# Spin-Flip Raman Scattering on Electrons and Holes in Two-Dimensional
(PEA)2PbI4 Perovskites

C. Harkort,1 D. Kudlacik,1 N. E. Kopteva,1 D. R. Yakovlev,1 M. Karzel,1 E.
Kirstein,1 O. Hordiichuk,2,3 M. Kovalenko,2,3 and M. Bayer1 1Experimentelle
Physik 2, Technische Universität Dortmund, D-44221 Dortmund, Germany  2
Laboratory of Inorganic Chemistry, Department of Chemistry and Applied
Biosciences, ETH Zürich, CH-8093 Zürich, Switzerland  3 Laboratory for Thin
Films and Photovoltaics, Empa-Swiss Federal Laboratories for Materials Science
and Technology, CH-8600 Dübendorf, Switzerland

###### Abstract

The class of Ruddlesden-Popper type (PEA)2PbI4 perovskites comprises two-
dimensional (2D) structures whose optical properties are determined by
excitons with a large binding energy of about 260 meV. It complements the
family of other 2D semiconductor materials by having the band structure
typical for lead halide perovskites, that can be considered as inverted
compared to conventional III-V and II-VI semiconductors. Accordingly, novel
spin phenomena can be expected for them. Spin-flip Raman scattering is used
here to measure the Zeeman splitting of electrons and holes in a magnetic
field up to 10 T. From the recorded data, the electron and hole Landé factors
($g$-factors) are evaluated, their signs are determined, and their
anisotropies are measured. The electron $g$-factor value changes from $+2.11$
out-of-plane to $+2.50$ in-plane, while the hole $g$-factor ranges between
$-0.13$ and $-0.51$. The spin flips of the resident carriers are arranged via
their interaction with photogenerated excitons. Also the double spin-flip
process, where a resident electron and a resident hole interact with the same
exciton, is observed showing a cumulative Raman shift. Dynamic nuclear spin
polarization induced by spin-polarized holes is detected in corresponding
changes of the hole Zeeman splitting. An Overhauser field of the polarized
nuclei acting on the holes as large as $0.6$ T can be achieved.

##  I Introduction

Lead halide perovskite semiconductors attract nowadays great attention due to
their remarkable potential for photonic applications [1, 2, 3, 4]. They are
available as bulk- and nanocrystals and also as two-dimensional (2D) layered
materials. 2D perovskites feature exceptional optical and electrical
properties. By changing the thickness of the semiconductor layers and varying
the organic barriers, their band gap energy changes from the infrared up to
the ultraviolet spectral range [5, 6, 7]. The 2D perovskites exhibit robust
environmental stability [8], which makes them promising for optoelectronic [4,
9, 8] and photovoltaic[10, 11, 12] applications. The strong quantum
confinement of electrons and holes results in excitons with large binding
energies, which are additionally increased by dielectric confinement,
approaching $200-500$ meV [13, 14]. The optical properties of 2D perovskites
are therefore determined by exciton absorption and emission even in ambient
conditions [15, 16], similar to 2D semiconductors like transition metal
dichalcogenides [17].

The band gap in lead halide perovskites is located at the R-point of the
Brillouin zone for cubic crystal lattice and at the $\Gamma$-point for
tetragonal or orthorhombic lattices [18, 19]. In all these cases, the states
at the bottom of the conduction band and the top of the valence band have spin
$1/2$. The perovskites band structure is inverted compared to conventional
III-V and II-VI semiconductors, i.e., in the vicinity of the band gap the
valence band is mostly formed by the s-orbitals of Pb, while the conduction
band states are contributed by the p-orbitals of Pb. As a result, the spin-
orbit interaction modifies mostly the valence band states (and thus the hole
effective mass and $g$-factor) [20, 21, 22], and the hyperfine interaction
with the nuclear spins is much stronger for the holes than for the electrons,
in contrast to conventional semiconductors [21]. Therefore, lead halide
perovskites of different dimensionalities are considered as novel model
systems for spin physics, offering interesting perspectives for spintronic and
quantum information applications [23].

Recent studies show that a similar level of optical spin control can be
achieved in perovskites as in conventional semiconductors. To that end, the
optical and magneto-optical techniques established for studying spin-dependent
phenomena were tested with respect to their suitability for lead halide
perovskites: optical orientation [24, 25, 26, 27], optical alignment [25],
polarized emission in magnetic field [28, 29, 30], time-resolved Faraday/Kerr
rotation [31, 32, 21] and spin-flip Raman scattering [33, 22] were
demonstrated. Some of them were also used to study spin properties including
their dynamics in 2D perovskites. Application of high magnetic fields up to 60
T provided information on the exciton fine structure and exciton Landé factor
($g$-factor) [34, 35, 36, 37, 38, 39, 40, 41]. The exciton spin dynamics down
to subpicosecond time scales were addressed by optical spin orientation
measured by time-resolved transmission [42, 43, 44, 45, 46]. Most of the
dynamical studies were carried out above liquid nitrogen up to room
temperature, where the spin relaxation times do not exceed a few picoseconds.
Recently, time-resolved Kerr rotation allowed measurements of the coherent
dynamics of electron spins in the (PEA)2PbI4 2D perovskite [47]. In these
experiments, longitudinal spin relaxation times up to 25 $\mu$s were found at
the temperature of $1.6$ K. In addition, the electron $g$-factor was measured,
showing a considerable anisotropy. At present, the experimental information on
the electron and hole $g$-factors in 2D perovskites, being the key parameters
for understanding and interpreting spin-dependent phenomena, is still limited,
and we are also not aware of corresponding theoretical considerations.

Spin-flip Raman scattering (SFRS) spectroscopy is another powerful magneto-
optical technique in spin physics, providing direct information on the Zeeman
splitting of electrons, holes, and excitons, and on the optical selection
rules due to the spin level structure of exciton complexes, determined by
their symmetries and exciton-carrier spin interactions [48, 49, 50, 51, 52,
53, 54]. SFRS signals are strongly enhanced when the laser photon energy is
tuned into resonance with the exciton. SFRS measurements are experimentally
challenging due to the close spectral proximity of the spin-flip signals and
the laser line, as the spin-flip Raman shift is on the order of a few hundred
$\mu$eV. Recently, however, the feasibility of SFRS for measuring the electron
and hole $g$-factors in CsPbBr3 and MAPbI3 lead halide perovskite crystals was
demonstrated [22].

In this paper, we report on an SFRS study of the electron and hole $g$-factors
in Ruddlesden-Popper type (PEA)2PbI4 two-dimensional perovskites. The
experiments are performed at cryogenic temperatures in magnetic fields up to
10 T, applied in different geometries in order to measure the $g$-factor
anisotropy. The spin-flip signals originate from resident electrons and holes
interacting with photogenerated excitons. Further, nuclear spin polarization
by spin polarized holes is evidenced through corresponding shifts of the hole
spin-flip line.

##  II Experimental results

###  II.1 Optical properties of two-dimensional perovskites (PEA)2PbI4

We study the 2D Ruddlesden-Popper type perovskite structure (PEA)2PbI4, which
consists of a corner-shared network of PbI6-octahedral monolayers constituting
quantum wells separated by van der Waals-bonded pairs of PEA
[phenethylammonium] molecules. Due to the strong quantum confinement of
electrons and holes in the 2D perovskite layers, the band gap energy increases
to $2.608$ eV at $T=2$ K [37]. The reduced dimensionality and the dielectric
confinement effect [19], provided by the difference of dielectric constants
between the perovskite and the PEA, strongly increase the exciton binding
energy in (PEA)2PbI4 to $260$ meV [37, 41], in comparison to $16$ meV in bulk
MAPbI3 [55].

Figure 1: Optical properties of excitons in (PEA)2PbI4 at $T=1.6$ K. (a)
Reflectivity (red) and photoluminescence (black) spectra. The PL is excited at
$2.412$ eV photon energy using $P=10.8$ W/cm2 excitation power. (b) Counter-
circularly polarized reflectivity spectra measured in Faraday geometry at
$B_{\rm F}=7$ T ($\mathbf{B}_{\rm F}\parallel\mathbf{k}\parallel c$). The
exciton Zeeman splitting of $E_{\rm Z,X}=0.63$ meV can be determined with good
accuracy. (c) Magnetic field dependence of the exciton Zeeman splitting
evaluated from magneto-reflectivity data (symbols). The green line is a
$B$-linear fit. (d) PL dynamics (symbols) measured at the PL maximum of
$2.343$ eV. Pulsed excitation is used at an energy of $3.493$ eV photon energy
with an average power of $P=3$ W/cm2. The line is an exponential fit of the
decay at longer time with the time constant of $40~{}\mu$s.

The pronounced exciton resonance in (PEA)2PbI4 is seen in the reflectivity (R)
spectrum, measured at the temperature of $T=1.6$ K, see Figure 1a. The
resonance line with the minimum at 2.341 meV and the full width at half
maximum of 6.6 meV originates from the free exciton. In external magnetic
field applied in the Faraday geometry ($\mathbf{B}_{\rm
F}\parallel\mathbf{k}\parallel c$), the exciton spin states $+1$ and $-1$
detected in $\sigma^{+}$ and $\sigma^{-}$ circular polarization, respectively,
are subject to Zeeman splitting by $E_{\rm Z,X}=g_{\rm X,c}\mu_{\rm B}B_{\rm
F}$. Here, the $c$-axis is perpendicular to the 2D planes, $\mathbf{k}$ is the
light wave vector, $g_{\rm X,c}$ is the exciton $g$-factor along the $c$-axis,
and $\mu_{\rm B}$ is the Bohr magneton. Reflectivity spectra at $B_{\rm F}=7$
T measured in $\sigma^{+}$ and $\sigma^{-}$ polarization are shown in Figure
1b. The different energies of the exciton resonance in the two spectra reflect
the Zeeman splitting. In Figure 1c we present the magnetic field dependence of
the exciton Zeeman splitting, from its linear fit the exciton $g$-factor
$g_{\text{X,c}}=+1.6\pm 0.1$ is evaluated. Note that in this experiment the
$g$-factor sign can be determined: a positive value corresponds to a high
energy shift of the $\sigma^{+}$ polarized resonance relative to the
$\sigma^{-}$ polarized one.

The photoluminescence (PL) spectrum shows a strong emission line with the
maximum at 2.343 eV and the full width at half maximum of about 10 meV, see
Figure 1a. The PL line coincides in energy with the free exciton resonance
measured in reflectivity. However, note that the PL line is broader than the
reflectivity line. It is plausible to assign the line to the exciton emission
of both free and weakly localized excitons. This assignment is supported by
time-integrated and time-resolved spectroscopic studies at cryogenic
temperatures reported in Refs. 39, 57, 58, 38, 56, showing that the PL band is
composed of at least two emission lines. Their recombination dynamics show
times in the range of 300 ps to 10 ns, highlighting the free- and bound-
exciton origin.

For the studied (PEA)2PbI4, the population dynamics are measured by time-
resolved differential reflectivity for resonant excitation of the exciton. The
results are reported in Ref. 47. The dynamics trace reveals decays with times
of 20 ps and 340 ps. Also a longer-lived component with a decay exceeding 1 ns
is observed. We attribute the short dynamics of 20 ps to the lifetime of the
bright excitons with a large oscillator strength in 2D perovskites. The
lifetime is given by their radiative recombination and their relaxation into
dark exciton states. This interpretation is in agreement with literature data
on the low temperature recombination dynamics in (PEA)2PbI4 [59, 57, 58]. The
slower 340 ps dynamics can be attributed to non-geminate recombination of
charge carriers.

In Figure 1d, the PL dynamics measured at the maximum of the PL line across a
much longer temporal range up to 100 $\mu$s are shown. Recombination processes
with a decay time of about 40 $\mu$s are observed, which greatly exceeds the
typical times in exciton dynamics. This evidences that long-living resident
carriers are present in the studied structures. These resident carriers can be
photo-generated electrons and holes which are localized at spatially separated
sites. We will term them as resident electrons and holes and will show that
they give the main contribution to the measured SFRS signals. Note that the
existence of resident carriers is typical for lead halide perovskites, as we
showed for bulk CsPbBr3 [32], FA0.9Cs0.1PbI2.8Br0.2 [21], and MAPbI3 [60]
crystals using optical techniques.

The weak low energy flank of the PL line at 2.330 eV, see Figure 1a, was
assigned in literature either to dark exciton emission [38, 61, 56] or to
phonon-assisted bright exciton recombination [57].

###  II.2 Spin-flip Raman scattering in close-to-Faraday geometry

We apply spin-flip Raman scattering to study the properties of the resident
carrier spins in the 2D (PEA)2PbI4 perovskite. In an external magnetic field,
$\mathbf{B}$, the spin sublevels of the electrons (e) and the holes (h) are
split by the Zeeman energy $E_{\rm Z,e(h)}=g_{\rm e(h)}\mu_{\rm B}B$, which is
proportional to the magnetic field strength and the electron (hole) $g$-factor
$g_{\rm e(h)}$. In the process of Raman light scattering, the carrier spin can
flip changing its orientation, which requires either absorption or dissipation
of the energy amount equal to $E_{\rm Z,e(h)}$, depending on whether the spin
flips from the lower to the upper energy level or vice versa. Therefore, the
energy of the scattered photon differs from the laser photon energy by $E_{\rm
Z,e(h)}$. In case of energy absorption, the Raman shift occurs to lower
energies (Stokes shift), note, however, that in SFRS experiments it is common
to refer to this case as positive Raman shift. In case of energy dissipation,
the shift is to larger energies (anti-Stokes shift), so that the Raman shift
values are negative. For light scattering in semiconductors, an exciton serves
as a mediator between light and spins [51, 52], because the light-matter
interaction is greatly enhanced at the exciton resonance.

Figure 2: Spin-flip Raman scattering in (PEA)2PbI4. (a) Sketch of the
experimental geometry. Upper diagram is for the Faraday
($\mathbf{B}_{\text{F}}\parallel c$) and Voigt
($\mathbf{B}_{\text{V}}\parallel(a,b)$) geometry with the laser light vector
$\mathbf{k}\parallel c$. Bottom diagram is for the tilted field geometry. The
angle $\theta$ specifies the tilt between $\mathbf{B}$ and the $c$-axis
($\mathbf{k}\parallel\mathbf{B}$). (b) SFRS spectrum in the anti-Stokes
spectral range (negative Raman shift) for $\theta=10^{\circ}$, measured for
$E_{\text{exc}}=2.345$ eV laser photon energy with the power $P=5.7$ W/cm2.
The spectrum is multiplied by a factor of 8. The shifts of the hole
$E_{\text{h}}$, the electron $E_{\text{e}}$, and their double flip
($E_{\text{e+h}}$ and $E_{\text{e-h}}$) lines are marked with arrows. (c) SFRS
spectrum in Voigt geometry at $B_{\rm V}=10$ T using linearly co-polarized
excitation and detection. (d) Reflectivity and photoluminescence spectra at
$B_{\rm V}=7$ T. Electron $g$-factor dependence on the excitation energy
(circles). (e) SFRS intensity resonance profile for the electron spin-flip at
$B_{\rm V}=7$ T. All data are measured at $T=1.6$ K.

The schematics of the applied experimental geometries are shown in Figure 2a.
In the Faraday geometry the magnetic field is parallel to the light $k$-vector
($\mathbf{B}_{\text{F}}\parallel\mathbf{k}$), which in turn is parallel to the
crystal $c$-axis ($\mathbf{k}\parallel c$). In the studied (PEA)2PbI4, SFRS
signal is absent in the pure Faraday geometry, because the carrier spin states
$+1/2$ and $-1/2$ are not mixed by magnetic field and, thus, the spin-flip
process is suppressed. Such mixing already occurs for small tilt angles, e.g.
at $\theta=10^{\circ}$, and then indeed SFRS signals become pronounced. We
refer to this geometry as ”close-to-Faraday geometry”, where the Zeeman
splitting is dominated by the $g$-factor component along the $c$-axis ($g_{\rm
e(h),c}$). The SFRS spectrum measured at $B=9.4$ T with the excitation laser
tuned to the exciton resonance at $2.345$ eV, is shown in Figure 2b. The spin-
flip lines are more pronounced in the anti-Stokes spectral range, as there the
contribution of background photoluminescence is minimized.

Four spin-flip lines in the SFRS spectrum labeled by $E_{\text{h}}$,
$E_{\text{e+h}}$, $E_{\text{e}}$, and $E_{\text{e-h}}$ are seen in Figure 2b.
They are absent at zero magnetic field, as expected from the vanishing Zeeman
splitting so that the spin-flip lines coincide with the exciting laser energy.
With increasing magnetic field the lines shift linearly from the laser energy
(referred to as zero). The details of their shifts are shown in Figures
3a,b,c. The $E_{\text{h}}$ line is only detected in high magnetic fields (see
the black circles in Figure 3c) due to its small shift amounting to only
$-0.078$ meV at 9.4 T, which is associated with the spin-flip of the hole
having $|g_{\text{h,c}}|=0.13$. The electron spin-flip line shows a much
larger shift of $E_{\text{e}}=-1.137$ meV at $B=9.4$ T. Its magnetic field
dependence in Figure 3a allows us to evaluate $|g_{\text{e,c}}|=2.11$,
agreeing well with $g_{\text{e,c}}=+2.05\pm 0.05$ determined from time-
resolved Kerr rotation on the same sample [47].

Identification of the hole and electron SFRS lines is done by comparing their
$g$-factors with the universal dependence of the carrier $g$-factors on the
band gap energy, that has recently been established for bulk lead halide
perovskites [22]. According to this dependence for materials with band gap
energies around 2.3 eV, $g$-factor values of $g_{\text{e}}\approx+2.0$ and
$g_{\text{h}}\approx+0.7$ are predicted. We expect some, but not drastic
deviations from this dependence for the 2D perovskites. Therefore, we assign
the spin-flip line with the larger shift to the resident electron with
positive sign of the $g$-factor.

Another approach to distinguish electrons from holes is based on their
interactions with the nuclear spin system, since in lead halide perovskites
the hole-nuclei interaction is about five times stronger than the electron-
nuclei one [21]. This also leads to a much stronger dynamic nuclear
polarization (DNP) by the holes. In Section II.6 we show that DNP can be
detected with the SFRS technique and that its effect is considerable for the
$E_{\text{h}}$ line. Note that it is absent for the $E_{\text{e}}$ line, in
accordance with our assignment. From this experiment, the sign of the hole
$g$-factor can be unambiguously determined. For the studied (PEA)2PbI4, the
hole $g$-factor is negative, i.e. $g_{\text{h,c}}=-0.13$.

The electron line $E_{\text{e}}$ has two satellites, $E_{\text{e-h}}$ and
$E_{\text{e+h}}$, which are shifted by the hole Zeeman splitting. The slopes
in their magnetic field dependence give $|g_{\text{e-h,c}}|=2.25$ and
$|g_{\text{e+h,c}}|=1.94$, see Figure 3b. These lines are provided by double
spin-flip processes, in which simultaneously electron and hole spin-flips are
involved. This is a rather unusual SFRS process. Double electron spin-flip was
found experimentally in 1972 for an exciton interacting with two donor-bound
electrons in CdS [62], later in ZnTe [63], and recently for two localized
electrons interacting with the same exciton in CdSe colloidal nanoplatelets
[54]. The according theoretical consideration can be found in Refs. 64, 66,
65. The $E_{\text{e-h}}$ and $E_{\text{e+h}}$ line shifts are much larger
compared to the $E_{\text{h}}$ line, and can therefore be resolved in a larger
range of magnetic fields starting from 4 T. We use the difference between the
double spin-flip line $E_{\text{e+h}}$ and the electron line $E_{\text{e}}$ to
evaluate the hole Zeeman splitting vs magnetic field in Figure 3c. Note that
the full width at half maximum, taken from the Gaussian fit of the electron
spin-flip line, is about 7 times larger ($50~{}\mu$eV) than that for the hole
($7~{}\mu$eV), which indicates a broader electron $g$-factor dispersion.

Commonly, SFRS signals have a pronounced polarization dependence, caused by
the optical selection rules and the involved scattering mechanisms. The
spectrum shown in Figure 2b is measured in a cross circularly-polarized
configuration with $\sigma^{+}$ polarized excitation and $\sigma^{-}$
polarized detection. The other polarization configurations are shown in the
Supporting Information, Figure S1a, for both the anti-Stokes and Stokes
spectral ranges. Surprisingly, the polarization dependence is weak. Possible
reasons for that are discussed in Section II.7.

###  II.3 Spin-flip Raman scattering in Voigt geometry

In order to determine the in-plane components of the electron and hole
$g$-factors, we perform SFRS measurements in the Voigt geometry, where
$\mathbf{B}_{\text{V}}\perp\textbf{k}$, $\mathbf{B}_{\text{V}}\parallel(a,b)$
and $\theta=90^{\circ}$. In Figure 2c the SFRS spectrum for linearly co-
polarized excitation and detection in the Voigt geometry at
$B_{\text{V}}=10~{}$T is shown. This geometry is favorable for SFRS
experiments because the spin states are mixed by the perpendicular magnetic
field, facilitating an efficient spin-flip process. The comparison of the SFRS
spectra in Figures 2b and 2c shows that the SFRS intensity in the Voigt
geometry is about five times higher than in the Faraday geometry. In the Voigt
geometry the Raman shift of the electron $E_{\text{e}}$ line corresponds to
$|g_{\text{e,(a,b)}}|=2.50$, see also Figure 3d. This value is in good
agreement with $g_{\text{e,(a,b)}}=+2.45\pm 0.05$ measured by time-resolved
Kerr rotation [47]. The slope of the linear fit to the double spin-flip
$E_{\text{e+h}}$ Raman shift corresponds to $|g_{\text{e+h,(a,b)}}|$ $=$
$1.98$, see Figure 3e. As the $E_{\text{h}}$ line cannot be resolved in this
geometry, we calculate its Raman shift from the shift difference between
$E_{\text{e+h}}$ and $E_{\text{e}}$. From the data in different magnetic
fields we determine the hole $g$-factor $g_{\text{h,(a,b)}}=-0.51$ (Figure
3f). Note that the $E_{\text{e-h}}$ line cannot be well detected in Voigt
geometry. The SFRS spectra are measured in different configurations of linear
polarization, however, a noticeable influence of selection rules is not found,
more information is provided in the Supporting Information, Figure S1b.

It is worth pointing out that the amplitude of the spin-flip lines is
sensitive to temperature. We show in the Supporting Information, Figure S2,
that the electron SFRS line amplitude decreases for temperatures exceeding 5 K
and becomes weak above 16 K. We suggest that thermal delocalization of the
resident electrons is the mechanism that reduces the efficiency of the SFRS
process. The estimated activation energy is about 2.1 meV.

###  II.4 Resonance profile of spin-flip Raman scattering

The SFRS intensity has a strong spectral dependence on the laser photon energy
as shown in Figure 2e for the $E_{\text{e}}$ line, measured in the Voigt
geometry at $B_{\rm V}=7$ T. The maximum of the resonance profile coincides
with the free exciton energy in the reflectivity spectrum shown in Figure 2d,
where also the PL line is given for comparison. This highlights the key role
of the exciton in the SFRS process. The exciton resonantly enhances the laser
excitation and scattering through the interaction with resident carriers,
whose spin-flip Raman shift is measured. Similar results were reported for
CdTe/(Cd,Mg)Te quantum wells with a low density of resident electrons [52] and
for singly-charged (In,Ga)As/GaAs quantum dots [53]. In Figure 2d, the
electron $g$-factor is shown as function of the excitation energy. It remains
constant across the investigated energy range.

###  II.5 $g$-factors of electrons and holes and their anisotropy

The electron and hole $g$-factors can be precisely determined from the Raman
shifts of the respective lines at different magnetic fields. The results in
the close-to-Faraday and Voigt geometries are presented in Figure 3. The
electron $g$-factors are taken from the shift of the $E_{\text{e}}$ line, see
Figures 3a,d. Figures 3b,e illustrate the shifts of the double spin-flip lines
$E_{\text{e+h}}$ and $E_{\text{e-h}}$, which are plotted relative to the
$E_{\text{e}}$ line shift. The differences between the $E_{\text{e}}$ and the
double spin-flip line shifts correspond to the hole Zeeman splitting, shown in
Figures 3c,f. Only in high magnetic fields the $E_{\text{h}}$ shift can be
directly measured. The corresponding values of the $g$-factors are given in
the panels of Figure 3 and are also collected in Table 1, in which the signs
of the $g$-factors are given.

Figure 3: Raman shifts of the spin-flip lines in magnetic field and evaluated carrier $g$-factors in (PEA)2PbI4. Magnetic field dependences of the anti-Stokes SFRS shifts measured in the close-to-Faraday ($\theta=10^{\circ}$) and Voigt ($\theta=90^{\circ}$) geometries. (a, d) Electron $E_{\text{e}}$ shift. (b, e) Double spin-flip $E_{\text{e+h}}$ and $E_{\text{e-h}}$ shifts after subtracting the shift of $E_{\text{e}}$. (c, f) Hole $E_{\text{h}}$ shift evaluated from the double spin-flip shifts (colored triangles). Black dots in panel (c) give direct measurements of the hole spin-flip shift of the $E_{\text{h}}$ line. In all panels, $B$-linear fits are shown by the solid lines. (g) $g$-factor anisotropy for the tilt angle $\theta$ tuned between Faraday and Voigt geometry. Lines are fits with Equation (1). All measurements presented here are performed at $T=1.6$ K with $E_{\text{exc}}=2.345$ eV laser photon energy using $P=7.5$ W/cm2 excitation power.  | close to Faraday geometry, $\theta=10^{\circ}$ | Voigt geometry, $\theta=90^{\circ}$
---|---|---
|  $g_{\text{e,c}}$ |  $g_{\text{h,c}}$ |  $g_{\text{e-h,c}}$ |  $g_{\text{e+h,c}}$ |  $g_{\text{e,(a,b)}}$ |  $g_{\text{h,(a,b)}}$ |  $g_{\text{e-h,(a,b)}}$ |  $g_{\text{e+h,(a,b)}}$
SFRS |  +2.11 |  $-0.13$ |  +2.25 |  +1.94 |  +2.50 |  $-0.51$ |  +2.93 |  +1.98
TRKR [47] |  +2.05 |  |  |  |  +2.45 |  |  |
Table 1: Overview of the $g$-factors in the close-to-Faraday geometry
($\theta=10^{\circ}$) and in the Voigt geometry ($\theta=90^{\circ}$) for
(PEA)2PbI4 measured by SFRS and time-resolved Kerr rotation [47]. The
measurement accuracy is $\pm 0.05$ in all cases. The exciton Zeeman splitting
measured by magneto-reflectivity in Faraday geometry is
$g_{\text{X,c}}=+1.6\pm 0.1$.

The anisotropy of the carrier $g$-factors is inherent for 2D structures and
originates from the reduced symmetry of the band structure. For the studied
(PEA)2PbI4 sample the anisotropy is shown in Figure 3g, where the experimental
data for the close-to-Faraday and Voigt geometries are complemented by
measurements at the magnetic field tilt angle of $\theta=22^{\circ}$. The
angular dependence of the $g$-factor can be described by

$g(\theta)=\sqrt{(g_{\text{c}}\cos\theta)^{2}+(g_{\text{(a,b)}}\sin\theta)^{2}}\,.$
(1)

The electron $g$-factor anisotropy measured by TRKR in a vector magnet with
smaller steps of the tilt angle can be found in Ref. [47]. It is interesting
to note that the anisotropies of $g_{\text{e}}$ and $g_{\text{h}}$ almost
compensate each other, so that their sum stays nearly isotropic,
$g_{\text{e,c}}+g_{\text{h,c}}$ $=$ $+1.98$ and
$g_{\text{e,(a,b)}}+g_{\text{h,(a,b)}}$ $=$ $+1.99$. A similar behavior was
recently found for bulk CsPbBr3 crystals [22].

The $g$-factor of the bright exciton in lead halide perovskites is the sum of
the carrier $g$-factors:

$g_{\rm X}=g_{\rm e}+g_{\rm h}\,.$ (2)

Therefore, the exciton $g$-factor in 2D (PEA)2PbI4 should be nearly isotropic
despite a clear crystal anisotropy. In fact, $g_{\rm X}$ may deviate from the
relation (2), as some $g$-factor renormalization can occur at finite carrier
$k$-vectors in the exciton. It is instructive to check this relation for
(PEA)2PbI4. Here $g_{\text{e,c}}+g_{\text{h,c}}=+1.98$ can be compared with
the $g_{\rm X,c}=+1.6$ measured by magneto-reflectivity (Figure 1c). Indeed,
the exciton $g$-factor is about 0.4 smaller than the sum. We attribute this
difference to the large exciton binding energies in the 2D (PEA)2PbI4
perovskite. Further model calculations are needed to identify the involved
mechanisms.

###  II.6 Dynamic nuclear polarization

The spin dynamics of electrons and holes in semiconductors are strongly
influenced by their hyperfine interaction with the nuclear spin system [67].
In conventional III-V and II-VI semiconductors the conduction band electrons
with s-type wave functions have stronger interaction with the nuclei spins
compared to the valence band holes with p-type wave functions. This situation
is reversed in lead halide perovskites, where the Pb ions greatly contribute
to the states around the band gap [21, 60]. Their p-orbitals form the
conduction band, while the s-orbitals contribute to the valence band. As a
result, the hyperfine interaction of the holes is about 5 times stronger than
that of electrons. Similar properties are expected for (PEA)2PbI4.

The hyperfine interaction of carriers with the nuclei can be assessed by the
effect of dynamic nuclear polarization (DNP). Spin polarized carriers, which
can be generated by circularly polarized light using optical orientation,
generate the Knight field ($\mathbf{B}_{\rm K}$) that acts as an effective
magnetic field on the nuclear spins. Thereby the carrier spin polarization can
be transferred to the nuclear spin system, so that it becomes polarized. In
turn, the polarized nuclear system induces the Overhauser field
($\mathbf{B}_{\rm N}$) that acts on the carrier spins and changes their Zeeman
splitting, see scheme in Figure 4d. Details of DNP model description are given
in Ref. [21]. Here for simplicity, we will consider only the hole
contribution, as we found experimentally that in (PEA)2PbI4 the holes are
dominant in polarizing the nuclear spins.

Figure 4:  Dynamic nuclear polarization of holes detected via SFRS in
(PEA)2PbI4. (a) Raman shift of the hole $E_{\text{h}}$ line measured in
$\sigma^{-}\sigma^{-}$ and $\sigma^{+}\sigma^{-}$ polarization for
$P=5.1~{}$W/cm2 excitation power. (b) Raman shift of the electron
$E_{\text{e}}$ and double spin-flip $E_{\text{e+h}}$ lines measured in
different polarizations for $P=13.5~{}$W/cm2. (c) Power density dependences of
the energy splitting $\Delta E_{\text{N}}=E^{+}-E^{-}$ for the electron and
hole shifts from panel (b). Right axis gives the corresponding Overhauser
field $B_{\text{N}}$. (d) Schematic illustration of the hyperfine interaction
in a carrier-nuclei spin system. The effective Knight field ($B_{\text{K}}$)
of the spin polarized holes $\langle\mathbf{S}_{\text{h}}\rangle$ acts on the
nuclear spin system. The average nuclear spin polarization
$\langle\mathbf{I}\rangle$ acts back via the Overhauser field
($B_{\text{N,h}}$) on the hole spin. (e) $\mathbf{B}_{\text{N,h}}$ orientation
scheme for $g_{\text{h}}<0$ with $\sigma^{+}$ or $\sigma^{-}$ excitation in an
external magnetic field applied in the Faraday geometry. (f) Schematic Raman
spectrum highlighting the effect of DNP on the Raman shift. The difference
between the Raman line shifts for $\sigma^{+}$ and $\sigma^{-}$ excitation is
proportional to $2B_{\text{N,h}}$.

The spin polarization of optically oriented holes
$\langle\mathbf{S}_{\text{h}}\rangle$ is transferred to the nuclei and induces
the average nuclear spin polarization $\langle\mathbf{I}\rangle$ given by

$\langle\mathbf{I}\rangle=l\frac{4I(I+1)}{3}\frac{\mathbf{B}(\mathbf{B}\langle\mathbf{S}_{\text{h}}\rangle)}{B^{2}}\,.$
(3)

Here $l$ is the leakage factor characterizing DNP losses due to relaxation
processes and $I$ is the nuclear spin. The nuclear spin polarization builds up
along the direction of projection of $\langle\mathbf{S}_{\text{h}}\rangle$
onto the magnetic field, and therefore its direction can be controlled by the
light helicity, which determines the $\langle\mathbf{S}_{\text{h}}\rangle$
orientation. The nuclear spin polarization can be converted into the
Overhauser field:

$\mathbf{B}_{\text{N,h}}=\frac{\alpha
A_{\text{h}}\langle\mathbf{I}\rangle}{g_{\text{h}}\mu_{\rm B}}$ (4)

with the positive hyperfine coupling constant for holes $A_{\text{h}}>0$. Here
$\alpha$ is abundance of nuclear isotops with nonzero spin. The sign of
$\mathbf{B}_{\text{N,h}}$ is determined by the sign of the hole $g$-factor,
which offers an experimental tool for evaluating the $g_{\text{h}}$ sign. In
Figure 4e, diagrams for the orientation possibilities of the magnetic and
effective fields as well as the spin polarization are given for $\sigma^{+}$
and $\sigma^{-}$ circular polarized excitation. Here, we take
$g_{\text{h}}<0$. Depending on the $g_{\text{h}}$ sign,
$\mathbf{B}_{\text{N,h}}$ can increase or reduce the hole Zeeman splitting
induced by an external magnetic field. Therefore, it changes the spin-flip
Raman shift and can be detected experimentally by SFRS. For example, we have
demonstrated that for (In,Ga)As/GaAs quantum dots [68].

In order to examine the DNP in (PEA)2PbI4, we apply the SFRS technique in
close-to-Faraday geometry ($\theta=10^{\circ}$). The signal is detected in
$\sigma^{-}$ circular polarization, while the excitation polarization was set
to either $\sigma^{+}$ or $\sigma^{-}$. As shown in Figure 4a the shift of the
hole spin-flip line is larger in the $\sigma^{-}\sigma^{-}$ configuration (we
label the shift as $E^{-}_{\text{h}}$ shown by the blue arrow) than in the
$\sigma^{+}\sigma^{-}$ configuration ($E^{+}_{\text{h}}$, the red arrow).
Their difference scales with twice the Overhauser field which thus can be
extracted from the relation

$\Delta
E_{\text{N,h}}=|E^{+}_{\text{h}}|-|E^{-}_{\text{h}}|=2|g_{\text{h,c}}|\mu_{B}B_{\text{N,h}}\,,$
(5)

as sketched in Figure 4f. The difference $\Delta
E_{\text{N,h}}=|E_{\text{h}}^{+}|-|E_{\text{h}}^{-}|=-1.6~{}\mu$eV measured at
$P=5.1~{}$W/cm2 corresponds to $B_{\text{N,h}}=-0.11$ T calculated using
$|g_{\text{h,c}}|=0.13$. The negative sign of $B_{\text{N,h}}$ means that
$g_{\text{h,c}}<0$, see Equation (4).

The nuclear-induced shift can be seen even more clearly in the double spin-
flip line $E_{\rm e+h}$, as for it the background contribution of the
scattered laser light is strongly reduced, see Figure 4b. Note that the DNP
shift is absent for the electron Zeeman splitting, as the $E_{\rm e}$ shift is
the same for the $\sigma^{-}\sigma^{-}$ and $\sigma^{+}\sigma^{-}$
configurations. However, the shift of the $E_{\rm e+h}$ line from $E_{\rm e}$
varies. For the used excitation density of 13.5 W/cm2 the energy splitting of
these lines amounts to $\Delta E_{\text{N,h}}=-5.5~{}\mu$eV and, therefore, to
$B_{\text{N,h}}=-0.36$ T.

The excitation density dependences of $\Delta E_{\text{N}}(P)$ and
$B_{\text{N}}(P)$ for electrons and holes are shown in Figure 4c. As already
noted, any effect on the electrons is absent, reflecting the expected weak
hyperfine interaction in the 2D (PEA)2PbI4 perovskite. The energy splitting is
pronounced for holes, for which the $\Delta E_{\text{N,h}}$ value increases up
to $-8.7~{}\mu$eV, which corresponds to $B_{\text{N,h}}=-0.6~{}$T at
$P=10.5~{}$W/cm2. For a further excitation density increase the energy
splitting becomes weaker, which we assign to heating of the nuclear spin
system.

The results of this section show that the SFRS technique is a valuable tool
for providing insight into the central spin problem of a carrier spin placed
in a nuclear spin bath in 2D perovskite materials and also for studying
perovskite bulk crystals and nanocrystals.

###  II.7 Discussion

Let us discuss the mechanisms that can be responsible for the observed spin-
flip processes. Recently a detailed theoretical analysis of the spin-flip
Raman scattering processes involving excitons and resident charge carriers in
perovskite semiconductors was published [65]. The model considerations were
made for bulk perovskites with cubic symmetry. Three mechanisms for the
observation of carrier spin-flips were suggested that can explain both the
single and double spin-flip processes. The first mechanism is the resonant
excitation of a localized exciton, followed by its exchange interaction with a
resident electron and/or hole. The second mechanism involves a biexciton as an
intermediate state of the SFRS. In this case, spin-flip shifts by the energies
of $E_{\text{e+h}}$ and $E_{\text{e+h}}/2$ are expected, but the process with
$E_{\text{e-h}}$ is forbidden. We observe, however, in the experiment the
$E_{\text{e-h}}$ process, which allows us to exclude the biexciton scenario.
The third mechanism is the direct excitation of propagating exciton-
polaritons, their scattering on resident carriers, and the conversion of the
polaritons into secondary photons at the sample boundary. In 2D perovskites
the semiconductor layers are electronically decoupled from each other which
prevents exciton-polariton motion along the $c$-axis. Therefore, we suggest
that the exciton-polariton mechanism can be neglected for them.

Our experimental results on the spectral dependence of the SFRS intensity
clearly show the exciton involvement. In turn, the Raman shift values and
their anisotropy allow us to refer them to resident carriers, which interact
with the exciton acting as a mediator of the SFRS. The considerations of Ref.
65 predict pronounced polarization dependencies for the carrier spin-flip
lines. So far, the reason why such dependencies are not observed here is
unclear, see the Supporting Information, Figure S1. Future analysis accounting
for the reduced symmetry and mixing of the bright exciton states in 2D
perovskites might clarify this property. Note that the 2D perovskites are
similar 2D CdSe colloidal nanoplatelets, but for the nanoplatelets we do
observe pronounced polarization dependences of the spin-flip lines [54]. The
SFRS theory for the CdSe nanoplatelets is presented in Ref. 66. Here, the
violation of polarization selection rules caused by the in-plane anisotropy of
the nanoplatelets, which induces exciton mixing and splitting, and by the
finite Zeeman splitting of the intermediate state were analyzed.

We have measured the exciton $g$-factor in (PEA)2PbI4 of $g_{\text{X,c}}=+1.6$
from the exciton Zeeman splitting in magneto-reflectivity, see Figure 1c. It
is in agreement with reported experimental data for 2D perovskite excitons
measured in pulsed magnetic fields up to 60 T, where either magneto-
transmission or magneto-reflectivity were used. The exciton $g$-factor of
about 1.2 was measured for (PEA)2PbI4 [37]. For the similar 2D perovskite
(C6H13NH3)2PbI4 it amounts to about 1.5 [69] and $+1.80$ [34]. For
(C10H21NH3)2PbI4 it is $+1.42$ [35], and for the halogen substitution for Br
in (C4H9NH3)2PbBr4 the $g$-factor is $+1.2$ [36].

Another type of spin-flip Raman scattering process was observed in the
(C4H9NH3)2PbBr4 2D perovskite [33]. These experiments were performed at zero
magnetic field, where the Raman shift by the large value of $28-32$ meV arises
from the scattering of a bright exciton with parallel electron and hole spins
into a dark exciton state with antiparallel spins. This shift corresponds to
the bright-dark exchange splitting of the excitons and not to the Zeeman
splitting of their states.

##  III Conclusions

We have investigated the spin properties of two-dimensional (PEA)2PbI4
perovskites using spin-flip Raman scattering. We have found spin-flip signals
from resident electrons and holes, as well as their combinations. This has
allowed us to measure the Landé factors and their anisotropy. The anisotropy
of the electron and hole $g$-factors is complementary, so that their sum
corresponding to the bright exciton $g$-factor remains isotropic. Also,
hyperfine hole-nuclei interaction is demonstrated in 2D perovskites by means
of the dynamic nuclear polarization. Due to the small $g$-factor of the hole,
we were able to achieve an Overhauser field value of $B_{\text{N,h}}=0.6$ T.
The direction of $\mathbf{B}_{\text{N,h}}$ allows us to unambiguously
determine the negative sign of the hole $g$-factor. We are convinced that
similar effects as those observed can manifest themselves in the large class
of 2D lead halide perovskites with different numbers of layers, as well as in
perovskites with various organic cations.

##  IV Experimental Section

###  IV.1 Samples

We studied Ruddlesden-Popper type two-dimensional (PEA)2PbI4 perovskites that
consist of a stack of monolayers formed by corner-shared PbI6 octahedra. The
monolayers are separated by van der Waals-bonded pairs of PEA
[phenethylammonium (C6H5)C2H4NH3] molecules. Details of the synthesis are
given in the Supporting Information, S1, and in Ref. 47. Due to the quantum
confinement of electrons and holes the band gap energy of (PEA)2PbI4 is
$2.608$ eV at $T=2$ K [37]. This value considerably exceeds the band gap
energy of $A$PbI3 lead iodine archetype bulk crystals with $E_{g}=1.5-1.7$ eV,
where $A=$ Cs+, MA+, or FA+. The reduced dimensionality and the dielectric
enhancement effect, provided by the contrast in dielectric constants between
the perovskite monolayers and the PEA, strongly increase the exciton binding
energy in (PEA)2PbI4 to $260$ meV [37, 41] in comparison to $16$ meV in bulk
MAPbI3 perovskite [55].

###  IV.2 Experimental details

####  IV.2.1 Spin-flip Raman scattering (SFRS) spectroscopy

The SFRS technique enables one to directly measure the Zeeman splitting of the
electron and hole spins from the spectral shift of the scattered light from
the laser photon energy. Resonant excitation of the exciton strongly increases
the SFRS signals, allowing one to measure resident electrons and holes
interacting with an exciton. For optical excitation we used a tunable single-
frequency continuous wave Ti:Sapphire laser (Matisse DS) equipped with a
MixTrain module from SIRAH. The emitted photon energy was tuned around 530 nm
(spectral range $2.33-2.36$ eV), provided by the sum frequency of the
Ti:Sapphire laser operating around $720$ nm and a fiber laser emitting at
$1950$ nm. The actual wavelength was measured and monitored by a fiber-coupled
high-resolution wavemeter (HighFinesse WSU). The laser power after the
MixTrain module was generally set to $0.7$ mW. The diameter of the laser spot
on the sample was 180 $\mu$m in diameter resulting in an excitation density of
$P=2.75$ W/cm2, if not specified otherwise. The linear or circular
polarizations of the laser beam and the Raman signal were set and analyzed by
combinations of $\lambda/2$ or $\lambda/4$ wave plates and a Glan-Thompson
prism, positioned in the excitation and detection paths. The linear
polarizations are denoted as V (vertical) and H (horizontal), and the circular
polarizations as $\sigma^{+}$ and $\sigma^{-}$.

The Raman signals were measured in backscattering geometry. The light
scattered from the sample was dispersed by a $1$ m double monochromator
(Yobin-Yvon U1000) equipped with a Peltier-cooled GaAs photomultiplier
providing a spectral resolution of $0.8$ $\mu$eV. This allows us to measure
$g$-factors with an accuracy of $0.05$. To protect the photomultiplier from
the highly intense laser light, a neutral density filter is placed in the
detection path while recording the laser. The SFRS measurements were performed
at the low temperature of $T=1.6$ K with the sample immersed in pumped liquid
helium. Magnetic fields up to $10$ T generated by a superconducting split-coil
solenoid were applied. In Figure 2a the used experimental geometries are
shown. The sample axes $a$ and $b$ are in-plane, while the $c$-axis is out-of-
plane. In the Faraday geometry, the magnetic field is parallel to the light
wave vector $k$ and to the $c$-axis
($\mathbf{B}_{\text{F}}\parallel\textbf{k}$, $\mathbf{B}_{\text{F}}\parallel
c$ and $\theta=0^{\circ}$). In the Voigt geometry the field is perpendicular
to these vectors ($\mathbf{B}_{\text{V}}\perp\textbf{k}$,
$\mathbf{B}_{\text{V}}\parallel(a,b)$ and $\theta=90^{\circ}$). In our
experiments we did not distinguish between the orientations of the $a$\- and
$b$-axes, and therefore the measured values are averaged over their random
orientations, while the differences between the two axes are not expected to
be large. The angle $\theta$ between the $c$-axis and the magnetic field
specifies the tilt of the field directions as shown in the bottom diagram,
where $\textbf{k}\parallel\mathbf{B}$ is kept.

####  IV.2.2 Photoluminescence (PL)

Nonresonant continuous wave excitation with the photon energy of 2.412 eV and
an excitation density of $P=10.8$ W/cm2 was used for the PL measurements
performed at $T=1.6$ K. The PL was detected by the same $1$ m double
monochromator (U1000) and GaAs photomultiplier, as in the SFRS measurements.

####  IV.2.3 Time-resolved photoluminescence (TRPL)

For the TRPL measurements, a pulsed excitation laser was used (pulse duration
of $10$ ns, pulse repetition rate of $800$ Hz, photon energy of $3.493$ eV,
and excitation density of $P=3$ W/cm2). The PL was detected again with the
Peltier-cooled GaAs photomultiplier coupled to the U1000. The time resolution
of the recombination dynamics was provided by a time-of-flight electronic
board (Fast ComTec MCS6A), which has a nominal time resolution of 100 ps. In
our experiment the time resolution of 10 ns was limited by the laser pulse
duration.

Supporting Information

Correspondence and requests for material should be addressed to D.R.Y.
(dmitri.yakovlev@tu-dortmund.de).

Acknowledgements

We are thankful to A. V. Rodina, E. L. Ivchenko, M. O. Nestoklon, M. M.
Glazov, and I. V. Kalitukha for fruitful discussions. We acknowledge the
financial support by the Deutsche Forschungsgemeinschaft in the frame of the
Priority Programme SPP 2196 (Project YA 65/26-1) and the International
Collaboration Research Center TRR160 (Projects A1 and B2). The work of O.H.
and M.V.K. was financially supported by the Swiss National Science Foundation
(grant agreement 186406, funded in conjunction with SPP2196 through DFG-SNSF
bilateral program) and by the ETH Zürich through the ETH+ Project SynMatLab:
Laboratory for Multiscale Materials Synthesis.

### Competing interests

The authors declare no competing interests.

ORCID
Carolin Harkort: 0000-0003-1975-9773
Dennis Kudlacik: 0000-0001-5473-8383
Nataliia E. Kopteva: 0000-0003-0865-0393
Dmitri R. Yakovlev: 0000-0001-7349-2745
Marek Karzel: 0000-0002-1939-5191
Erik Kirstein: 0000-0002-2549-2115
Oleh Hordiichuk: 0000-0001-7679-4423
Maksym V. Kovalenko: 0000-0002-6396-8938
Manfred Bayer: 0000-0002-0893-5949

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Supporting Information:

Spin-flip Raman scattering on electrons and holes in two-dimensional
(PEA)2PbI4 perovskites

##  S1 Preparation of the (PEA)2PbI4 thin films

The monolayer-thick 2D hybrid organic-inorganic lead halide perovskites have
the stoichiometry $A_{m}$Pb$X_{4}$, with the halide $X$ of the corner shared
[PbX6]4- octahedra forming the monolayers, the bigger organic molecule $A$
separating these monolayers, and $m=1$ for the divalent Dion-Jacobson or $m=2$
for the monovalent Ruddlesden-Popper configuration [1]. While in the bulk case
$A$ is limited by the tolerance factor to {Cs, formamidinium, methylammonium},
in the case of 2D perovskites $A$ can be chosen from a plethora of organic
molecules [1].

For this study Ruddlesden-Popper $m=2$ thin films of PEA [phenethylammonium
(C6H5)CH2CH2NH3] lead iodide, (PEA)2PbI4, were chosen. For the synthesis,
(PEA)I and PbI2 were dissolved in N,N-dimethylformamide in 2:1 molar ratio to
obtain a solution of 8.3 wt.% concentration of (PEA)2PbI4. The solution was
spin-coated on glass substrates (the substrates had been washed by sonication
at $60^{\circ}$C with detergent, water, acetone, isopropanol, and then UV-
ozone treated) for 5 s at 400 rpm followed by 30 s at 3000 rpm. The obtained
films were annealed on a hotplate at $100^{\circ}$C for 10 min. Spin-coating
and annealing were carried out in a N2-filled glovebox. The procedure
described here is an adaptation of that described in Ref. 2.

The lead(II) iodide (PbI2, 99%) and Phenethylamine ($\geq$99%) were purchased
from Sigma-Aldrich. The hydriodic acid (57% aqueous solution, stabilized with
1.5% hypophosphorous acid) was purchased from ABCR. The N,N-Dimethylformamide
(99.8%, Extra Dry over Molecular Sieve, AcroSeal) was purchased from Acros.
All chemicals were used as received without further purification. The
synthesis of phenethylammonium iodide ((PEA)I) was performed in-house and is
described in the Supporting Information, S1.1.

Results of XRD, AFM, and profilometer characterization of the samples are
given in Ref. [3]. The crystals consist of a stack of about 54 perovskite
monolayers, separated from one another by a pair of PEA molecules. The
perovskite monolayers are formed by PbI4 corner shared octahedra. The length
of the octrahedra is $2\times 3.17$ Å [4], and the pair of PEA molecules
separate those monolayers by 10.05 Å at the closest iodine to iodine contact
[5]. The unit cell of the layered perovskite structure is larger due to PEA
twisting and an octrahedral tilt. The $a$, $b$, $c$ axis lengths reported in
Ref. 2 are $a=b=8.74\,$Å, $c=33.00$ Å for the room temperature crystal
configuration.

###  S1.1 Synthesis of phenethylammonium iodide (PEA)I

As a special detail in the description of the sample growth, the synthesis of
(PEA)I is presented. 13 ml of hydriodic acid was added dropwise to a mixture
of 10 ml of phenethylamine and 20 ml of ethanol (anhydrous) while stirring.
The mixture was cooled with an ice bath and stirred for 1 hour. The resulting
solution was evaporated in a rotary evaporator at $50^{\circ}$C until the
liquid was completely removed. The obtained solid was washed three times with
diethylether and recrystallized from ethanol with diethylether. The final
product of (PEA)I was obtained after drying under vacuum at $50^{\circ}$C
overnight (14 g).

##  S2 Experimental results

###  S2.1 Polarization of SFRS

Figure S1:  SFRS spectra measured in the anti-Stokes and the Stokes ranges for
$E_{\text{exc}}=2.345$ eV photon energy using a power $P=5.7$ W/cm2 at $T=1.6$
K. (a) SFRS in tilted field geometry with $\theta=22^{\circ}$ for both co- and
cross-circular polarization at $B=6$ T. (b) SFRS in Voigt geometry for co- and
cross-linear polarization at $B_{\rm V}=7$ T. The linear polarizations $H$ and
$V$ are given for excitation / detection. The anti-Stokes spectra are
multiplied with a factor of 7 to increase the visibility of the SFRS lines.
The electron $E_{\text{e}}$ and the combined $E_{\text{e+h}}$ spin-flip Raman
peak positions are marked by arrows.

In Figure S1(a), the SFRS spectra in circularly co-polarized and cross-
polarized configuration at $\theta=22^{\circ}$ for $B=6~{}$T are shown. In the
anti-Stokes and Stokes ranges, the electron spin-flip is clearly visible with
a Raman shift of $|E_{\text{e}}|=0.75~{}$meV. Note that the absolute SFRS
intensities of the electron spin-flip Raman peaks do not differ in the co- and
cross-polarization configurations. The minor changes are originating from
variations of the resonant photoluminescence background which is weaker in the
$\sigma^{+}/\sigma^{+}$ configuration (blue spectrum).

In Figure S1(b) the SFRS spectra for the different linear co- and cross-
polarizations are presented, measured in the Voigt geometry
($\theta=90^{\circ}$) at $B_{\rm V}=7$ T. The Raman shift of the electron
spin-flip is

$|E_{\text{e,(a,b)}}|=1.03~{}$meV. With increasing tilt angle, the spin-flip
process efficiency increases, so that the electron spin-flip intensity in the
Stokes and anti-Stokes ranges increases approximately five times in comparison
to $\theta=22^{\circ}$. The comparison of the different linear polarization
configurations shows that the absolute electron SFRS peak intensity is only
20% weaker in the cross-linear configurations than in the co-linear
configurations, both for Stokes and anti-Stokes.

###  S2.2 SFRS temperature dependence

Experimental data on the temperature dependence of SFRS measured in the Voigt
geometry are given in Figure S2. The SFRS anti-Stokes spectra at temperatures
of $5$ K and $12$ K are presented in Figure S2a. At $T=5$ K the electron
($E_{\rm e}$) and double ($E_{\rm e+h}$) spin-flip lines are pronounced
compared to $12$ K, where only the weak electron spin-flip remains visible.
The Raman shift is not affected by temperature as shown by the temperature
dependence of the electron g-factor in Figure S2c: the electron $g$-factor
remains constant, $g_{\text{e,(a,b)}}=2.5\pm 0.1$, in the temperature range
from 1.6 K up to 16 K, as one would expect from the negligible changes of the
band structure in this range.

Figure S2: Temperature dependence of SFRS in (PEA)2PbI4 measured in the Voigt
geometry. (a) Anti-Stokes SFRS spectra at $T=5$ K (blue) and $12$ K (red),
measured at $B_{\rm V}=7$ T. Both spectra are multiplied by a factor of 10 in
order to increase the visibility of the spin-flip signals. (b) Temperature
dependence of the electron SFRS intensity (green circles) and the full width
at half maximum (blue squares). The temperature behavior of the electron
intensity follows the Arrhenius-like equation (S1) shown by the green line
fit. (c) Temperature dependence of the electron $g$-factor.

The amplitude of the electron spin-flip line decreases with increasing
temperature, but is hardly detectable above 16 K. The temperature dependence
of the SFRS intensity is shown by the green circles in Figure S2b and can be
described by the Arrhenius-like equation

$I(T)=\Big{(}A\exp{{\Big{(}\frac{E_{\text{A}}}{k_{B}T}}\Big{)}}+C\Big{)}^{-1}\,,$
(S1)

with the activation energy $E_{\text{A}}$ and the Boltzmann constant $k_{B}$.

From fitting the data, the parameters amount to $E_{\text{A}}=2.1~{}$meV, with
the amplitude $A=0.22$ and the constant $C=0.0075$ (see the line in Figure
S2b). We suggest that the thermal delocalization of resident electrons is the
mechanism that leads to the reduction of the efficiency of the SFRS process.
Moreover, in Figure S2b the temperature dependence of the full width at half
maximum (FWHM) of the electron spin-flip line is presented which has a rather
constant value of about 0.1 meV within the examined temperature range.

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