Ferroelectricity Modulates Polaronic Coupling at Multiferroic Interfaces

Physics of the multiferroic interfaces is currently understood mostly within a phenomenological framework including screening of the polarization field and depolarizing charges. Largely unexplored still remains the band dependence of the interfacial charge modulation, as well as the associated changes of the electron-phonon interaction, coupling the charge and lattice degrees of freedom. Here, multiferroic heterostructures of the colossal-magnetoresistance manganite La1-xSrxMnO3 buried under ferroelectric BaTiO3 and PbZrxTi1-xO3 are explored using soft-X-ray angle-resolved photoemission. The experimental band dispersions from the buried La1-xSrxMnO3 identify coexisting two-dimensional hole and three-dimensional electron charge carriers. The ferroelectric polarization modulates their charge density, changing the band filling and orbital occupation in the interfacial region. Furthermore, these changes in the carrier density affect the coupling of the 2D holes and 3D electrons with the lattice which forms large Froelich polarons inherently reducing mobility of the charge carriers. We find that the fast dynamic response of electrons makes them much more efficient in screening of the electron-lattice interaction compared to the holes. Our k-resolved results on the orbital occupancy, band filling and electron-lattice interaction in multiferroic oxide heterostructures modulated by the ferroelectric polarization disclose most fundamental physics of these systems needed for further progress of beyond-CMOS ferro-functional electronics.


Introduction
The proximity of the hole-doped manganite La 0.7 Sr 0.3 MnO 3 (LSMO) and a FE material with a well-defined orientation of the FE polarization (P), provides a local tuning of the doping level close to the interface 1,2 . Charge modulation in the interfacial region of LSMO occurs in order to compensate the unscreened depolarizing field due to the discontinuity in the ferroelectric polarization [3][4][5] , with its spatial localization related to the Thomas-Fermi screening length 6 . An electrostatic picture of compensating the FE polarization assumes a charge depletion in LSMO when P points towards the interface, and a charge accumulation when it points in the opposite direction 2,7,8 . However, the final picture of the interface-altered electronic structure extends beyond electrostatic-derived arguments. On one hand, the Schottky barrier height between the two joining materials and the FE state control the band alignment and band bending at the interface, and thus the transfer of electrons and holes accounting for compensation of the FE phase 3,4,9,10 . Then, the orbital and lattice degrees of freedom (DOF) come into play when strain 11,12 in conjunction with ferroelectric-like distortions 5 and octahedral tilts, 13 propagating into the interfacial region, modulate the Mn-O bond lengths as compared to the bulk. By lifting orbital degeneracy, it changes the orbital-dependent charge occupations and itinerancy of the carriers 7,8,14 .
The coupling between the charge and lattice DOFs expresses the polaronic nature of the propagating electron/hole, dressed by the local lattice distortion in the form of a phonon cloud.
Such coupled charge-lattice quasiparticles explain the superconductive pairing mechanism 15 , the transition from high to low mobility in colossal magnetoresistance materials 1 and the strong charge localization close to the metal-to-insulator transition in Mott insulators 16,17 . Hence, understanding how electron-phonon interaction (EPI) renormalizes the electron and hole effective mass (m eff ) and therefore their mobility is essential for pushing forward oxide electronics beyond the known paradigms. However, addressing the impact of EPI on the interface electronic structure is experimentally challenging since most spectroscopic techniques, by probing the whole heterostructure depth, can rarely isolate the contribution of the contact region only. One way of extracting such information is from the spectral function, A(k,ω) 18 which contains the effect of all many-body (electron-electron and electron-boson) interactions. It is directly accessed by angle-resolved photoelectron spectroscopy (ARPES), with the EPI signature being a dip-hump structure of A(k,ω) accompanying the quasiparticle peak (QP) at low band filling and kinks in the experimental band dispersion 18,19 at large occupations of the conduction band. Our study uses soft X-ray ARPES 20,21 , whose probing depth matches the interfacial region and whose sharp intrinsic resolution in the out-of-plane momentum k z allows precise sampling of the 3D k-space, to access electronic properties of the LSMO interface buried under thin FE layers of BaTiO 3 (BTO) and PbZr 0.2 Ti 0.8 O 3 (PZT), which propagate the hole-depletion state into the joining LSMO region. We reveal aspects which so far remained hidden due to either the extreme surface sensitivity and consequently large k z broadening 20 of conventional ultra-violet ARPES, or the angle-integrated nature of the transport measurements 14 , X-ray photoelectron spectroscopy 4,10 , 4,10 and X-ray absorption spectroscopies 1,2,7,14 , previously used to probe such interfaces.
Our results establish the coexistence of hole-coupled 2D and electron-coupled 3D Fröhlich polarons (FP) in LSMO. We show that the polaronic-coupling strength can be tuned by the FE polarization through the preferential occupation of the e g (3z 2 -r 2 ) orbitals vs e g (x 2 -y 2 ) ones.
Such altered orbital occupation modifies in turn the relative electron/hole density and changes their contribution at the screening of the electron-phonon coupling. In addition, we resolve the subtle balance between hole depletion and electron accumulation which stabilize the well-defined polarization state of the FE top layer in multiferroic heterostructures.

Results and Discussion
The essential aspect of our experiments is the preparation of multiferroic heterostructures, where the FE layer is thin enough to access the electronic structure of the buried interface with soft X-ray photoemission, and in the same time stays above the critical thickness of~3-6 unit cells at which PZT and BTO lose their FE character 5,22 . Such thin FE films, epitaxially grown and strained at the in-plane lattice constant of the substrate, stabilize as a single FE domain due to their high coercive field. P pointing either towards (P -) or away from the interface (P + ) 5 are opposed by corresponding depolarizing field, compensated by the modulation of the LSMO charge carriers. Other possible extrinsic mechanisms such as such as adsorption of polar molecules at the FE surfaces may also have a contribution in stabilizing the ferroelectric state 23,24 For details on the FE state of the top layers see Section 1 and The high coercive field of the 3 nm-thin FE layers means that in-situ switching of the ferroelectric state between two opposed states P -/P + is excluded. We will focus instead on comparing the signature of the bare LSMO surface, unmodified by the proximity effect of FEs with the Pinterface which is stabilized by the LSMO substrate. We will follow the gradual evolution of charge density and orbital order induced at the interface by ferroelectrics with different magnitude of P; with P BTO~ 20 -30 μC/cm 3 and P PZT~ 60 -80 μC/cm 25,23 .
Different occupation probabilities of the otherwise degenerated e g orbitals in half-filled LSMO result from a competition between the substrate-induced strain and breaking of the symmetry at the surface and interface 11,12 . The strain lowers the crystal symmetry 25 , and Jahn-Teller octahedral rotations lift the orbital degeneracy 8,25 . In-plane tensile strain (c/a<1) lowers the energy of the e g (x 2 -y 2 ) orbitals, increasing their occupation probability, while compressive strain (c/a>1) lowers the energy and increases occupation of the e g (3z 2 -r 2 ) ones 8 .
These effects alter hopping probabilities between Mn orbitals with the in-plane and out-of-plane symmetries. On the other hand, breaking of symmetry near the surface always favors the e g (3z 2 -r 2 ) occupation 11,12 . Joining strained LSMO and epitaxially grown FE oxides further modulates the orbital occupation such that P -, oriented towards the LSMO contact, increases the e g (3z 2 -r 2 ) occupation, while the opposite P + direction enhances the e g (x 2 -y 2 ) occupation 7,8 .
Electron microscopy images with atomic and chemical resolution in Fig. 1A reveal mostly the LaSrO|TiO 2 transition sequence from LSMO to PZT, with some intermixing limited at the first interface layer (see MM). Details on the signatures of the substrate strain in X-ray diffraction and microscopy images of the BTO|LSMO interface are in Fig. S2. Hence, our LSMO/FE interfaces prepared mostly in the LaSrO|TiO 2 sequence, minimise the e g splitting e g between the 3z 2 -r 2 and x 2 -y 2 orbitals 12 due to competing strain and termination effects, while P oriented towards LSMO to increase occupation of the e g (3z 2 -r 2 ) states 7,8 . For details on growth methodology see Materials and Methods (MM) and SM 2. The heavy quasi-2D holes define the FS pocket around the R point, with carriers having predominantly the e g (x 2 -y 2 ) character 26 . The experimental in-plane FS maps recorded at two photon energies hv near the ГXM and X Z AR planes of the Brillouin zone (BZ) are represented in

FE-induced charge density modulation
First, we will analyze the FE-induced modulation of the charge density represented by the ARPES data. The images in Fig. 2A  The microscopic mechanism of interface coupling is a combined effect of: 1. charge building up in LSMO close to the interface with the FE in order to compensate the bound FE charges and the resulting depolarizing field, stabilizing the well-defined orientation of P 9 . This charge depends on both the magnitude of P and on the amount of intrinsic compensation charges already available in the FE through self-doping mechanisms 23 . For the same layer thickness~3 nm, the density of free carriers in BTO, with its oxygen vacancy-assisted n-type conduction, exceeds by at least one order of magnitude that of PZT 3 . Hence, it requires less compensation charges in the metallic electrode to stabilize the inwards Pstate. Accordingly, the alteration of the LSMO electronic structure expressed by the experimental n h values is weaker when interfacing to BTO than to PZT 3 .

2.
FE instability, consisting in off-centering of the cations, modified tetragonality and octahedral tilts in the top layer which propagates into LSMO within the first unit cells, lowering energy of the e g orbitals and favoring their preferential occupation [6][7][8] . This effect has also been shown to directly scale with the magnitude of P through the cation displacement with respect to the centro-symmetric configuration, propagating into LSMO. Such instability induced by the PZT layer 23,29 is at least by a factor of two larger compared to BTO 14 . Consequently, its impact on the electronic structure through the induced displacement of the Mn atoms from the central position, modified tetragonality ratio (c/a) and octahedral conformation is also stronger 5,8,13 .  For the electron states, the effect of the FE polarization is clear from the ARPES data in The experimental k F values and the corresponding electron densities, evaluated assuming approximately spherical shape of electron pockets and also presented in Table 1 We will see below that although n e is significantly smaller than n h , its increase predominates in screening of EPI and corresponding renormalization of the charge carrier's m eff . Finally, we will analyze the mechanism of FE-induced electron accumulation in terms of atomic orbitals. Fig. 4 A,B presents the ARPES images collected along the ΓM direction using s-polarized light. In principle, the dipole selection rules at our experimental geometry suggest that these images reveal only the antisymmetric bands with the e g (x 2 -y 2 ) character 21 . However, the low-temperature rhombohedral phase of LSMO lacks exact symmetry planes, and the mixture of domains with 3 different axis orientation 26,30 relaxes this strict linear dichroism, surviving only at the Γ point, where the symmetry prevents e g (x 2 -y 2 ) and e g (3z 2 -r 2 ) bands from hybridization even under octahedral tilt and rotations 30 . In Ref. 8   The kink position in the 40-70 meV range corresponds to the phonon modes active in thin LSMO layers 25,31,32 , and indicates that it originates in the EPI. We stress that the observed kinks are no artifacts due to energy or k variations of the ARPES matrix element, but intrinsic properties of the A(k,ω) spectral function in LSMO as evidenced by qualitatively similar kink structures observed through higher BZs in k || as seen in Fig. 2 D-E, G-H and S3-S5.

LSMO LSMO|BTO LSMO|PZT
Linear fits of the experimental dispersions in the bare-band and renormalized-band regions below and above the kink, respectively, yield the corresponding Fermi velocities and an estimate for the m eff renormalization.
Here, m b and m eff are the bare and renormalized effective masses, and v F b and v F * are bare and renormalized Fermi velocities, respectively.
The obtained m eff values are compiled in Table 2. The enhancement of m eff by a factor of~3 for bare LSMO's hole band is consistent with the previous reports on epitaxially grown and substrate-strained LSMO from photoemission 27 , optical conductivity 32 and transport data 33 .
Intriguingly, the experimental m eff dramatically decreases under the FE polarization in LSMO|PZT.
The mechanism of EPI in LSMO 32,33 involves coupling of electrons with optical phonons through long-range Coulomb interaction as captured by the Fröhlich term 34 : where ⍺ is the dimensionless coupling constant, d = 2 or 3 the polaron dimensionality, q the phonon wavevector, and κ the screening wavevector. Note that a d-dimensional polaron means that the electron is confined in d-dimensional space while the polarization is three-dimensional. Polaronic effective-mass renormalization. 3D electron polarons We will now return to the ARPES data for the e g (3z 2 -r 2 ) derived electron bands in Fig. 3 for LSMO and the LSMO|PZT interface. Their dispersions in low-energy region, zoomed-in in  Table 2. The kinks around other symmetry-related k F points in Fig. 3 (A,B) show smaller spectral intensity, but yield essentially identical renormalization values. The corresponding coupling parameters 3D , found from the DMC calculations in 3D case 37 , are also given in Table 2 The electrons attracted by the FE polarization into the interfacial region resolve the above puzzle why the depletion of the hole charge carriers goes along with the EPI reduction in the hole bands. Such effect has been observed in other manganites and is related to the fact that the electrons have much smaller m eff compared to the holes. Being light, they are faster than the lattice oscillation and can therefore screen the EPI much more efficiently compared to the holes, whose m eff in the third dimension is very large 16 . Hence, the light electrons are the carriers which set the interface to the weak-coupling regime of the Fröhlich polarons. Remarkably, the density of light electrons, n e is smaller by more than one order of magnitude compared to that of the heavy holes n h as seen in Table 1. However, the FE-induced increase of the light electron's n e is enough to drive LSMO from the strong-to weak coupling regime. Moreover, the 3D character of interface electrons (Fig. 1H) suggests that the identified decrease of the polaronic coupling extends into the bulk beyond the Thomas-Fermi screening length 17 , implying the concomitant conductivity increase in a region exceeding the sharp interface region. This is because the distribution of the 3D electrons, deriving from a complex interplay between interface potential and mutual dynamic screening, is not governed by the Thomas-Fermi theory. Hence the light electrons, with their 3D character, spread larger distances from the interface than the Thomas-Fermi length, providing static screening of slow lattice distortions even far from the interface.
Consequently, at the Pinterface we identify the expected electron accumulation and hole depletion. This translates in smaller adimensional polaronic coupling constant which indicates weaker electron-phonon interaction at the P -.
This results shows that the light electron accumulation/depletion controlled by the FE state of the top material, by better/weaker screening the EPI is the key player in the modulated polaronic coupling at the FE/LSMO interface. at 575°C to prevent Pb migration. Then, they were transferred in N 2 atmosphere from the preparation chamber to the analysis one, which we notice to bring only a minimum surface contamination easy to overcome by the high probing depth of the soft X-ray range.

SX-ARPES
Experiments were carried out at ADRESS beamline at Swiss Light Source which delivers high photon flux in soft X-ray range 21 , allowing the band structure investigation of buried interface with the additional benefit of a remarkably sharp momentum resolution along the out-of-plane direction k z 20 and thus full 3D momentum. The relationship between electron momentum (k || ,k ⊥ ), photoelectron kinetic energy and the photoelectron emission angle are given in Ref. 21 . The geometry of the experimental setup 21 is such that the incoming s-polarized (p-polarized) photon beam has the electric field oscillating perpendicularly (parallel) to the measurement plane, thus the selection rules of the photoemission process permit to probe only the antisymmetric (symmetric) states with respect to that measurement plane. ARPES measurements have been performed in pressure better than 10-10 mbar and a temperature of 12 K. Fermi level is calibrated using a gold foil in electrical contact with the sample. A combined resolution (thermal broadening in addition to the photon beam and the ARPES analyzer) was~70 meV.

First-principles calculations
The calculations were performed within the generalized gradient approximation (GGA) using the quantum ESPRESSO plane-wave code 40,41 , and the exchange-correlation functional in the

Data availability
All data presented in this work are available from the corresponding authors upon request.

X-ray photoelectron spectroscopy measurements
The compensation of the FE polarization and screening of the localized depolarizing charges by mobile electrons and holes close to the FE/vacuum interface manifest in downwards or upwards band bending, and further reflects in rigid shifts of all corel levels towards lower (P -) or higher (P + ) binding energies.
In our case, the Pstate of the ferroelectric is in accordance with previous observations when LSMO was used as a substrate 4,5,[44][45][46] . Our established FE state comes from following the FE-dependent shift of the core levels, related to the evolution of the band bending potential going from the surface of the ferroelectric towards the interface. Fig S1A shows the shift towards higher energies of Ti 2p level in BTO when we gradually increase the probing depth (Fig. S1B) confirming the variation of the band bending potential as expected for its Pstate. The PZT layer lying in the same FE state as BTO is confirmed by comparing the Ti 2p and Pb 4f core level energies (Fig. S1 C,D) with the corresponding ones when PZT is deposited on Nb-doped STO, which is known to feature P + FE state 9 . The relative shift of 0.9 eV towards lower binding energies of both Pb and Ti core levels is consistent with the values corresponding to opposed FE state.

ARPES data:
Isoenergetic scans in k z direction ( Figure 1D), performed by varying the incoming energy from 480 eV to 750 eV while keeping the k || in the X Y MR and in ΓX x M' planes, reveal respectively the heavy-hole cuboids and light-electron spheres structure of the interface k space, in accordance with our calculated Fermi surface. The 643 eV energy brings the electron states close to the Γ point in k z for k || in the second Brillouin zone, while the hole bands are ideally probed with the 708 eV energy (Fig. 1E,F). The 643 eV radiation, in resonance with Mn 2p -Mn 3d intraatomic transition, selectively enhance the Mn 3+/ Mn 4+ interface states, thus allowing their identification at a better signal-to-noise ratio 18,20,26,47 .

Hole bands in extended k-space and fit of the momentum distribution curves
The electron dynamics as the result of electron interaction with other quasiparticles can be described by the Green function: (S1) ( , ) = 1 −ε( )−Σ( ,ω) related to the spectral function, which is the essential result in ARPES by: In Eq. S3, is the bare band dispersion and is the complex self energy which captures effects going beyond the single particle picture. The non-interacting case is described by .      Table 1) and determine the splitting between the two bands, Δe g = 0.15 eV associated with the lifting of the degeneracy at the LSMO/BTO interface under combined effect of substrate-strain, termination and FE polarization pointing towards LSMO.

XRD measurements
The lattice parameters of the epitaxial structures have been determined by high resolution X-ray diffraction, using a Bruker D8 Advance X-ray diffractometer with nickel-filtered Cu Kα radiation, parallelized with a Göbel mirror. Symmetric scans with miscut correction (2θ-ω scans) were performed to evaluate the structural characteristics perpendicular to the substrate.
Reciprocal-space mappings (RSM) around the STO node were performed to confirm the epitaxy on the whole area and thickness of the thin layers, and to estimate the in-plane lattice parameters and the epitaxial strain. The lattice parameters of the thin films were determined using the reflections of the cubic STO substrate (a=3.905 Å) as the reference.