Detection of Rashba spin splitting in 2D organic-inorganic perovskite via precessional carrier spin relaxation

Hybrid organic-inorganic perovskites have gained considerable attention in recent years due to their outstanding performance as absorbing layers in photovoltaics.¹ This success has led to a comprehensive research effort with the aim to unravel their photophysical properties^2–18 and to move beyond CH₃NH₃PbI₃ and explore other material compositions including 2D perovskites.^19–24 This burgeoning family of materials offers properties that can be tailored to a broad range of applications in optoelectronics, including photovoltaics,^1,23,25 field-effect transistors,^26,27 hard radiation detectors,²⁸ light-emitting diodes,^29–31 lasers,³² and optical sensors.³³ 

Hybrid perovskites are characterized by strong spin-orbit coupling (SOC) tied to the constituent heavy elements.³⁴ These strong spin-orbit effects make the perovskite family of materials attractive for applications in semiconductor spintronics and spin opto-electronics.^35–45 SOC leads to a giant (∼1 eV) splitting of the lowest two conduction bands and influences the band gap and carrier effective masses.^46,47 In conjunction with a lack of inversion symmetry, SOC also leads to an effective magnetic field that lifts the degeneracy of the carrier spin states within each band.³⁵ While this effect has many origins in semiconductors tied to different sources of inversion asymmetry,^48–52 it is most commonly referred to as the Rashba effect after Bychkov and Rashba analyzed the case of structural inversion asymmetry in a two-dimensional electron gas.⁵⁰ In a spintronic device, the effective magnetic field associated with the Rashba effect may be used to operate on the spin state of carriers by inducing precession in a spin field-effect transistor.^36,37 The Rashba spin splitting can also enable spin-dependent transport without the need for an external magnetic field or magnetic materials by using a resonant tunnel diode structure.⁵³ 

Rashba effects in organic-inorganic perovskites have been the subject of numerous theoretical investigations in recent years.^54–60 The predicted Rashba splittings (∼10’s of meV) are large compared to the conventional III-V semiconductors upon which most spintronic devices have been based.³⁴ Switchable Rashba coupling exploiting the ferroelectric response has also been predicted.^56,57 Experimental observation of the Rashba effect in the valence band in single crystal CH₃NH₃PbBr₃ was recently demonstrated using angle-resolved photoemission spectroscopy (ARPES).⁶¹ The magnitude of the observed Rashba spin splitting (160 meV) was comparable to the largest values predicted theoretically in any of the hybrid perovskite systems.^54–60 While it has been suggested that this observed Rashba effect is due to the symmetry breaking at the surface,^62–64 since the strong dipole tied to surface reconstruction is expected to penetrate several hundred nanometers,⁶⁵ the ultralarge splitting observed is, nevertheless, promising for developing thin-film based spintronic devices. Experimental evidence of Rashba effects have been seen in perovskites using the photogalvanic effect,⁶⁶ transient anisotropy,⁶⁷ and electro-absorption⁶⁸ in recent years, highlighting the need for further experimental studies of Rashba effects in the hybrid perovskite family of materials.

Here, we report detection of the Rashba splitting in the 2D perovskite (BA)₂MAPb₂I₇ through measurement of carrier spin relaxation using time-resolved circular dichroism techniques. Measurements of carrier spin dynamics have proven extremely valuable in the study of Rashba coupling in inorganic III-V semiconductor systems,³⁵ in which the spin population relaxation time (T₁) is sensitive to both the magnitude and wavevector-dependence of the Rashba effective magnetic field.^48,52 (BA)₂MAPb₂I₇ exhibits a Ruddlesden-Popper structure with two layers of corner-sharing lead-iodide octahedra separated by long organic cations of butylammonium forming an interdigitating bilayer. Our experiments indicate that T₁ decreases with increasing photoexcitation energy and increases with optically injected carrier density, both signatures of Rashba precessional spin relaxation.^48,69,70 Our simulations of the electron spin dynamics yield a Rashba spin splitting of 10 meV at an electron energy 50 meV above the band gap, a value that is 20 times larger than in GaAs quantum wells.⁴⁸ Our findings highlight the utility of spin relaxation studies as a probe for Rashba coupling in the organic-inorganic hybrid perovskite family of materials.

In systems with no center of inversion symmetry, the spin-orbit interaction leads to an effective magnetic field $Ωk$ with a direction that determines an effective spin quantization axis at each value of the electron wavevector k and a magnitude that determines the energy separation between spin-up and spin-down band states. The crystal structure will dictate the wavevector dependence of Ω(k). For the 2D organic-inorganic perovskites, symmetry breaking is tied to tilting and associated polar distortions of the metal-halide octahedra, which are determined by the interplay between the long organic BA cations and the smaller MA cations that induce out-of-plane and in-plane octahedral distortions, respectively.²⁴ For the n = 2 structure studied in this work [Fig. 1(a)], x-ray diffraction indicates a noncentrosymmetric structure with a polar (⁠$C2v$⁠) space group at room temperature.^24,71 As a result, a nonzero Rashba spin splitting is expected for this system. The Rashba Hamiltonian is given by^50,58

where k = (k_x, k_y) is the electron wavevector in the x-y plane perpendicular to the stacking direction, σ is the vector of Pauli spin matrices, and

In this case,

and the spin eigenstates are given by

where λ_R is the Rashba coupling parameter. The Rashba effective magnetic field and the dispersion relations for the two spin eigenstates are shown in Fig. 1(b).

The Rashba effective magnetic field leads to precessional carrier spin relaxation. This mechanism was first discussed in the context of III-V semiconductors by D’yakonov and Perel⁶⁹ and later refined for semiconductor quantum wells by D’yakonov and Kachorovskii.⁷⁰ Due to the optical selection rules [Fig. 1(c)], excitation with circularly polarized light leads to a fully spin polarized distribution of electrons and holes. The carrier spins will be initially aligned parallel or antiparallel to the light propagation direction [the z direction in Fig. 1(b)] depending on the carrier type (electron or hole) and the circular polarization state of the light field. These initially polarized carrier spins will begin to precess about Ω(k) with frequency |Ω(k)|. Since the direction of Ω(k) varies with k, the net spin polarization of the ensemble, after summing over k decays. Our interest here is on the longitudinal spin lifetime in the absence of an external magnetic field (T₁). The spin relaxation rate is

where τ is the carrier scattering lifetime. A characteristic feature of this spin relaxation mechanism is that T₁ is proportional to the carrier scattering rate,⁷⁰ referred to as motional narrowing. The instantaneous magnitude and direction of Ω(k) change as carriers scatter from one k value to another. The larger the rate of scattering, the slower the spin relaxation because the carrier spins do not have as much time to undergo precession between scattering events. This mechanism of spin relaxation is dominant in III-V semiconductors such as GaAs at room temperature.^35,48

Since the rate of precessional spin relaxation is proportional to the square of the Rashba effective magnetic field,⁴⁸ measurement of T₁ provides a sensitive probe of the strength of Rashba coupling in a semiconductor material. For instance, in GaAs quantum wells, the spin lifetime at 300 K is 100 ps⁷² and the corresponding spin splitting has been calculated to be <1 meV.⁴⁸ In contrast, in quantum wells formed from the InAs/GaSb/AlSb system possessing a much larger SOC, calculated spin splittings are ∼10 meV or larger,^48,53 and measured spin lifetimes in these materials under 1 ps have been reported.^42,52

The results of differential transmission measurements [(⁠$T−T0T0$⁠), where T (T₀) is the transmission of the probe pulse in the presence (absence) of the pump beam, see Fig. 2(a)] for linearly polarized pump and probe pulses are shown in Fig. 2(b). The use of linearly polarized pulses enables measurement of the average state filling signal associated with both spin populations. The magnitude of the differential transmission signal at τ = 2 ps is plotted alongside the linear absorption spectrum in the lower panel of Fig. 2(b). A Tauc analysis of the linear absorption results (see the supplementary material) indicates a band gap of (2.12 ± 0.05) eV. The peak at 2.05 eV is therefore attributed to the state filling response of excitons, and the peak at higher energies is due to unbound electron-hole pairs on interband transitions above the band gap. Fitting the results in Fig. 2(b) for the above band gap excitation to a double exponential decay yields a carrier thermalization time of (7 ± 1) ps, followed by recombination on a time scale ∼1 ns. These spin-independent relaxation kinetics are in line with previous studies in phenylethylammonium lead iodide (PEA)₂(MA)_n−1Pb_nI_3n+1 2D perovskite.⁷³ 

T₁ was measured using time-resolved circular dichroism. A circularly polarized pump pulse is used to inject a spin-polarized carrier distribution. When the probe has the same (opposite) circular polarization as the pump, the state filling signal is tied to the majority (minority) spin population. The convergence of these two state filling signals with increasing interpulse delay indicates carrier spin relaxation. Figure 2(c) shows the results of circular dichroism experiments for the same pump pulse fluence as in Fig. 2(b) under excitation at 2.15 eV (30 meV above the band gap). A strong oscillatory signal associated with the coherent artifact⁷⁴ is superimposed on the state-filling response for delay values within the range of overlap between the pump and probe pulses. Beyond this overlap region, the differential transmission signals for the same circular polarization (SCP) and opposite circular polarization (OCP) are clearly resolved, indicating a difference in the magnitude of the state-filling response tied to the majority and minority carrier spin populations. The degree of spin polarization of the carrier distribution may be extracted from the results in Fig. 2(c) by taking the difference of the SCP and OCP responses and dividing by the sum (see the supplementary material for further details). The result of this analysis is shown in the inset of Fig. 2(c). The decay of the carrier spin polarization fits to a single exponential, yielding T₁ = (10 ± 1) ps. Recent calculations indicate similar effective masses for electrons and holes in this system.⁷⁵ The resulting similarity in the density of states in the valence and conduction bands has the consequence that the two carrier species contribute to a similar extent to the magnitude of the measured state filling signal. The observation of a single exponential decay, together with the large value of the initial degree of spin polarization, points to a similar spin lifetime for electrons and holes.

The measured spin lifetimes for a range of laser tunings (E_ex) and pump pulse fluence values are shown in Figs. 3(a) and 3(b), respectively. In order to detect evidence of Rashba precessional spin relaxation, the spin lifetime for carriers above the band gap is of interest. Figure 3(a) shows the spin lifetime vs laser detuning (E_ex − E_g), which together with the carrier masses determines the electron and hole energies relative to the band edges. The spin lifetime decreases for increasing laser detuning, indicating that spin relaxation is more rapid for carriers with larger kinetic energies. The spin lifetime was also observed to increase with increasing pump pulse fluence [Fig. 3(b)]. Increasing the density of optically injected carriers therefore results in a longer spin lifetime.

The fluence and detuning energy dependences in Figs. 3(a) and 3(b) indicate precessional spin relaxation—the D’yakonov Perel mechanism. Since the precession vector Ω(k) has a magnitude and direction that varies with wavevector, precession causes the initially spin-polarized distribution of carriers to decay. Scattering of carriers with phonons, impurities, and each other will slow this spin relaxation process by inducing rapid changes in the value of Ω(k), resulting in a smaller degree of precession between scattering events. This motional narrowing feature is clearly reflected in the observation of an increase in T₁ with increasing carrier density, indicating slower spin relaxation with an increased rate of carrier-carrier scattering. The observation of a decrease in T₁ with increasing excess energy is also consistent with Rashba precessional spin relaxation. Since the carrier thermalization time was found to be similar to the spin lifetime, the carriers remain hot during spin relaxation, with a temperature determined by the laser detuning. A higher average carrier kinetic energy will lead to the occupation of states at larger k values. Since the magnitude of the effective magnetic field increases with |k|, hot carriers will undergo more rapid spin relaxation.

We note that the results in Fig. 3(b) are opposite to the trend expected for the Elliott Yafet spin relaxation process,^76,77 for which scattering events themselves lead to spin decay rather than precession between scattering events. The spin relaxation process tied to spin-flip scattering between electrons and holes (the Bir Aronov Pikus mechanism),⁷⁸ which would lead to the opposite trend vs excited carrier density to that measured here, is expected to be weak in perovskite materials due to the small value of the exciton exchange splitting,⁴⁴ a feature that has been attributed to the spatial separation of the electron and hole wave functions within the unit cell.

An estimate of the magnitude of the Rashba spin splitting in the 2D perovskite structure studied here was obtained from simulations of the measured carrier spin dynamics. Calculation of the momentum scattering time enables the strength of the Rashba coupling to be determined from the measured spin lifetime using Eq. (4), where τ is the carrier scattering lifetime associated with all scattering processes neglecting the spin texture. The faster the carrier scattering, the slower the rate of spin relaxation for a given magnitude of the Rashba effective magnetic field. These simulations incorporated polar optical phonon scattering, which is expected to be stronger than acoustic phonon scattering at 300 K,⁷⁹ as well as 2D electron-electron scattering mediated by the Coulomb interaction in the nondegenerate limit. Electron-phonon scattering and electron-electron scattering both contribute to motional narrowing, decreasing the rate of spin relaxation. In this case, the momentum scattering rate is $τ−1=τep−1+τee−1$⁠. Since the experiment indicates a similar spin relaxation rate for electrons and holes, only the spin relaxation of electrons in the conduction band was included for simplicity. The polar coupling in 2D can be expressed as

where α is the dimensionless polar coupling. Note that the polar coupling has different q dependences in 2D and 3D, being $1/q$ and 1/q, respectively. The momentum scattering rate due to polar optical phonons is

Here, ω₀ is the LO phonon frequency, $n0≡[exp(ħω0/kBT)−1]−1$ is the phonon number, $k0=(2meω0/ħ)1/2$⁠, E_k is the electron energy, and K(x) and E(x) are the complete elliptical integral of the 1st and 2nd kind, respectively. We emphasize that the apparent divergence of V_q in Eq. (5) at q → 0 does not give rise to any singularity in the scattering rate in Eq. (6), which changes little if a potential V_q that is finite at q = 0 is used.⁸⁰ 

For carrier-carrier scattering, we consider electron-electron scattering via the Coulomb interaction, e²/ϵr, where ϵ is the dielectric constant. For 2D systems, the electron-electron scattering in the nondegenerate limit can be expressed as

where N is the carrier density and E_B ≡ m_ee⁴/2ϵ²ħ² is the effective Rydberg energy with m_e being the electron effective mass. The calculated phonon and electron-electron scattering rates are shown vs electron energy in Fig. S4.

In our calculations, the carrier effective masses m_e = 0.291m₀ and m_h = 0.328m₀ were taken from recent first principles calculations for (BA)₂PbI₄,⁷⁵ the LO phonon energy (ħω₀ = 12.4 meV) was taken from Ref. 79, and α = 2.12 was used. The effective dielectric constant ϵ ≡ (ϵ_al_a + ϵ_bl_b)/(l_a + l_b) is the volume average with ϵ_a(b) and l_a(b) being the dielectric constant and width of the inorganic (organic) layer, respectively. Taking ϵ_a = 6.5 and ϵ_b = 2 gives an estimate of ϵ = 3 for our structure.³ The detuning energy E is the summation of electron and hole energies. From the momentum conservation, we obtain the electron energy,

When E < k_BT = 25 meV, we take the electron energy to be E_k = k_BT/(1 + m_e/m_h). λ_R was varied to obtain the best fit to the experimental results and was the only adjustable parameter in the simulations. The resulting fits are shown as the solid curves in Figs. 3(a) and 3(b). Quantitative agreement was obtained over the full range of carrier energy above gap and excitation carrier density, yielding λ_R = 0.08 eV Å. The Rashba spin splitting extracted from the fitting process is shown in Fig. 3(c). A splitting of 10 meV is found at an energy of 50 meV above the conduction band minimum. For comparison, for GaAs quantum wells at 300 K, a much smaller spin splitting of 0.5 meV at this energy was found from the analysis of spin lifetime results.⁴⁸ The spin-independent pump probe experiments in Fig. 2(b) indicated a thermalization time of 7 ps, resulting in an effective carrier temperature somewhat cooler than determined by the laser detuning alone. Our simulations, which neglect thermalization effects, therefore provide a lower bound to the Rashba spin splitting in this material.

Since the measured trends we observe for T₁ indicate dominant precessional spin relaxation, being inconsistent with all other spin relaxation mechanisms, our findings provide an unambiguous experimental detection of Rashba coupling in the 2D perovskite structure investigated here. The precessional spin relaxation mechanism has not been identified previously in the hybrid organic-inorganic perovskites,^43,44 despite the fact that this mechanism dominates the room temperature spin dynamics in the majority of III-V semiconductors.³⁵ An experimental verification that the physics of spin relaxation in traditional III-V’s semiconductors can be transferred to the perovskite’s is highly significant because III-V materials have been the primary focus for spintronic device development. The value we estimate from our theoretical simulations for the spin splitting (10 meV at an excess energy of 50 meV above the band gap) is 20-fold larger than GaAs⁴⁸ but is in line with other inorganic systems possessing large spin-orbit coupling that are strong contenders for the realization of practical spintronic devices including GaSb quantum wells⁴² and InAs/GaSb superlattices.^37,52,53 Our findings therefore highlight the promise of perovskite materials for applications in semiconductor spintronics, offering a solution-processable alternative for facile, low-cost device fabrication.

While the value of the Rashba coupling parameter we extract (λ_R = 0.08 eV Å) is a lower bound due to the influence of carrier thermalization as discussed above, this value is smaller than some recent reports of Rashba effects in the organic inorganic perovskites.^61,68 The value of the spin splitting in the family of 2D perovskites will be dictated by the net distortions of the lead-iodide octahedra induced by competition between the long organic cations and the small cations.²⁴ Varying the type of long organic cation while keeping the number of lead-iodide octahedra layers constant would therefore provide a useful extension to the present work by probing the extent to which the strength of Rashba coupling may be engineered in these systems. The first observation of the Rashba effect in an organic-inorganic perovskite (in the valence band of a single crystal sample of the 3D perovskite CH₃NH₃PbBr₃) was carried out using ARPES,⁶¹ yielding a record Rashba coupling parameter of 7 eV Å. Recent reports suggest that this large Rashba effect was due to inversion asymmetry breaking at the surface.^62–65 Such a surface Rashba effect is consistent with the observation of strong Rashba coupling in thin films of 3D CH₃NH₃PbI₃ using the photogalvanic effect.⁶⁶ In another study using ARPES on a similar single crystal sample, however, no k-dependent spin splitting was detected,⁸¹ indicating that the sample preparation conditions may influence the measured results.⁶³ Strong Rashba coupling (λ_R = 1.6 eV Å) was recently found using electro-absorption techniques and density functional theory (DFT) calculations in the 2D perovskite (PEA)₂PbI₄ (PEPI, with a single layer of lead-iodide octahedra).⁶⁸ In that measurement, the Rashba splitting was determined from a low-energy peak in the electro-absorption spectrum attributed to transitions between the Rashba spin split bands.⁶⁸ Signatures of dynamic Rashba effects were also seen using transient polarization anisotropy in thin films of 3D CH₃NH₃PbI₃.⁶⁷ While the large size of the Rashba coupling observed in the perovskites in recent years is promising for spintronic applications, the wide spread of reported values highlights the need for further experimental studies of Rashba coupling using a range of experimental techniques. Our findings illustrate the utility of spin lifetime measurements for studying such effects, building upon the extensive existing literature probing precessional spin relaxation in inorganic semiconductors.

We have measured the spin relaxation time for optically injected carriers in thin films of the 2D perovskite (BA)₂MAPb₂I₇ using time-resolved circular-dichroism techniques. The measured dependence of the spin lifetime on the laser excess energy and excited carrier density indicate precessional spin relaxation caused by the Rashba effect. Simulations of the measured carrier spin dynamics incorporating LO phonon and electron-electron scattering enabled the extraction of a Rashba spin splitting of 10 meV at an electron energy of 50 meV above the band gap. Our experiments, which confirm the presence of a Rashba spin splitting experimentally in a 2D perovskite material, open the door to studies of spin relaxation kinetics as a probe of Rashba effects in a wide range of 2D and 3D perovskite materials. For instance, the extension to larger thicknesses of the inorganic layer [e.g., (BA)₂(MA)_n−1Pb_nI_3n+1 with n > 2] would enable an interesting comparison to the quantum well-width dependence in III-V semiconductors,⁸² and spin lifetime studies may be used to complement structural characterization of the temperature-dependent distortions of the metal halide octahedra within each crystal phase in the perovskites.^83,83 Our findings shed-light on the spin-related properties of the organic-inorganic perovskites and point to the potential for spintronic devices based on these materials.

See supplementary material for details of sample preparation, linear absorption and x-ray diffraction, description of pump probe techniques, method of extraction of spin lifetimes from measured circular dichroism, and additional details of theoretical model including calculated scattering rates for electrons.

Work at Dalhousie University was supported by the Natural Sciences and Engineering Research Council of Canada. Work at Northwestern University was supported by Grant No. SC0012541 from the US Department of Energy, Office of Science. Work at Washington State University was supported by Grant No. W911NF-17-1-0511 from the US Army Research Office.