Interfacial strain induced giant magnetoresistance and magnetodielectric effects in multiferroic BCZT/LSMO thin film heterostructures

Ferroelectric/ferromagnetic (FE/FM) thin film heterostructures have shown superior magnetoelectric (ME) coupling behavior, enabling the electrical control of magnetocrystalline anisotropy,^1–3 exchange bias,^4,5 and spin transport phenomenon,^6–10 along with the ability to adjust magnetization at lower voltages compared with their bulk counterparts. These effects have the potential to revolutionize various technological applications such as low-power memory storage, sensors, energy-efficient electronics, and advanced computing.^11–14 ME thin film heterostructures of FE perovskites such as BaTiO₃ (BTO) or its derivatives such as Ba_1−yCa_yTi_1−xZr_xO₃ (BCZT) with the FM half-metallic manganite, La_1−xSr_xMnO₃ (LSMO), are well-known multiferroic systems, explored for potential applications in ME random-access-memories and energy-efficient spintronics.^15–19 In such layered FE/FM heterostructures where the LSMO layer also serves as the bottom electrode, the ME coupling relies on either the interfacial strain or the charge ordering between the layers.^20–22 In particular, LSMO/BTO multilayered thin films can exhibit strong ME coupling, as each layer can sustain its ferroic orders at room temperature and above.^23–26 Eerenstein et al. reported a giant ME coupling constant, α∼ 2.3 × 10⁻⁷sm⁻¹, in a ME BTO/LSMO epitaxial thin film heterostructure of around 200 K temperature, near the rhombohedral to orthorhombic (R–O) phase transition of BTO.²⁴ Enhanced voltage tunability (∼0.6 at 1 MHz frequency) has been reported in a BTO/LSMO multilayer thin film due to remarkable interfacial polarization contributions (∼13.62%).²⁶ A large electrical modulation (>10%) at room temperature has been reported by Lu et al. at the BTO/LSMO interface due to polarization reversal in BTO.²¹ A strain-mediated converse ME effect in a LSMO thin film grown on a BTO (100) substrate has been reported to change up to ∼55% of coercivity (ΔH/H) and ∼36% of squareness (M_r/M_s) under the application of a 8 kV/cm electric field at 210 K temperature due to the phase transition in BTO.¹⁹ The orientation of FE polarization has been reported to tune the magnetic as well as electrical properties at the interface of FE/FM, influencing the overall ME properties.^22,27,28 Chen et al. have performed an ab initio calculation suggesting a strain-mediated ferroelectric polar displacement into the interfacial layer of a BTO/LSMO bilayer epitaxial thin film.²⁹ So far, electric control over the ME coupling at the BTO/LSMO interface has been reported in several investigations, but the magnetic control at the interfacial polarization remains difficult to understand. It is speculated that depending on the direction of the polarization of the FE layer whether pointing toward or away from the interface, screening charges could be attracted or repelled toward the interface from the LSMO layer, leading to hole accumulation or depletion, respectively.^29,30 Consequently, this may lead to the modulation of magnetotransport properties such as magnetoresistance (MR). On the other hand, external magnetic fields may cause variations in the polarization properties, leading to enhanced magnetodielectric (MD) properties in the FE layer in such ME heterostructures.^31–33 

One important prerequisite for efficient ME coupling is the growth of high-quality thin film heterostructures for overcoming weak mechanical connections and impurity development at the interfaces.^34,35 It is known that epitaxial LSMO thin films and their multilayered hybrid systems may exhibit unique magnetotransport properties such as colossal magnetoresistance (CMR) due to the interfacial lattice strain introduced during their growth.^36–44 Due to lattice compression of the LSMO unit cell in strained epitaxial thin films, there is a reduction in the electron–phonon interaction causing a Jahn–Teller-type octahedral distortion in MnO₆ octahedra. This, in turn, enhances the electronic hopping probability due to a decrease in the Mn–O bond length and an increase in the Mn–O–Mn bond angle.²³ These alterations collectively contribute to raising T_C in LSMO thin films.⁴⁵ Conversely, in the case of FE/FM heterostructures, the introduction of an external magnetic field could induce changes in polarization and capacitance within the FE layer.^33,46,47 Large MD effects along with CMR could be achieved in FE/FM thin films where the ferroic phase transitions of the FE layer and the FM layer coincide at a specific temperature.^48,49 Besides this, different other factors could also contribute to large MD effects such as strain, Maxwell–Wagner polarization at the interface, thickness, and resistivity of the thin films.^48,50–52 However, detailed information on interfaces and mutual influence between adjacent layers is still lacking, and such information is crucial for developing multifunctional hybrid devices based on the heterostructures. On the other hand, the FE perovskite BCZT, a derivative of the parent BTO, holds promise due to its impressive dielectric properties, significant remanent polarization and coercive field, and large piezoelectric coefficient.^53–55 Depending on the composition of Ba_1−yCa_yTi_1−xZr_xO₃, there have been reports to show interesting relaxor FE behavior distinguished by diffuse phase transition and high electrostriction properties.⁵⁶ Recently, we have reported on the large FE polarization, dielectric relaxor mechanisms, and superpoling phenomena in epitaxial BCZT thin films.^53,57,58 Here, we focus on the strain engineering of epitaxial BCZT/LSMO heterostructures that may lead to unconventional properties with promising applications.

This study focuses on the structure–property relationships in epitaxial BCZT and LSMO bilayer thin films grown on different single-crystal LaAlO₃ (LAO) (100) and MgO (100) substrates using the pulsed laser deposition (PLD) technique. This work offers a fundamental understanding of the mechanisms of temperature-dependent variations in magnetic, electric, and magneto-induced MD properties by investigating the phase transition of LSMO and examining the interplay between BCZT and LSMO at interfaces.

BCZT/LSMO heterostructures were grown on single-crystal LaAlO₃ (LAO) (100) and MgO (100) substrates using a commercial pulsed laser deposition (PLD; Neocera Pioneer 120 Advanced) system. Briefly, high-purity ceramic targets of La_0.80Sr_0.20MnO₃ (LSMO) and Ba_0.85Ca_0.15Ti_0.9Zr_0.1O₃ (BCZT) (Kurt J. Lesker Company) were sequentially ablated using a KrF excimer laser (λ = 248 nm, frequency = 10 Hz, fluences = 4 J/cm²) inside a deposition chamber equipped with a multitarget carousel allowing the in situ deposition of multilayers with clean interfaces. A distance of 5 cm was maintained between the substrate and the targets during the depositions. Before growing the LSMO layer, the LAO and MgO substrates were annealed inside the PLD chamber at 800 °C under an ambient oxygen pressure (⁠ $P O 2$⁠) of 500 mTorr for 2 h. The details of the deposition conditions have been reported in our previous works.^57,58 Briefly, an initial layer of LSMO (thickness ≈ 50 nm) was deposited at 800 °C under a $P O 2$ of 10 mTorr, followed by a layer of BCZT (thickness ≈ 50 nm) at 750 °C under a high $P O 2$ of 1000 mTorr. Open access to the initial LSMO bottom electrode was maintained throughout the process using shadow masks. Finally, top LSMO electrodes of 200 μm diameter were deposited using a shadow mask at 750 °C under a $P O 2$ of 10 mTorr. After deposition, the samples were gradually cooled down to room temperature (approx. 4h) under $P O 2$ of 1000 mTorr.

The crystallinity and crystallographic orientations of the heterostructures were measured using x-ray diffraction (XRD) with a Rigaku Smart Lab 9 kW XG diffractometer provided with a 5-axis goniometer sample stage employing collimated parallel beam Cu Kα radiation (λ = 1.5406 Å). The chemical composition of the films was determined using an x-ray photoelectron spectrometer (XPS, Omicron, model 1712-62-11) with a nonmonochromatic Al Kα (1486.7 eV) x-ray source that operates at 150 W (15 kV and 10 mA). Electrical transport and magnetic properties of the thin film samples were measured using a physical property measurement system (PPMS) (Quantum Design Inc. DynaCool 9T). Magnetization vs magnetic field M(H) hysteresis loops were measured for both in-plane and out-of-plane configurations in magnetic fields up to 5 kOe. The M(H) hysteresis loops shown here were plotted after subtracting the diamagnetic contributions from the substrates. For the measurement of dielectric response below room temperature, a Keysight E4980A Precision LCR meter was used, which was attached to a commercial low-temperature cryostat (CFMS, Cryogenic Ltd.). For magnetodielectric measurement, a vibration isolation system (Newport S-2000) equipped with a Hioki (IM 3635) LCR meter and cryogenic temperature controller (Cryo.con 22C) was used. The ferroelectric polarization measurements of the fabricated BCZT/LSMO thin films (using LSMO top and bottom electrodes) were performed at room temperature using a commercial Precision LC Ferroelectric tester (from Radiant Technologies, Inc.) equipped with a microprobe station.

The single-crystalline natures of the BCZT/LSMO heterostructures are evidenced by their XRD θ–2θ patterns as shown in Fig. 1(a). Here, peaks corresponding to BCZT and LSMO are represented by α and β, respectively, with subscripts 1, 2, and 3 denoting (001), (002), and (003) Bragg reflection planes. In both cases, only (00l) (l = 1, 2, and 3) diffraction peaks of the tetragonal BCZT phase (JCPDS No. 96-901-4669) and the pseudocubic perovskite LSMO phase (JCPDS No. 01-089-4461) are observed, indicating the epitaxial growth of the individual layers. The insets (I) and (II) to Fig. 1(a) show the XRD detector (2θ) scan performed around the (111) plane of BCZT and LSMO thin film layers for BCZT/LSMO/LAO and BCZT/LSMO/MgO heterostructures, respectively. Rocking curves performed around the BCZT (001) crystallographic planes for the heterostructures [Fig. 1(b)] yield peaks with a narrow full-width-at-half-maxima FWHM (0.06° ≤ Δω ≤ 0.16°), confirming the excellent in-plane orientation of the BCZT layers. As expected, the BCZT/LSMO film grown on the lower lattice mismatched LAO substrate (∼2.3%) exhibits a lower FWHM of 0.06°, while the BCZT/LSMO film grown on a larger mismatched MgO substrate (∼8.1%) shows slightly a larger FWHM of 0.16°. Figures 1(c) and 1(d) show the XRD pole figures for the BCZT/LSMO/LAO and BCZT/LSMO/MgO films, respectively, measured around the (111) asymmetric plane. The four distinct bright spots at intervals of 90° conform the fourfold cubic symmetry and excellent in-plane orientation of the BCZT layers in the heterostructures. The out-of-plane (⁠ $a ⊥$⁠) and in-plane (⁠ $a ∥$⁠) lattice parameters of the BCZT and LSMO layers have been calculated from symmetric and asymmetric XRD scans, respectively [see Fig. 1(a)]. The lattice parameters, tetragonal distortion (⁠ $a ⊥ a ∥−1$⁠), in-plane strain (⁠ $ε ∥$⁠), and out-of-plane strain (⁠ $ε ⊥$⁠) relative to the bulk lattice parameters have been calculated for the BCZT and LSMO film layers and are listed in Table I. For BCZT/LSMO/LAO, both the LSMO and the BCZT layers experience in-plane lattice compression to match the underlying layers; while for BCZT/LSMO/MgO, the LSMO layer undergoes in-plane relaxation, while the BCZT layers experience in-plane compression. It is also noted that for both BCZT and LSMO layers, the BCZT/LSMO/LAO sample exhibits a higher tetragonal distortion and out-of-plane tensile strain compared with the BCZT/LSMO/MgO thin film. A schematic representation of unstrained bulk unit cells and strained unit cells of BCZT and LSMO after the epitaxial film growth for the BCZT/LSMO/LAO and BCZT/LSMO/MgO heterostructures is shown in Fig. S1 in the supplementary material.

Further confirmation of the epitaxial growth and estimation of unit-cell parameters for the BCZT/LSMO thin films were obtained from high-resolution XRD reciprocal space maps (RSMs) using asymmetrical reflections. Figures 2(a) and 2(b) show representative RSMs performed around the LAO (111) and MgO (111) planes for the BCZT/LSMO/LAO and BCZT/LSMO/MgO thin films, respectively. Single peaks corresponding to LSMO (111) and BCZT (111) reflections are observed near the LAO (111) and MgO (111) substrate peaks, certifying the epitaxial growth of the heterostructures. While the LSMO peak is very close to LAO in Fig. 2(a) as expected given their small lattice mismatch of ∼2.3% (i.e., using LAO, a = 3.79 Å; LSMO, a = 3.88 Å), the position of the LSMO peak is highly separated from the MgO peak in Fig. 2(b) due to their larger lattice mismatch of ∼8.1% (i.e., using MgO, a = 4.22 Å; LSMO, a = 3.88 Å). The out-of-plane (⁠ $a ⊥$⁠) and in-plane (⁠ $a ∥$⁠) lattice parameters of the BCZT and LSMO film layers as calculated from the RSM, the resulting tetragonal distortion (⁠ $a ⊥ a ∥−1$⁠), out-of-plane strain (⁠ $ε ⊥$⁠), and in-plane strain (⁠ $ε ∥$⁠) relative to their bulk lattice parameters have been calculated and are listed in Table I. The lattice parameters and the tetragonality in the BCZT/LSMO films as calculated from the RSMs show the same trend as those obtained from XRD symmetric and asymmetric scans shown in Fig. 1(a). From the above XRD analyses, it is observed that there are different strain states in the BCZT and LSMO layers as a consequence of the epitaxial growth of the heterostructures of different lattice mismatched LAO and MgO substrates.

Figures 4(a)–4(d) display the core level XPS spectra representing the constituent atoms of the BCZT and LSMO layers of the BCZT/LSMO/LAO and BCZT/LSMO/MgO thin films, respectively. Specifically, the spectra for Ba 3d, Ti 2p, Ca 2p, and Zr 3d are shown for the BCZT layer, while La 3d, Sr 3d, and Mn 2p are presented for the LSMO layer in Fig. 4. Peaks have been deconvoluted and relative peak areas have been calculated after Shirley background correction. The peak positions of each atom are listed in Table S1 (see the supplementary material). The binding energies for various atoms in BCZT and LSMO remain relatively constant in both BCZT/LSMO/LAO and BCZT/LSMO/MgO films, showing no significant changes. The XPS analyses of the BCZT thin film layers reveal that the calculated compositions for the samples closely match the nominal composition of BCZT [(Ba_{0.85 ± 0.02}Ca_{0.15 ± 0.01}Ti_{0.9 ± 0.03}Zr_{0.1 ± 0.02})O₃] and LSMO (La_{0.80 ± 0.02}Sr_{0.20 ± 0.02}MnO₃), indicating good stoichiometric growth of the heterostructures using an optimized PLD process.

To detect any structural phase transitions in the BCZT and LSMO layers, temperature-dependent XRD scans were performed on the heterostructures. Figure 5(a) shows the high-resolution XRD θ–2θ patterns of the BCZT (002), LSMO (002), and MgO (200) peaks for the BCZT/LSMO/MgO film as measured from a 50–300 K temperature range (as shown in the scale bar). A zoom-in-view of the (002) planes of BCZT (marked as α₂) and LSMO (marked as β₂) is shown in the inset. The MgO (200) peaks are deconvoluted into two peaks arising from Cu Kα₁ and Kα₂ lines as observed from the XRD patterns. From the figure, it is seen that the BCZT (002) and LSMO (002) peaks show a change in the XRD pattern profile over temperature, as shown in the zoomed-in view in the inset of Fig. 5(a). The out-of-plane lattice parameters calculated at different temperatures for the BCZT and LSMO layers are shown in the upper and lower panels of Fig. 5(b), respectively. The out-of-plane lattice parameters at 300 K temperature for BCZT and LSMO match with the calculated values obtained from the room temperature XRD θ–2θ scan. The error bars in Fig. 5(b) are calculated from the FWHMs of the BCZT and LSMO peaks in Fig. 5(a). Notably, the out-of-plane lattice parameter of the BCZT shows a slight change in slope near 170 K; which most probably corresponds to the orthorhombic to rhombohedral structural phase transition in BCZT as reported earlier.⁵⁷ However, surprisingly, a distinct change in lattice parameters has been observed near the BCZT transition temperature at around 176 K temperature for the LSMO layer, indicating a possible structural phase transition around this temperature. Since the LSMO system does not undergo any intrinsic structural phase transition around this temperature, we presume that this possible structural transition in the LSMO layer is extrinsic in nature and arises from the strain-mediated feedback from the BCZT layer in the heterostructure. The observation of concurrent phase transitions in both the BCZT and the LSMO layers near the same temperature is plausibly due to the excellent mechano-elastic coupling within the layers in the heterostructure.

To investigate the magnetic transitions in the heterostructures, the magnetization vs temperature M(T) curves were measured for the BCZT/LSMO/LAO and BCZT/LSMO/MgO heterostructures under the application of an in-plane magnetic field of 0.5 kOe as shown in Figs. 6(a) and 6(b), respectively. The ZFC-FC M(T) curves for BCZT/LSMO/LAO and BCZT/LSMO/MgO show a cusp with a drop in magnetization at 145 and 137 K, respectively, which in this case corresponds to the known FM to AFM phase transition in LSMO.⁶⁴ The Néel temperatures (T_N) for the BCZT/LSMO/LAO and BCZT/LSMO/MgO films are thus identified as 145 and 137 K, respectively. The T_C values as measured from the peak positions of the dM/dT curves shown in Fig. S3 in the supplementary material are 185 and 175 K for the BCZT/LSMO/LAO and BCZT/LSMO/MgO films, respectively. It is observed that the larger in-plane compressive strain in the LSMO layer (⁠ $ε ⊥=−1.54$⁠) in BCZT/LSMO/LAO (see Table I) leads to increased T_N (=145 K) and T_C (=185 K) as compared to the in-plane tensile strain in the LSMO layer (⁠ $ε ⊥=0.77$⁠) in the BCZT/LSMO/MgO film.

It is known that in LSMO (001) thin films, the magnetic properties are primarily a consequence of a combination of the in-plane FM double-exchange (along the MnO₂ planes arising from the itinerant e_g electrons via oxygen atoms) and out-of-plane AFM super-exchange (along the MnO₂ out-of-planes resulting from the localized t_2g electrons via oxygen atoms) mechanisms. Thus, the in-plane compressive strain in the LSMO layer shortens the Mn–O–Mn bond length and increases the hopping probability of e_g electrons, which, in turn, stabilizes the FM double exchange ordering and results in enhanced T_C as observed in the BCZT/LSMO/LAO heterostructure.⁴⁵ Notably, the FM–PM phase transition temperature shown in Fig. 6 coincides with the temperature where the LSMO layer experiences a distinct change in lattice parameter, as obtained from the temperature-dependent XRD for BCZT/LSMO/MgO shown in Fig. 5(b), implying that the transitions are most likely magnetostructural in nature in the heterostructure.

It is known that in LSMO thin films, the A-type AFM state exhibits metallic behavior due to the efficient conduction of spin-polarized carriers through double-exchange hopping.^65–70 Further, the T_C and metal-to-insulator (MIT) transition temperature is strongly influenced by lattice strain⁶⁹ and/or ionic vacancies in epitaxial LSMO thin films.⁷⁰ To correlate the magnetic transitions in Figs. 6(a) and 6(b), with the electrical properties, the temperature dependent resistivity ρ(T) of the LSMO layers in the BCZT/LSMO/LAO and BCZT/LSMO/MgO films were measured at 0, 1, and 2 T magnetic fields as shown in Figs. 7(a) and 7(b), respectively. In both Figs. 7(a) and 7(b), it can be seen that at 0 T field, the ρ(T) curve shows a peak at temperatures of 228 and 197 K for the BCZT/LSMO/LAO and BCZT/LSMO/MgO films (i.e., MIT temperature corresponding to the maxima value of dρ/dT), respectively. Further, the peak maxima in the ρ(T) curves shift toward higher temperatures with an increasing field for both the thin films. Since the XPS analysis in Fig. 4 revealed that the LSMO layers were stoichiometric, it is inferred that the observed changes in M(T) and ρ(T) are primarily governed by the lattice distortions induced by the interfacial strain in the heterostructures. AFM super-exchange coupling of the t_2g electrons sustained along the $a ⊥$ axis and should be stronger for shorter distances between MnO₂ planes as in the case of BCZT/LSMO/MgO with a larger out-of-plane contraction of the LSMO unit cell. Hence, ρ(T) values are higher in BCZT/LSMO/MgO (ρ_max ∼350 mΩ cm) than in the BCZT/LSMO/LAO (ρ_max∼260 mΩ cm) film. As a result of the lattice distortion in the LSMO unit cell, the consequential deviation of the Mn–O–Mn bond angles from 180° and the elongation of the Mn–O bonds lead to a reduction in electronic bandwidth. This reduction, in turn, weakens the FM double exchange interaction in the in-plane LSMO layer. Figures 7(c) and 7(d) show a representational unit cell schematic diagram of LSMO layer distortion grown on LAO and MgO substrates, respectively. The distortion induced by strain in the MnO₆ octahedron may result in the crystal field splitting of the e_g level, causing a reduction in either the (3z²–r²) or the (x²–y²) state.⁶⁴ The tensile strain in the LSMO layer on MgO encourages occupancy of the (x²–y²) orbital, stabilizing the A-type AFM structure and consequently suppressing the FM double exchange interaction.⁶⁸ The reduced double exchange interaction results in lower transition temperatures, diminished magnetization, and increased resistivity.⁶⁶ In the BCZT/LSMO/LAO system, the smaller lattice mismatch leads to weaker lattice distortion in LSMO. Consequently, larger magnetization, higher transition temperatures, and smaller resistivity are observed. Conversely, BCZT/LSMO/MgO samples with a significant lattice mismatch exhibit strong lattice distortion, enhancing the localization of e_g electrons. This, in turn, results in smaller magnetization, lower transition temperatures, and larger resistivity.

Figures 9(a) and 9(b) show the temperature dependent dielectric response of BCZT/LSMO/LAO and BCZT/LSMO/MgO heterostructures measured at different frequencies from 1 kHz to 1 MHz at a temperature range of 60–270 K. Dielectric peaks show a broad diffusive nature over temperature and the dielectric maxima temperature (T_m) shifts toward a higher temperature with increasing frequency (shown by the dotted arrow), hence indicating dielectric relaxation present in the heterostructures.⁵⁷ Room temperature ferroelectric hysteresis loops of the two films are shown in Fig. S4 in the supplementary material. Narrow loops without saturation indicate the relaxor-type nature of the films. T_m for the samples measured at 10 kHz frequency is listed in Table II. It is noted that T_m as well as the dielectric permittivity (⁠ $ε r ′$⁠) is higher in the BCZT/LSMO/LAO film than in the BCZT/LSMO/MgO film. The enhanced dielectric constant value and higher transition temperature in the film may be attributed to the epitaxial strain leading to a higher tetragonal distortion in the BCZT layer of the BCZT/LSMO/LAO film.⁵³ 

Figure 10(a) shows the frequency dependence of dielectric permittivity (⁠ $ε r ′$⁠) at 200 K temperature (the temperature at which maximum MR effect for the LSMO layer is observed in Fig. 8) for the BCZT/LSMO/LAO and BCZT/LSMO/MgO films in the upper and lower panels, respectively, at 0 and 2 T magnetic fields. From the figure, it is observed that the $ε r ′$ values are higher under the 2 T field at all frequencies. Similar behavior is observed in the frequency-dependent dielectric permittivity at 0 and 2 T magnetic fields measured at other temperatures (100, 150, 250, and 300 K) as shown in Fig. S5 in the supplementary material. Figure 10(b) shows the temperature dependent dielectric permittivity at 75 kHz frequency under 0 and 2 T applied magnetic fields for BCZT/LSMO/LAO (upper panel) and BCZT/LSMO/MgO (lower panel). The magnetodielectric (MD) effect calculated¹² using $MD(%)=( ε H − ε 0)× 100 ε 0$ for these two films is shown in Fig. 10(c). Maximum $MD(%)$ observed in the BCZT/LSMO/LAO and BCZT/LSMO/MgO films are 2.3% and 6.4%, respectively, as calculated under the application of 2 T magnetic field at 200 K temperature, where the magnetoresistance effect of the underlying LSMO layer is the most dominating. The BCZT/LSMO/MgO film shows almost twice the MD effect compared with the BCZT/LSMO/LAO film. A similar observation of MD has been shown at a different frequency of 95 kHz in Figs. S6(a) and S6(b) in the supplementary material. The MD value calculated in our BCZT/LSMO bilayer film is higher than that in other BTO/LSMO based systems reported in the literature (see Table III). In the bilayer multiferroic heterojunction, several factors induce the magnetoelectric coupling, such as elasticity,^76,77 magnetic exchange bias,⁴ charged-based coupling,⁷⁸ interfacial polarization,^79,80 etc. In the BCZT/LSMO bilayer, our focus of discussion is on the BaO/MnO₂ ferroelectric/manganite interface. Previous investigations through first-principles calculations have reported that at the FE/LSMO interface, the termination of ferroelectric polarization and the presence of a surface-bound charge attract screening charges to the interface.^81,82 Within BCZT, polarization aligns with the out-of-plane [001] direction. Two distinct scenarios may take place at the BCZT/LSMO interface: (i) polarization directed toward the interface and (ii) polarization directed away from the interface. This polarization direction modulates whether hole accumulation or depletion occurs at the BCZT/LSMO interface. For an in-plane compressive strain (⁠ $a ⊥> a ∥$⁠), the octahedral cage surrounding the interfacial Mn, the O ion is pushed away from the Mn atom, and the polarization is directed away from the interface, as shown in Fig. 11(a). The out-of-plane $d 3 z 2 − r 2$ is more stabilized and hole depletion across the interface takes place. For an in-plane tensile strain (⁠ $a ⊥< a ∥$⁠), the BaO layer's O atom is shifted toward the Mn atom, and the polarization is directed toward the interface as shown in Fig. 11(b). The in-plane $d x 2 − y 2$ stabilization and hole accumulation is favored at the interface. Due to the coupling at the BaO–MnO₂ interface, the polarization of the FE BCZT layer could be continued over several layers of LSMO unit cell depending upon the nature of hole accumulation or depletion at the FE/FM interface. Chen et al.²⁹ performed an ab initio calculation on the polar distortion (continuation of ferroelectric displacement) within the interfacial MnO₂ layer. The displacement amplitude (δ) exhibits a smaller value when $a ⊥> a ∥$ and a higher value when $a ⊥< a ∥$⁠, suggesting an enhanced polarization effect in the BCZT/LSMO interface due to the FE distortion from BCZT into the interfacial LSMO layers. Figures 11(c) and 11(d) show the BCZT/LSMO interface on LAO and MgO substrates, respectively. A higher δ value has been shown for the BCZT/LSMO interface under an in-plane tensile strain. The observed polar distortion is a distinct interfacial phenomenon resulting from the propagation of ferroelectric polarization and the finite screening length of LSMO. Under the application of a magnetic field, LSMO is known to exhibit a positive magnetostriction effect.⁸³ While the magnetostriction effect is not prominent near the LSMO/substrate interface due to a strong substrate clamping effect, this influence gradually diminishes as one moves toward the FE/FM interface. When an in-plane magnetic field is applied, LSMO experiences in-plane tensile strain near the BCZT/LSMO interface. This, in turn, encourages a greater δ shift into the interfacing LSMO layer and enhances the effective polarization at the interface. In the BCZT/LSMO/MgO film, a larger substrate–LSMO lattice mismatch induces higher lattice relaxation near the BCZT/LSMO interface. Consequently, the BCZT/LSMO/MgO heterostructure demonstrates a higher MD effect than the BCZT/LSMO/LAO film. The good mechanoelastic coupling within the layers in the heterostructures has also been observed in temperature-dependent XRD analysis as shown in Fig. 5.

BCZT/LSMO/LAO and BCZT/LSMO/MgO thin film heterostructures have been grown using the PLD technique. Different lattice mismatches between the substrates and the film layers give rise to a variation in tetragonal distortion, epitaxial strain, and residual stress in both BCZT and LSMO thin film layers, as observed from different XRD measurements. XPS analysis indicates the identical composition of BCZT and LSMO layers in both films grown in similar ambiance. Low-temperature XRD measurement of the BCZT/LSMO/MgO film reveals a change in lattice parameters around the temperature 170 K for BCZT and 176 K for the LSMO layer. An A-type AFM behavior has been observed in both films below T_N. The magnetization, T_N, and T_C have been strongly influenced by the LSMO–substrate lattice mismatch. A colossal magnetoresistance has been observed in the BCZT/LSMO/LAO film that may arise due to the larger out-of-plane lattice parameter of the LSMO layer. The lower value of resistivity in the BCZT/LSMO/LAO film in comparison with BCZT/LSMO/MgO suggests a stronger FM interaction in the former film. The larger tetragonal distortion of the BCZT layer in the BCZT/LSMO/LAO thin film is attributed to a higher dielectric permittivity value, as well as higher T_m. The larger PNR size of BCZT in the BCZT/LSMO/LAO film (∼12 nm) than in BCZT/LSMO/MgO (∼8 nm) supports the higher dielectric freezing temperature in the BCZT/LSMO/LAO film. The magnetodielectric measurement exhibits almost twice the MD effect in the BCZT/LSMO/MgO film than in BCZT/LSMO/LAO, which is attributed to a higher strain-induced interfacial polarization distortion in the FE/FM layer. This work opens up a new possibility of strain-induced magnetic field-controlled dielectric modulation in FE/FM multilayer thin film heterostructures.

See the supplementary material for a schematic representation of tetragonal distortion in BCZT and LSMO unit cells in the heterostructures, surface morphology of the top BCZT thin film layer, XPS binding energy values of different constituent atoms of BCZT and LSMO layers, dM/dT curves for T_C calculation, room temperature ferroelectric hysteresis loops, and frequency dependence and temperature dependence of dielectric permittivity with and without an applied magnetic field for BCZT/LSMO/LAO and BCZT/LSMO/MgO thin film heterostructures.

D.M. expresses gratitude for financial support received from the Technical Research Centre (TRC), Department of Science and Technology (DST), Government of India (Grant No. AI/1/62/IACS/2015). S.C. acknowledges fellowship from DST-INSPIRE, Government of India.

The authors declare no conflict of interest.

Subhashree Chatterjee: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). Kusampal Yadav: Data curation (supporting). Nasiruddin Mondal: Data curation (supporting). Ganga S. Kumar: Data curation (supporting). Dipten Bhattacharya: Data curation (supporting); Resources (supporting); Writing – review & editing (supporting). Devajyoti Mukherjee: Conceptualization (lead); Formal analysis (equal); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Resources (lead); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (equal); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.