Motional Narrowing Effects in the Excited State Spin Populations of Mn-Doped Hybrid Perovskites

Spin–orbit coupling in the electronic states of solution-processed hybrid metal halide perovskites forms complex spin-textures in the band structures and allows for optical manipulation of the excited state spin-polarizations. Here, we report that motional narrowing acts on the photoexcited spin-polarization in CH3NH3PbBr3 thin films, which are doped at percentage-level with Mn2+ ions. Using ultrafast circularly polarized broadband transient absorption spectroscopy at cryogenic temperatures, we investigate the spin population dynamics in these doped hybrid perovskites and find that spin relaxation lifetimes are increased by a factor of 3 compared to those of undoped materials. Using quantitative analysis of the photoexcitation cooling processes, we reveal increased carrier scattering rates in the doped perovskites as the fundamental mechanism driving spin-polarization-maintaining motional narrowing. Our work reports transition-metal doping as a concept to extend spin lifetimes of hybrid perovskites.


EDX
For investigations of the atomic composition of the doped sample a Bruker XFlash6130 energy-dispersive X-ray spectrometer, mounted in a Zeiss EVO MA10 for sample alignment imaging, was used.For this measurement the sample was spin-coated on an FTO substrate for better conductivity to prevent charging of the sample.T1: Atomic ratios and mass ratios obtained by the series fit deconvolution.

Magnetization measurements
The magnetization measurements were performed at a superconducting quantum interference device (SQUID, MPMS3 Quantum design) capable of temperatures down to 1.8 K and magnetic fields up/down to ± 7 T. Quantification of Mn content:

Supporting
The EDX measurements showed that the actual Mn content in the thin film, starting from a precursor solution in which 50% of the lead was replaced by Manganese, was about 35%.Since EDX measurements are not sensitive to the valence state of the elements, magnetization measurements were performed to find a lower limit for the Mn 2+ content in the nominally 50 % Mn-doped material.The magnetization shown in Figure 1e in the main text was fitted with the function with the saturation magnetization where   stands for the number of free moments with total magnetic moment J per formula unit which here implies the number of Mn 2+ ions, the Brillouin function describing a system with a total angular momentum J where the -factor was assumed to be 2, 2 the Bohr magneton   , the magnetic field strength  0 , the Boltzmann constant   , and the temperature .An additional linear term  0  0  was required to account for a linear contribution to the total magnetization.The presence of a linear term may be interpreted as signature for an antiferromagnetic contribution.The fit results in   = 0.183 1 ..
(18.34 %) for the nominally 50 % Mndoped material.We conclude that at least a minimal doping concentration of 18.34 % of Mn 2+ ions are present.The linear contribution is in the range of  0 = 0.06 ± 0.001

Ultrafast broadband circularly polarized transient absorption spectroscopy (CTA)
All transient absorption measurements were conducted at a home-built pump-probe setup with the sample being located inside a closed-cycle magneto-optic cryostation (Montana Instruments).The CTA measurements were performed at 5 kHz repetition rate of the laser system (Pharos by Light Conversion).The fundamental of 1030 nm was frequency-doubled and also used to generate white light (Hiro by Light Conversion).The 515 nm beam was running via a delay stage (Newport DLS325) used to pump the material and chopped down to 2.5 kHz while the generated white light was used to probe in the spectral region of interest detected by a spectrometer with a mounted sCMOS camera (Kymera 193i and Zyla 5.5 by Andor Oxford Instruments).Pump and probe were both circularly polarized by the same superachromatic quarter-wave plate (specified for 310 -1100 nm by B-Halle) right in front of the entrance window of the cryostation.Switching between co-and counter polarized combinations of pump and probe was achieved via rotation of the linearly polarized pump with a superachromatic half-wave plate (specified for 310 -1100 nm by B-Halle) before passing the quarter wave plate.

Spin relaxation mechanism:
Spin relaxation mechanisms of excited charge carriers in semiconductors can be very complex and depend on numerous parameters like the material itself (crystal symmetry, spinorbit coupling, quantum confinement…), temperature, charge carrier density and excess energy.Depending on these parameters one mechanism can be more dominant than the other and via changing one or more of these parameters the material can be tuned from one spin relaxation regime to another.Most research on this topic was done for III-V inorganic semiconductors.Except for the charge carrier recombination which is also one way of spin relaxation that usually happens orders of magnitude slower than the actual spin relaxation, three main relaxation mechanisms were identified.The Elliot-Yafet (E-Y), the D'yakonov Perel (D-P) and Bir-Aronov-Pikus (BAP) effect.The BAP mechanism describes spin relaxation in p-doped semiconductors or in confined systems, where spin flip happens via Coulomb exchange coupling between electrons and holes.This effect can be neglected for MAPbBr3.Concerning the E-Y mechanism scattering events of the charge carriers with phonons or impurities e.g.cause spin flip.For III-V semiconductors and the E-Y mechanism, the spin lifetime can be written as 3 where τp is the momentum relaxation time, Eg the band gap,  = Δ/(  + Δ) with the spinorbit splitting Δ, and A a dimensionless constant.In the D-P mechanism spins relax due to precessional motion in the presence of effective magnetic fields caused by the Dresselhaus or Rashba effect.Momentum scattering between the precession prevents spins from relaxation.The spin lifetime can be written as 3 with Q a dimensionless constant and α given by where mc and m0 are the effective mass of the electron and the free electron mass, respectively.We see that both E-Y and D-P effect show a strong temperature dependence which is not trivial because of the momentum scattering time that also depends strongly on the temperature.To summarize, the behaviors for both mechanisms depend on the temperature and the spin lifetimes are directly and inversely proportional to the momentum scattering time τp for the E-Y and the D-P mechanism, respectively.In the E-Y mechanism, with decreasing temperature the spin lifetime should increase proportional to   ()  2 , while for the D-P mechanism the spin lifetime should increase proportional to 1  3

𝜏 𝑝 (𝑇)
. In case of the D-P mechanism the increase of the spin lifetime with decreasing temperature will be slowed down by the increase in the momentum scattering time so that the overall temperature dependence deviates strongly from the T 3 behavior.In lead halide perovskites it was shown that the momentum scattering time   () scales with T m with m in the range of -1.4 to -2.5. 4,5onsidering the two extreme cases with m = -1.4 and m = -2.5,    should be proportional to  S5 shows the relative spin lifetime change as a function of temperature.The spin lifetime increases by a factor of three from room temperature to 4.5 K. Connecting the relative change in spin lifetime to the crystal structure one can clearly see the crystal phase change from cubic to tetragonal to orthorhombic which leads to a decrease of the spin lifetime (around 150 K) that can be traced back to a further reduction in symmetry of the crystal structure, probably transition from on spin relaxation regime to another (E-Y to D-P).A power law fit (dashed line in Figure S5) of the spin lifetime for the orthorhombic phase results in   ()   −0.55 , clearly underlining D-P as the dominating spin relaxation mechanism in this regime.
Supporting Figure S5: Spin lifetime of MAPbBr3 normalized to the maximum spin lifetime at 4.5 K with a pump fluence of ~0.2 μJ/cm 2 as a function of temperature.The shaded areas indicate the three different crystal structures MAPbBr3 forms depending on the temperature 6 (from left to right: blue -orthorhombic, green -tetragonal, red -cubic).The fit with a power law of the spin lifetime as a function of temperature is shown with the dashed line for the orthorhombic phase.Supporting Figure S6: Time constants obtained from polarization dynamics by biexponential fits.The first initial fast decay t1 is assigned to the hole spin lifetime, the second time constant τs to the spin lifetime of electrons.The hole spin lifetimes of the pristine and Mn-doped materials increase similarly with decreasing fluences.Due to the s-like valence band, holes are most likely less affected by the SOI leading to a reduced impact of the Mn-doping to the holes' spin via the D-P mechanism.
Supporting Figure S7: (a) The optically induced circular dichroism, which is responsible for the emergence of the PIALow/PIAHigh features also leads to a shift of the GB in energy.The splitting in energy of the GB between co-and counterpolarized combinations of pump and probe is plotted as a function of delay time for Mn-doped and undoped MAPbBr3 for three different fluences.The fluences ~(0.25; 0.75; 2.25) μJ/cm 2 are represented by the intensity of the color-plot from dark to light, respectively.The position of the GB was extracted with a fitting routine which locally fits the GB peak and finds the position of the maximum.The kinetics of the GB-splitting were fitted with mono-exponential (undoped MAPbBr3) and biexponential (Mn-doped MAPbBr3) functions.The obtained time constants are depicted in (b).The Mn-doped material shows a second long-lived spin lifetime component t2 compared to the undoped material.
Undoped Mn-doped t 1 Mn-doped t 2 t S (ps) Fluence (mJ/cm 2 ) Supporting Figure S8: Direct comparison of the spin lifetimes extracted by the PIALow feature and the transient energy splitting of the GB between co and counter polarized spectra for undoped (a) and Mn-doped MAPbBr3 (b).In case of the undoped material the GB energy splitting can be perfectly fitted with a mono-exponential function while the polarization extracted by the PIALow feature scales more bi-exponential.As expected, the spin lifetimes for the GB energy splitting method are between t1 and t2, but follow the same trend pretty well.In case of the Mn-doped sample the comparability is better since the polarization dynamics extracted from both methods follow a bi-exponential function, resulting in the same overall trend with overall slightly higher lifetimes in case of the GB energy splitting method.

Quantitative analysis of charge carrier cooling
We make the usual assumption, when analyzing TA experiments, that the differential transmission at energy ԑ, ΔT/T(ԑ), is proportional to the carrier population at this energy, f(ԑ), which essentially amounts to neglecting the contribution to the signal from the photoinduced refractive index change of the sample.Since we restrict our fit to the high-energy tail of the GB, we approximate f(ԑ) by a Maxwell-Boltzmann distribution.Hence, we fit to our signal a function of the form: with ԑ G the bandgap energy, ԑ F the quasi-Fermi level, kB Boltzmann's constant, Tc the carrier temperature and A1 and A2 fit constants relating to the bandfilling and bandgap renormalization contributions, respectively.We further simplify this by assuming  G =  F , which is commensurate with our assumption of Boltzmann statistics, so that there are four free parameters in our fits: A1, A2, eF and Tc.No widespread consensus exists regarding the definition of the high-energy tail of the signal when performing this analysis; here, we define it as the signal in the energy window between, at the lower end, the energy corresponding to half the maximum bleach at a delay time of 0.35 ps and, at the higher end, by the zerocrossing of the TA signal at this delay.
It is typical to obtain a value for ԑ F by fitting the function specified in (4) to the signal for the longest measured delay time, with Tc set to the lattice temperature (i.e., it is assumed the carrier population has fully cooled at the longest measurement time).This, then, reduces the number of free fit parameters to three for all other delay times.However, here, we find that (4) with Tc fixed to the lattice temperature of 5 K gives a poor fit to the measured signal at the longest delay of 1686.75 ps.Instead, we set Tc to 20 K for this delay, which we find gives a much better fit to the data for both samples, obtaining values for ԑ F of 2.3160 eV for the undoped sample and 2.3048 eV for the Mn-doped sample.Beyond the improved fit to our measurements, we further justify the use of the supra-lattice temperature of 20 K by making the point that, for carrier populations at such low temperatures, the number of carriers with energy above the emission threshold for even the lowest frequency optical phonon mode becomes extremely small and the carrier cooling rate becomes very slow.Thus, that the carrier population has not fully cooled even after > 1 ns is conceivable.
For all other delay times, we fix the value of ԑ F in (4) to the appropriate value obtained from the fit for a 1685.75 ps delay and allow the values of A1 and A2 to vary ±50 % compared with the fitted values at this longest delay, which should allow for a physical variation of the amplitudes of the bandfilling and bandgap renormalization contributions with delay time.Hence, we get Tc as a function of delay time from our fits, to which we fit biexponential decays for both samples.

Figure S2 : 1 T
Magnetization measurements of pristine and Mn-doped MAPbBr3 in presence of an external magnetic field of 0.1 T. The nominal doping level 50% corresponds to the doping level in the precursor solution.Undoped MAPbBr3 shows a very weak paramagnetic response (χ ≈ 1*10 -3 erg/G 2 mol).The Mn-doped material shows dominant Curie paramagnetism for low temperatures, which is indicated by the fit of the data with the Curie law (black line).A shoulder around 90 K and 125 K for the 50% Mn-doped sample could indicate the existence of an additioal Mn-phase like MnO or MnO2.No additional magnetic transitions which would imply the existence of other magnetic impurities and clusters can be observedSupporting FigureS3: Magnetization measurements as a function of the external magnetic field of pristine and Mn-doped MAPbBr3 at 1.8 K. Magnetization of the undoped material shows a very weak positive magnetic susceptibility while the Mndoped material shows a pronounced paramagnetic response.
Brillouin function could indicate the presence of paramagnetic Mn 3+ /Mn 4+ ions in an impurity phase, to some extent.
Differential circularly polarized transient absorption map of MAPbBr3 at 5 K with a fluence of ~0.75 μJ/cm 2 and excitation energy of ~2.41 eV for co-and counter-polarized combinations of pump and probe plotted in a) and (b), respectively.Co-polarized map shows distinct PIA feature on the high energy side while counter-polarized map shows PIA feature on the low energy side.