Unravel Spin Relaxation Mechanism in Hybrid Organic-Inorganic

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Unravel Spin Relaxation Mechanism in Hybrid Organic-Inorganic Perovskites Zhi-Gang Yu, and Yan S. Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04261 • Publication Date (Web): 15 May 2019 Downloaded from http://pubs.acs.org on May 15, 2019

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The Journal of Physical Chemistry

Unravel Spin Relaxation Mechanism in Hybrid Organic-Inorganic Perovskites Zhi-Gang Yu∗,† and Yan S. Li‡ †ISP/Applied Sciences Laboratory, Washington State University, Spokane, Washington 99210, USA Department of Physics and Astronomy, Washington State University, Pullman, Washington 99164, USA ‡Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA E-mail: [email protected]

1

ACS Paragon Plus Environment


Abstract Hybrid organic-inorganic perovskite (HOIP) CH3 NH3 PbI3 exhibits a long spin coherence despite its strong spin-orbit coupling. Elucidation of spin relaxation mechanism is a prerequisite to harness this spin coherence for spintronic applications. Here we show that exciton spin relaxation behaviors can be quantitatively accounted for by the Rashba splitting in the exciton bands together with piezoelectric (PE) coupling, both arising from structural inversion asymmetry of HOIPs. Large exciton size and Debye screening influence piezoelectric scattering and result in the unusual temperature and photoexcitation dependences in spin relaxation. Our results suggest that the strong PE coupling helps retain spin coherence in HOIPs with strong spin-orbit coupling and Rashba splittings.

Graphical TOC Entry

10

10

3

2

τs (ps)

1 0.5

10

1

Sz

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Introduction Hybrid organic-inorganic perovskites (HOIPs) such as MAPbI3 (MA=CH3 NH3 ), with photovoltaic efficiencies exceeding 20% in solution-processed samples, represent a revolutionary breakthrough for low-cost solar cells. 1–3 For a material with heavy elements like Pb that have an strong spin-orbit coupling (SOC), 4 spin coherence is generally deemed too ephemeral to be seen. The situation is exacerbated in HOIPs by the Rashba effect (RE), resulting from the concomitant SOC and structural inversion asymmetry (SIA). 5–9 The RE introduces a momentum-dependent effective magnetic field, around which the spins precess erratically. Surprisingly, recent time-resolved Faraday rotation (TRFR) measurements revealed a long spin lifetime in MAPbI3 , exceeding 1 ns at 4 K. 10 Here we show that this apparent paradox can be unraveled by another consequence of SIA: pronounced piezoelectric (PE) coupling between electrons and acoustic phonons. The PE suppresses the exciton spin relaxation via the D0 yakonov-Perel0 (DP) mechanism, 11 while both Elliot-Yafet (EY) 12 and Bir-Aranov-Pikus (BAP) 13 mechanisms are insignificant. Thus HOIPs provide a paradigm of achieving a long spin coherence in the presence of large SOC and RE. Moreover, we demonstrate that spin relaxation can be tuned by modifying the effective PE coupling via photoexcited carriers.

Methods and Results Exciton states under magnetic field The optical excitations in MAPbI3 , as created in the TRFR experiment, are loosely bound Wannier excitons, 14,15 with conduction-band electrons cjez and valence-band holes v¯jhz characterized by angular momenta je(h)z = ±1/2. In the TRFR experiment, circularly polarized light excites Γ5 excitons (c 1 v¯ 1 or c− 1 v¯− 1 ) with spin polarization along the z-axis. The Γ5 2

2

2

2

excitons are a superposition of exciton eigenstates in a transverse magnetic field B, and quantum-beating signal emerges. 10 The spin Hamiltonian of the 1s exciton under B = Bex

3


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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reads 1 Hex = Jk σez σhz + J⊥ (σex σhx + σey σhy ) + (ge σex + gh σhx )µB B, 2

(1)

where σe(h) are the Pauli matrices for electron (hole) pseudo spin je(h) , ge and gh are the electron and hole g-factors in the x-y plane, µB is the Bohr magneton, and Jk (J⊥ ) is the exchange between electron and hole spins parallel (perpendicular) to the crystal axis. The RE is not explicitly included in Eq. (1) because it contributes mainly to spin relaxation (see below) but little to quantum-beating frequencies. The TRFR signal can be obtained from a time evolution of the exciton density matrix, defined as ρêx =

P

mm0 ;nn0

ρmm0 ;nn0 |cm v¯n ihcm0 v¯n0 |,

∂ ρêx /∂t = i[ˆ ρex , Hex ]/¯ h − ∂ ρêx /∂t|sr , which includes both quantum beating and irreversible spin relaxation. The latter can be written as X X 1 1 1 1 ∂ρmm0 ;nn0 =− ρmm0 ;nn0 − δmm0 ρm00m00;nn0 − ρmm0 ;nn0 − δnn0 ρmm0 ;n00n00 , (2) sr ∂t τse 2 τsh 2 m00 n00

with τse(h) being the relaxation time of Se(h) = T rρêx σe(h) . Here we neglect exciton recombination, a much slower process than spin relaxation in HOIPs. If the exchange coupling is temporarily neglected [see Supporting Information (SI)], dynamics of Se and Sh are decoupled, and their z-components, Sez ≡

P

n

ρ 1 1 ;nn −ρ− 1 − 1 ;nn and Shz ≡ 22

2

2

P

m

ρmm; 1 1 −ρmm;− 1 − 1 , 22

2

2

are described by a damped oscillation, Se(h)z ∝ cos[ωe(h) t]e−t/τse(h) , with oscillation frequency ωe(h) = ge(h) µB B/¯h. The TRFR signal, Sz ≡ ρ 1 1 ; 1 1 − ρ− 1 − 1 ;− 1 − 1 = Sez + Shz , contains two 22 22

2

2

2

2

components with distinct oscillation frequencies, as shown in Fig. 1a. The corresponding exciton energies and the electron’s and hole’s Larmor frequencies are displayed in Fig. 1d as a function of B. The exchange coupling Jk(⊥) in Eq. (1) competes with B and their interplay is analogous to that of SOC and B in the Paschen-Back effect. 16 When the exchange dominates over the Zeeman energy caused by B, the exciton states are more appropriately characterized by the total angular momentum, J = je + jh , being J = 1 or J = 0, and it would be the total J that precesses around B. This is reflected in Figs. 1c and 1f, where excitons

4


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with J = 1 and with J = 0 have very different energies, and the oscillations of Sez and Shz are virtually synchronic, with a common frequency h ¯ ω = (ge + gh )µB B/2. Experimentally, the TRFR signal in MAPbI3 can be unambiguously decomposed into a superposition of electron and hole spin dynamics, from which the g-factors and spin lifetimes τse and τsh are obtained. Indeed, by fitting the TRFR data, the exchange in MAPbI3 is found to be around Jk(⊥) ∼ 10−6 eV, which can be overcome by a field of B > 10 mT. In this weak-exchange regime, the TRFR signals, as well as exciton energies and Larmor frequencies, are displayed in Figs. 1b and 1e. c

b

0.6

0

0 1 kG

-0.6

1 kG

1 kG

-0.6

0.6

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0

0 4 kG

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t (ns)

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-0.6 2

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t (ns)

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e

d

30 µ

4 kG

4 kG

f

0

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-200 µ

-30 µ 60 µ

60 µ

30 µ

30 µ

0

0 0

2000

4000 0

B (Gauss)

2000

4000

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B (Gauss)

2000

Eex (eV)

-0.6

Eex (eV)

Sz, Sez, Shz

a

ωe,h (eV)

Sz, Sez, Shz

0.6

ωe,h (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4000

B (Gauss)

Figure 1: Upper panel: Time evolution of exciton spin Sz (black), and constituent electron and hole spins, Sez (orange) and Shz (green) in magnetic fields of Bx = 1000 and 4000 G. The spin lifetimes for the simulation are τse = τsh = 1 ns. Lower panel: Energies of exciton states Eex and beat frequencies ωe (black and red lines) and ωh (blue and green lines). ωe(h) are extracted from exciton states whose expectation values of electron (hole) spin change sign but of hole (electron) spin do not. The left, middle, and right panels correspond to Jk = J⊥ = 0, 10−6 , and 10−4 eV.

5



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Exciton spin relaxation The electronic structure of low-temperature orthorhombic and tetragonal CH3 NH3 PbI3 can be well described by an effective-mass model, 15 in which the valence and conduction bands are derived from Pb’s 6s and 6p orbitals. Because of Pb’s strong SOC, the 6p orbitals are more appropriately characterized by the total angular momentum j = l + s with l (l = 1) and s being orbital and spin angular momenta. The SOC is reflected in the energy splitting between the lowest conduction band (j = 1/2) and higher conduction bands (j = 3/2). In addition, the lack of inversion symmetry in orthorhombic and tetragonal CH3 NH3 PbI3 breaks the spin degeneracy at a given wavevector k in the conduction and valence bands, i.e., the Rashba effect, R Hc(v) = αc(v) (ky σx − kx σy ),

(3)

where αc(v) is the Rashba strength in the conduction (valence) bands and directly related to the material’s inversion asymmetry parameter. 15 In a semiconductor spin relaxation can be caused by EY, DP, and BAP mechanisms. A direct spin-phonon process, which may become important in spin relaxation under strong magnetic fields (> 1 T), 17 is not effective at low magnetic fields (< 1 mT), under which exciton spin lifetimes are obtained. 10 Since the measured material is bulk CH3 NH3 PbI3 and the strong SOC associated with heavy elements has been consistently included in the electronic structure, we neglect extrinsic heavy-element or magnetic impurities 18 and structural/composition fluctuations, 19–21 which can contribution to spin relaxation in III-V semiconductors and alloys, particularly in low-dimensional structures. The BAP mechanism originates from exchange-induced spin flip scattering between electrons and holes. The weak exchange coupling of 10−6 eV renders such spin flips negligible in HOIPs. The DP mechanism is operative if the spin degeneracy in the band structure is lifted, which happens in MAPbI3 because of the RE. To include the RE in the exciton spin relaxation we augment

6


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the exciton Hamiltonian with the RE in both conduction and valence bands,

Hex ≡ H0 +H1 , H0 = −

h ¯2 2 h ¯2 2 e2 ∇e − ∇h − , H1 = −iαc (σe ×∇e )z −iαv (σh ×∇h )z , 2me 2mh |re − rh | (4)

where me (mh ) is electron (hole) effective mass and re (rh ) its location. The exciton wave function of H0 , characterized by the center-of-mass wavevector K, is a linear combination of electron-hole pairs with respective wavevectors K + k and −k, 22

|λ; cm v¯n Ki =

X

fλ (K + k, k)|cm ; K + ki|¯ vn ; −ki,

(5)

k

where fλ (K + k, k) is the momentum-space envelope function with λ characterizing the hydrogenic wave function for the electron-hole relative motion. For the 1s exciton, the hydrogenic wave function φ1s (r) = (πa30 )1/2 e−r/a0 with a0 being the exciton radius, f1s (K + q

k, k) = 8 πa30 /V [1 + (k + pe K)2 a20 ]−2 with pe(h) = mh(e) /(me + mh ) ≡ mh(e) /M (see SI) and V the volume. The exciton’s size and binding energy are determined by dielectric constant and reduced mass µ = me mh /M , resulting in a0 = h ¯ 2 /e2 µ and EB = µe4 /22 h ¯ 2. The RE can be written as H1 = (¯h/2)

P

k (σe

· Ωek + σh · Ωhk ), where h ¯ Ωe(h)k =

2αc(v) (ky , −kx , 0), and thus is equivalent to a momentum-dependent effective magnetic field acting on the electron or hole spin, with the corresponding Larmor frequency of |Ωek | or |Ωhk |. If we include K in the exciton’s density matrix, ρêx (K) =

P

mm0 ;nn0

ρmm0 ;nn0 (K)|cm v¯n Kihcm0 v¯n0 K|,

where we have confined ourselves to the 1s excitons and omitted symbol λ, the density matrix of the electron in such an exciton is

ρê (K) = T rρêx (K)δnn0 δkk0 =

X mm0 ;n

ρmm0 ;nn

X

|f (K + k, k)|2 |cm ; K + kihcm0 ; K + k|, (6)

k

whose time evolution is described by the Redfield equation,

dˆ ρe dt

= − ¯hi [H1 , ρê ]− ¯h12

R∞ 0

[Hp (t), [Hp (t−

τ ), ρê ]]dτ. Here Hp describes the scattering potential, which, for MAPbI3 , is the electronphonon coupling because of the material’s weak impurity scattering. Introducing electron 7



Page 8 of 19

spin polarization SeK = T rρê (K)σe , we have X dSeK = ΩeK × SeK + WKK 0 SeK − SeK 0 . dt K0

Here ΩeK ≡

P

k

(7)

|f (K + k, k)|2 ΩeK+k = 2αc ph K/¯ h is the precession frequency for the

electron spin in an exciton with K, i.e., the Rashba strength is “renormalized” from αc for free electrons to αc ph for the electron in an exciton. The electron scattering rate is WKK 0 =

2π h ¯

P

q

|hK 0 |Hp |Ki|2 δK 0 ,K±q δ(EK 0 − EK ± h ¯ ωq ) with h ¯ ωq being the phonon energy.

It should be noted that the scattering of the electron in an exciton differs from that of a free electron by a form factor, hK 0 |Hp |Ki ≡ hcK 0 + k|Hp |cK + kiϕe (|K 0 − K|) with ϕe (|K 0 − K|) =

X

h

f (K + k)f (K 0 + k) = 1 +

k

p |K 0 − K|a 2 i−2 e 0

2

.

(8)

The corresponding form factor for holes, ϕh (q), has the same form with pe replaced by ph = me /M . ϕe(h) (q) can be regarded as an effective electron (hole) charge for a particular momentum change q when the electron (hole) is in the 1s exciton, and limits scattering to small q such that qa0 ≤ 1. If no scattering is present, precession ΩeK in Eq. (6), sets a free-induction time scale of τf ≡ 1/h|ΩeK |i = h ¯ M/(2αc me K0 ), where K0 is the typical exciton momentum, K0 = √ 3M kB T /¯ h according to equipartition. Thus oriented spins tend to lose their coherence at a rate of h|ΩeK |i ∝ T 1/2 , as shown in Fig. 2a. When the scattering WKK 0 is strong, the spin precession ΩeK is frequently interrupted as K changes to K 0 . When the momentum scattering is much faster than the precession, τp /τf ≡ η −1 1, where τp (K) = P

K0

WK 0 K (1 − cos θKK 0 ) is the momentum scattering time, the spin relaxation times ob-

tained from Eq. (6) are 11

−1 −1 τsk (K) = 2τs⊥ (K) = {[ΩeK ]2x + [ΩeK ]2y }iτp (K) =

8

4αc2 m2e 2 (Kx + Ky2 )τp (K) ∼ τf−2 τp , (9) M2


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where τsk (K) and τs⊥ (K) are the spin relaxation times for longitudinal (z) and transverse spin components (x, y). Hence a strong scattering can help retain spin coherence by extending the spin lifetime from τf to τp−1 τf2 = ητf . The spin lifetime τse at a given temperature is 2

−1 obtained by averaging τsk (K) throughout the Maxwell distribution, F (K) ∝ e−¯h

τse−1 =

R

K 2 /2M kB T

,

−1 dKτsk (K)F (K)/ dKF (K).

R

The above discussions can be readily extended to the hole in an exciton. The “renormalized” Rashba splitting is ΩhK = 2αv pe (Ky , −Kx , 0) for the hole spin in an exciton with K and the PE coupling for the hole is equal to that for the electron, except the sign. Consequently, the ratio of electron and hole spin lifetimes, at low temperatures where the form factors are unimportant, would have a simple relation, τse /τsh = (αv mh /αc me )2 , which is consistent with comparable τes and τhs observed in the TRFR experiment. 10 In addition to the DP mechanism, spin relaxation occurs via spin-flip scattering caused by SOC-induced spin mixing–the EY mechanism. Using the newly developed effectivemass model for HOIPs, 15 we can express the spin-flip Hamiltonian as HK 0 ↓K↑ = γ(K 0 × K)hK|Hp |Ki, where γ = sin ξ cos ξP⊥ Pk /Eg2 with P⊥(k) being the Kane parameter and Eg the band gap. γ is directly related to the deviation of hole’s g-factor from the freeelectron value (g0 = 2). The spin relaxation rate due to the EY mechanism is τse0−1 ' (gh⊥ − g0 )(me /m)2 (kB T /Eg )2 τp−1 (see SI), where spin mixing is characterized by the factor me kB T /(mEg ) with m is the free-electron mass. Thus in spite of large SOC in MAPbI3 , the large Eg as compared to the thermal energy prevents a significant spin mixing. To quantitatively account for the spin lifetime in HOIPs, we need to reliably evaluate the momentum scattering time τp , as required in both DP and EY mechanisms.

Acoustic-phonon scattering Carrier momentum scattering can be caused by impurities and phonons in a solid. Native defects such as vacancies and interstitials can form in HOIPs. 23 Experimentally, it is found that the performance of optoelectronic devices based on HOIPs is insensitive to these defects 24 9



Page 10 of 19

and that carrier transport can be satisfactorily described by phonon scattering over a broad temperature range. 26,27 This defect tolerance has been ascribed to the strong screening 25 in ionic HOIPs. Hence we focus on phonon scattering in evaluating τp . It has been recognized that polar optical phonon scattering limits carrier mobility in HOIPs for T > 150 K, 28 because of their strong ionic nature. At low temperatures where polar optical phonons are scarce, acoustic-phonon scattering should be dominant. In this case, scattering potential Hp can be the short-range deformation potential and, in systems with SIA as in MAPbI3 , the long-range piezoelectric (PE) potential, 29 Hp = ±

iq·r bλq λq (Cλq e

P

+

∗ −iq·r † e bλq ), where + and − are for electrons and holes, respectively, because of the PE Cλq

coupling’s electrostatic origin. b†λq creates an acoustic phonon with eigen vector ξ(qλ) in branch λ at a wave vector q, and the coupling strength 30 (see Supporting Information)

Cλq =

2πg 1/2 h ¯ cλ q 3/2 λ

V

, gλ = 2

q 2 + q0

e2

h ¯ cλ

p¯λ , p¯λ =

4π Dh ek,ij qk qj ξi (qλ) i2 E . ρ qωλ

(10)

Here ek,ij is the PE tensor with subscripts being Cartesian component x, y, or z, q0 is the reciprocal Debye screening length, ρ is the density, and the dimensionless coupling gλ is the product of the fine structure constant for the speed of sound cλ and electro-mechanical coupling p¯λ , which measures the percentage of mechanical energy that is converted into electric energy. Table I lists the PE and mechanical properties 31,32 reported in literature as well as calculated gλ values for MAPbI3 . The PE coupling strength is exceptionally large, even higher than that in CdS (gT = 3.7 and gL = 0.21), 33,34 where PE scattering is known to be the dominant scattering channel at low temperatures. 35 The huge gT in MAPbI3 is the result of a strong electromechanical coupling due to its ionic feature and a low speed of sound due to its elastic softness for the transverse modes, particularly in the tetragonal phase. 36 Since PE and polar couplings share the same electrostatic origin, the strong PE coupling in MAPbI3 is consistent with its large polar coupling. Figure 2b compares the momentum scattering times due to the PE and deformation

10


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Table 1: Effective PE coupling for MAPbI3 . The units of ek,ij and cλ are 10−4 C/cm2 and 105 cm/s. p¯λ and gλ are dimensionless. L and T represent longitudinal and transverse modes, respectively. ex,zz −0.4651

ex,xz 0.0661

ez,zz 0.171

cL 2.042

p¯L 0.0032

gL cT 0.30 0.932

p¯T 0.0702

gT 13.8

coupling, showing that the PE scattering is an order of magnitude stronger for T < 200 K. Moreover, the PE scattering time decreases with temperature as T −1/2 for free carriers, as compared to the T −3/2 dependence of deformation scattering. This weak temperature dependence suggests that the PE scattering becomes more dominant at cryogenic temperatures. For T > 100 K, the temperature dependence of PE scattering levels off, as shown in Fig. 2b, even though the number of acoustic phonons increases with temperature. This arises from the exciton’s form factor ϕe(h) (q), which limits effective scattering to long-wave length phonons q < a−1 0 . The PE scattering time τp over the entire temperature range varies from 0.1 to 1 ps, much shorter than the free induction time τf , and therefore the spin lifetime is greatly enhanced through frequent scattering. The enhancement factor η is shown in Fig. 2c, which is about 50 for T < 10 K, but reduces to 5 for T > 100 K, where spin precession becomes much faster while scattering of the electron in an exciton remains largely unchanged. The averaged spin lifetime in Eq. (8), delineated in Fig. 2d, quantitatively explains the experimentally measured spin lifetime over the entire temperature range. Contributions from the EY mechanism is orders-of-magnitude weaker than those from the DP mechanism. The dominant PE scattering in spin relaxation should be the limiting factor of carrier mobility at low temperatures in HOIPs as well. Using the PE strength to estimate carrier mobility, νe = eτp /me , we find that the free electron mobility in an MAPbI3 crystal would be 102 − 103 cm2 /Vs for T < 100 K. Based on the results from carrier scattering and spin dynamics in HOIPs at low temperatures, the long spin lifetime in MAPbI3 can be unraveled via an auspicious combination of several factors: 1) the weak exchange coupling inhibits the BAP mechanism, 2) the minimal spin mixing due to the large energy gap makes the EY mechanism ineffec11



12

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0

10 10

-1

10

4

2

100

10

Temperature (K)

100

Temperature (K)

Figure 2: Free induction rate caused by the Rashba splitting (a), momentum scattering time (b), spin lifetime enhancement factor (c), and spin lifetime (d) as a function of temperature. In (b), blue and red lines describe acoustic phonon scattering via deformation and piezoelectric coupling, respectively. Solid and dashed lines represent results with and without the exciton form factor φe . In (d), dots are experimental data, and orange and red lines correspond to the EY and the DP mechanisms. Parameters are αc = 0.007 eV˚ A and = 11.9.

12


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tive, and most importantly 3) the strong PE coupling suppresses spin relaxation induced by the Rashba splitting via the DP mechanism. With the information of the momentum scattering time and spin lifetime at low temperatures, we can estimate the Rashba strength q

as αc = (M/me )/ 3τes τp M kB T . Using the calculated τp (T ) we find that αc = 7 × 10−3 eV˚ A can explain the measured spin lifetime as a function of temperature. This value is considerably smaller than the Rashba splitting from earlier first-principles calculations reported in the literature, αc ≥ 1 eV˚ A , 8,9 but in line with recent studies 37 and consistent with values estimated from second harmonic generation experiments. 38 It should be noted that when the Rashba splitting is large enough to have τf < τp , the spin lifetime would be determined by the free induction, τes ' τf ; for T = 10 K and αc = 1 eV˚ A, τes = 5 × 10−14 s, which is several orders of magnitude shorter than the measured value. The effective PE coupling in Eq. (9) depends on the Debye screening q0 , which changes the electrostatic potential from 1/r to e−q0 r /r. Since q0 , according to the Debye-Huckel theory, 39 can be influenced by excess electron and hole densities, ne and nh , q02 =

4πe2 (ne + nh ), kB T

(11)

PE scattering, and accordingly, spin relaxation, can be tuned by varying photoexcitation intensity. Figures 3a and 3b describe screening q02 and momentum scattering time τp due to deformation and PE couplings as a function of photoexcitation intensity. The measured spin lifetimes of different MAPbI3 samples, as plotted in Fig. 3c, follows a common intensity dependence. We see that while photoexcitation does not affect the short-range deformation coupling, it weakens PE scattering and reduces spin lifetime, which satisfactorily accounts for the observed intensity dependence of spin lifetime, as shown in Fig. 3c. In summary, we have unravelled the puzzling long exciton spin lifetime and its dependence on temperature and photoexcitation in MAPbI3 . Our microscopic theory provides a solid foundation for achieving a long spin coherence in HOIPs, which, together with versatile

13



-2

(q0) (Ang )

10

a

c 10

-4

0

2

10

-3

-5

2

10

10

b

10

-1

τs(I)/τs(I0)

10

10

τp (ps)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 19

1

0

0.1

1

10 0.1 2

10 10

1

-2

2

I (W/cm )

I (W/cm )

Figure 3: Debye screening parameter q02 (a), momentum scattering time (b), spin lifetime (c) as a function of photoexcitation intensity. In (b), blue and red lines correspond to deformation and piezoelectric scatterings. In (c), circles and squares are experimental data on two similarly prepared MAPbI3 samples. I0 = 0.25 W/cm2 .

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spin manipulation afforded by strong SOC and RE, promises great potential for HOIPs in spintronics.

Acknowledgement This work was partly supported by the US Army Research Office under Contract No. W911NF-17-1-0511. Y.S.L. was supported by the Center for Hybrid Organic Inorganic Semiconductors for Energy (CHOISE) funded by the Office of Basic Energy Sciences, US Department of Energy, under Contract No. DE-AC36-08G028308.

Supporting Information Available Detailed derivations and discussions on the electronic structure, exciton states, exciton spin dynamics, exciton bands, the Elliot-Yafet mechanism, and piezoelectric coupling in HOIPs (PDF).

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Unravel Spin Relaxation Mechanism in Hybrid Organic-Inorganic

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