Ferroelectricity modulates polaronic coupling at multiferroic interfaces

Physics of the multiferroic interfaces is currently understood mostly within a phenomenological framework based on screening of the polarization field and depolarizing charges. Additional effects still unexplored are the band dependence of the interfacial charge modulation and 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 investigated 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, affecting the coupling of the 2D holes and 3D electrons with the lattice which forms large Fröhlich polarons inherently reducing mobility of the charge carriers. 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. A deeper understanding of the coupling at the interface of multiferroics heterostructures is being achieved by the use of synchrotron radiation techniques. Here, the authors use k-resolved soft X-ray photoemission spectroscopy and first principles calculations to investigate the band structure of several multiferroic heterostructures, isolating the distinct signature of the interface.

T he proximity of the hole-doped manganite La 0.7 Sr 0.3 MnO 3 (LSMO) and a ferroelectric (FE) material with a welldefined 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 for 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. Firstly, 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 orbitaldependent 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 (electronelectron 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 at 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 in the 250-350 kV cm −1 range [23][24][25] , which increases at low temperatures 26,27 . P pointing either towards (P − ) or away from the interface (P + ) 5 are opposed by the corresponding depolarizing field and compensated by the modulation of the LSMO charge carriers. Other possible extrinsic mechanisms such as adsorption of polar molecules at the FE surfaces may also have a contribution in stabilizing the ferroelectric state 27,28 . Additional details on the FE state of the top layers are presented in Supplementary Note 1 and Supplementary Fig. 1.
The combined high leakage currents and 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 extremely challenging. We will focus instead on comparing the signature of the bare LSMO surface, unmodified by the proximity effect of FEs with the P − interface which is stabilized by the LSMO substrate. We note that the probing depth in our soft X-ray ARPES experiment exceeds the thickness of the possibly appearing magnetic dead layer at the LSMO surface, which lies in the 3 unit cells range 29 . Hence, our approach still correctly delivers information on the spin-integrated intrinsic electronic structure of strained LSMO. 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~2 0-30 μC/cm 3 and P PZT~6 0-80 μC/cm 225, 28 .
Different occupation probabilities of the otherwise degenerate 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 30 , and Jahn-Teller octahedral rotations lift the orbital degeneracy 8,30 . 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 the hopping probabilities between Mn orbitals with the in-plane and out-ofplane symmetries. On the other hand, breaking of symmetry near the surface has been shown to always favor 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 2y 2 ) occupation 7,8 .
Our LSMO/FE interfaces are prepared in the LaSrO|TiO 2 sequence, such that the competing strain and termination effects minimize the e g splitting Δe g between the 3z 2 -r 2 and x 2 -y 2 orbitals 12 , with P oriented towards LSMO to increase occupation of the e g (3z 2 -r 2 ) states 7,8 . The details on the growth methodology are given in Methods section (Sample growth: Pulsed Laser Deposition).
Electron microscopy images with atomic and chemical resolution in Fig. 1a reveal the sharp LaSrO|TiO 2 transition sequence from LSMO to PZT, with no intermixing within the sensitivity range of our measurements. The signatures of the substrateinduced strain in X-ray diffraction and large area microscopy images of both the BTO|LSMO and PZT|LSMO interfaces are given in Supplementary Fig. 2 and discussed in Supplementary Note 2.
First-principles density-functional-theory (DFT + U) calculations of LSMO, strained to the in-plane STO lattice constant, are represented in Fig. 1b. They indicate a coexistence of two types of charge carriers at the Fermi level E F : light electrons and heavy holes. The effective mass of the electrons lying in the e g (3z 2 -r 2 ) derived 3D bands is m eff~0 .4 m e , where m e is the free-electron mass. The effective mass of the holes lying predominantly in quasi-2D, e g (x 2 -y 2 ) derived bands is m eff~1 .4 m e , along the RAR direction of the BZ while the expected m eff along the undispersive directions is expected to be even larger. This makes the overall hole m eff significantly larger than that of the electrons. The effects of correlations and substrate-induced strain on the calculated electronic structure of LSMO are summarized in Supplementary  Fig. 4. The corresponding Fermi surface (FS), represented in Fig. 1c is qualitatively similar with previous works and experimental results 31,32 . It features the 3D electron pocket around Γ, with only a slight mass anisotropy along the ΓM and ΓX directions. These electron states have e g (3z 2 -r 2 ) character with an admixture of e g (x 2 -y 2 ). The heavy quasi-2D holes define the FS pocket around the R point, with carriers having predominantly e g (x 2 -y 2 ) character 31 . 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 Fig. 1d, f for bare LSMO and in Fig. 1e, g for the LSMO|BTO heterostructure. Superimposed on the experimental FSs are the calculated FS of the strained LSMO. The out-of-plane FS map in Fig. 1h identifies the 3D character of the LSMO electrons in the 2-3 unit cells close to the interface. The Luttinger volume 33 of the electron and hole pockets, represented by their areas in the experimental FS cuts, quantifies the corresponding concentrations of electrons (n e ) and holes (n h ). Additional details on the analysis of the ARPES data are given in Supplementary Note 3. Having established the kspace structure of the electron and hole states, we will now explore the impact of the FE-induced charge density modulation on the concentration and polaronic effective-mass renormalization of the electrons and holes.
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, b, recorded with 708 eV, represent band dispersions within the cube-like hole pocket along the RAR direction of the BZ for bare LSMO (Fig. 2a) and for the PZT|LSMO interfaces (Fig. 2b). Superimposed on top are the fits of the momentum distribution curves (MDC) maxima through the binding energies (traced by blue dotted line) and the MDCs at E F (yellow line) whose gradient indicates the Fermi momentum k F . ARPES images of the BTO|LSMO system recorded in the same conditions are shown in Supplementary Fig. 6. Further details on data analysis are given in Supplementary Note 3. The k F extraction procedure in several points of the BZ is included in Supplementary Note 3.1 for the hole bands and Supplementary Note 3.2 for the electron bands. The results are presented in Supplementary Figs. 5-7 for the holes and in Supplementary  Fig. 8 for the electrons. Table 1 reports the hole densities, calculated using the Luttinger formula 33 from the experimental k F values as: assuming the approximately cubic shape of hole pockets. These results demonstrate that the FE polarization significantly depletes n h at the LSMO|FE interfaces compared to bare LSMO surface. The gradual decrease of n h manifests the expected hole-depletion state, induced in the LSMO substrate by the P − state of the FE top layer, where the FE field is compensated by carriers from LSMO 2,4 . This evolution scales with the increasing value of P in BTO and PZT. 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 28 . 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 P − state. 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 the 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 28,34 is at least by a factor of two larger than 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 Fig. 3. The latter compares the ARPES images for the LSMO|PZT interface and bare LSMO recorded at the Mn 2p resonance in the ΓX direction. These images represent band dispersions for the e g (3z 2 -r 2 ) derived electron pockets centered at the Γ point ( Fig. 1d-f) through two BZs. The experimental k F values and the corresponding electron densities, evaluated assuming approximately spherical shape of electron pockets and also presented in Table 1, and show the increase when going from LSMO to the buried LSMO|PZT interface (Fig. 1d). The ARPES images for the LSMO|BTO interface are shown in Supplementary Fig. 8. Therefore, the FE polarization oriented inwards (P − ) results indeed in accumulation of additional electrons in the interfacial region of the LSMO|FE heterostructures compared to the LSMO surface, in agreement with previous experiments 2,7 . However, our measurements allow for the first time a distinct separation of the electron and hole contribution to the total FE-induced charge density n = n h − n e . 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. 4a, 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 lowtemperature rhombohedral phase of LSMO lacks exact symmetry planes, and the mixture of domains with 3 different axis orientation 31,35 relaxes this strict linear dichroism, surviving only at the Γ point. There, the symmetry prevents e g (x 2 -y 2 ) and e g (3z 2r 2 ) bands from hybridization even under octahedral tilt and rotations 35 . It was shown 8 that the FE instability propagating in LSMO alters the ideal overlap of the wavefunctions, their hopping probabilities and bandwidths, with the energy of e g orbitals varying such that P pointing towards LSMO interface lowers the e g (3z 2 -r 2 ) energy and increases its occupation, while opposite  orientation of P increases the e g (x 2 -y 2 ) occupation. Assuming well-defined orbital character of the bands in the Г point, the split of our e g -derived bands, with the e g (x 2 -y 2 ) -like band shifted towards E F and consequent smaller k F at the interface with PZT (Fig. 4b) compared to the bare LSMO (Fig. 4a) is consistent with the mechanism established before 8 . Hence the splitting Δe g = E[(3z 2 -r 2 )]-E[(x 2 -y 2 )], between the corresponding bands bottom relates to the different energy of the e g (3z 2 -r 2 ) and e g (x 2 -y 2 ) orbitals at our interfaces 35 . For the bare LSMO surface, the positive Δe g = 0.18 eV is a direct indication of the higher energy and thus lower occupation of the e g (3z 2 -r 2 ) orbital compared to the e g (x 2 -y 2 ) one 11,12 . At the interface with PZT, on the contrary, the negative Δe g = -0.2 eV indicates the preferential occupation of the 3z 2 -r 2 orbital. The value Δe g = 0.15 eV at the BTO|LSMO interface ( Supplementary Fig. 8) manifests an intermediate trend, with the relative e g (x 2 -y 2 ) and e g (3z 2 -r 2 ) energy only weakly modified by the smaller P of BTO. This is possibly due to partial relaxation of the BTO layer as revealed by the XRD measurements and consequent decrease of the FE polarization close to the interface. The electron concentrations on the three systems are comparatively presented in Supplementary Table 1. On the theoretical side, our supercell DFT calculations confirm that such changes in the interfacial charge distribution depend on the magnitude of P. The difference between the charge density of Mn computed between atoms lying at the interface and in bulk Δρ = ρ interface (SCF) -ρ bulk (SCF) shows that the magnitude of the charge density variation at the LSMO interface scales with the value of the FE polarization (Fig. 4f). More exactly, Δρ > 0 indicate additional charge accumulation in the t 2g orbitals and charge depletion mostly in the e g (x 2 -y 2 ) ones. The picture of the FEdependent band filling of e g (3z 2 -r 2 ) states (Fig. 4c, d) is consistent with the trend established before in XAS measurements 7,14 , which identify different relative energies of LSMO e g states triggered by the FE switch of the top layer (Fig. 4e).
Polaronic effective-mass renormalization. Quasi-2D hole polarons. We will now turn to the analysis of EPI manifested by renormalization of the charge carrier's m eff . The ARPES images in Fig. 2a, b are overlaid by the MDC maxima, identifying the experimental band dispersions of bare LSMO and PZT|LSMO interface. Closely following the theoretical band structure, upon approaching E F , these dispersions go through a kink, which manifests as a renormalization of the bare bands and corresponding increase of m eff . The kink position in the 40-70 meV range corresponds to the phonon modes active in thin LSMO layers 30,36,37 . It is reasonable then to assume that the kink origin is 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. 2d, e, g, h and Supplementary Figs. 5-7. 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 32 , optical conductivity 37 and transport data 38 . Intriguingly, the experimental m eff decreases under the FE polarization in LSMO|PZT.
It was previously established that the mechanism of EPI in LSMO 37,38 involves coupling of electrons with optical phonons through long-range Coulomb interaction as captured by the Fröhlich term 39 : where α 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. This identifies the phononcoupled charge carriers in the hole band as 2D polarons. For large Fröhlich polarons, the EPI strength is determined by the constant α. Except for extremely weak EPI, there is no analytic expression for α, and evaluation of the polaron properties requires unbiased exact numeric methods such as Feynman's path integral formalism 40 or Diagrammatic Monte Carlo (DMC) 41,42 Based on the experimental m eff , we extracted the corresponding values of α 2D (Table 2) from DMC calculations for the 2D case 41 relevant for the hole bands. Whereas for bare LSMO the α 2D value lies in the intermediate-coupling regime of EPI, the FE polarization forces the Fröhlich polarons to transition to the weak-coupling regime. Equation (3) shows that this can only be forced by the screening constant κ, which increases with mobile charge density 18,19 . However, the experimental n h in Table 1 shows the opposite trend, decreasing under the FE polarization at the LSMO|FE interface. Therefore, an explanation could be that the additional electrons building up in the interface region 4 , play the decisive role in screening of the EPI and undressing the charge carriers from the phonons.
Due to insufficient statistics, the BTO|LSMO analysis of the hole band in terms of renormalized effective mass derived from the fit of the kink region is more challenging, hence we will formulate our conclusions on band renormalization based on the bare LSMO and PZT|LSMO data. However, the BTO|LSMO dataset is enough to establish the interface doping trend from the k F variation (Table 1), which suggests a transition of the coupling strength to low coupling regime going from the LSMO surface to the P − interface.
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 of LSMO surface, presented in Fig. 3a and of the LSMO|PZT interface in Fig. 3b. Their dispersions in the low-energy region, zoomed-in in respectively Fig. 3c, d, show the kink similar to the hole bands. Mapped by the MDC maxima in Fig. 3d for LSMO surface and in Fig. 3f for LSMO|PZT interface, the kink appears at approximately the same energy as in the hole  bands, indicating its origin due to the EPI. Whereas for LSMO the kink and the corresponding renormalization of m eff are distinct, for its interface with PZT they are barely visible. From the linear fit of the band dispersions below and above the kink, we extracted the corresponding Fermi velocities of the bare and renormalized bands for LSMO and the LSMO|PZT interface, which yielded the m eff -renormalization values compiled in Table 2. The kinks around other symmetry-related k F points in Fig. 3a, b show smaller spectral intensity, but yield essentially identical renormalization values. The corresponding coupling parameters α 3D , found from the DMC calculations in 3D case 42 , are also given in Table 2. Similarly to the hole bands, the α 3D values exhibit a transition from the intermediate coupling regime in LSMO (α 3D~4 .1) to weak coupling at the LSMO|PZT interface (α~1.5). This trend signals that the modulation of n e due to the FE polarization provides better EPI screening. The same trend is identified for the bands dispersing along ΓM direction as seen in Supplementary Fig. 9 and in Supplementary Table 2. Although for BTO|LSMO we could not estimate α 3D with enough accuracy, the trend in n e suggests an α 3D value intermediate between those of LSMO and PZT|LSMO. The electrons attracted by the FE polarization into the interfacial region resolve the above puzzle of why the depletion of the hole charge carriers goes along with the EPI reduction in the hole bands. Such an effect has been observed in other manganites 16 where it was 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, we believe that a similar argument might operate here as well, with the light electrons as the carriers which set the interface to the weak-coupling regime of the Fröhlich polarons. Indeed, 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, presumably 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 P − interface we identify the expected electron accumulation and hole depletion, translating into a smaller adimensional polaronic coupling constant. This result indicates weaker electron-phonon interaction at the P − .
This finding shows that the light electron accumulation/ depletion controlled by the FE state of the top material, and the accompanying better/weaker screening of the EPI is the key player in the modulated polaronic coupling at the FE/LSMO interface.

Conclusions
Our k-resolved soft X-ray photoemission results on multiferroic LSMO/BaTiO 3 and LSMO/PbZrTiO 3 heterostructures resolves (A) the missing ferroelectric, band-dependent electron/hole accumulation/depletion induced at the interface, extending the previous understanding of P dependent modulation of orbital energies under FE switch 7,8 .
Specifically, the FE instability propagating into the interfacial region of LSMO pushes the e g (x 2 -y 2 ) derived bands defining the hole pockets around the R point, up in energy by~0.2 eV, in accordance with the expected order of the LSMO e g orbitals at the P − interface 7,8 . With the energy of the (3z 2 -r 2 ) orbitals, and their corresponding bands defining the electron pocket bands around the Г point below the (x 2 -y 2 ) ones, charge accumulation occurs in the former and charge depletion in the latter. This effect further propagates into (B) modulation of the EPI strength, expected changes in conductivity, allowing to tune the functionality of the interface. At relatively small influence of the heavy holes in the x 2 -y 2 bands, the fast dynamic response of the light electrons in the 3z 2 -r 2 band effectively screens the EPI. Therefore, the electron accumulation in this band reduces the EPI strength from intermediate for bare LSMO to weak at its interface with the FE overlayer. This regime, with the charge excitations undressed from the lattice vibrations, increases the electron and hole itinerancy. The P − FE polarization should therefore increase the charge carrier mobility, although this phenomenon still awaits verification in transport experiments, while the opposite FE state, by increasing the EPI strength, should decrease interface mobility. Such an effect of the FE polarization on the renormalization of m eff through the EPI strength, which has escaped identification in the previous works, should be taken into account in functional interfaces between the FE and oxide materials, in addition to the other existing mechanism of FE-assisted enhanced carrier mobility 43 .
The detailed band-resolved picture disclosed by our results on how the P affects the orbital occupancy, band filling and electronlattice interaction unveils a number of novel avenues towards further progress not only focused on the multiferroic oxide heterostructures discussed above, but also in the whole vast field of oxide electronics and spintronics. For example, P can be used to tune the mobility of the charge carriers in oxides through modified EPI, in turn modulated by the electron concentration. Particularly promising in this respect are systems where electron correlations increase the population of light-electron bands compared to heavy-hole ones similarly to Ce-doped CaMnO 3 16 The electron correlations themselves can also be tuned through the band filling changing under the FE polarization (electroncorrelation engineering). Furthermore, in multiband systems such as LSMO, where 2D charge carriers coexist with 3D ones, the polarization can tune their relative concentration and thus the dimensionality of the overall electron transport. Still to be explored is the oxide FE/superconductor heterostructures, where the polarization could be utilized to change the effective doping and the regime of phonon-mediated superconductivity 44 through the polarization-induced modulation of the EPI strength identified here for LSMO. Such mechanisms could be used, for example, for realization of switches for power-saving electronics based on Josephson junctions. These ideas open only a few possible novel avenues towards realization of oxide electronic, spintronic, and superconducting devices based on our findings of the multifaceted effect of FE polarization on the orbital occupancy, band filling, electron correlations and electron-boson interaction.

Methods
Sample growth: pulsed laser deposition. Epitaxial LSMO samples were grown on SrTiO 3 (STO) substrates using a thin (5 unit cells) SrRuO 3 (SRO) buffer layer between STO and LSMO. Heterostructures have been prepared by pulsed laser deposition using a well-established recipe to result in epitaxial growth as well as smooth surfaces and sharp interfaces 3,9,28  The ablation of the FEs, SRO and LSMO targets was performed by using a KrF laser (λ = 248 nm) and a repetition rate of 5 Hz for SRO and FEs and 1 Hz for LSMO. The laser fluence was 2 J/cm 2 for the deposition of LSMO, SRO and PZT films, and 1.5 J/cm 2 for BTO. The substrate temperature was maintained at 700°C and the oxygen pressure during deposition was 0.14 mbar for BTO and PZT, 0.13 mbar for SRO and 0.27mbar for LSMO. The as-grown LSMO, SRO and BTO films were post-deposition annealed, in the deposition chamber, at 700°C, for one hour, in O 2 atmosphere while post-annealing of PZT was performed 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 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 21 are given in Supplementary Note 3. 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 ( Supplementary Fig. 3). 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.
Transmission electron microscopy (TEM). Transmission electron microscopy observations have been performed using a probe-corrected analytical highresolution JEM ARM 200 F electron microscope operated at 200 kV, equipped with a Gatan Quantum SE Image Filter for EELS. Atomic resolution images have been recorded in STEM mode (0.08 nm point resolution) using the High-Angle Annular Dark Field (HAADF) detector. Chemical maps at atomic resolution have been obtained by EELS-SI in the STEM mode. Images and spectral data processing have been made using specialized routines under Gatan Digital Micrograph. For the atomic-resolution spectrum-image experiments the electron beam has been scanned inside a 25 nm 2 across the interface region. The probe dwell time was set at 20 ms/pixel. The chosen convergence angle was 2.6 mrad using a condenser aperture of 30 µm diameter, while the collection angle was 18 mrad at 3 cm camera length and for the spectrometer entrance aperture of 2.5 mm. The energy dispersion and the spectral window were set in such a way to allow the simultaneous acquisition of the Ti L, O K, Mn L, Ba L and La M signals.
First-principles calculations. The calculations were performed within the generalized gradient approximation (GGA) using the quantum ESPRESSO plane-wave code 45,46 , and the exchange-correlation functional in the Perdew-Burke-Ernzerhof (PBE) parametrization. We used norm-conserving pseudopotentials from PseusoDojo 47 . The heterostructure was modeled by a 1 × 1 × 14 supercell geometry starting from the relaxed structure of the LSMO unit cell, but imposing the calculated in-plane lattice constant a = 3.903 Å of SrTiO 3 . This supercell contained 7 unit cells (u.c.) of BTO and PTO in contact with 7 u.c. of LSMO. This thickness ensures that the FE property remains stable, because the FE-polarization states tend to merge starting from a thickness of 5 u.c. 48 . The z-coordinates were allowed to relax until the Hellman-Feynman forces on each atom were less than 2.5 meV/Å. La-Sr substitutional doping was treated by means of virtual crystal approximation (VCA) replacing each A-site of the perovskite with a fictitious atom with fractional valence, instead of explicit doping which would be computationally expensive due to larger supercells. The VCA generation of the pseudopotential has been checked to reproduce the correct electronic properties of bulk LSMO. The coordinates of the slab are given in Supplementary Data 1. The kinetic-energy cut-off for the plane waves was set at 60 Ry and for the charge density at 240 Ry. The BZ integration was performed on an automatically generated Monkhorst-Pack 3 × 3 × 3 k-mesh, for all slabs, with Gaussian energy-level smearing of 0.02 Ry. For bulk LSMO band structure, a U Mn = 2 eV Hubbard parameter was employed, which reproduces well the half-metallic character of the LSMO.
X-ray diffraction. 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. Reciprocalspace 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 inplane 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.