell-shaped electron sections and cross-shaped hole surfaces.With hindsight of ∼50 years and present knowledge of DNL materials, the interpretation in terms of a complicated Fermi surface was not off the mark.Figure 9 shows magnetoresistance data from [192] obtained at 1.2-4.2K at a fixed magnetic field of 10 T. The current was applied along [001] and the orientation of the magnetic field was varied over two angles (θ and ϕ in the figure) to reveal Shubnikov-de Haas oscillations attributed to different Fermi surface cross-sections.
More recently, Lin et al [98] re-examined the electronic transport properties of single crystals of IrO 2 and RuO 2 over the temperature (T) range 0.3 K to 300 K.Both TMOs adopt the same rutile structure and exhibit similar metallic transport properties, meaning that the electrical resistivity drops monotonously with decreasing T. The IrO 2 , in particular, showed pronounced metallic behavior with resistivity ratios between 300 K to 4 K of 224-826.A fit of resistivity vs T to scattering of electrons with acoustic phonons (Bloch-Grüneisen model) and with optical phonons (Einstein model) showed good agreement with the models, demonstrating the importance of phonon scattering in accordance with the standard theory for metals.A Debye temperature of θ D ≈ 290 K was deduced for IrO 2 .While substantially more studies have been performed on thin films and nanowires, undoped IrO 2 in bulk form presents properties in accordance with good metallic behavior [100].

Thin film electrical transport properties.
In thin film form, the additional parameter of lower dimensionality leads IrO 2 to display a richer spectrum of properties stemming from its crystal structure, DNL, and competition between energy scales as discussed earlier.At a fundamental level, the exotic behavior is however underpinned by good metallic properties, as shown in the transport properties of polycrystalline thin film IrO 2 obtained by RF sputtering on glass substrates measured in [194], between 15 K and 300 K (for similar RF sputtered polycrystalline films see [195]).The films exhibited the usual metallic behavior, dominated by acoustic and optical phonon scattering and impurity scattering, but also show that the additive Matthiessen's rule for phonon and impurity scattering is not followed for T < 0.1 θ D .At low T, phonon and impurity scattering are not independent and an interference term due to scattering by vibrating impurities functions as an additional scattering mechanism (Reizer-Sergeev scattering).The interference term leads to a contribution to resistivity scaling as T 2 which was distinguished from electron-electron scattering.In IrO 2 the interference term can, at low T, dominate by a factor 10 over the Bloch-Grüneisen acoustic phonon scattering contribution.At higher T, acoustic phonon scattering dominates, succeeded at the highest T by optical phonon scattering.
Progressing from thin to ultra-thin films, IrO 2 shows thickness-dependent properties that illustrate a typical controllability of properties on external parameters, including dimensionality that affects the competition between bandwidth, correlations, and disorder, and may induce magnetic properties.Egido et al [113,196] studied transport properties of IrO 2 thin films (grown by PLD and sputtering) as a function of film thickness down to few monolayers (MLs).A metal-insulator transition appears for the thinnest films in the 1.5 nm-2.5 nm range (3-5 unit cells), as illustrated in figure 10(a).Films above 3 nm are metallic over the measurement range (10 K-300 K), films of 2.5 nm-thick films show insulating behavior below 50 K, of 2.2 nm below 150 K, of 1.7 nm below 250 K, and films of 1.5 nm are insulating over the measurement range.The tunable properties of IrO 2 thin films include the bandwidth W, where W drops with decreasing thickness (similar to strain engineering).The ratio of U/W, where W and U denote the kinetic energy or electron hopping and the electron correlation energy, respectively, determines the importance of electron correlations.Higher U/W can lead to a Mott metal-insulator transition due to the formation of a Coulomb gap.Thinner films also accentuate the role of disorder, quantified by disorder potential D. A higher D/W in thinner films can yield the formation of an Anderson insulator.Whereas IrO 2 in bulk or thicker film form does not show magnetic ordering, magnetic ordering was reported in the magnetization measurement of the thinnest films, within the ultrathin film limit [113].This antiferromagnetic order can lead to a Slater insulator.Mott, Anderson or Slater insulators are all candidates to explain the metal-insulator transition.For films of thickness 1.5 nm, the temperature dependent resistivity can be well fitted by the Efros-Shklovskii variable range hopping model due to Coulomb gap opening, indicative of a Mott insulator.Yet at 125 K a weak ferromagnetic-like transition is detected in the 1.5 nm (100) film, possibly developed from a canted antiferromagnetic order as observed in strontium iridate (SrIrO 3 ) thin films which also shows a metalinsulator transition as the film thickness is reduced to the ultrathin limit [197,198].As a result, a mixed Mott and Slater insulator may underlie the metal-insulator transition, as observed in figure 10(a).
The dimensionality also brings out properties associated with the DNL, as demonstrated by Kawasaki et al [125] describing ARPES and transport measurements (figures 10(b) and (c)) on MBE-grown ultrathin single crystalline IrO 2 (110) films on TiO 2 (110) substrates.The resistance vs T shows an overall metallic behavior, yet with a slight upturn in resistance with decreasing T < 40 K for films of 3 ML and 4 ML thickness (figure 10(b)).Such an upturn in ultrathin films was also observed in [113,196].While in these works a transition to a mixed Mott and Slater insulator was invoked, the upturn in [125] is ascribed to a confinement-induced quantization of the momentum vector normal to the growth plane for films below 10 ML.It is indeed evidenced that the carrier density, as expressed in 3D, drops sharply in films below 10 ML due to the formation of quantized subbands with accompanying energy gaps.In fact, the resistivity as expressed in 3D increases by about two orders of magnitude between 50 ML and 3 ML.Comparing results of [113,196] with [125], it is plausible that contributions from either an interaction-induced Mott insulator or confinement-induced quantization can contribute to insulating behavior in ultrathin films, depending on disorder and growth conditions.Thurs, results have to be interpreted in the light of a specific experiment.Further, ARPES shows an enhancement of effective mass in the ultrathin films due to the quantum confinement in the specifically non-parabolic bands expected for a DNL semimetal.It is shown that electronelectron interactions do not have a large role in the effective mass enhancement, unlike in several other materials systems amenable to quantum confinement, such as in GaAs/AlGaAs heterostructures.The examples above demonstrate the tunability of IrO 2 thin films as hosts for quantum states of matter.
Tunability of the carrier type is demonstrated by Uchida et al [126] and is based on the rutile structure assumed by IrO 2 .The rutile structure of IrO 2 is a typical nonsymmorphic crystal structure, which can lead to very anisotropic folded Fermi surfaces near the Brillouin zone boundaries.As a result, the dominant charge carrier type (electron or hole) can be expected to be anisotropic in crystal orientation and sensitive to the details of external stimuli.Indeed, Uchida et al [126] showed that the carrier type in IrO 2 indicated by the Hall effect switches depending on the measurement's magnetic field orientation, as depicted in figure 11(a).Making IrO 2 a good testbed for the switching of properties is also the fact that IrO 2 is a metal with Fermi energy at a half-filled level, without magnetic ordering (except tentatively in ultrathin films [113]) or other phase transitions down to low temperatures.The IrO 2 singlecrystal films were grown by MBE with orientations ( 110), ( 100), (001), (101), and (111) on single-crystal TiO 2 of corresponding orientations.The Hall effect was measured from 300 K to 2 K with the magnetic field applied normal to the film plane, hence along different crystallographic directions (figure 11(a)).The dominant carrier type indicated by the Hall effect is found to be controlled by the crystallographic direction of the magnetic field, indicating a pronounced anisotropy of the Hall coefficient.Hole contributions dominate for magnetic fields along [100] and [110], and electron contributions along [001] and [101], while [111] shows nearly compensated behavior, consistent over the range of measurement  [100] and [110] orientations, electron contributions in [001] or [101], and compensated behavior in [111].Reprinted (figure) with permission from [126], Copyright (2015) by the American Physical Society.
temperatures (figure 11(b)).First-principles calculations of the band structure complemented by Boltzmann transport theory show that the observed dependence of dominant carrier type on magnetic field direction has its origin in the anisotropic and non-trivial electronic structure and Fermi surface of the nonsymmorphic IrO 2 .The nonsymmorphic structure of IrO 2 hence allows a unique switching of carrier type based on the magnetic field direction, a phenomenon of potential use in electronics applications.
4.1.3.Nanowire electrical transport properties.Spurred by progress in 1D nanostructure synthesis methods, recent studies have turned to electronic properties of IrO 2 nanorod/ nanowires, where rich phenomena and unanticipated quantum states that rely on the existence of the DNL, strong SOC, and controlled disorder and doping have been uncovered.
While studying single-crystal IrO 2 nanorods, Lin et al [199,200] observed a metallic behavior from 300 K to 50 K, with a weak upturn in resistivity with decreasing T below 50 K.Such an upturn is in fact regularly observed in IrO 2 of lower dimensionality (wires and thin films).The nanorods show a substantially higher resistivity over the range of T compared to bulk IrO 2 (at 300 K about 270 mΩ cm compared to 85 mΩ cm), and also show residual resistivity ratios (300 K resistivity/4 K resistivity) of only ∼1.2, compared to ∼500 for bulk crystals [98].Both observations point to a high level of point defects.An analysis of resistivity vs T shows that the T-dependent part of the resistivity is due to standard acoustic and optical phonon scattering, with θ D ≈ 315 K, similar to θ D ≈ 290 K found in bulk crystals [98].
As an example of an uncommon quantum state observation, Yeh et al [201] investigated the transport properties of IrO 2 (and RuO 2 ) nanowires as a function of T (figure 12), where they found the crystal symmetries that enforce the DNL of IrO 2 also give rise to nonmagnetic Kondo correlations.The O vacancies in the IrO 2 nanowires drive an orbital two-channel Kondo effect, where the degree of freedom is a pseudospin from orbital degrees of freedom.The near-degeneracy of the Ir d xz and d yz orbitals near an O vacancy is due to symmetry properties of IrO 2 and these orbitals form the pseudospin basis.The two defect electrons from the vacancy act as two independent Kondo screening channels.The O vacancy system can thus support an orbital two-channel Kondo effect.The resistivity of the nanowires drops linearly in T 1/2 below a characteristic Kondo temperature T K ≈ 20 K, as shown in figure 12.The resistivity shows metallic behavior for T > T K .The dependence on T is consistent with the existence of a two-channel Kondo effect.Other origins of the dependence on T, including effects of electron-electron interactions and disorder, are counted as unlikely by the authors.Yeh et al [201] hence showed that defect engineering in IrO 2 nanowires can provide unique unconventional non-Fermi-liquid quantum phenomena.
Closer to established mesoscopic quantum coherence effects in metallic nanowires, Chien et al [202] and Lin et al [203] demonstrated quantum interference effects in IrO 2 nanowires that were annealed in vacuum to generate O vacancies.Noise measurements in electronic transport from 1.7 K to 350 K show an increase in 1/f noise for T < 20 K due to time-dependent universal conductance fluctuations (UCFs, here TUCFs) generated by scattering off mobile defects in the nanowires.UCFs are a fingerprint of quantum interference in disordered mesoscopic conductors, originating from constructive and destructive interference of quantum-coherent carrier trajectories defined by the spatial defect configuration.In a mesoscopic conductor the resulting conductance fluctuations (versus a parameter such as magnetic field, temperature or time) are not averaged out and appear in the measurements at low T where quantum-coherence survives thermal broadening of energy levels.The mobile defects leading to TUCFs in the IrO 2 nanowires are thought to have the same microscopic origin in O vacancies as the defects leading to the two-channel Kondo effect.The TUCFs were used to quantify the quantum phase coherence length of the carriers, showing a length of 90 nm at 1.7 K and 10 nm at 8 K.
The presence of both strong SOC and electron correlations can lead to correlated topological states of matter, and searching for these states with an enhancement of electron correlations in IrO 2 is advantageous.An enhancement in electron correlations was noted in vanadium-doped IrO 2 (Ir 1−x V x O 2 ) nanowires [161].Since strong electron correlations are present in 3d TMO VO 2 , the enhancement in electron correlations was pursued as a deliberate result of the V-doping, with the aim to increase correlations in the otherwise relatively weakly interacting IrO 2 system.The nanowires in this work had rectangular cross-sections and effective diameters from 87 nm to 149 nm.T-dependent electrical resistivity measurements were carried out to study the effects of V-doping, where the doped nanowires had electrical resistivity orders of magnitude higher than undoped IrO 2 (figure 13(a)).Significantly, the nanowires showed a mild non-metallic upturn in resistivity with decreasing T starting in a certain range of low T (figure 13(b)).Several mechanisms can contribute to the weak upturn in resistivity, including a Kondo effect, localization effects, and corrections due to electron-electron interactions.Analysis of the resistivity vs T shows that in this doped disordered system, both an orbital two-channel Kondo effect and the resistivity correction from electron-electron interactions can account for the observations, with no ready means of distinguishing their contributions individually.It is noted that both mechanisms rely on strengthened electron correlations, and that the V-doping succeeded in enhancing electron correlations in the IrO 2 nanowires [161].
The above examples demonstrate that in nanowire form, the tunability of the IrO 2 electronic properties can be fully exploited in the search for new quantum phenomena and states of matter.Future experiments and theoretical developments have a fruitful path to follow up on the initial studies.

Spin transport
The strong SOC in IrO 2 leads to a large spin Hall angle, which makes the material attractive in spintronics for charge-to-spin conversion (spin Hall effect, for spin-current generation) or spin-to-charge conversion (inverse spin Hall effect, for spincurrent detection).To date, studies have confirmed large spin Hall angles θ SH , of which the sign and magnitude however vary with crystallinity and preferential surface or interface texture ((100), (110), etc) and can depend on T. The variation and dependence on T are attributed to different intrinsic SOC mechanisms and different spin-dependent scattering mechanisms (skew scattering, side jump mechanism) prevailing depending on conditions.The studies so far clearly indicate that controlling the surfaces and interfaces is necessary for use of IrO 2 in spintronics applications.
The pioneering work by Fujiwara et al [51] studied the inverse spin Hall effect in amorphous and polycrystalline IrO 2 thin films using a nonlocal spin valve geometry in the shape of a triple cross bar, with Ag as spin transport bar, two permalloy cross bars as spin-current injection electrodes, and an IrO 2 cross bar for spin-current detection by the inverse spin Hall effect (figures 14(a) and (b)).Inverse Hall effect was clearly observed in both the polycrystalline and amorphous samples (figures 14(c) and (d)).At 300 K, the spin Hall angles are found to be: θ SH = 0.040 for the polycrystalline IrO 2 and θ SH = 0.065 for the amorphous IrO 2 .These values are comparable to θ SH in Pt, Pd, β-W, β-Ta, and other metals often used for spin-current detection (figure 14(e)).Moreover, the inverse spin Hall voltage is proportional to the product of θ SH with electrical resistivity (the product is the spin Hall resistivity, which determines the efficiency of spin-current detection).The relatively higher resistivity of IrO 2 compared to elemental metals creates an additional advantage for spin-current detection.The work also found that the Ag/IrO 2 interface is well-defined.The θ SH changes sign at T = 90 K (θ SH > 0 above 90 K to θ SH < 0 below 90 K), which was ascribed to the coexistence of different SOC mechanisms yielding different signs.While a large θ SH is a promising hallmark in IrO 2 thin films, the complexities introduced by competing SOC mechanisms and a sensitivity to film orientation, morphology and strain have also been emphasized in subsequent work, as discussed below.
Various experimental approaches have recently been applied to obtain values for θ SH .These include measurements on spin valves, ferromagnetic resonance (FMR), and measurements of the spin Seebeck effect, with examples reviewed below.The spin Hall conductivity and θ SH were studied by Bose et al [205] in single-crystalline IrO 2 (001) and ( 110) thin films, with results shown in figure 15.The measurements occurred by spin-torque FMR to obtain an effective spin Hall conductivity.For (001) IrO 2, the spin Hall angles are determined to be θ SH = 0.45 at 300 K and θ SH = 0.65 at 30 K, among the highest θ SH measured on IrO 2 (figure 15) [140,141] and of opposite sign to some other results [124].In (110) films, θ SH is much reduced and is anisotropic for different current directions; both effects ascribed to anisotropic strain in the (110) films contrasted with the isotropic strain in the (001) films (figure 15).The contributions to the spin Hall conductivity near the DNLs are indeed expected to be very sensitive to strain.The work demonstrates the tunability and effect of orientation and strain on the spin Hall effect in IrO 2 .Deeper understanding of SOC mechanisms in IrO 2 is desired for better control of spin-to-charge conversion in the material [206], as illustrated by the varying sign and magnitudes for θ SH reported so far.To illustrate, Jiménez-Cavero et al [124] studied θ SH in polycrystalline Fe 2 O 3 /IrO 2 bilayers using the spin Seebeck effect for the measurements, where they found θ SH is negative and is scaling proportionally to the film resistivity throughout the range of T (50 K-300 K) and of thickness (2 nm-22 nm).Several mechanisms contributing to the spin Hall effect were discussed, including skew scattering, the side jump mechanism and the intrinsic SOC mechanism, and conclude that, in their work, the likely dominant contribution arises from the intrinsic SOC mechanism.Because one mechanism dominates, the sign of θ SH remains consistent.The results indicate that crystallinity and preferential texture (here (100)) can be used to control the sign and magnitude of the inverse spin Hall effect and that low θ SH values in the literature may be due to coexisting and competing mechanisms in one given sample leading to different signs.
In conventional spin-orbit torques (SOTs), the spin polarization directions generating the torque on magnetization are constrained to be orthogonal to both spin-current and chargecurrent directions, limiting magnetization switching to just one direction.While lower-symmetry materials offer more choices for the spin polarization, high-symmetry IrO 2 can be used with surfaces having lower-symmetry orientations, like (110) or (111), and with lower-symmetry crystallographic directions for applied current.The lower-symmetry surfaces and current  [16] to measure spin-charge conversion in polycrystalline thin films of IrO 2 .(b) The spin Hall angles measured at room temperature vs IrO 2 thickness.Tokura and Nagaosa [16] finds spin Hall angles up to 0.31 in the polycrystalline IrO 2 , about 4x larger than that found in Pt in comparable Pt/CoFeB bilayers.Reprinted from [141], with the permission of AIP Publishing.directions form a route for breaking the constraints inherent in conventional SOTs.IrO 2 has formed the basis for a search for such unconventional SOTs in [142], where spin-currents with unconventional spin polarizations can then be produced.The work studied the spin Hall effect in (001), (110), and ( 111) oriented films along different in-plane crystallographic directions using spin-torque FMR.The films were grown on TiO 2 via RF magnetron sputtering with a permalloy overlayer used as spin detector.
Examples of the various magnitudes and signs for spin-tocharge conversion in IrO 2 observed in the growing literature are discussed below [207], in conjunction with the nature of the films and the measurement method, both of which may play a role in the results.Sahoo et al [140] applied FMR spin pumping in IrO 2 /CoFeB bilayers (figure 16) to study inverse spin Hall voltages.Polycrystalline IrO 2 was obtained in the bilayer, through DC magnetron sputtering on Si (100).Spin pumping transfers spin angular momentum from a ferromagnet (CoFeB) to an adjacent nonmagnetic material (IrO 2 ) under an external magnetic field and a microwave excitation field, and the inverse spin Hall effect converts the spin-current to charge-current for measurements.Damping of the FMR signal was also used for measurements.The results show high θ SH = 0.26 in the polycrystalline IrO 2 at 300 K, comparable to results of [205].Using similar approaches Sahoo et al [141] reported large θ SH in polycrystalline IrO 2 /CoFeB bilayers using spin-torque FMR experiments, linewidth modulation experiments and line shape analysis, with the setup and typical sample depicted in figure 16.The films were vacuumannealed, resulting in improved intergrain conductance and lower roughness.The spin Hall angle is θ SH = 0.31 in the optimized polycrystalline IrO 2 (figure 16), which is about 4x larger than that found in Pt in a comparable Pt/CoFeB bilayer studied in parallel (θ SH = 0.07).The improved conductivity and low roughness in the optimized polycrystalline films likely contributed to the high θ SH = 0.31, which is comparable to the crystalline film result in [205].Using spin-torque generation in permalloy (Ni 81 Fe 19 )/IrO 2 bilayers and measuring second-harmonic Hall resistance, Ueda et al [143] reported an effective θ SH = +0.093± 0.003 and a spin-diffusion length = 1.7 ± 0.2 nm at 300 K.The work again shows that θ SH in IrO 2 is comparable to that in Pt and in fact 7x higher than that in elemental Ir.Furthermore, the same group studied a stacking-order effect, where the magnetic and spintransport properties for two distinct stacking configurations, i. Qiu et al deposited IrO 2 film on a Y 3 Fe 5 O 12 (YIG) film to form an all-oxide spintronics device for the observation of the spin Seebeck effect in the IrO 2 [216].All-oxide spintronics devices, in many cases, have promising applications where optical transparency is required.IrO 2 with its high θ SH is an attractive component in this quest.In the experiments, via the spin Seebeck effect, a temperature gradient maintained across the YIG/IrO 2 interface injects a spin current into the IrO 2 which is then detected by the inverse spin Hall voltage over contacts on the IrO 2 .The small magnitude of the measured inverse spin Hall voltage indicates a small spin-mixing conductance at this particular YIG/IrO 2 interface.Realization of all-oxide spin Seebeck devices hence requires engineering of the oxide interface for optimum spin-mixing conductance, which can be achieved by interlayers, annealing, or doping.

Thermal transport
Like many other TMOs, the thermal transport properties of IrO 2 have been far less studied than their electrical and spin transport properties.This may be due to the conventional wisdom that TMOs have relatively low thermoelectric figure of merit in comparison to other families of materials such as metal chalcogenides.The thermal transport of IrO 2 , however, is of particular interest for fundamental research owing to its unique material properties, including the large atomic mass difference between the light oxygen and heavy iridium atoms, the strong interatomic bonding, the relatively complex crystal structure that contains six atoms in a unit cell, as well as the possible interactions between electrons and phonons.
The first thermal transport measurement was performed by Tao et al [204] on single crystalline IrO 2 nanowires grown by the vapor phase method.Figure 17(a) shows a SEM image of a representative IrO 2 nanodevice for thermal measurement using a standard micro-thermal bridge method [161,204,[217][218][219].The IrO 2 nanowire was positioned between two suspended membranes in proximity which have embedded serpentine platinum coils.Each of the coils was connected electrically to four contact pads for both joule heating and four-terminal resistance measurement.One coil was used as a resistance heater and the other as a resistance thermometer.Pt/C composites were typically deposited at the contacts of the nanowire to minimize the contact thermal resistance.In a typical measurement, a DC voltage was applied to the heater to heat one side of the nanowire by Joule heating.Part of the heat was conducted to the resistance thermometer through the nanowire and increased its temperature.The thermal conductance of the nanowire was derived by solving 1D heat transport equations.
The thermal conductivity of a material is composed of two terms, the electronic thermal conductivity (κ e ) and the lattice/ phonon thermal conductivity (κ ph ).The κ e is related to the electrical conductivity σ e , as described by the Wiedemann-Franz law: κ e = LTσ e , where L is the Lorentz number and T is the temperature.Because of the high electrical conductivity of IrO 2 , the electrons have a notable (∼20%) contribution to the κ tot (figure 17(b)).The dominant contribution (80%), however, is from phonon transport, differing from many other metals.The high phonon thermal conductivity κ ph is unexpected as each unit cell of IrO 2 contains 6 atoms, corresponding to 15 optical phonon branches, which would promote threephonon scattering and lead to a low κ ph .
Theoretical studies based on DFT calculations and Boltzmann transport suggest that the high phonon thermal conductivity κ ph is due to two remarkable characteristics of IrO 2 .First, the atomic mass of Ir is 12 times as large as that of the O atom; this large atomic mass difference leads to a sizable band gap (between 11 THz and 16 THz) in the phonon dispersion (figure 18(a)).As a result, the Umklapp scattering involving high energy optical branches is significantly suppressed.Indeed, as shown in figure 18(b), the rate of the Umklapp scattering (which poses resistance to thermal transport) is about an order of magnitude lower than the normal scattering rate.Therefore, the three-phonon scattering process is dominated by the normal scattering which satisfies the conservation of phonon momentum with no influence on the thermal conductivity.Second, the interatomic bonding in IrO 2 is strong, leading to high group velocities for the acoustic phonons.Some of the low energy optical branches also have high phonon group velocities, as shown in figure 18(c).Consequently, the phonon thermal conductivity of IrO 2 is relatively high.
It is worth noting, however, that the theoretically calculated κ ph including only the three-phonon scattering is higher than the experimentally measured values (figure 18(d)).To explain this discrepancy, Tao et al [204] added the electron-phonon (e-ph) scattering in their model, where they demonstrated that the e-ph scattering plays an essential role in suppressing the κ ph above ∼50 K[figure 18(d)].The calculated e-ph scattering rate, shown in figure 18(b), is overall higher than the Umklapp scattering rate.The strong influence of e-ph on thermal conductivity is not often seen in either elemental metals such as Cu, Ag, and Au where three-phonon scattering rate dominates, or semiconductors/insulators which have low conduction electron density and smaller e-ph scattering rate.Furthermore, reduction of κ ph by surface boundary scattering of phonons was also observed both experimentally and theoretically in nanowires with a diameter of ∼100 nm.This suggests that the intrinsic mean free path for phonons is ∼100 nm or longer in bulk IrO 2 .The competing effects of the large atomic mass difference and strong inter-atomic bonding against the e-ph scattering and surface boundary scattering gives rise to a relatively high phonon thermal conductivity which is comparable with that of the Si nanowires of a similar diameter [220].
Vanadium doping drastically suppresses the thermal conductivity of the IrO 2 nanowires [161].As shown in figures 19(a)-(c), both the κ e and κ ph were reduced by about an order of magnitude at room temperature with 29% vanadium.The reduction of κ e is related to the suppressed electrical conductivity σ upon doping.At low temperatures, the suppression of κ ph is attributed to the enhanced impurity scattering of phonons by doping, whereas its dramatic decrease at room temperature is due to the enhanced phonon-phonon Umklapp scattering.When some of the Ir atoms are replaced by V, the number of atoms in a primitive unit cell increases and the crystal symmetry is lowered, which gives rise to more complex phonon dispersion (figure 19(d)).Furthermore, since V is lighter than Ir, the atomic mass difference between the metals and oxygen is decreased, yielding a reduction in energy gap between the phonon branches.The increased complexity in the phonon dispersion and the reduction in energy gap collectively enhances the phonon-phonon Umkapp scattering and hence reduces κ ph .Comparisons of (a) κtot, (b) κ ph , and (c) κe of V-doped and undoped IrO 2 nanowires, which suggests a significant suppression of thermal conductivity by V-doping.The undoped data were originally adapted from [204] in [161].(d) The calculated phonon dispersion relation of 25% V-doped IrO 2 .Reproduced from [161].CC BY 4.0.

Summary and perspectives
In quantum systems, degeneracy as a manifestation of internal symmetry can be observed in experiments.For instance, the paramagnetic nature of molecular oxygen is attributed to the presence of two degenerate antibonding orbitals at the outer shell and to the Hund's rule.Here, in IrO 2 , which is a binary oxide with rutile structure, the nonsymmorphic symmetry causes the doubling of degeneracy along A-M and X-M directions in the momentum space.Originally, the timereversal symmetry and inversion symmetry guarantee that every Bloch state is at least doubly degenerate and with the nonsymmorphic symmetry, the fourfold degeneracy is protected along A-M and X-M.Thus, it is interesting to wonder whether the fourfold degeneracy can be broken in a realistic system in the presence of, for example, magnetic impurities.IrO 2 is also unique in the sense that the DNLs cross the Fermi level.Therefore, further exploration of the scattering of the corresponding Bloch states with impurities and defects is critical for understanding the spin and/or charge transport properties [221,222].
Another form of perturbation is the presence of magnetic field, which also breaks the time-reversal symmetry and can be used to map the Fermi surface.The fourfold degeneracy along the A-M and X-M directions, has been experimentally verified in IrO 2 with the ARPES [50,71].These DNLs occur when the electron-like band is in contact with the hole-like bands around the Fermi level [50].The richness of such Fermi surfaces may manifest itself through the carrier dynamics in the presence of a weak magnetic field.In a semiclassical picture, carriers are traversing the closed loops inside the Fermi surface in the plane perpendicular to external field [223,224].The possibility of carrier tunneling from one electron-like orbit to a holelike one through the DNL is an interesting question for modeling the carrier dynamics under weak magnetic field.
Experimental study of exotic physical properties strongly relies on the growth of high-quality materials.Bulk crystals, epitaxial thin films, and single-crystalline nanostructures of IrO 2 have been synthesized via a variety of synthetic approaches.Some of these growth techniques (e.g.vapor transport) utilize the high volatile nature of the IrO 3 to realize mass transport for the growth; the high volatility, on the other hand, poses challenges in controlling the stoichiometry of IrO 2 in other deposition processes (e.g. in PLD).Fine tuning of the growth parameters in a coherent way to minimize the loss of Ir and meanwhile to avoid metal dissociation would be essential to those growths.Strain engineering of the oxidation chemistry as used in a recent metal-organic MBE growth [128] is a novel approach to control the formation of competing phases.It would certainly be interesting to study if the same approach is applicable to other growth processes, such as PLD or electron-beam-assisted MBE growth.
Single crystalline nanowires with a sufficiently long length suitable for device fabrication have been realized via vapor transport growth.The diameters of the nanowires are typically on the order of tens of nanometers or larger.It would be of great interest to achieve ultra-thin wires down to sub-10 nm to explore potentially new transport properties arising from the dimensionality effect.This 1D nanowire growth, however, may not be a trivial task as the IrO 2 nanowires are synthesized via a direct VS mechanism (instead of metal-catalyzed VLS), in which case the wire diameter is less controlled.The anisotropy in the VS growth is strongly influenced by the surface energy difference between facets; therefore, enhancing the surface energy difference by tailoring the growth parameters would be a viable approach to realize 1D ultra-thin wires.
Electronic and magnetotransport properties of IrO 2 have extensively been used as a diagnostic for the numerous phenomena harbored by the bulk crystals, thin to ultrathin films, and nanowires.The richness and tunability of the properties consistently mirror the physics of the competition between the energy scales of SOC, U, and ∆, which yields quantum states depending on strain, doping, dimensionality, film thickness by confinement quantization, temperature, and magnetic field.Apart from the competition, also the presence of DNLs, the strong SOC, and the crystal symmetries bring out unique electronic properties.While from a materials viewpoint IrO 2 appears as a single entity, from the viewpoint of transport properties the material is multifaceted and versatile.Future work should keep the multifaceted nature in mind and analyze electronic transport results accordingly and will undoubtedly add to the list of phenomena hitherto observed.Examples of non-trivial electronic properties include a strong anisotropy of the Hall coefficients, insulating behavior of several possible origins in ultrathin films, and the presence of a rare twochannel Kondo effect in nanowires.
The strong SOC has led to consistent observations of a large spin Hall angle, beneficial in spintronics for spin-current generation and spin-current detection.Future work, particularly regarding control of surfaces and interfaces, will help resolve open questions regarding the sign and magnitude of the spin Hall angle, where variations have been observed.The variations are not entirely surprising given the susceptibility of IrO 2 films to strain, disorder, film thickness, and other parameters.More refined knowledge about the different SOC mechanisms and spin-dependent scattering mechanisms will also contribute to propelling IrO 2 as a prominent spintronics material.Furthermore, the thermal conductivity of IrO 2 turns out to be high among oxides due to the large atomic mass difference between Ir and O, as well as the strong interactomic bonding.The high electrical and thermal conductivities, accompanied by its outstanding spin-based properties, will offer great opportunities for applications in oxide-based electronics and spintronics.

Figure 1 .
Figure 1.(a) Rutile crystal structure of IrO 2 .(b) Upper panel: a generic J eff = 1/2 model describing the splitting of 5d states by a perfect octahedral crystal field and strong SOC; bottom panel: a schematic illustrating the distortion of an IrO 6 octahedron; (c) IrO 6 octahedra with shared corners and edges in IrO 2 .(d) Projected density of states of the three t 2g orbitals and two eg orbitals in IrO 2 .Reprinted (figure) with permission from [44], Copyright (2016) by the American Physical Society.

Figure 2 .
Figure 2. Calculated electronic band structures of IrO 2 (a) with and (b) without SOC.The bands highlighted with the green color in (a) represent the DNLs which are fourfold degenerate due to the nonsymmorphic symmetries.The dashed circles denote two Dirac points in the absence of SOC: the one along Γ − Z path is sixfold degenerate, whereas the one along A-M is eightfold degenerate.Reprinted (figure) with permission from [71], Copyright (2019) by the American Physical Society.

Figure 3 .
Figure 3. Fermi surfaces projected at (110) and (001) directions obtained by ARPES as demonstration of Dirac nodal lines in IrO 2 .(a) Two hole-like Fermi surfaces (red) and one electron-like Fermi surface (blue).(b) Color-coded representation of Dirac nodal line dispersion along A-M and X-M.(c) The Fermi surface projected onto (110) central plane (inset), obtained from DFT (left) and ARPES (right).(d) The Fermi surface projected on (110) boundary plane.(e) and (f) Projections onto the (001) central and boundary planes, respectively.Reprinted (figure) with permission from [50], Copyright (2019) by the American Physical Society.

Figure 4 .
Figure 4. One-dimensional band dispersion along the path joining the Dirac points OP and HP on the (110) mirror plane.(a) and (b) are the results with and without SOC, respectively.Note that in (b)the band degeneracy is fully lifted at HP while the two-band touching remains at OP (OP located along A-M).(c) Displays the distribution of the spin Berry curvature along the (110) plane passing through the Dirac points as well as these highly symmetric momenta Γ , A, M, and Z.The gap opening [blue curve in (a) is split into their counter parts in (b)] due to the SOC results in significant spin Berry curvature.Reprinted (figure) with permission from [48], Copyright (2017) by the American Physical Society.

Figure 5 .
Figure 5. (a) A schematic illustrating the crystal structure of IrO 2 (100) thin film on TiO 2 (100) substrate.(b) X-ray diffraction (XRD) θ − 2θ scan of a PLD-grown IrO 2 film on a single crystalline TiO 2 (100) substrate.(c) Cross-sectional scanning transmission electron microscopy (STEM) image showing a sharp interface of the epitaxial IrO 2 film and TiO 2 substrate.The scale bar is 2 nm.(d) X-ray reciprocal space mapping around the (301) Bragg reflections.(e) A PLD growth phase diagram describing the influence of O 2 pressure and deposition temperature on the IrO 2 films: no films are formed at high O 2 pressure regime, pure IrO 2 at intermediate O 2 pressures and relatively low temperatures, and films with Ir metal cluster at intermediate O 2 pressures and high temperatures.Each dot denotes a growth at the corresponding condition.The yellow dashed line and the arrow mark the optimal and the best growth conditions, respectively.(f) A cross-sectional TEM image showing the height difference between grains in a PLD grown IrO 2 film.(b), (d) Reprinted (figure) with permission from [44], Copyright (2016) by the American Physical Society.(c) Reproduced from[113] with permission from the Royal Society of Chemistry.(e), (f) Reprinted from[114], Copyright (2017), with permission from Elsevier.

Figure 8 .
Figure 8. SEM images of (a) needle-like IrO 2 nanowires grown by vapor transport and (b) less-tapered nanowires grown by a modified vapor transport approach where IrO 2 powder was coated on the substrate to facilitate growth.(c) An optimum bright-field (OBF) STEM image demonstrating the high crystalline quality of an IrO 2 nanowire near its surface.(d) and (e) OBF images taken at different magnifications with the e-beam parallel to the nanowire axis to show its cross-section.(f)-(g) SEM images at different magnifications revealing the enhanced nanowire density in the scratched region of a Si substrate.(h) A schematic drawing illustrating the different diffusion preferences of adatoms in the flat region and near an edge.Atoms diffuse isotopically in the former case, whereas they tend to diffuse towards the edge in the latter case, which generally enhances nucleation.(i) High-angle annular dark-field STEM image and (j) energy-dispersive x-ray spectroscopy (XEDS) maps of a V-doped IrO 2 nanowire near its tip.The inset shows the XEDS line scans of Ir (cyan) and V (purple) across the nanowire diameter.(a) Reprinted with permission from [158].Copyright (2012) American Chemical Society.(c)-(e) Reprinted from [160], Copyright (2023), with permission from Elsevier.(f)-(h) and (j) Reproduced from [161].CC BY 4.0.

Figure 9 .
Figure 9. Magnetoresistance in rutile single-crystal IrO 2 at 1.2-4.2K and at a fixed magnetic field of 10 T. The current was applied along [001].Using sample rotation, the direction of the magnetic field was varied over two angles θ (crystallographic direction indicated on top axis) and ϕ to obtain Shubnikov-de Haas oscillations due to various Fermi surface cross-sections.The magnetoresistance is expressed as the relative change in resistivity (∆ρ/ρ) and its scale is arbitrary.The zero is offset for each ϕ (indicated by Z on the left axis).From the data, a model of a complicated Fermi surface was deduced.Reprinted (figure) with permission from [192], Copyright (1972) by the American Physical Society.

Figure 10 .
Figure 10.(a) Resistivity vs temperature in PLD-grown IrO 2 films on TiO 2 substrate with (001) orientation for different film thicknesses (measured in van der Pauw configuration).The upturn into insulating behavior, indicated by an arrow, denotes a metal-insulator transition appearing for the thinnest films of thickness 1.5 nm-2.5 nm.(b) Resistance vs temperature measured along the [001] direction of the [110]-oriented thin films grown by MBE with varied thicknesses down to 3 monolayers.(c) Effective 2D hole density of the MBE-grown films as a function of temperature.(a) Reproduced from [113] with permission from the Royal Society of Chemistry.(b), (c) Reprinted (figure) with permission from [125], Copyright (2018) by the American Physical Society.

Figure 11 .
Figure 11.Measurements of the Hall resistivity obtained with magnetic fields along different crystallographic directions of IrO 2 indicate different carrier types (electron or hole).(a) A sketch of the magnetic field directions and film orientations for the Hall resistivity measurements, with the IrO 2 rutile structure shown in the same orientation.(b) The Hall resistivity vs magnetic field obtained at 2 K for different magnetic field orientations.The measurements indicate hole contributions in the[100] and[110] orientations, electron contributions in [001] or[101], and compensated behavior in[111].Reprinted (figure) with permission from[126], Copyright (2015) by the American Physical Society.

Figure 12 .
Figure 12.Measurements of resistivity vs T in IrO 2 nanowires indicate a two-channel Kondo effect.The main panel shows the T 1/2 insulating behavior of resistivity for three nanowires, characteristic of the two-channel Kondo effect.Nanowire (NW) A has a diameter of 130 nm, NW B1 and B2 have 190 nm diameters, while NW 3 is of diameter 330 nm and was oxygenated to have low O vacancy concentration.The left inset (scale bar 1 µm) shows a SEM micrograph of NW A. The right inset shows resistivity vs T in NW A over wider range of T, and in reference metallic NW.Reproduced from [201].CC BY 4.0.

Figure 13 .
Figure 13.(a) Temperature dependent resistivity of undoped and V-doped IrO 2 nanowires, revealing significantly increased resistivity upon V-doping.The undoped data were originally adapted from[204] in[161].(b) Resistivity of the V-doped nanowires normalized at 300 K to display its temperature dependence for nanowires with different diameters.The resistivity values at 300 K are shown in the inset.Reproduced from[161].CC BY 4.0.

Figure 14 .
Figure 14.The lateral nonlocal spin-valve geometry used in [51] to study the inverse spin Hall effect via the spin Hall resistivity and spin Hall angle.(a) The spin-valve geometry has the shape of a triple cross bar, with a Ag spin transport bar, two permalloy cross bars as spin-injection electrodes, and an IrO 2 cross bar for spin-current detection by the inverse spin Hall effect.The spin Hall angles obtained in [51] are comparable to those measured in other metals often used for spin-current detection.(b) A SEM micrograph of a typical spin-valve, with scale bar of 500 nm.The dotted lines indicate the edges of the IrO 2 wire.The inverse spin Hall resistance versus magnetic field measured on (c) a polycrystalline wire and (d) an amorphous wire.(e) A summary of measured spin Hall resistivity ρ SH and electric resistivity ρc for different metals, which shows considerably large ρ SH in IrO 2 compared with some typical heavy metals and alloys.Reproduced from[51], with permission from Springer Nature.

Figure 15 .
Figure 15.Spin Hall angles vs T, measured on thin film IrO 2 via spin-torque ferromagnetic resonance in [12].The spin Hall angles are the damping-like ξ DL and the field-like ξ FL as measured from the spin torques, where ξ DL is of relevance for comparisons of the spin Hall resistivity in materials.(a) Spin Hall angles for (001) IrO 2 , showing large values of 0.45 at 300 K and 0.65 at 30 K, among the highest measured on IrO 2 .(b)-(c) Spin Hall angles for anisotropically strained (110) IrO 2 , showing much reduced and anisotropic values.Reprinted with permission from [205].Copyright (2020) American Chemical Society.

Figure 16 .
Figure 16.(a) A schematic of the spin-torque ferromagnetic resonance setup and a picture of the IrO 2 /CoFeB bilayer samples used in[16] to measure spin-charge conversion in polycrystalline thin films of IrO 2 .(b) The spin Hall angles measured at room temperature vs IrO 2 thickness.Tokura and Nagaosa[16] finds spin Hall angles up to 0.31 in the polycrystalline IrO 2 , about 4x larger than that found in Pt in comparable Pt/CoFeB bilayers.Reprinted from[141], with the permission of AIP Publishing.
e. substrate/TaO x /Ni 81 Fe 19 /IrO 2 (IrO 2 -T) and substrate/IrO 2 / Ni 81 Fe 19 / TaO x (IrO 2 -B), were compared [144].The IrO 2 -B sample possesses a positive sign for the field-like SOT, whereas a negative sign was observed in the IrO 2 -T sample which was attributed to the oxidation of the Ni 81 Fe 19 at the Ni 81 Fe 19 /IrO 2 interface.Since O 2 gas was introduced in the deposition of IrO 2 , the surface oxidation of Ni 81 Fe 19 was more significant in the IrO 2 -T sample than in the IrO 2 -B.The oxidation possibly enhances the interface Rashba-Edelstein effect, yielding a negative sign in the field-like SOT [208-212].The damping-like SOT is positive for both samples, but its magnitude is lower in the IrO 2 -T sample than in the IrO 2 -B sample, possibly due to an intermixing effect which reduces the spin transparency at the interface [213-215].

Figure 17 .
Figure 17.(a) A false-colored SEM image showing a top view of anIrO 2 nanowire device for thermal transport measurement using a micro-thermal bridge method.The nanowire is denoted by the green color.Red and blue indicate the platinum coils embedded in suspended membranes as resistance heater and thermometer, respectively.The inset is an SEM image showing the cross-sectional shape of the nanowire (with the e-beam tilted away from the nanowire axis).The total thermal conductivity κ total , phonon thermal conductivity κ ph and electronic thermal conductivity κe of two IrO 2 nanowires with a diameter of 126 nm.Reprinted from[204], Copyright (2021), with permission.

Figure 18 .
Figure 18.(a) The phonon dispersion of bulk IrO 2 calculated by DFT.(b) A comparison of the calculated scattering rate for normal scattering, Umklapp scattering and electron-phonon (e-ph) scattering.The accumulated thermal conductivity with and without e-ph scattering are compared in the inset.(c) The calculated phonon group velocity for the transverse acoustic (TA) modes, longitudinal acoustic (LA) mode, and optical modes along the Γ − Z path.(d) A comparison of the calculated (lines) and measured (dots) κ ph of two nanowires with different diameters.The dashed lines are without considering e-ph scattering, whereas the solid lines are with the e-ph scattering.κ ph of bulk IrO 2 with and without e-ph scattering are shown in the inset.In all cases, a dramatic suppression of κ ph by e-ph scattering is evidenced.Reprinted from [204], Copyright (2021), with permission.