Abrupt enhancement of spin–orbit scattering time in ultrathin semimetallic SrIrO₃ close to the metal–insulator transition

The Ruddlesden–Popper series iridates (Sr_n+1Ir_nO_3n+1) exhibit highly tunable electronic and magnetic ground states due to the strong spin–orbit coupling (SOC), which competes with the electron itineracy, the on-site Coulomb energy U, and the crystal fields associated with the spatially extended 5d-orbitals.^1–4 As the end member of the series in the large bandwidth limit (n = ∞), SrIrO₃ (SIO) is a paramagnetic semimetal^3–5 and has been suggested to exhibit nontrivial topological phases in the orthorhombic phase [Fig. 1(a)], such as Weyl/Dirac semimetals and topological Mott insulators.^6,7 While the perovskite SIO is metastable in the bulk,^8,9 it has been realized in high quality epitaxial thin film form,^4,10 where a range of interesting phenomena have been observed, including strain tunable Dirac node^11–13 and metal–insulator transition (MIT)^14–16 and thickness-driven dimensionality crossover.^17,18 Due to the highly tunable electronic state, intrinsically large SOC, and emerging interfacial Dzyaloshinskii–Moriya interaction,¹⁹ SIO thin films and heterointerfaces are promising material candidates for developing novel spin transistors²⁰ and skyrmion-based topological electronics.^21,22 Despite the emerging fundamental and practical research interests, the dominant spin relaxation mechanism in ultrathin SIO films, especially in the presence of enhanced electron correlation, remains elusive to date.

In this work, we report a comprehensive magnetotransport study of spin relaxation in high quality epitaxial SIO thin films coherently strained on SrTiO₃ (STO) substrates. SIO films with thicknesses down to 2.0 nm show semimetallic transport with complete charge compensation, while the thinner films exhibit insulating behavior. From the two-dimensional (2D) weak localization (WL) and weak anti-localization (WAL) effects, we extract the temperature and film thickness dependences of the phase coherence and spin–orbit scattering behaviors. The spin–orbit scattering time τ_so exhibits a quasi-linear dependence on the momentum scattering time τ_p, pointing to Elliott–Yafet (EY) mechanism dominated spin relaxation. The films approaching the critical thickness of MIT show an abrupt enhancement in τ_so with concomitantly reduced carrier density and increased charge mobility. A likely scenario for such unusual enhancement is that spin scattering is suppressed due to an emerging charge gap.

We deposited 1.4–21.2 nm epitaxial SIO thin films on (001) STO (1.4% compressive strain) using off-axis radio frequency magnetron sputtering (see the supplementary material for growth conditions). Atomic force microscopy (AFM) measurements reveal smooth sample morphology for all samples with a typical surface roughness of 1–2 Å [Fig. 1(b)].²³ X-ray diffraction (XRD) spectra show (001) growth (pseudo-cubic notation) with no appreciable impurity phases [Fig. 1(c)]. The c-axis lattice constant is ∼4.02 Å, larger than the bulk value of 3.96 Å, which is consistent with strained SIO on STO.¹⁵ Reciprocal space mapping (RSM) shows that even the thickest film is fully strained to the substrate [Fig. 1(d)]. For magnetotransport studies, we patterned the SIO samples into Hall bar devices with the channel length of 10–40 µm and the length/width ratio of 1:1 or 2:1. Magnetotransport measurements were performed in a Quantum Design PPMS system combined with an external SR830 Lock-In or Keithley 2400 SourceMeter at an excitation current of 100 nA–10 µA.

Figure 1(e) shows the temperature dependence of sheet resistance R_□(T) for SIO films with various thicknesses. The 2.0 nm and thicker films exhibit metallic temperature dependence (dR/dT > 0) over a wide temperature range, followed by an upturn below a transition temperature T_m that can be described by ln(T) dependence of sheet conductance G [Fig. 1(e), inset],

and

Here, R₀ (G₀) is the residual sheet resistance (conductance), and A, α, p, and T₀ are fitting parameters (see Fig. S2 of the supplementary material for fitting details). Distinct from the hexagonal SIO single crystals,⁵ the high temperature R_□(T) exhibits a very weak T-dependence with a room temperature resistivity ρ(300 K) of 0.5–0.9 mΩ cm. The power exponent α in Eq. (1a) is about 1.1–1.2, revealing a non-Fermi-liquid behavior. The low temperature ln(T) correction to the conductance [Fig. 1(f)] is the signature behavior of a 2D electron system due to WL or electron–electron interaction.²⁴ The thinner films show higher T_m, which increases from 7 K to 21 K as the film thickness reduces from 21.2 nm to 2.0 nm [see Fig. S2(a) of the supplementary material]. The 1.6 nm film becomes insulating over the entire temperature range, and the low temperature R_□(T) can be well described by the 2D variable range hopping (VRH) model: $R□∝expT0T1/3$ [Fig. 1(g)].²⁵ This transition to the strongly localized behavior occurs as R_□ exceeds h/2e² ≈ 12.9 kΩ. The 1.4 nm film, on the other hand, exhibits a crossover from thermally activated semiconducting behavior exp[Δ/2k_BT] at high temperature to 2D VRH at about 155 K [Fig. 1(h)]. The extracted activated energy Δ ≈ 102 meV is consistent with the previous reports for ultrathin SIO.¹⁷ Such thickness-driven MIT in SIO has been attributed to enhanced correlation energy in the 2D limit¹⁷ and lattice distortion imposed by the substrate symmetry.¹⁸ The critical thickness (about 4 unit cell) in our samples is comparable with that reported for SIO films encapsulated with STO top-layers¹⁷ and approaches the limit for charge gap formation.¹⁸ 

Previous band structure mapping via angle-resolved photoelectron spectroscopy (ARPES) has revealed a light mass electron pocket and a heavy mass hole pocket at E_F in epitaxial SIO thin films.^11,13 The semimetallic nature of SIO is clearly manifested in the Hall effect and magnetoresistance (MR) measurements. As shown in Figs. 2(a) and 2(b), the magnetic field H-dependences of Hall resistance R_xy and R_□ can be well described by the semiclassical two-band model,²⁶ 

and

Here, ρ_xy = R_xyt is the Hall resistivity, t is the film thickness, ρ is the longitudinal resistivity, $ne$ (⁠$nh$⁠) is the electron (hole) density, and μ_e (μ_h) is the electron (hole) mobility. The linear H-dependence of R_xy and H²-dependence of R_□ have been observed in films of all thicknesses, which can be satisfied for close to be fully compensated electron and hole densities, i.e., $ne$ ≈ $nh$⁠, with Eq. (2) reducing to

and

Another possibility for having a linear Hall behavior is that there is only a single type of charge carrier (electron). The single carrier model, however, would lead to about two orders of magnitude discrepancy between the mobility value deduced from MR, i.e., Δρ/ρ(0) = μ²H², and the Hall mobility, i.e., $μ=σne=|RH|ρ0$⁠. Combining this fact with the previous ARPES results, we can rule out the single carrier scenario.

Fitting the Hall and MR data to Eq. (2) and assuming $ne$ = $nh$⁠, we extracted the carrier density and mobility as a function of film thickness. At T_m, the carrier density falls in the range of 10¹⁹–10²⁰ cm⁻³ [Fig. 2(c)], similar to previously reported results.^15,16 At 10 K, the 2.0 nm and 2.8 nm films show considerably lower carrier density than those at T_m, consistent with an emerging charge gap at the ultrathin limit.^17,18 The carrier mobility, on the other hand, is significantly enhanced in the thinner films [Fig. 2(d)], with μ_e at 10 K increasing from 45 cm²/V s in the 21.2 nm film to 140–150 cm²/V s in the 2.0 nm films. The mobility difference for electron and hole, defined as $β=μe−μhμe+μh$⁠, is less than 1.5% for all samples. The mobility values are orders of magnitude higher than those observed in strongly correlated oxides in the paramagnetic metallic phase²⁷ and comparable with the non-interacting electrons in thin films of high mobility perovskite semiconductor BaSnO₃.²⁸ A possible scenario is that these samples are close to the fully charge compensated regime with low density of states in both the conduction and valence bands,¹¹ which suppresses the intra-band elastic scattering. The inter-band scattering does not play a significant role at low temperature due to the large momentum transfer required between the electron and hole bands at the Fermi level E_F.^11,13 A likely origin for the film thickness dependence of mobility is the progressively reduced structural defects associated with the epitaxial strain in thinner films. As orthorhombic SIO is meta-stable in the bulk, it has been shown that the film crystallinity degrades in the thicker films, where the lattice strain is released through oxygen vacancies, dislocations, and even formation of polycrystalline grains above a critical thickness (20–40 nm).^4,10

Figure 3(a) shows the magnetoconductance (MC) Δσ(H) = σ(H) − σ(0) of the 2.8 nm SIO film at low temperatures. The sample exhibits a negative MC at low field followed by a positive MC at high field. The positive MC is widely observed in 2D electron systems due to the WL effect, where the magnetic field suppresses the constructive backscattering of electrons. The negative MC, known as WAL, originates from spin–orbit scattering, which leads to destructive interference of backscattered electrons that can be suppressed by the magnetic field. The WAL effect has previously been used to deduce the SOC induced spin splitting in semiconductor heterostructures.^29,30 In SIO films, the transition from WAL to WL dominated MC occurs at progressively higher field at increasing temperatures, suggesting that the dephasing/scattering mechanisms contributing to these two quantum conductance correction effects have different temperature-dependences.

Given the strong SOC in SIO and considering the effect of Zeeman splitting, we employed the Maekawa–Fukuyama (MF) model to fit Δσ(B),³¹ 

Here, Ψ = ln(x) + ψ(1/2 + 1/x), ψ(x) is the digamma function, and σ₀ = e²/πh is the quantum conductance. The dephasing driven by inelastic scattering and spin–orbit scattering are captured in $Hi=ℏ4eDτi$ and $Hso=ℏ4eDτso$⁠, respectively, where $D=12vF2τp$ is the diffusion constant, v_F is the Fermi velocity, τ_p is the momentum relaxation time, and τ_i is the inelastic scattering time. The parameter γ = gμ_BH/4eDH_so couples H_so and the g factor, which describes the Zeeman effect correction. At 2–5 K, the MC data can be well described by the MF model [Fig. 3(a)]. Given the sample mobility (μ_e,h ∼ 140 cm²/V s at 10 K), the criterion of low magnetic field condition (μ_e,hB < 1) is satisfied in the entire range of the magnetic field investigated. The quantum corrections to the MC persists to a very high field (up to 4 T), where the classical parabolic contribution is negligible.

Figure 3(a) (inset) plots the extracted H_i and H_so for the 2.8 nm film, which exhibit linear and quadratic T-dependences, respectively. Similar temperature dependences have been observed in the 2.0–5.4 nm films, while thicker films do not show prominent WL and WAL in MC above 3 K. From H_i and H_so, we obtained the inelastic scattering and spin–orbit scattering lengths using $Li,so=Dτi,so1/2=ℏ4eHi,so1/2$⁠. As shown in Figs. 3(b) and 3(c), both scattering lengths exhibit power-law dependences on temperature L_i,so ∼ T^−β. For L_i, β = 0.4 ± 0.1, close to the expected value of β = 0.5 for electron–electron scattering induced dephasing.²⁴ The exponent for L_so is β = 1.0 ± 0.1, in sharp contrast to the nearly T-independent L_so observed in semiconductor quantum wells,³⁰ where spin–orbit scattering is related to the spin precession process induced by the intrinsic spin-splitting in the 2D band.

Figure 4(a) summarizes the L_i and L_so obtained from the 2.0–10.2 nm SIO samples at 2 K. For films thicker than 2.8 nm, neither L_i nor L_so exhibits any apparent thickness dependence. We can thus rule out the film surface/interface states as the major electron dephasing/spin scattering source. The L_i value is always higher than L_so, which satisfies the strong spin–orbital scattering condition in the MF model, i.e., $τiτso>0.183$⁠,³¹ justifying the observation of WAL at ow field and WL at high field.

To confirm that these samples are in the 2D diffusive region, we calculated the elastic mean free path in these samples. The mean free path can be estimated using the Drude model L_p = v_Fτ_p. With $vF=ℏkFm*$ and τ_p = μ_e,hm^*/e, where m^* is the effective mass and $kF=2πn2D$ is the Fermi wave vector, L_p only depends on the mobility and 2D charge density n_2D = n_e,ht. Given the electron and hole bands possess closely matched density and mobility values, their mean free paths are also similar. In Fig. 4(a), we used the condition of L_p exceeding the film thickness to gauge if the system can be characterized as 2D. While the 10.2 nm sample sits right at the L_p = t boundary, the thinner films reside well within the 2D regime, confirming the thickness-driven dimensionality crossover. Nevertheless, the condition for the WAL regime, L_p² < L_so² ≤ L_i², is always satisfied for the electrons and holes.³¹ The magnetic length at 4 T $LB=ℏ/eH≈13 nm$ also exceeds L_p, confirming that the system is in the diffusive regime for the entire field range.

We consider two commonly observed spin relaxation mechanisms: the D’yakonov–Perel’ (DP) type and the Elliot–Yafet type.³² The DP mechanism describes the spin precession induced by the spin splitting of the energy level that is randomized by the elastic scattering^32–34 and can have both the bulk (Dresselhaus) and interface (Rashba) contributions. The bulk term is important in noncentrosymmetric materials.²⁹ The Rashba effect is due to the inversion field at the hetero-interfaces and surfaces, as observed in semiconductor quantum wells³⁰ and complex oxide heterostructures,^35,36 and is expected to be more prominent in thinner films. The EY mechanism, on the other hand, depicts spin dephasing via momentum scattering, e.g., due to impurities or electron–phonon interactions, in the presence of SOC.^32,37,38 Structural defects commonly occurring in epitaxial thin films, such as cation vacancies, dislocations, and grain boundaries, can all contribute to spin scattering through the EY mechanism. One way to distinguish these two mechanisms is to examine the relation between τ_so and τ_p.³² In the DP mechanism, the SOC induced spin splitting acts effectively as a magnetic field that causes electron precession. The elastic scattering randomizes this process so that the related spin dephasing time scales with 1/τ_p.²⁹ The spin-flip process in the EY mechanism, in contrast, is facilitated by momentum scattering with the associated τ_so depending linearly on τ_p.³⁹ In SIO thin films, while the WL–WAL type measurements have previously been performed to extract τ_so,^14,16 the relation between τ_so and τ_p remains elusive due to the lack of effective approaches to control the charge mobility.^4,14–16 For example, in the study of WAL in SIO thin films grown on LaAlO₃ substrates, only less than 2% variation of τ_p has been reported.¹⁴ The film thickness of our samples, on the other hand, presents a powerful control parameter to tune carrier mobility, making it feasible to identify the dominant spin relaxation mechanism in epitaxial SIO thin films.

Figure 4(b) shows τ_so at 2 K as a function of τ_p for the electrons. Considering that the Dirac node is lifted by the compressive strain, we assumed a parabolic conduction band with m^* ≈ m₀.^11–13 This assumption is supported by the observed carrier density, which is significantly higher than what is expected for a linear dispersion (see a detailed discussion in the supplementary material).^9,11 To avoid the complicating effect of quantum conductance correction, we used the diffusion constant at 10 K to calculate τ_so. As all SIO films show highly consistent, very weak T-dependence in ρ_xx [Fig. 1(e)], the diffusion constant exhibits little variation below 20 K [see Fig. S2(f) of the supplementary material]. For the thicker films, τ_so exhibits a quasi-linear relation with τ_p, increasing from 0.093 ± 0.008 ps in the 10.2 nm film to 0.36 ± 0.04 ps in the 3.2 nm film [Fig. 4(b), lower inset], which points to an EY mechanism dominated spin relaxation. The absence of Dresselhaus contribution is not surprising given that the orthorhombic structure of SIO preserves inversion symmetry. The carrier density and film thickness dependences of H_so also rule out a dominant presence of the Rashba effect (see Fig. S3 of the supplementary material). We then consider the possible spin scattering sources in epitaxial SIO films. As τ_so is enhanced in the thinner films, it is natural to rule out the roughness and defect states related to the film interface/surface as the dominant spin scattering sources. A possible bulk mechanism that contributes to the lower τ_so in thicker films is the structural defects associated with the epitaxial strain, such as oxygen vacancies, dislocations, and polycrystalline grain formation above a critical thickness (20–40 nm), whose density can increase progressively with film thickness.^4,10 The last mechanism is not relevant as our samples are well below the critical thickness, and XRD studies yield no sign of impurity phase growth. We also note that the charge mobility increases in thinner films, which possess lower carrier density [Figs. 2(c)–2(d)]. This rules out a pronounced presence of charged impurities, e.g., cation or oxygen vacancies, as they are highly susceptible to the screening effect. On the other hand, misfit dislocations can be present even in ultrathin films¹⁴ and are a viable source for spin scattering.

In the EY mechanism, the momentum scattering induces spin flipping between two neighboring bands with admixed spin-up and spin-down states. The emerging energy gap Δ can suppress the spin transition probabilities, leading to enhanced τ_so.³⁹ As the spin scattering rate scales with the momentum scattering rate as $1τsoEY≈LΔ21τp$⁠, where L is the SOC matrix element,⁴⁰ we deduced L/Δ ≈ 0.55 for the thicker films [Fig. 4(b)]. This result is in excellent agreement with the previously reported values of Δ ≈ 28 meV at the strain lifted Dirac point in SIO¹³ and the SOC induced band splitting of L ≈ 15 meV.¹¹ It is important to note that the assumption of the effective mass does not change the extracted slope, as both τ_so and τ_p are scaled by the same m^*. In contrast, ARPES studies showed that the energy separation between the valence band and a neighboring band at the same momentum space is more than 0.5 eV. We thus expect the spin–orbit scattering rate associated with holes to be more than two orders of magnitude lower than that for electrons and rule out the notable contribution of holes in the temperature and magnetic field range investigated.

The EY-mechanism also naturally accounts for the unusually strong T-dependence of τ_so [Fig. 4(b), upper inset]. In the presence of a nearby band, spin flipping involves the electron–electron inter-band scattering,^37,41 which can yield a T²-dependent scattering rate.⁴² In fact, the T²-dependence of resistivity has been observed in thick SIO films on GdScO₃ substrates below 10 K.¹⁵ In thin films, this effect cannot be directly observed in low temperature R(T) due to the conductance correction from WL and electron–electron interaction.²⁴ 

Close to the critical thickness of MIT, there is an abrupt enhancement in τ_so, reaching 2.0 ± 0.1 ps for the 2.8 nm film, and 1.9 ± 0.1 ps and 2.2 ± 0.1 ps for the two 2.0 nm films [Fig. 4(b), lower inset]. The two 2.0 nm films exhibit qualitatively similar magnetotransport properties (see the supplementary material), showing that such an effect is robust and reproducible. For the 2.0 nm and 2.8 nm films, the $τsoτp$ ratio is 7.6 times of that for thicker films. There are three possible scenarios that can lead to the enhanced τ_so observed in ultrathin films. The first one is a sudden reduction of the defect density, which can lead to the reduced momentum scattering rate $1τp$⁠. There are, however, no abrupt changes observed in the mean free path L_p and the inelastic scattering length L_i in ultrathin SrIrO₃ films [Fig. 4(a)], strongly suggesting that there is no sudden change in the density or type of defect in the SrIrO₃ films as the film thickness approaches the critical value for MIT.

In the second scenario, there is a sudden reduction in $LΔ$ to 0.2. Assuming L remains unchanged, we obtained an emerging energy gap of Δ′ ≈ 75 meV. Considering the band parameters extracted from thicker SIO films (L ≈ 15 meV, Δ ≈ 28 meV, E_F > 50 meV),^11,13 this Δ′ value is not sufficient to induce a MIT, while E_F is getting close to the corresponding conduction band edge. This is consistent with the sudden drop of the carrier density in this thickness range and the clear temperature-dependence of the carrier density, which is absent in thicker films [Fig. 2(c)]. It is also in line with the charge gap extracted in the insulating phase (∼100 meV).¹⁷ The 2.0–2.8 nm samples thus retain the metallic behavior, while the spin-flip rate for the electron being scattered to the neighboring band is substantially reduced. With E_F falling in the vicinity of the region for SOC band splitting, this scenario can also contribute to the suppressed scattering and enhanced mobility in ultrathin films [Fig. 2(d)].

We also consider the third possible scenario, where the abrupt change in τ_so signals a transition from the EY to DP dominated spin flip scattering mechanism. Given that the SrIrO₃ films preserve the inversion symmetry, the crossover to the DP-type can only occur when the Bloch state broadening $Γ≈ℏ2τp$ well exceeds the energy separation from a neighboring band Δ, as theoretically proposed in Ref. [40]. Using τ_p = 0.075 ps as the critical value for the transition, we estimated Γ to be about 4.4 meV. This value, however, is much smaller than the reported gap value Δ ≈ 28 meV for thick SIO films.¹³ Therefore, the DP mechanism is not a critical spin flip mechanism in this transport regime. We thus conclude that the enhanced τ_so is intrinsic to ultrathin SIO due to the interplay between SOC and the onset of strong correlation energy.

In summary, we report a weak (anti)localization study of spin relaxation in high quality epitaxial SrIrO₃ thin films. In the 2D regime, the spin–orbit scattering time in SIO exhibits quasi-linear dependence on electron mobility, pointing to the EY mechanism dominated spin relaxation, and is strongly enhanced in films close to the critical thickness of MIT. Our study reveals the complex interplay of SOC, impurity scattering, and electron correlation on spin transport in this emerging quantum material. The ultrathin films exhibit enhanced mobility and spin scattering time, making them an ideal platform for realizing novel spintronic devices such as spin transistors and SOC enhanced multiferroic tunnel junctions.

See the supplementary material for details of sample growth and characterization, additional magnetotransport studies, and data modeling.

We thank Allen MacDonald and Kirill Belashchenko for valuable discussions. This work was primarily supported by the National Science Foundation (NSF) through Grant No. DMR-1710461. Additional support was provided by the Nebraska Materials Research Science and Engineering Center (MRSEC) (NSF Grant No. DMR-1420645) (materials preparation). This research was performed, in part, in the Nebraska Nanoscale Facility: National Nanotechnology Coordinated Infrastructure and the Nebraska Center for Materials and Nanoscience, which were supported by the National Science Foundation under Award No. ECCS: 1542182, and the Nebraska Research Initiative.

All relevant data that support the findings of this study are available from the corresponding authors upon request.