Interface phenomena and emerging functionalities in ferroelectric oxide based heterostructures

Abstract

Capitalizing on the nonvolatile, nanoscale controllable polarization, ferroelectric perovskite oxides can be integrated with various functional materials for designing emergent phenomena enabled by charge, lattice, and polar symmetry mediated interfacial coupling, as well as for constructing novel energy-efficient electronics and nanophotonics with programmable functionalities. When prepared in thin film or membrane forms, the ferroelectric instability of these materials is highly susceptible to the interfacial electrostatic and mechanical boundary conditions, resulting in tunable polarization fields and Curie temperatures and domain formation. This review focuses on two types of ferroelectric oxide-based heterostructures: the epitaxial perovskite oxide heterostructures and the ferroelectric oxides interfaced with two-dimensional van der Waals materials. The topics covered include the basic synthesis methods for ferroelectric oxide thin films, membranes, and heterostructures, characterization of their properties, and various emergent phenomena hosted by the heterostructures, including the polarization-controlled metal–insulator transition and magnetic anisotropy, negative capacitance effect, domain-imposed one-dimensional graphene superlattices, programmable second harmonic generation, and interface-enhanced polar alignment and piezoelectric response, as well as their applications in nonvolatile memory, logic, and reconfigurable optical devices. Possible future research directions are also outlined, encompassing the synthesis via remote epitaxy and oxide moiré engineering, incorporation of binary ferroelectric oxides, realization of topological properties, and functional design of oxygen octahedral rotation.

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1. Introduction

Ferroelectrics possess nonvolatile, spontaneous polarization that is switchable via an external electric field (Fig. 1). When they are prepared in thin film forms, the ferroelectric free energy is highly susceptible to the electrostatic and mechanical boundary conditions, which can be utilized to engineer the polar properties and control domain formation.^1–3 The heterostructures interfacing ferroelectrics with other nanoscale functional materials thus present a versatile platform for designing emergent ferroic orders and exploring novel control mechanisms that are not viable in single-phase materials. Leveraging the voltage-controlled nature and nanoscale programmable polarization, ferroelectric thin films have been widely adopted to construct energy-efficient electronic devices, including ferroelectric field effect transistors (FeFETs),⁴ ferroelectric tunnel junctions (FTJs),⁵ memristors,⁶ and negative capacitance (NC) transistors,⁷ which are promising building blocks for developing low-power memory and logic applications as well as neuromorphic computing. Their polar properties have also been exploited in intriguing mechanical⁸ and optical⁹ applications.

Fig. 1 Overview of research on ferroelectric perovskite oxide-based heterostructures, including material systems, emergent phenomena, and potential device applications. P_up/P_down: polarization up/down.

Compared with the widely studied ferroelectric polymer and van der Waals (vdW) materials, ferroelectric perovskite oxides are known for their large polarization, high dielectric constant, high ferroelectric Curie temperature (T_C), low coercive field (E_c), and unit-cell-scale sharp domain walls (DWs).¹ For ferroelectric perovskite thin films and membranes, the interfacial layers play a critical role in determining the material parameters and even affecting the ferroelectric instability. Capitalizing on the interfacial coupling mediated by charge, strain, and polar symmetry, ferroelectric oxides have been utilized to modulate the electronic, magnetic, and optical properties of the neighboring materials.^4,10–14 Various emergent phenomena have been reported in ferroelectric oxide-based heterostructures, including polarization-controlled quantum phase transitions,^15,16 polar vortices,^17,18 negative capacitance mode,^19,20 enhanced polar alignment,^21,22 periodic domain structure imposed superlattices,²³ and unconventional nonlinear optical filtering effects.^24,25 The ability to synthesize single crystalline ferroelectric oxide membranes^26–29 and stack them with controlled twist angles²⁹ lifts the lattice constraints for building multifunctional heterointerfaces and opens up the opportunity to develop oxide-based twistronics. The advancements in the growth of crystalline ferroelectric perovskites on conventional semiconductors such as Si^30,31 and Ge³² herald the potential to integrate these emergent functionalities with the mainstream semiconductor industry.

In this feature article, we focus on two types of ferroelectric oxide-based heterostructures, the epitaxial complex oxide heterostructures and the ferroelectric thin films and membranes interfaced with two-dimensional (2D) van der Waals materials, discussing the basic synthesis methods and property characterization and surveying a range of interface phenomena and emerging functionalities. In Section 2, we discuss the synthesis and characterization of different types of heterostructures. Section 3 summarizes the effects of the interfacial layer on the ferroelectric properties of epitaxial oxide thin films and freestanding membranes. Section 4 focuses on the epitaxial ferroelectric oxide heterostructures, discussing the polarization control of the electronic and magnetic properties of correlated oxides, the ferroelectric-to-dielectric transition, domain formation, and transient NC effect in ferroelectric/dielectric oxide heterostructures, as well as related device concepts such as Mott FeFETs and all-oxide FTJs. Section 5 centers on the ferroelectric/2D van der Waals heterostructures, discussing the ferroelectric field effect, domain induced superlattice modulation, tuning of second harmonic generation, and enhanced polar alignment and piezoelectric response in 2D ferroelectrics, as well as highlighting the potential applications in electron lensing, NC FETs, and programmable nonlinear optical filters. Section 6 summarizes the research progress and provides an outlook on possible future directions, such as novel synthesis via remote epitaxy and oxide moiré engineering, incorporation of doped ferroelectric hafnia and zirconia, realization of topological properties, and functional design of oxygen octahedral rotation.

2. Materials synthesis and characterization

2.1 Epitaxial ferroelectric oxide heterostructures

The rapid development of advanced physical vapor deposition (PVD) techniques enables scalable growth of high quality epitaxial thin films of ferroelectric oxides. For perovskite transition metal oxides, their structural and chemical similarities allow the combination of ferroelectric oxides with various functional oxides, ranging from dielectrics to Mott insulators, magnets, and superconductors, into high-quality epitaxial heterostructures.¹¹ The atomic registration between interfacial constituent layers can not only eliminate dangling bonds, minimizing defect formation, but also enable novel lattice design via controlling lattice strain³³ and oxygen octahedral rotation.³⁴ In addition to the charge mediated coupling mechanism, strain-induced lattice distortion and migration of defects such as oxygen vacancies can also have a profound impact on the physical properties.

For epitaxial complex oxide thin film deposition, widely used PVD techniques³⁵ include molecular-beam epitaxy (MBE), pulsed laser deposition (PLD), and off-axis radio-frequency (RF) magnetron sputtering. In this paper, we center on the discussions of epitaxial ferroelectric thin films and heterostructures prepared via the off-axis RF magnetron sputtering approach. Examples include the ferroelectric/correlated oxide and ferroelectric/dielectric perovskite heterostructures. Compared with the MBE and PLD methods, magnetron sputtering has the advantages of low growth temperature, compatibility with industrial scale deposition, and low cost. The sputtering technique has recently been utilized to prepare polar nitride perovskites,³⁶ which broadens the class of materials viable for exploring polarization-based phenomena and device applications.³⁷ One limitation of the sputtering growth is that the strong magnetic field precludes the implementation of the reflection high-energy electron diffraction (RHEED) technique for in situ characterization of sample crystallinity and growth mode. Efforts have been made to incorporate RHEED into sputtering via special sputtering chamber design, such as adopting antisymmetric sputter sources.³⁸

The PVD techniques can yield single crystalline thin films and heterostructures with high crystallinity, atomically flat surfaces, and unit-cell-level precise control of film thickness. Fig. 2 shows the surface, structural, and chemical properties of ferroelectric PbZr_0.2Ti_0.8O₃ (PZT) interfaced with dielectric oxide SrTiO₃ (STO) and strongly correlated oxides such as RNiO₃ (RNO with R = Sm, Nd, or La) and La_0.67Sr_0.33MnO₃ (LSMO). These samples possess smooth surface morphology, as revealed by atomic force microscopy (AFM). Fig. 2(a) shows the AFM image taken on a 50 nm PZT/10 nm LSMO heterostructure deposited on a (001) STO substrate with a root-mean-square (RMS) roughness of 4–5 Å.²³ X-ray diffraction (XRD) measurements of these heterostructures reveal the (001) growth of all layers (Fig. 2(b) and (c)).^23,39Fig. 2(c) shows the XRD spectra taken on a series of PZT/STO heterostructures with about 100 nm total thickness deposited on 10 nm LaNiO₃ (LNO) buffered STO.³⁹ Regardless of the layer thickness, the c-axis of PZT is about 4.17 ± 0.1 Å, consistent with the strained value on STO, showing that epitaxial strain can sustain in 100 nm thickness films.

Fig. 2 Characterization of epitaxial PZT heterostructures. (a) AFM topography image and (b) XRD θ–2θ scan taken on 50 nm PZT/10 nm LSMO on (001) STO, with a fit to the Laue oscillations around the (001) peak of PZT (red line). Reproduced from ref. 23 with permission from American Physical Society, copyright 2024. (c) XRD θ–2θ scans taken on PZT/STO heterostructures with a total thickness of about 100 nm deposited on LNO buffered STO substrates with different PZT and STO layer thickness ratios (r = t_PZT/t_STO). (d) XRR performed on a PZT/STO heterostructure. Reproduced from ref. 39 with permission from American Physical Society, copyright 2021. (e) HRSTEM and (f) in-plane lattice constants of different layers normalized to that of STO substrate for a PZT/3 nm SNNO/2 nm LSMO heterostructure. Reproduced from ref. 40 with permission from Wiley-VCH GmbH, copyright 2017. (g) HRSTEM (left panel) and EELS element mapping performed on a PZT/3 uc LNO/3 uc LSMO heterostructure. Reproduced from ref. 41 with permission from Springer Nature, copyright 2023. (h) EELS line scans for five elements taken on the sample shown in (e) and (f). Reproduced from ref. 40 with permission from Wiley-VCH GmbH, copyright 2017.

Even though real-time monitoring of the growth rate is not available for these sputtered samples, the highly smooth sample surfaces/interfaces allow post-growth thickness characterization via either the Laue oscillations around the main Bragg peaks (Fig. 2(b) and (c))^23,39 or X-ray reflectivity (XRR) (Fig. 2(d))³⁹ measurements, which can be used to calibrate the deposition rate. Transmission electron microscopy (TEM) studies confirm that precise thickness control has been achieved. Fig. 2(e) shows the high-resolution scanning TEM (HRSTEM) image of a PZT/3 nm Sm_0.5Nd_0.5NiO₃ (SNNO)/2 nm LSMO heterostructure,⁴⁰ which reveals high crystallinity and atomically sharp interfaces. The in-plane lattice constant for each atomic layer has been deduced from the TEM data, confirming that the entire heterostructure is fully strained to the STO substrate (Fig. 2(f)).⁴⁰Fig. 2(g) shows the electron energy loss spectroscopy (EELS) elemental mapping of a PZT/1.2 nm LNO/1.2 nm LSMO heterostructure,⁴¹ showing that the interfaces are also chemically sharp. The line profiles of the EELS data (Fig. 2(h)) indicate that the diffusion of interfacial atoms is typically within one-to-two unit cell (uc) scale.^40,41

2.2 Free-standing ferroelectric oxide membranes

Recent developments in the synthesis of single crystalline complex oxide membranes^42,43 further broaden the material design portfolio for ferroelectric oxide-based heterostructures, opening up new avenues for exploring novel interface phenomena and achieving tailored functionalities.^{25,28,29,44–47} In particular, it is possible to construct heterostructures with the same constituents either in the epitaxial heterointerface form or via direct contact of membranes. Comparing the physical properties of these two types of systems helps differentiate the effects of electrostatic and mechanical boundary conditions on the ferroelectric instability in perovskite thin films. Building twisted ferroelectric oxide heterostructures further broadens the parameter space for engineering novel polar states,²⁹ which are not bound by the intrinsic crystal symmetry. Epitaxial ferroelectric oxide thin films can be suspended from the substrate via depositing on a water soluble layer such as Sr₃Al₂O₆ (SAO) (Fig. 3(a)) followed by water etching^28,42 or through selected chemical etching of a buffer layer such as (La,Sr)MnO₃.^29,44 The freestanding membranes can then be transferred on any designated base layer using Gel-Film²⁸ or PMMA⁴⁷ with precision control of position and orientation (Fig. 3(b)).

Fig. 3 Preparation and characterization of PZT membranes. (a) Schematic of a PZT/SAO heterostructure on STO. (b) Schematic of dry transfer of a PZT membrane on a designated base layer. (c) XRD θ–2θ scan and (d) AFM topography image taken on 50 nm PZT/20 nm SAO on (001) STO. (e) XRD θ–2θ scan of the same sample after water etching of the SAO layer. (f) AFM topography image a PZT flake transferred on a LSMO/STO base layer. Inset: Optical image of the flake. Reproduced from ref. 28 with permission from American Chemical Society, copyright 2023.

Fig. 3(c)–(f) compares the crystallinity and surface roughness of a 50 nm PZT film deposited on 20 nm SAO buffered STO before and after water-etching. The epitaxial heterostructure possesses single crystalline (001) PZT and SAO layers with no impurity phases (Fig. 3(c)) and smooth surface morphology with an RMS roughness of about 5 Å (Fig. 3(d)). After water-etching, the SAO peaks disappear, while the suspended PZT layer retains the crystallinity (Fig. 3(e)) and shows the same c-axis lattice constant of 4.15 Å, suggesting that the PZT membrane remains fully strained even after suspension from the substrate. Fig. 3(f) shows the AFM image of a 20 nm PZT membrane transferred on a LSMO/STO base layer. The flake exhibits clear ripples, with the RMS roughness (∼1 nm) significantly higher than the roughness of the base layer (∼4 Å) (Table 1). In contrast, the 20 nm PZT/10 nm LSMO membrane on LSMO/STO exhibits a surface roughness similar to the base layer, suggesting that atomic bonding with the LSMO layer effectively reduces rippling.

Table 1 Effect of the buffer/base layer on the properties of epitaxial PZT films, PZT membranes, and PZT/LSMO membranes. The T_C values are extracted from the thermal-quenching experiments performed on 50 nm PZT thin films and membranes. The data for epitaxial thin films are from ref. 48. The data for membranes are from ref. 28

Sample	Buffer/base layer	Surface roughness (film thickness) (nm)	E c (MV cm^−1)		T C (°C)
			P up	P down
Epitaxial PZT	LSMO	0.4 (50)	−0.5	+1.1	775 ± 25
	LaNiO3	0.2 (50)	−0.56	+0.38	738 ± 12
	SrIrO3	0.3 (50)	−0.1	+0.36	775 ± 25
PZT membrane	Au	2.0 (20)	−3.0	+1.7	763 ± 12
	LSMO	1.0 (20)	−1.70	+1.09	725 ± 25
	MoS2	0.3 (20)	−1.60	+0.75	588 ± 12
PZT/LSMO membrane	Au	0.8 (20)	−0.18	+0.74
	LSMO	0.5 (20)	−0.26	+0.28
	MoS2	0.4 (20)	−0.6	+1.01

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2.3 Ferroelectric oxide/2D van der Waals heterostructures

Integrating ferroelectric oxides with 2D van der Waals materials can enable functional design of the electronic, mechanical, and optical responses via ferroelectric field effect doping, strain modulation, and nanoscale domain control.^4,14 The van der Waals layers can be interfaced with single-crystalline^49–53 and polycrystalline ferroelectric thin films,^54–56 ferroelectric single crystals,^57,58 and ferroelectric oxide membranes.^{25,28,44–46} Compared with the epitaxial thin films, large-scale, low-cost synthesis of polycrystalline ferroelectric oxide films can be achieved by chemical vapor deposition (CVD) methods such as the metal–organic CVD⁵⁹ approach and the sol–gel method.⁶⁰ While these techniques are desirable for industrial processing, the polycrystalline samples exhibit compromised polarization and high density structural defects such as grain boundaries.

The 2D van der Waals layers can be prepared on the ferroelectric oxide substrates via direct mechanical exfoliation,^49,50 dry transfer,^23,25,28 or direct CVD growth.⁵⁸ The direct mechanical exfoliation method exploits adhesive tape to peel off 2D atomic layers from high-quality single crystals and lay the resulting flakes directly on the ferroelectric substrates.⁶¹ It preserves to the maximum extent the intrinsic properties of the 2D materials, while the limitations include low yield, lack of thickness control, presence of tape residue, and difficulty in identifying atomically thin flakes on ferroelectric oxides due to low optical contrast.^49,56 To increase the yield and flake size for mechanical exfoliation, substrate treatments with oxygen plasma⁶² or metal-film-coating⁶³ have been developed to enhance the interaction between the substrate and van der Waals materials. By pre-patterning interaction-enhanced regions, it is possible to have 2D vdW flakes directly exfoliated onto specific locations on the substrate, resulting in complex architectures unattainable with conventional exfoliation and dry-transfer methods. While these interaction-enhancement approaches have been successfully applied to a wide range of 2D materials to achieve up to millimeter-scale exfoliation,^62–65 they may alter the surface chemistry of the ferroelectric oxides or produce undesired interfacial layers, which compromise the device functionality.

In the dry-transfer method, viscoelastic polymer films such as polydimethylsiloxane (PDMS),⁶⁶ polypropylene carbonate (PPC),^67,68 and polycarbonate (PC)⁶⁹ serve as transfer stamps to pick up and drop down pre-prepared 2D vdW flakes, which facilitates precise positioning and stacking-order control for heterostructure fabrication. The pick-up and drop-down processes are controlled by adjusting the vitrification of polymer films at different temperatures, while the transfer process is guided by an actuated x–y–z–θ-stage, enabling sub-micron-scale precision in alignment and placement of 2D flakes on the oxide substrate, as well as control over interlayer twist angles. The dry nature of the transfer process ensures that the interface remains uncontaminated, as it avoids solvent exposure until the final cleaning step for removing polymer residues. Additionally, encapsulation with air-stable top layers such as hexagonal boron nitride (h-BN) protects the vdW surface from direct exposure to the ambient conditions, which is critical for preserving the intrinsic properties of 2D materials that are sensitive to moisture.⁷⁰

Bottom-up synthesis techniques, such as CVD, physical vapor transport, and MBE, have also been developed for fabricating 2D vdW flakes, thin films, and heterostructures.^71–73 For example, monolayer MoS₂ has been directly grown on a periodically poled LiNbO₃ substrate, which shows a preferred growth on the P_up domains.⁵⁸ It is conceivable that scalable synthesis of 2D vdW thin films directly on the ferroelectric substrate can facilitate the development of industrial applications of ferroelectric oxide/2D vdW heterostructures. A major material challenge is that most of these techniques involve high temperature synthesis in high/ultrahigh vacuum, which can exceed the structural phase transition temperatures of some widely used ferroelectric oxides (e.g., BaTiO₃)⁷⁴ and introduce oxygen vacancies,⁷⁵ therefore compromising the device performance.

3. Interface effects on ferroelectric properties

3.1 Epitaxial ferroelectric thin films

Various ferroelectric properties of ferroelectric oxide thin films, including polarization, E_c, T_C, and domain wall roughness and creep behaviors, have been investigated using electrical measurements and scanning probe microscopy. The results reveal the profound effects of electrostatic and mechanical boundary conditions on ferroelectricity and domain formation. Fig. 4(a) shows the characterization of polarization vs. electric field (P–E) loops taken on an Au/100 nm PZT/10 nm LaNiO₃ capacitor, where the polarization is calculated by integrating the charging and discharging current through the circuit upon polarization switching.³⁹ The deduced remanent polarization is about 78 μC cm⁻², consistent with those obtained from Hall effect measurements of epitaxial FeFETs.^41,76 The coercive field increases with increasing frequency (f) of the bias voltage (V_bias) wave, with E_c exhibiting a power-law dependence on f (Fig. 4(b)),³⁹ which can be well described by the domain nucleation and growth dominated polarization switching process.⁷⁷

Fig. 4 Ferroelectric properties of PZT thin films. (a) P–E loops at different V_bias frequencies, and (b) 2E_cvs. f for an Au/100 nm PZT/10 nm LaNiO₃ capacitor on STO. Reproduced from ref. 39 with permission from American Physical Society, copyright 2021. (c)–(f) PFM studies of a 50 nm PZT/10 nm LSMO heterostructure on STO. (c) PFM phase and (d) amplitude images of concentric square domains. (e) PFM amplitude and (f) phase switching hysteresis. Reproduced from ref. 48 with permission from American Physical Society, copyright 2021.

Conductive AFM and piezoresponse force microscopy (PFM) have been used to assess polarization switching, write/image domain structures, and quantify the piezoelectric coefficients. Fig. 4(c) and (d) shows the PFM images of concentric square domains written on a PZT/LSMO heterostructure via conductive AFM, which shows that the as-grown sample is uniformly polarized in the P_up state.⁴⁸Fig. 4(e) and (f) shows the PFM switching hysteresis taken on this sample, which reveals a smaller coercive voltage for the P_up state than that for the P_down state, consistent with the as-grown polarization, confirming that the P_up state is energetically favorable. The polarization asymmetry has been widely observed in epitaxial PZT thin films and depends sensitively on the choice of correlated oxide electrodes (Table 1).⁴⁸ Quantitatively analyzing the PFM amplitude response vs. V_bias below the coercive field can yield the piezoelectric coefficient.^21,22

PFM studies have also been utilized to assess T_C, polarization switching dynamics, and the static configuration of DWs in epitaxial ferroelectric thin films. Due to the compressive strain, epitaxial PZT thin films deposited on (001) SrTiO₃ substrates normally exhibit significantly higher T_C compared with the bulk value (T_C ∼ 450 °C⁷⁸). Fig. 5(a) shows the PFM images of stripe domains written on a PZT/LSMO heterostructure on SrTiO₃, where the sample has been heated at progressively higher temperatures and quenched rapidly to room temperature.⁴⁸ The domain structure remains stable after thermal-quench (TQ) cycles at temperatures of up to 600 °C. Bubble domains start to emerge at 650 °C, while the originally straight DWs become barely recognizable at 750 °C. Similar results have been observed in PZT films with LaNiO₃ and SrIrO₃ (SIO) bottom electrodes, showing that T_C for PZT strained on SrTiO₃ is above 700 °C (Table 1).⁴⁸ The high thermal stability makes epitaxial PZT thin films viable for high temperature applications.

Fig. 5 PFM characterization of ferroelectric perovskite oxide thin films. (a) PFM phase images of a domain structure in PZT/LSMO on STO at selected TQ temperatures. Reproduced from ref. 48 with permission from American Physical Society, copyright 2021. (b) PFM amplitude response vs. time with fits to t^−α taken on a 15 nm SZTO film on Ge. The power exponents are labelled. Adapted from ref. 32 with permission from American Chemical Society, copyright 2017. (c) DW roughness correlation relation B(L) vs. L for 50 nm PZT films on 10 nm correlate oxide electrodes. Inset: Schematic of a rough DW. (d) ζ vs. TQ temperature. (e) Schematic of thermally activated DW motion in a disorder energy landscape tilted by an external field. (f) Schematic ζ–T diagram. Reproduced from ref. 48 with permission from American Physical Society, copyright 2021.

For industrial applications, there has been extensive research interest in integrating ferroelectric perovskites with conventional semiconductors.^79,80 Besides canonical ferroelectrics such as PZT³⁰ and BaTiO₃,³¹ perovskite oxides that are non-ferroelectric in bulk such as STO⁸¹ and Sr(Zr,Ti)O₃ (SZTO)³² can develop a ferroelectric relaxor phase in strained thin films. Fig. 5(b) shows the PFM amplitude response of P_up and P_down domains patterned on a 15 nm SZTO film deposited on Ge. The amplitude signal relaxes initially with a power-law time dependence t^−α and then stabilizes at about 10 hours, remaining stable after 48 hours of domain writing. The exponents are α = 0.22 for the P_up state and α = 0.23 for the P_down state, which are consistent with strained STO that exhibits relaxor behavior.⁸²

Despite the similar T_C, the PZT films deposited on different correlated oxide electrodes exhibit distinct thermal evolution of DW roughness due to the collective contributions of interfacial screening condition and defect migration. For ferroelectrics, the DW roughness carries important information about the dimensionality, disorder type, and nature of interaction of the system,^83,84 which can be quantitatively assessed by calculating the correlation function of the relative transverse displacement (u) of two points along the DW separated by a distance L (Fig. 5(c) inset): , which averages over position and disorder distribution. Treating DW as an elastic manifold in a disordered medium, B(L) exhibits a power-law dependence on L, B(L) ∝ L^2ζ, where ζ is the roughness exponent. Previous PFM studies have shown that the DW roughening of epitaxial PZT thin films exhibits 2D random bond (RB) disorder dominated behavior with long range dipole interaction (ζ_2D,RB = 0.31) at room temperature⁸⁵ and evolves to a one-dimensional (1D) thermal roughening (ζ_1D,TF = 0.5) dominated behavior at high temperatures.^48,86 DW roughening due to 1D RB behavior (ζ_1D,RB = 2/3) has been theoretically predicted⁸⁷ but has been scarcely observed experimentally in epitaxial thin films, which can be affected by the artificial domain writing process, the ambient screening condition, and the relative energy and length scales of DW elasticity, thermal fluctuation, and disorder pinning.^87–90

In ref. 48, Wang et al. investigated the effect of the correlated oxide electrode on the thermal evolution of DW roughness in PZT. Fig. 5(d) shows ζ vs. TQ temperature for 50 nm PZT films deposited on SrTiO₃ buffered by 10 nm LSMO, LaNiO₃, and SrIrO₃ electrodes. For all samples, the ζ values exhibit 2D RB behavior at room temperature and approach 1D thermal roughening behavior close to T_C. The DW growth can be treated as the creep motion of particles in a disorder energy landscape, where thermal fluctuation promotes the de-trapping of DW from the local pinning potential (Fig. 5(e)). The transition temperatures where ζ starts to deviate from ζ_2D,RB (T_cr) and where ζ approaches ζ_1D,TF (T_th) correspond to the lower and higher bound of the pinning energy, respectively (Fig. 5(f)).⁴⁸ PZT on LSMO exhibits the highest transition temperatures, while PZT on SrIrO₃ exhibits the lowest, which can be attributed to the effects of lattice distortion and the oxygen migration induced interfacial biasing field. In the former mechanism, LSMO possesses the largest oxygen octahedral rotation and SrIrO₃ is the closest to the cubic structure that is closely matched with PZT.^91–94 For the latter, the oxygen migration energy is the lowest in LSMO and the highest in SrIrO₃, which can result in different trapping energies at the PZT interface.^95–98 For devices using ferroelectric domains as the information storage unit, the DW roughness determines how closely two bits can be placed without interfering with each other, its temperature response determines the thermal stability of the bit, and E_c determines the writing voltage. Understanding the effect of the electrode material is thus critical for designing the storage density, operation temperature, and energy consumption of PZT-based memory applications, as further illustrated in the ferroelectric membranes.

3.2 Ferroelectric membranes

In ref. 28, Wu et al. examined the E_c (Fig. 6(a) and (b)) and T_C (Fig. 6(c)) of PZT and PZT/LSMO membranes prepared on three types of base layers with distinct screening capacities and surface roughness, the metallic Au, correlated LSMO, and semiconducting MoS₂ (Table 1). For single-layer 20 nm PZT membranes, E_c is the highest on Au and lowest on MoS₂ (E_c(Au) > E_c(LSMO) > E_c(MoS₂)), which has been attributed to the change in membrane surface roughness and base layer screening capacity. The rippling of membranes induces a flexoelectric effect, which suppresses DW motion and enhances E_c.²⁶ The base layer with low conductivity can lead to a high depolarization field, suppress the ferroelectric double well energy, and thus reduce E_c. For comparison, the membranes of PZT/LSMO heterostructures possess a smoother surface morphology compared with the PZT membranes and exhibit significantly smaller E_c on the same type of base layer (Fig. 6(b)). Among these samples, the PZT/LSMO membrane on the LSMO base layer exhibits symmetric switching with the smallest average E_c value (Table 1). This is significantly lower than those of PZT membranes on LSMO and epitaxial PZT/LSMO heterostructures, despite the same screening electrode (LSMO), clearly illustrating the critical role of the mechanical boundary conditions (e.g., interface roughness and epitaxy) in determining the polarization switching dynamics.

Fig. 6 PFM characterization of PZT and PZT/LSMO membranes. (a) and (b) PFM phase and amplitude switching hysteresis taken on a 20 nm PZT membrane (a) and a 20 nm PZT/10 nm LSMO membrane (b) on LSMO base layers. (c) PFM phase images of stripe domains on a 50 nm PZT membrane on Au at selected TQ temperatures showing a T_C > 750 °C. Reproduced from ref. 28 with permission from American Chemical Society, copyright 2023.

Fig. 6(c) shows the PFM images of thermally quenched stripe domains written on a 50 nm PZT membrane on Au. For all three types of base layers, the PZT membranes exhibit enhanced T_C well exceeding the bulk value (Table 1), consistent with the XRD result showing that the membranes can retain the strain state (Fig. 3(c) and (e)). The membrane on MoS₂ possesses the lowest T_C (>575 °C), suggesting that the atomically smooth van der Waals type interface may facilitate strain relaxation. At room temperature, PZT membranes thicker than 10 nm and PZT/LSMO membranes on all types of base layers exhibit 2D RB disorder dominated behavior with ζ close to ζ_2D,RB (Fig. 7(a)). For the 10 nm PZT membrane on Au, ζ approaches ζ_1D,TF. As the Au film possesses the highest surface roughness, the rippled membrane is partially decoupled from the substrate, which may release it from interface-induced DW pinning, allowing 1D thermal fluctuation dominated DW roughening. Similar to that of epitaxial PZT films (Fig. 5(d)), ζ increases with increasing TQ temperatures (Fig. 7(b)). For the 50 nm PZT membrane on MoS₂, ζ increases to ζ_1D,TF at T_th ∼ 500 °C. Despite the much higher T_C, PZT membranes on LSMO and Au base layers exhibit a much lower T_cr. The ζ values quickly exceed ζ_1D,TF and approach ζ_1D,RB, suggesting a DW creep behavior within the quasi-equilibrium-nucleation model.⁸⁷ Such 1D RB disorder dominated DW roughness has not been observed in epitaxial PZT films at large length scales,⁸⁸ and the equilibrium configuration may be established in the PZT membranes due to partial decoupling from the LSMO and Au base layers. The distinct E_c and thermal evolution of DW roughness for PZT membranes on different base layers illustrate the convoluted effects of rippling induced flexoelectric effects, local strain distribution, interface induced DW pinning, and mobility of charged disorders in determining DW motion.²⁸

Fig. 7 DW roughness in PZT membranes. (a) ζ vs. PZT thickness at room temperature for PZT and PZT/LSMO membranes on different base layers. (b) ζ vs. TQ temperature for 50 nm PZT membranes on different base layers. Reproduced from ref. 28 with permission from American Chemical Society, copyright 2023.

4. Epitaxial ferroelectric oxide heterostructures

4.1 Ferroelectric/correlated oxide heterostructures

4.1.1 Ferroelectric polarization control of correlated transport. For a correlated oxide channel, a ferroelectric gate can be utilized to impose electric field effect doping, strain modulation, and interfacial orbital design, which are powerful means to tune the competing energy scales without introducing additional defect states.^10,11 It also facilitates the development of novel high density, energy-efficient electronic devices, such as Mott FeFETs^39,40 and all-oxide ferroelectric or multiferroic tunnel junctions.⁹⁹ The ferroelectric field effect has been exploited to tune the transport properties of a wide variety of correlated oxides. As shown in Fig. 8(a), switching the polarization of a ferroelectric top-gate can either accumulate or deplete charge carriers at the interfacial layer of the correlated oxide channel, which can induce conductivity modulation or even a metal–insulator transition. Fig. 8(b) shows the temperature dependence of sheet resistance R_□ of a 4 nm La_0.8Sr_0.2MnO₃ channel in both polarization states of the PZT gate. Switching the polarization leads to a nonvolatile shift of 25 K of resistance peak temperature,¹⁰⁰ which is related to the modulation of T_C.^15,101

Fig. 8 Ferroelectric field effect in PZT-gated correlated channels. (a) Device schematic. (b) R_□(T) of 4 nm La_0.8Sr_0.2MnO₃ on STO for both polarization states. Adapted from ref. 100 with permission from American Physical Society, copyright 2019. (c) R_□(T) of 2.5 nm and 4 nm SNNO channels on LaAlO₃ for both polarization states. Inset: Resistance on/off ratio vs. temperature. Reproduced from ref. 40 with permission from Wiley-VCH GmbH, copyright 2017. (d) R_□(T) of a 1.5 nm LaNiO₃ channel for both polarization states. (e) Resistance on/off ratio of single-layer RNiO₃ channels vs. channel thickness at 300 K. Adapted from ref. 41 with permission from Springer Nature, copyright 2023.

The optimal channel thickness for the ferroelectric field effect modulation is determined by the interfacial charge screening effect and electronic finite size effect. As switching the polarization field yields a fixed 2D density modulation, 2P = Δn_2D, the fractional change of 3D carrier density in the channel scales inversely with the channel thickness. On the other hand, the thickness scaling cannot be sustained when the film becomes electrically dead, a phenomenon widely observed in epitaxial correlated oxide thin films,^{16,41,102,103} as strongly localized charges cannot provide proper screening for the polarization field, which leads to poor retention behavior for the off state.^40,76Fig. 8(c) shows the R_□(T) of 4 nm and 2.5 nm Sm_0.5Nd_0.5NiO₃ devices for both polarization states of PZT.⁴⁰ At 300 K, the resistance switching ratio ΔR/R_on for the 2.5 nm channel is about one order of magnitude higher than that of the 4 nm SNNO. For 4 nm SNNO, ΔR/R_on exhibits a peak at 160 K, which is in the vicinity of the metal–insulator transition temperature. Such transition is absent in the 2.5 nm channel as it is below the electrical dead layer thickness. Close to the electrical dead layer thickness, it is possible to induce a carrier density-driven metal–insulator transition via the ferroelectric field effect.¹⁶Fig. 8(d) shows the R_□(T) of a 1.5 nm, or 4 uc, LaNiO₃ channel for both polarization states of the PZT gate. Bulk LaNiO₃ is a correlated metal, while the P_down state of PZT depletes holes from LaNiO₃ and induces an insulating state.⁴¹

Fig. 8(e) summarizes the channel thickness (t_RNO) dependence of ΔR/R_on at 300 K in single-layer RNiO₃ channels.⁴¹ NdNiO₃ (NNO), SNNO, and SmNiO₃ (SNO) are charge-transfer type Mott insulators with progressively lower charge itinerancy due to a higher degree of lattice distortion.^91,104 Despite the distinct metallicity, the LaNiO₃, NdNiO₃, and SNNO channels exhibit highly consistent exponential growth of ΔR/R_on with decreasing t_RNO until the electrical dead layer thickness is reached, clearly pointing to the interfacial charge screening scenario. LaNiO₃ possesses the smallest electrical dead layer thickness of about 2 uc, and the 2 uc LaNiO₃ channel exhibits the largest resistance modulation. The corresponding resistance on–off ratio is about 17, which is the highest room temperature value reported for oxide FeFETs with single-layer Mott channels.⁴¹ The maximum ΔR/R_on are smaller in NNO (2.5 uc channel) and SNNO (6.5 uc channel), which can be attributed to the larger electrical dead layer thicknesses. The field effect is negligibly small in SNO, which is insulating in bulk at 300 K. The channel thickness scaling behavior reflects the convoluted effects of carrier density modulation and charge itinerancy in determining the ferroelectric field effect, while strain-induced lattice distortion, interfacial lattice/orbital effects, and size-induced dimensionality crossover can all affect the metallicity of the system.^105–107 Understanding their impacts is critical for developing device applications such as the Mott FeFETs and all-oxide FTJs discussed below.

4.1.2 Interfacial charge engineering of high-performance Mott FeFETs. Mott FETs with metallic carrier density have been proposed as a promising device solution to transcend the size scaling limit of Si-based CMOS technology.^108,109 However, the sheet carrier density in nanoscale correlated oxide thin films can reach 10¹⁴–10¹⁶ cm⁻² in the metallic state, well exceeding the doping capacity of conventional dielectrics such as SiO₂ and HfO₂.⁴ Ferroelectric perovskites such as PZT provide a viable gate choice for Mott transistors as switching the polarization field corresponds to Δn_2D ∼ 1 × 10¹⁵ cm⁻² (Fig. 3(b)).^41,76 Moreover, the nonvolatile, voltage-controlled nature of FeFETs is desirable for energy-efficient device operation. Capitalizing on the high quality epitaxial heterointerface, all-perovskite FeFETs based on a correlated oxide channel has been extensively investigated over the last three decades for developing low-power electronic applications such as nonvolatile memories.¹¹⁰ The key challenges for practical implementation of this device concept is the competing material requirements for enhancing the resistance switching ratio and optimizing the device retention. As shown in Fig. 8(e), the channel thickness scaling of ΔR/R_on is limited by the electrical dead layer thickness, beyond which strong depolarization field causes severe polarization back-switching and fast relaxation of the resistance states,^40,76 compromising the field effect modulation. To date, the highest room temperature on–off ratio in a single-layer correlated channel is about 17, observed in 2 uc LaNiO₃.⁴¹

One solution to reduce the net carrier density in the Mott channel without causing severe depolarization in the ferroelectric gate is to exploit the charge transfer effect between two correlated oxides to create a tailored density profile in the Mott channel. It has been shown that inserting an LSMO buffer layer with intrinsically low carrier density in RNO₃-based Mott FeFETs can significantly enhance the resistance on–off ratio by orders of magnitude.^40,41 The interfacial charge transfer between RNiO₃ and LSMO corresponds to the valence change of Ni³⁺ + Mn³⁺ → Ni²⁺ + Mn⁴⁺. Fig. 9 shows the high-angle-annular-dark-field (HAADF) STEM image and EELS elemental mapping of Mn L spectra taken on a PZT/3 uc LNO/3 uc LSMO heterostructure. The atomic layer-by-atomic layer mapping of the Mn valence state (Fig. 9(c) and (d)) reveals about 0.7 eV shift of the Mn L₃ peak position, corresponding to 0.06 e⁻/Mn transfer from Mn to Ni ions. XAS and XPS studies also point to a charge transfer of 0.08–0.09 e⁻/Mn at the Sm_0.5Nd_0.5NiO₃/LSMO interface,⁴⁰ and the experimental results are well corroborated by density functional theory calculations.^40,41 The charge transfer effectively reduces the carrier density in RNiO₃ within 1–2 uc at the LNO/LSMO interface (Fig. 9(d)), while the high carrier density at the PZT/LNO interface is sustained.

Fig. 9 TEM characterization of a PZT/3 uc LNO/3 uc LSMO heterostructure. (a) Cross-sectional HRSTEM image. (b) EELS elemental mapping of Mn. (c) Layer-by-layer EELS spectra of the Mn L edge. The unit cell positions are labeled in (a). (d) Mn L₃ peak position (top) and L₃/L₂ intensity ratio (bottom) as a function of unit cell position. Adapted from ref. 41 with permission from Springer Nature, copyright 2023.

Fig. 10 compares the resistance switching of FeFETs with single-layer and bilayer correlated channels with similar total channel thickness. For a 4 uc LaNiO₃ channel (Fig. 10(a)) and a 3 uc LNO/1 uc LSMO channel (Fig. 10(b)), the resistance on/off ratio (r_off/on) in the bilayer channel is more than 40 times higher. Increasing the LNO single-layer channel thickness to 5 uc leads to smaller resistance modulation (Fig. 10(c)), as the bottom layer can be treated as a shunting resistor. On the other hand, the ferroelectric field effect in the LNO/LSMO bilayer cannot be modeled as parallel conduction of two independent channels. Increasing the LSMO layer thickness by 1 uc significantly enhances, rather than attenuates, the resistance modulation (Fig. 10(d)), clearly illustrating the effect of interface synergy between LNO and LSMO. Fig. 10(e) summarizes the ΔR/R_on of RNO/LSMO bilayer channels with different layer thickness combinations, which increases exponentially with decreasing total channel thickness (t_tot). The universal channel thickness scaling behavior for the Mott FeFETs with both single-layer and bilayer channels clearly testify to the interfacial screening nature of the ferroelectric field effect. For the same t_tot, r_off/on in the bilayer channel can be over two orders of magnitude higher than that of single-layer RNiO₃, pointing to a highly effective approach for designing the ferroelectric field effect. Fig. 10(f) compares the maximum room temperature ΔR/R_onvs. channel thickness (t_channel) obtained on epitaxial complex oxide FeFETs with different correlated oxide channels, including cuprate,^111,112 cobaltate,¹¹³ manganite,^16,114 ruthenate,¹¹⁵ single-layer nickelate,^40,41 and bilayer RNiO₃/LSMO^40,41 channels. The PZT/2.5 uc LNO/2 uc LSMO device exhibits a record high room temperature r_off/on of 385.4, well exceeding the state-of-the-art results for MRAM.¹¹⁶

Fig. 10 Room temperature resistance modulation in ferroelectric-gated LNO and LNO/LSMO channels. (a) and (b) R_□ switching upon pulsed gate voltage V_g taken on 4 uc LNO (a) and 4 uc LNO/1 uc LSMO (b) channels. (c) and (d) R_□vs. V_g switching hysteresis taken on 5 uc LNO (c) and 3 uc LNO/2 uc LSMO (d) channels. (e) ΔR/R_onvs. t_tot in RNO/LSMO channels, with the layer thickness in the unit of uc labeled. (f) Maximum ΔR/R_onvs. t_channel for various correlated oxide channels. Inset: ΔR/R_onvs. V_g switching hysteresis taken on a PZT/2.5 uc LNO/2 uc LSMO sample. Adapted from ref. 41 with permission from Springer Nature, copyright 2023.

For the bilayer channels, the presence of LSMO further provides an extended screening layer for minimizing the depolarization field in PZT, yielding excellent retention compared with the single-layer devices (Fig. 10(c) and (d)). For the 3 uc LNO/2 uc LSMO channel, r_off/on stabilizes at 55% of the initial value after a few hours (Fig. 11(a)).⁴¹ The cycling behavior shows a characteristic three-stage fatigue behavior consistent with previous reports of PZT thin films:¹¹⁷ (I) slow fatigue stage until 10⁶ cycles, (II) logarithmic stage until 10⁸ cycles, and (III) saturated stage settling at 76% of the initial value until 10¹⁰ cycles (Fig. 11(b)). The high frequency conductivity has been investigated by microwave impedance microscopy (MIM) (Fig. 11(c)), which shows that the on–off ratio is stable up to 1 GHz (Fig. 11(d)), confirming that the resistance switching originates from the modulation of carrier density rather than ionic defects (e.g., oxygen vacancies).¹¹⁸ The high on–off ratio,⁴¹ excellent retention and endurance,⁴¹ fast switching,¹¹³ robust high frequency response,¹¹⁸ and potential for constructing epitaxial three-dimensional architectures¹¹⁹ make the Mott FeFETs highly competitive for developing nonvolatile memories and neuromorphic computing, which can be potentially integrated with the main stream Si technology.^30–32

Fig. 11 Room temperature performance of RNiO₃-based Mott FeFETs. (a) Retention and (b) cycling behaviors of a PZT/3 uc LNO/2 uc LSMO sample. Reproduced from ref. 41 with permission from Springer Nature, copyright 2023. (c) MIM imaginary (top) and real (bottom) signal images (bottom) of a 3 uc LNO/2 uc LSMO channel underneath square domains of PZT, and (d) the extracted conductance on/off ratio vs. imaging frequency. Adapted from ref. 118 with permission from AIP Publishing, copyright 2024.

4.1.3 All-oxide ferroelectric tunnel junctions with correlated oxide electrodes. The device concept of ferroelectric tunnel junction has been intensively investigated in recent years for developing energy-efficient electronics and neuromorphic computing.^6,120 For FTJs adopting electrodes with different screening capacities, switching the ferroelectric polarization modifies the tunneling potential profile, leading to a nonvolatile electroresistance (ER).^121,122 Epitaxial complex oxide heterostructures are a promising platform for developing FTJs due to the high quality interface, precise thickness control, scalable growth, and high switching speed.¹²³ Critical considerations for designing all-oxide FTJs include the room temperature ER, which calls for strong potential asymmetry, and the retention behavior, as the depolarization effect is more severe in ultrathin ferroelectric oxide tunnel barriers close to the finite size limit. While semiconducting electrodes¹²⁴ or ferroelectric/dielectric composite tunnel barriers¹²⁵ have been adopted to produce high ER, these material choices provide insufficient interfacial screening and can lead to poor retention due to the strong depolarization effect. Working with correlated oxide electrodes with high carrier density can effectively minimize the depolarization field. The ER of correlated oxide-based FTJs, however, is often small due to the similar screening capacity of different correlated oxides.

In ref. 99, Zhang et al. showed that a giant room temperature ER can be achieved in all-oxide FTJs by pairing a correlated metal LaNiO₃ with a narrow bandgap Mott insulator Sr₃Ir₂O₇ as electrodes (Fig. 12(a) and (b)). Switching the PZT polarization in LaNiO₃/PZT/Sr₃Ir₂O₇ FTJs into the P_up and P_down states results in high (I_on) and low (I_off) tunneling current, respectively. At room temperature, the ER, defined as (I_on − I_off)/I_off, is 6500% (1000%) for the FTJ with 4 nm (2.8 nm) PZT barrier (Fig. 12(c)), which is one to three orders of magnitude higher than those of all-oxide FTJs with correlated oxide electrodes and similar tunnel barrier configurations (Fig. 12(d)).^126–128 The giant enhancement has been attributed to the polarization induced metal–insulator transition in the interfacial Sr₃Ir₂O₇, which is feasible as Sr₃Ir₂O₇ is a narrow-gap Mott insulator with a bandgap of about 0.1 eV,¹²⁹ leading to a highly asymmetric tunnel barrier energy profile for the P_up and P_down states (Fig. 12(e)). Moreover, Sr₃Ir₂O₇ exhibit moderate conductivity even in the insulating state, effectively reducing the depolarization field. For the FTJ with thicker (4 nm) barrier, no apparent relaxation has been observed in the tunneling conductance. At 100 K, the ER ratio increases to 1.62 × 10⁵% (1.46 × 10⁵%) for the FTJ with 4 nm (2.8 nm) PZT barrier (Fig. 12(c)), which has been attributed to the pyroelectric increase of ferroelectric polarization.²³ The larger coercive field and the suppressed on-state relaxation behavior even for the FTJ with ultrathin (2.8 nm) barrier are consistent with the suppressed domain wall depinning of PZT at low temperature.⁴⁸ The giant ER, nonvolatile reversible switching, and superb retention make the all-oxide FTJs with narrow bandgap Mott electrodes highly competitive for nonvolatile memory and neuromorphic computing applications.

Fig. 12 Fabrication and characterization of LaNiO₃/PZT/Sr₃Ir₂O₇ FTJs. (a) Device schematic. SIO: Sr₃Ir₂O₇. (b) Optical image of a sample patterned with four tunnel junctions. (c) Tunneling conductance G vs. writing voltage V_write at room temperature and 100 K for FTJs with 2.8 nm and 4 nm PZT barriers. (d) Room temperature ER vs. tunnel barrier thickness t for various all-oxide FTJs.^126–128 LCMO: (La,Ca)MnO₃. BTO: BaTiO₃. BSTO: (Ba,Sr)TiO₃. (e) Schematic band diagrams for the on and off states. Adapted from ref. 99 with permission from AIP Publishing, copyright 2024.

4.1.4 Ferroelectric polarization control of magnetism. For correlated oxides, the electronic state is closely intertwined with magnetism. The ferroelectric field effect is a powerful tool for identifying the individual contributions of charge, lattice, and defect effects in determining the magnetic properties.^10,11 It has been shown that in epitaxial ferroelectric/correlated oxide heterostructures, the polarization control of carrier density in the ultrathin correlated oxide channel can lead to the modulation of the magnetic T_C and magnetic anisotropy,^{92,100,130,131} which has been assessed by magneto-optics,¹³² X-ray spectroscopy,^131,133 and magnetotransport studies.^{15,92,100,130} The nonvolatile voltage-control of magnetism has been extensively studied for developing energy-efficient spintronics.^4,12,13

In ref. 100, Rajapitamahuni et al. demonstrated the manipulation of magnetic anisotropy energy (MAE) in 4 nm La_0.8Sr_0.2MnO₃ on (001) SrTiO₃via the ferroelectric field effect. For nanoscale magnetic materials, where the sample volume is too small for detection with conventional magnetometry, the anisotropic magnetoresistance (AMR) and planar Hall effect (PHE) are sensitive tools for assessing the magnetic state.^134,135 In the coherent rotation model, the PHE and AMR resistance are given by:¹³⁵

R_PHE = (R_‖ − R_⊥)sin φ cos φ,

R_AMR = R_⊥ + (R_‖ − R_⊥)cos² φ. (1)

Here, φ is the angle between the current and in-plane magnetization (Fig. 13(a)). Fig. 13(b) shows R_AMR and R_PHE taken on a PZT/4 nm La_0.8Sr_0.2MnO₃ heterostructure at 125 K as a function of the angle θ between current and the in-plane magnetic field. At high magnetic fields, the magnetization follows the field direction (φ ≈ θ), and R_AMR and R_PHE exhibit sinusoidal θ-dependence. At low magnetic fields, the MAE dominates the Zeeman energy, and the magnetization is pinned to the easy axis ([110] or [11̄0]). As a result, R_PHE exhibits two distinct resistance states with sharp switching behavior. The switching hysteresis between these two R_PHE states in magnetic fields closely resembles those of MRAM (Fig. 13(c)), offering a simple material design for magnetic memories based on a single-layer LSMO thin film.¹³⁵

Fig. 13 Effects of the field effect doping and strain on magnetic anisotropy in LSMO. (a)–(d) AMR and PHE in PZT/4 nm La_0.8Sr_0.2MnO₃ on STO. (a) Schematic measurement geometry. (b) θ-dependence of R_AMR and R_PHE at different magnetic fields. (c) R_PHE(H) at 125 K for both polarization states of PZT. (d) Normalized MAE vs. hole doping level x extracted from PZT/La_0.8Sr_0.2MnO₃ (open symbols) and single-layer La_1−xSr_xMnO₃ thin films (solid symbols). The dotted line illustrates the DFT modeled doping dependence. Adopted from ref. 100 with permission from American Physical Society, copyright 2019. (e) R_PHEvs. θ at 100 K taken on a 6 nm LSMO with half of the channel patterned into nano-stripes (250 nm width, 1.2 nm depth) perpendicular to I. The red dashed line is a fit to eqn (1). The blue solid lines illustrate the pinning of R_PHE. Reproduced from ref. 136 with permission from the Society of Photo-Optical Instrumentation Engineers (SPIE), copyright 2018.

Switching the ferroelectric polarization not only shifts the T_C of LSMO (Fig. 8(b)),^12,132,133 but also modulates the AMR and PHE.^92,100,130 For the 4 nm La_0.8Sr_0.2MnO₃, the resistance ratio between the two polarization states for R_AMR and R_PHE is about 3.5 ± 0.2 and independent of the magnetic field (Fig. 13(b)). The larger switching fields for R_PHE in the P_up state suggest the change in MAE (Fig. 13(c)). The MAE has been quantified by analyzing the angular dependence of R_PHE: the anisotropy field marks the critical magnetic field for aligning the magnetization to the field direction (φ ≈ θ).¹³⁷Fig. 13(d) shows the deduced E_MAE of the La_0.8Sr_0.2MnO₃ channel for both polarization states of PZT as well as single-layer La_1−xSr_xMnO₃ with x = 0.2 and 0.33. The field effect induced change of MAE agrees well with the doping induced modulation of d-orbital occupancy predicted via density functional theory (DFT) calculations. In contrast, the change in MAE for the chemically doped sample is smaller than that expected from the doping variation, which can be attributed to the chemical substitution induced strain effect: La_1−xSr_xMnO₃ with larger x possesses a smaller lattice constant and thus is subjected to larger tensile strain on SrTiO₃,¹⁰¹ which suppresses the in-plane MAE.¹⁰⁰ The strain effect on MAE has been leveraged to design the magnetocrystalline anisotropy in nanostructured La_0.67Sr_0.33MnO₃ thin films, where the top layers are patterned into periodic nano-stripes. The depth modulated regions host a large strain gradient, yielding giant enhancement of uniaxial magnetocrystalline anisotropy and multilevel resistance switching (Fig. 13(e)).^136,137 It is conceivable that combining the ferroelectric field effect with the nanostructured LSMO thin films can lead to novel magnetic memory devices with multilevel information storage unit and voltage-controlled switching.

4.2 Ferroelectric–dielectric oxide heterostructures

4.2.1 Ferroelectric-to-dielectric transition. For ferroelectrics, the free energy vs. polarization P exhibits a double well profile, where the ground states settle at a finite remnant polarization P_r (Fig. 14(a)). Polarization switching between different orientations requires an external field higher than the coercive field E_c, yielding a P–E hysteresis loop (Fig. 14(b)). When a ferroelectric is interfaced with a dielectric layer, the matching of displacement field results in strong depolarization, which reduces the double well energy and net polarization in the ferroelectric layer. By tuning the thickness ratio between the ferroelectric (FE) and dielectric (DE) layers, it is possible to induce a ferroelectric-to-dielectric phase transition in the FE/DE stack structure. In ref. 39, Hao et al. investigated the FE-to-DE transition in a series of epitaxial PZT/STO heterostructures with a total thickness of 100 nm by tuning the layer thickness ratio r = t_PZT/t_STO (Fig. 14(c)). The P–V loops show that the remanent polarization P_r of the PZT/STO stack decreases with decreasing r (Fig. 14(d)). Single-layer PZT exhibits a butterfly-shape of capacitance vs. V_bias (C–V) loop (Fig. 14(e)). In PZT/STO stacks with high PZT content, the butterfly first broadens, consistent with the higher E_c observed in the P–V loop (Fig. 14(d)), which can be attributed to the partial voltage drop across STO. With r further decreasing, the switching hysteresis in P–E and C–V loops gradually closes. There is a shoulder-like feature in the hysteresis for heterostructures with r = 9 and 6, reflecting the competition between the fast nuclear and growth process and the slower DW propagation upon emergence of a multidomain state.¹³⁸

Fig. 14 FE-to-DE transition in PZT/STO stacks. (a) and (b) Schematics of ferroelectric free energy density g vs. P (a) and P–E loop (b). The dotted lines represent the dielectric responses. (c) Schematic of a PZT/STO stack hosting a DW. (d) P–E loops and (e) effective dielectric constant vs. V_bias for PZT/STO stacks with different PZT/STO thickness ratios r. Reproduced from ref. 39 with permission from American Physical Society, copyright 2021.

Fig. 15(a) and (b) summarizes the P_r (a) and effective dielectric constant ε_eff = C[(t_PZT + t_STO)/ε₀A] (b) measured for PZT/STO and STO/PZT stacks with different r values.³⁹ Sharp quenching of P_r occurs at r = 7–8, indicating a FE-to-DE phase transition. Such a transition can be well described by the Landau–Ginzburg–Devonshire (LGD) theory incorporating domain formation (Fig. 14(c)), where the free energy density of the PZT/STO stack (Fig. 15(c)) is expressed as:

Here α, β, and γ are the Landau coefficients, which can be extracted by fitting the P–E loop of PZT (Fig. 4(a)), k is the DW coupling constant, and D is the displacement field. The three terms in eqn (2) describe the contributions from the ferroelectric layer, the dielectric layer, and the electrostatic energy associated with the applied electric field, respectively.

Fig. 15 Characterization and modeling of PZT/STO stacks. (a) 2P_rvs. 1/r for PZT/STO (open symbols) and STO/PZT (solid symbol) stacks. The dashed line is the simulation result using a single-domain model. (b) ε_effvs. 1/r for PZT/STO stacks. The dashed line indicates the dielectric constant for single-layer STO. (c) Simulated g(P) for PZT/STO stacks with different r within the single-domain model. Adapted from ref. 39 with permission from American Physical Society, copyright 2021. (d) Simulated free energy contour plot of PZT hosting a DW as functions of P₁ and P₂. Reproduced from ref. 139 with permission.

Under the single-domain conditions (D ≈ P and ∇P = 0), this model predicts a FE–DE transition at a critical thickness ratio r_c = 7.8, where P_r vanishes (Fig. 15(a)) and the free energy evolves from a double-well to a single energy minimum at P = 0 (Fig. 15(c)). Even though the simulated r_c agrees well with the experimental result (Fig. 15(a)), the residue hysteresis window and gradual decrease of P_r in PZT/STO stacks beyond r_c cannot be captured by the single-domain model.³⁹ The possible explanations include the contribution of STO, an incipient ferroelectric with nonzero P_r at high bias,⁸² and the emergence of a multidomain state between the FE and DE phases.^19,138,140Fig. 15(d) shows the simulated energy profile of PZT hosting a 180° DW between two polar domains with independent polarizations of P₁ and P₂ based on eqn (2).¹³⁹ Switching between the fully polarized single-domain states (two diagonal corners: P₁ = P₂ = ±P_r) can either go through the dielectric state (center point: P₁ = P₂ = 0) or detour to the off-diagonal local energy minima, which correspond to the multidomain state (both P₁ and P₂ are finite). For the PZT/STO stack, the off-diagonal points can evolve into global energy minimum in a certain range of r, preferring the multidomain state rather than the dielectric state. The slow DW motion during polarization switching results in residual P_r. This multidomain state can be suppressed by further reducing the ferroelectric content, and the PZT/STO stack eventually settles at a nonpolarized, dielectric state with entirely quenched P_r.

4.2.2 Transient negative capacitance effect. For ferroelectrics, the free energy profile in the vicinity of P = 0 exhibits a negative curvature (Fig. 14(a) and 15(c)), which corresponds to a negative slope in the P–E relation (Fig. 14(b)). It can be characterized as an effective negative capacitance. The NC effect has garnered intensive research interest as it can be leveraged to anchor steep-slope switching, or sub-60 mV decade⁻¹ room temperature subthreshold swing (SS), in transistors adopting a ferroelectric gate.^141,142 As shown in Fig. 15(b), for the PZT/STO stacks with certain layer thickness ratios (e.g., r = 1.5 and 1), the ε_eff values become higher than those of single-layer PZT (ε_PZT ≈ 90) and STO (ε_STO ≈ 120),³⁹ suggesting the existence of a steady-state NC mode in the ferroelectric layer. The negative curvature of the ferroelectric free energy has previously been assessed by evaluating the charge dynamics during polarization switching in ferroelectric capacitors, known as the transient NC effect.^143–145

Hao et al. investigated the transient NC effect in the PZT/STO stacks.³⁹ As shown in Fig. 16(a), when a square wave of source voltage (V_s) larger than the coercive voltage is applied to the PZT/STO stack with r = 8, the voltage across the capacitor (V_cap) exhibits a prominent damping during the initial charging (Fig. 16(a) and (b)), the characteristic behavior of the transient NC effect. In the Q–V curves deduced by integrating the charging current, an S-shape emerges (Fig. 16(c)), which is the direct manifestation of the NC mode (Fig. 15(c)). The voltage damping behavior and S-shape in Q–V gradually diminish with increasing STO content, becoming barely visible in the r = 6 sample (Fig. 16(c)), which is consistent with its vanishing ferroelectric order (Fig. 15(c)).

Fig. 16 Transient NC effect in PZT/STO stack capacitors. (a) Voltage across a PZT/STO capacitor with r = 8 (V_cap) upon applied square wave source voltage (V_s). Inset: Schematic experimental setup. (b) V_cap(t) in the transient NC regime (open symbols) for the r = 8 and 7 samples with fits to the KAI/NLS model (solid line) and LK model (dotted line). (c) Q_svs. V_cap in PZT/STO stacks with r = 8, 7, and 6. Adapted from ref. 39 with permission from American Physical Society, copyright 2021.

As shown in Fig. 16(b), the transient NC behavior in the PZT/STO stack cannot be described by the Landau–Khalatnikov (LK) dissipative model based on single-domain polarization switching.¹⁴⁶ Instead, the nucleation-limited-switching (NLS) model can quantitatively describe the fast V_cap damping followed by slow recovery.^146,147 Phenomenologically, this model considers polarization switching involving multiple independent nucleation sites, where the domain growth is constrained by defect pinning and grain size. The polarization switching within a single-domain region is characterized by the Kolmogorov–Avrami–Ishinashi (KAI) factor 1 − exp[−(t/t₀)ⁿ], where t₀ characterizes the time scale of DW propagation between different nucleation regions. Modeling the transient NC behavior using the KAI/NLS model reveals a narrow distribution of t₀ for the r = 8 sample, consistent with the single-domain scenario, and a notably broader distribution of t₀ for the r = 7 sample.³⁹ The latter points to a multidomain state, where the DW motion is hindered by the formation of quasi-static, soft DWs, resulting in heterogeneous switching dynamics across different switching regions with a large variation in t₀. The emergence of the multi-domain state can be utilized to anchor the steady-state NC effect, which is essential for the operation of NC-FETs, as illustrated in Section 5.1.3.

5. Ferroelectric oxide–2D van der Waals heterostructures

5.1 Ferroelectric field effect in van der Waals materials

5.1.1 Ferroelectric-gated van der Waals transistors. Compared with polymer and van der Waals ferroelectrics, the large polarization, high dielectric constant, and high T_C of ferroelectric oxides make them powerful gate materials for tuning the electronic and optical properties of 2D van der Waals materials, including graphene and transition metal dichalcogenides (TMDCs).^4,14 Combining the ferroelectric field effect with nanoscale domain control also enables local modulation of carrier densities, which can be utilized to impose the pn junction state and superlattice modulation.^23,57,148 On the other hand, the 2D material can serve as a sensitive tool to probe the polarization of ferroelectric thin films, which is challenging for conventional characterization methods due to the large leakage current. For example, Hall effect measurements have been conducted in monolayer (1L) graphene back-gated by Ba_0.6Sr_0.4TiO₃ (BSTO)^52,149 and PZT²³ thin films to examine the remnant polarization, coercive field, dielectric constant, and pyroelectric coefficients of the ferroelectric gates.

Fig. 17(a) shows the longitudinal resistivity ρ_xxvs. V_g at 2 K taken on a 1L graphene FET back-gated by a BSTO thin film, which exhibits switching hysteresis that is consistent with ferroelectric polarization doping.¹⁴⁹ The corresponding carrier density has been deduced from Hall measurements, n = 1/eR_H, where R_H is the Hall coefficient (Fig. 17(b)). Beyond the hysteresis window, BSTO behaves as a typical high-κ dielectric, with low temperature κ close to 100. Due to the efficient dielectric screening, the ferroelectric-gated graphene FETs exhibit high mobilities,⁴⁹ with a field effect mobility of up to 23 000 cm² V⁻¹ s⁻¹ and nonvolatile modulation of the quantum Hall effect (Fig. 17(c) and (d)) observed in BSTO-gated 1L graphene.^52,149

Fig. 17 Ferroelectric field effect in vdW FETs. (a)–(d) A 1L graphene FET with a BSTO back-gate. (a) ρ_xx(V_g) and (inset) σ vs. −n at 2 K. (b) 1/eR_Hvs. V_g at 2 K. Inset: ρ_xyvs. B at V_g = −1 V for up-sweep. Adapted from ref. 149 with permission from AIP Publishing, copyright 2022. (c) ρ_xx and (d) ρ_xyvs. V_g at 2 K and 9 T. Reproduced from ref. 52 with permission from American Chemical Society, copyright 2013. (e)–(g) A few-layer MoS₂ FET with an SiO₂ back-gate and a PZT membrane top-gate. (e) Device schematic. (f) Optical device image. (g) I_dsvs. V_bg at 300 K for the no poling, P_up, and P_down states of the PZT top-gate. (insets) PFM images of PZT (right) and device retention for the P_up and P_down states of PZT (bottom). Adapted from ref. 28 with permission from American Chemical Society, copyright 2023.

For 2D FETs back-gated by PZT and BSTO, the high temperature switching hysteresis is often opposite to that expected for ferroelectric polarization doping, known as an anti-hysteresis.^50,52,53 When the van der Waals layer is transferred on the ferroelectric oxide at temperatures below T_C, the bound charge on the ferroelectric surface is pre-screened by the ambient charged adsorbates⁵⁰ or surface defect states,⁵³ whose dynamic response to the applied electric field can over-screen the ferroelectric polarization and lead to the anti-hysteresis. To achieve appropriate switching hysteresis in 2D vdW FETs at room temperature, it is preferrable to exploit high-temperature transfer above T_C⁵³ or work with a top-gate geometry. In ref. 28, Wu et al. fabricated few-layer MoS₂ FETs sandwiched between a SiO₂ back-gate and a PZT membrane top-gate (Fig. 17(e) and (f)), using conductive AFM to switch PZT's polarization. These devices exhibit nonvolatile modulation of the source–drain current (I_ds) that agrees with ferroelectric polarization switching, with a current on–off ratio of up to 2 × 10⁵ and no apparent decay for 3 days at 300 K (Fig. 17(g)).

The ferroelectric oxides possess high dielectric constants (Fig. 14(e)), resulting in soft remote surface optical (RSO) phonon modes that can significantly impact the mobility of the 2D channel.^4,149–151Fig. 18(a) shows ρ_xx(T) at different carrier densities for a BSTO-gated 1L graphene FET.¹⁴⁹ Beyond the electron–hole puddle region, ρ_xx decreases upon lowering temperature due to phonon scattering, which can be well described by:

Here ρ₀(n) and ρ_LA(T,n) account for the scattering contributions from impurities and intrinsic longitudinal acoustic (LA) phonons in graphene, respectively. The RSO phonon scattering is captured by ρ⁽ⁱ⁾_RSO(T,n) ∝ (e^ħω_i/k_BT − 1)⁻¹, with four RSO phonon modes ħω_i = 15.1 meV, 35.8 meV, 57.9 meV, and 86.8 meV for BSTO. Modeling using eqn (3) shows that ρ_xx(T) is dominated by the LA phonon scattering below 80 K, yielding ρ_xx ∝ T, and the RSO phonon scattering at high temperatures. Fig. 18(b) summarizes the 300 K mobility limits of BSTO-gated graphene imposed by various phonon modes, revealing the dominant role of the 35.8 meV RSO phonon mode. The overall mobility limit is about 3 × 10⁴ cm² V⁻¹ s⁻¹ with weak density dependence, highly competitive compared to graphene gated by a conventional dielectric.¹⁵¹ The ability to sustain high mobility in the 2D channel means it is possible to combine the ferroelectric field effect with nanoscale domain patterning for constructing programmable junction states and inducing superlattice modulation in a 2D channel. The presence of domains also introduces a new functional entity, the ferroelectric DW, as a control knob for designing 2D FETs. Next, we discuss two examples of ferroelectric oxide gate-enabled phenomena and device concepts in van der Waals materials.

Fig. 18 Effect of RSO phonons on a BSTO-gated 1L graphene FET. (a) ρ_xx(T) at various hole doping levels with fits to eqn (3). (b) Mobility limit at 300 K imposed by the LA and four RSO phonon modes and the overall contribution (total). Reproduced from ref. 149 with permission from AIP Publishing, copyright 2022.

5.1.2 1D Graphene superlattice with high transport anisotropy. For graphene subjected to one-dimensional Kronig–Penney (KP) potential (Fig. 19(a)), its band structure becomes highly anisotropic, with enhanced Klein tunneling along the superlattice vector direction (ŝ) and flattened band perpendicular to ŝ.^152,153 There is intensive research interest in realizing the 1D graphene superlattice (GSL) in the high KP potential limit for achieving the electron lensing or supercollimation effects.^154,155 Experimentally, 1D KP potential has been imposed on graphene through modulated dielectric gates^156,157 and periodic domain patterning in ferroelectric gates.²³ In the former approach, the KP potential is limited by the gating capacity of the dielectrics, which is in the moderate regime (i.e., the scaled dimensionless KP potential up to , with V₀ the KP barrier, L the superlattice period, and v_F = 10⁸ cm s⁻¹, the Fermi velocity of graphene).¹⁵⁷ The dielectric thickness separating the gate electrode and graphene channel also leads to spatially dispersed potential profiles. In contrast, the ferroelectric domain approach can generate a step-like potential profile through direct contact with graphene, and the polarization doping of ferroelectric oxides such as PZT can be orders of magnitude higher than those of dielectric gates.

Fig. 19 PZT induced 1D graphene superlattice. (a) Schematic Kronig–Penney potential. (b) Sample schematic. (c) and (d) Optical images of an h-BN/graphene/PZT sample before (c) and after (d) the deposition of the Au top-gate electrode. (e) R_□(δn) for pristine graphene and a 1D GSL sample (L = 205 nm) in the R_xx configuration, with (f) R_xxvs. δn and B. (g) R_□(δn) for a 1D GSL sample (L = 199 nm) in the R_yy configuration, with (h) R_yyvs. δn and B. The dashed lines illustrate the modeled Landau fans, with the filling factors labeled. (i) Calculated band structure for 1D GSL with scaled dimensionless KP potent u = 90π. (j) Δn_DPvs. L with a fit (dashed line) on linear and (inset) semi-log scales. Adapted from ref. 23 with permission from American Physical Society, copyright 2024.

In ref. 23, Li et al. have achieved high KP potential (u ∼ 90π) in 1D GSL by fabricating graphene FETs sandwiched between an h-BN top-gate and a PZT back-gate with prepatterned stripe domains of period L = 200–300 nm (Fig. 19(b)–(d)).²³ A polarization doping difference of up to 3 × 10¹³ cm⁻² between the P_up and P_down states has been induced in graphene at low temperatures due to the pyroelectric effect, corresponding to a high KP potential of 0.9 eV. For the 1D GSL with ŝ parallel to the current direction (denoted as R_xx), two satellite Dirac points emerge in R_□vs. electron doping induced by the top-gate (δn) (Fig. 19(e)), indicating the formation of higher-order bands due to superlattice Brillouin zone folding. In magnetic fields, R_xx develops into three sets of Landau fans, originating from the original Dirac point and two satellite Dirac points (Fig. 19(f)). For the 1D GSL with ŝ perpendicular to the current direction (denoted as R_yy), R_□(δn) exhibits a single peak (Fig. 19(g)) and only one set of Landau fans (Fig. 19(h)), confirming the highly anisotropic magnetotransport properties of the 1D GSL.

For V₀ = 0.9 eV and L = 200 nm, the scaled dimensionless KP potential reaches u = 90π. The corresponding band structure exhibits a highly flattened band along k_y (E = ±ħv_F(k_x + 2Nπ/L)) with strongly suppressed Fermi velocity v_y ∼ 0.01 v_F (Fig. 19(i)). Experimentally, the relation between the average carrier density interval between two consecutive Dirac points and the superlattice period can be described by: Δn_DP = AL^β, with β = −1.18 ± 0.06 (Fig. 19(j)). This quasi-inverse relation is a hallmark of the 1D GSL in the high KP potential limit, and the proportionality constant A = 2/a₀ yields a₀ = 2.40 Å, which is in excellent agreement with the graphene lattice constant 2.46 Å.

5.1.3 Domain wall enabled 2D negative capacitance transistors. For semiconductor FETs, the gate voltage (V_g) required to change the channel source–drain current (I_d) by one order of magnitude, known as the subthreshold swing (SS), is given by: , where C_ch and C_g are the channel and gate capacitance, respectively. For a conventional dielectric gate with positive capacitance, the Boltzmann statistics impose a fundamental limit of SS ≈ 60 mV decade⁻¹ at 300 K. It has been proposed that the effective negative capacitance in a ferroelectric gate close to P = 0 (Fig. 14(a)) can be exploited to achieve steep-slope switching, or sub-60 mV decade⁻¹ SS at room temperature,^141,142 which can lead to energy-efficient logic devices with reduced operation voltage. Previous studies of NC-FETs have focused on utilizing a ferroelectric/dielectric stack gate to stabilize the steady-state NC mode,⁷ and it is challenging to quench the ferroelectric hysteresis and achieve steep-slope switching at low gate-voltage. In ref. 55, Song et al. showed that it is possible to leverage the metastable polar state in ferroelectric DWs to enable steep-slope switching in a MoS₂ based NC-FET at ultra-low V_g towards hysteresis-free operation. Fig. 20(a) shows the 300 K transfer curves (I_dvs. V_g) of a few-layer (FL) MoS₂ FET back-gated by polycrystalline PbZr_0.35Ti_0.65O₃, which exhibits a current switching ratio of up to 8 × 10⁶ over a small gate window of V_g = ±0.5 V that is below the coercive voltage V_c. The SS is below the Boltzmann limit over three decades of I_d for the forward V_g-sweep and over one decade of I_d for the backward V_g-sweep. The minimum SS for this device is SS_min = 37 mV decade⁻¹ and reaches SS_min = 9.7 mV decade⁻¹ in a bilayer MoS₂ FET at 300 K (Fig. 20(b)).

Fig. 20 DW enabled MoS₂ NC-FET gated by polycrystalline PbZr_0.35Ti_0.65O₃. (a) I_dvs. V_g of a few-layer MoS₂ FET at 300 K. Insets: Device schematic (top) and deduced SS vs. I_d (bottom). (b) I_dvs. V_g of a bilayer MoS₂ FET at 300 K. Insets: AFM image of the device (top) and deduced SS vs. I_d (bottom). (c) Average SS vs. T taken on 2 bilayer FETs and 3 FL FETs. The dashed lines in (a)–(c) indicate the Boltzmann limit. (d) Comparison of the room temperature current on/off ratio vs. operation voltage window ΔV_g for various NC-FETs and FeFETs with MoS₂ channels.^158–168 (e) Force field simulation of a flux-closure type domain structure (left) and the change of local polarization upon small bias below V_c (right) in PZT. (f) L-PFM images of a domain structure on PZT with progressively higher DC V_bias, with the DW position highlighted. (g) Areal density of DW length l_DW/A vs. V_bias extracted from (f) and SS_avgvs. V_g-scan range taken on bilayer MoS₂ FETs. Adapted from ref. 55 with permission from Springer Nature, copyright 2022.

Compared with conventional NC-FETs, these MoS₂-based NC-FETs exploit a single-layer polycrystalline PZT gate. The steep-slope switching and nearly hysteresis-free behavior at low V_g have been consistently observed in multiple bilayer and FL devices at different temperatures (Fig. 20(c)) and remain stable across different source–drain voltages and gate-voltage scan rates. The high I_on/I_off achieved over a small operation voltage window of ΔV_g = 0.75 V makes the device performance highly competitive compared with other MoS₂-based NC-FETs and FE-FETs (Fig. 20(d)).^158–168 This quasi-static NC mode has been attributed to the high density DWs in the polycrystalline PZT back-gate. Force field simulation shows that frustrated dipoles with flux-closure-type chiral rotation within the PZT DW can be polarized at an electric field well below E_c. It results in an abrupt jump in local polarization (Fig. 20(e)), which can quantitatively account for the steep-slope switching in surface MoS₂ at V_g = −0.25 V. While the 180° DW in bulk PZT is known to be of Ising type with unit-cell-scale width,¹⁶⁹ it has been shown that the flux-closure-type DW emerges in the presence of strong depolarization field, e.g., at the ferroelectric surfaces,¹⁷⁰ grain boundaries,¹⁷¹ and ferroelectric/dielectric interfaces.^19,20

The suppression of DW density at low bias voltage has been confirmed by PFM studies. Fig. 20(f) shows the lateral PFM (L-PFM) image of a polycrystalline PZT film, which hosts a high density of DWs at zero V_bias. The sample is subsequently imaged with progressively higher DC V_bias that is below V_c applied, which reveals a suppressed DW density with increasing V_bias. Studies of bilayer MoS₂ NC-FETs show that the SS_min increases monotonically with increasing V_g-range (Fig. 20(g)), which correlates well with the reduced DW areal density, pointing to the critical role of the metastable polar state in the DW in stabilizing the NC effect.

5.2 Ferroelectric oxide interfaced with polar 2D materials

5.2.1 Nonlinear optical tuning effect in PZT/MoS₂ heterostructures. Despite the intensive studies of the heterostructures composed of ferroelectric oxides and 2D transition metal dichalcogenides, previous work has mostly focused on charge mediated interface effects, i.e., ferroelectric field effect tuning of the electronic properties^4,14 and optical responses such as photoluminescence (PL) in 2D TMDCs.^{24,45,46,172,173} The polar nature of ferroelectric oxides, on the other hand, can lead to a strong nonlinear optical signal such as second harmonic generation (SHG). For example, polarized SHG signals have been observed at DWs of PZT, which has been attributed to the chiral dipole rotation induced in-plane polarization at the DW surface.^174,175 An even stronger tuning effect of both the intensity and polarization of SHG signals has been demonstrated recently by interfacing PZT thin films and membranes with a polar 2D TMDC, monolayer MoS₂ (Fig. 21(a)),^24,25 leveraging the interfacial coupling of the polar symmetry.

Fig. 21 Characterization of the PZT/1L MoS₂ heterostructure. (a) Schematic experimental setup. (b) PFM phase images of 1L MoS₂ transferred on a 50 nm PZT film prepatterned with square domains. (c) Room temperature PL spectra of 1L MoS₂ on the P_up and P_down domains shown in (b). Inset: PL mapping of the peak intensity (upper), width (middle), and position (lower) of 1L MoS₂ on P_up and P_down domains of PZT, with DW positions marked. (d) Fits to the PL spectra revealing the modulation of neutral excitons (A⁰) and negative trions (A⁻). Adapted from ref. 24 with permission from Springer Nature, copyright 2020.

Fig. 21(b)–(d) shows a 1L MoS₂ flake transferred on a 50 nm PZT film pre-patterned with square domains, which reveals nonvolatile tuning of the PL signal. The intensity areal ratio between the negative trions (A⁻) and neutral excitons (A⁰), extracted by fitting the PL spectra (Fig. 21(d)), suggests that the induced doping is dominated by the interfacial screening charge rather than ferroelectric polarization.²⁴ For (001) PZT thin films, normal-incidence light yields prominent SHG signals at the DW regions (Fig. 22(a)).²⁴ The light polarization of the SHG signal is perpendicular to the DW, which points to the presence of in-plane polarization at the Néel-type DWs, consistent with previous reports.^174,175 For 1L MoS₂/PZT heterostructures, there is a strong filtering effect of the SHG signal that depends on the relative alignment of polar axes as well as the measurement geometry.

Fig. 22 DW filtering of SHG signals at 1L MoS₂/PZT interfaces. (a) R-SHG mapping of a domain structure on PZT with no analyzer applied before (a) and after (b) the transfer of 1L MoS₂ on top. (c) Schematic of a flux-closure type polar rotation at the surface of a 180° DW. (d) Schematic of the polar alignment at a 1L MoS₂/PZT interface. The arrows mark the local polarization directions. Reproduced from ref. 24 with permission from Springer Nature, copyright 2020. (e) PFM phase image and (f) R-SHG mapping of a hexagonal domain on bare PZT, and (g) R-SHG mapping after a 1L MoS₂ transferred on top. The open arrows show the direction of the incident light polarization. The dashed (solid) arrows mark the polarization directions of the DWs (MoS₂). (h) Polar plots of normalized R-SHG intensity vs. ϕ taken at different DWs in (g) with fits to nonlinear electromagnetic theory (dashed lines). Reproduced from ref. 25 with permission from Wiley-VCH GmbH, copyright 2022.

Fig. 22(b) shows the SHG mapping of a 1L MoS₂/PZT heterostructure, where one of the polar axes of MoS₂ is aligned with the vertical DWs. In the reflected mode (R-SHG), the SHG signal is modulated at the DWs, remaining unchanged at the polar domains. The SHG signal on the horizental DWs shows alternating enhancement and suppression in intensity, which reflects the alignment between the polar axis of MoS₂ and the in-plane polarization of DW. DFT calculation shows that the in-plane polarization of a flux-closure type DW in PZT (Fig. 22(c)) is comparable with that of 1L MoS₂.²⁴ Combining these two can lead to about four times of the SHG intensity when the two polar axes are aligned and close to zero SHG intensity when they are anti-aligned (Fig. 22(d)).²⁴ The SHG signal on the the vertical DWs, on the other hand, cannot be differentiated from the background MoS₂, as the two polar axes are orthogonal to each other. The 1L MoS₂ can thus serve as an atomic-scale polarizer that can modulate the strength of the SHG signal based on its polar alignment with the DW. The modulation of the SHG strength and polarization can be quantitatively modeled using the nonlinear electromagnetic theory considering the coupling of second-order nonlinear optical susceptibility tensors for MoS₂ and PZT DW. As shown in Fig. 22(e)–(h), both the amplitude and polarization of the SHG signal can be tuned by varying the angle between the polar axes of MoS₂ and PZT DW, which have been well captured by theoretical modeling.²⁵

In the transmitted mode (T-SHG) for 1L MoS₂ on top of PZT thin films (MoS₂/PZT), the polar domain also exerts a strong tuning effect on the SHG signal (Fig. 23(a)). A similar effect has been observed in R-SHG for reversed sample geometry (PZT/MoS₂), i.e., with 1L MoS₂ underneath a PZT membrane (Fig. 23(b)). The coupling with the PZT polar domain leads to three-fold polarization of the SHG signal, or C_3v symmetry, with the intensity peaking along the zig-zag directions of MoS₂ (Fig. 23(c)–(h)). This is in sharp contrast to the C_6h symmetry observed in standalone MoS₂¹⁷⁶ and C_2v symmetry observed in R-SHG of 1L MoS₂/PZT heterostructures (Fig. 22(h)), which can be well explained by considering the coupling of second-order nonlinear optical susceptibility tensors for MoS₂ and PZT (Fig. 23(e) and (h)).²⁵ For the PZT/MoS₂ geometry, the domain structure in the top PZT membrane is reconfigurable, facilitating in operando device operation.

Fig. 23 Ferroelectric domain control of SHG signals. (a) Schematic of a 1L MoS₂/PZT thin film. (b) Schematic of PZT membrane/1L MoS₂. (c)–(e) T-SHG studies of MoS₂/PZT. (c) PFM phase image and (d) T-SHG mapping of a domain structure on MoS₂/PZT. The excitation laser power is 30 mW. (e) Polar plots of normalized T-SHG intensity vs. ϕ taken on the P_up and P_down domains in (d) with fits (solid lines). (f)–(h) R-SHG studies of PZT membrane/MoS₂. (f) PFM phase image and (g) R-SHG mapping of a domain structure on PZT/MoS₂. The excitation laser power is 7 mW. (h) Polar plots of normalized R-SHG intensity vs. ϕ taken on the P_up and P_down domains in (g) with fits (solid lines). Reproduced from ref. 25 with permission from Wiley-VCH GmbH, copyright 2022.

5.2.2 Enhanced polar alignment in van der Waals ferroelectrics. In addition to the coupling of polar symmetry, the interfacial synergy between the polar vdW materials and ferroelectric oxides can also be mediated by lattice. In ref. 22, Wang et al. reported controlled domain formation, enhanced ferroelectricity, and tunable piezoelectricity in thin CuInP₂S₆ (CIPS) flakes interfaced with PZT (Fig. 24(a)). The vdW ferroelectric CIPS has attracted intensive research interest in recent years due to large bandgap,¹⁷⁷ large out-of-plane polarization,¹⁷⁸ above room temperature T_C,¹⁷⁹ and stackable nature with other 2D vdW materials.¹⁴ Its unconventional quadruple energy well¹⁸⁰ also leads to negative piezoelectricity¹⁷⁸ and inter-correlated out-of-plane/in-plane polarization switching.¹⁸¹ Due to its high ionic conductivity,¹⁸² it is challenging to have an electric field well confined at the nanoscale in CIPS, which leads to diffusive DWs. As shown in Fig. 24(b), for 13–14 nm CIPS flakes on PZT, the polar domains fully conform to those prepatterned on PZT, in sharp contrast to the spontaneously formed small domains for CIPS of the same thickness on Si and Au base layers. The enhanced polar alignment only occurs in thin CIPS flakes, i.e., with thickness below 25 nm (Fig. 24(c)). In this region, the flake on PZT also exhibits an enhanced, positive piezoelectric coefficient d^CIPS₃₃, in contrast to the negative d^CIPS₃₃ for flakes on Si and Au (Fig. 24(d)), with the value increasing substantially with reducing CIPS thickness (Fig. 24(e)).

Fig. 24 Enhanced polar alignment in thin CIPS on PZT. (a) Sample schematic. (b) PFM phase images of 13–14 nm CIPS flakes transferred on PZT, Si, and Au base layers. (c) PFM phase and (inset) AFM topography images of CIPS flakes with various thickness transferred on a prepatterned domain structure on PZT. (d) Averaged d₃₃ for 14 nm CIPS on Au, Si, and PZT. (e) d^CIPS₃₃ of CIPS on PZT as a function of flake thickness. Adapted from ref. 22 with permission from American Chemical Society, copyright 2023.

The enhanced polar alignment and d^CIPS₃₃ in ultrathin CIPS flakes point to the interfacial coupling with the PZT underneath. The sign change of d^CIPS₃₃ further suggests that the sample is settled at the metastable state (MS) rather than the ground state (GS) of the quadruple energy well (Fig. 25(a) and (b)).¹⁷⁸ DFT calculations of the CIPS/PbTiO₃ heterointerface reveal a strain-induced lattice distortion in the interfacial CIPS layer, which results in a tilted free-energy profile that favors the anti-alignment between the polarization of CIPS and PbTiO₃ and settles at the metastable state (Fig. 25(b)).

Fig. 25 Interface tuning of ferroelectricity in CIPS via PZT. (a) and (b) Schematics of sulfur and copper ion arrangements (upper panels) and ferroelectric quadruple-well energy profiles (lower panels) for standalone CIPS (a) and CIPS on PbTiO₃ with polarization antialigned (b). (c) In situ PFM images at selected temperatures taken on 13 nm and 55 nm CIPS on PZT, corresponding to the red boxed areas in Fig. 24(c). (d) Monte Carlo simulations of the mean Cu position at different temperatures. Reproduced from ref. 22 with permission from American Chemical Society, copyright 2023.

The titled free energy well further enhances the ferroelectric ordering energy. Fig. 25(c) shows the in situ PFM images of CIPS on PZT at elevated temperatures. For the 55 nm flakes, the domain structure becomes blurred at 100 °C, suggesting that it is above T_C, which is consistent with the bulk value (T_C ∼ 42 °C).¹⁷⁹ For the 13 nm CIPS, T_C is substantially enhanced to above 200 °C. Monte Carlo simulations based on atomic positions of CIPS strained on PbTiO₃ predict a 63% increase of T_C compared with that of standalone CIPS (Fig. 25(d)), which is in excellent agreement with the experimental results.²² The enhanced polarization and T_C for thin CIPS on PZT, as well as their anti-aligned polarization, have been confirmed via in situ, temperature-dependent PL studies, which reveal an interface-strain induced lattice change in CIPS.¹⁸³ A similar enhancement of polar domain formation and the piezoelectric coefficient has been observed in the organolead trihalide perovskite CH₃NH₃PbI₃ interfaced with PZT,²¹ which has been attributed to the over-screened ferroelectric polarization induced dipole field that promotes the polar alignment in a polar liquid state of the hybrid perovskite.¹⁸⁴

6. Conclusions and perspectives

In this feature article, we use ferroelectric perovskite oxide-based heterostructures as model systems to illustrate various emergent phenomena mediated by interfacial coupling of charge, lattice, and polar symmetry. The discussion centers on epitaxial complex oxide heterostructures and ferroelectric thin films and membranes interfaced with 2D van der Waals materials. The electrostatic and mechanical boundary conditions have profound impacts on the polar properties of ferroelectric oxide thin films, leading to large variations in the ferroelectric Curie temperature and coercive field. The T_C of epitaxial ferroelectric films can be over 300 °C higher than the bulk value due to compressive strain. It is interesting to note that the strain level can be sustained in suspended oxide membranes after being transferred on a different base layer, and the properties of the base layer (e.g., surface roughness and bonding type) can affect the level of strain relaxation. The DW roughness and its thermal evolution have been systematically analyzed, which reveal the critical role of the base layer and the complex interplay of interfacial screening capacity, atomic bonding, surface morphology, and defect migration in determining the static distribution and dynamic response of the DW. The effect of the depolarization field is manifested in the ferroelectric–dielectric transition, transient negative capacitance mode, and domain formation in ferroelectric/dielectric heterostructures. The gained information is critical for understanding the polarization switching dynamics, domain size limit, and thermal stability and can facilitate the development of domain/DW-based memory and logic devices with high density, high speed, low power, and high operation temperature.

We also survey the coupling mechanisms and emergent functionalities of ferroelectric oxide-based heterointerfaces, including the ferroelectric field effect control of the electronic and magnetic states in correlated oxides and quantum transport in graphene, as well as the filtering effect of nonlinear optical response of MoS₂via ferroelectric polarization and DWs. Nanoscale domain patterning further allows the design of 1D graphene superlattices and programmable second harmonic generation in ferroelectric/MoS₂ heterostructures. The interfacial strain coupling with ferroelectric thin films have been leveraged to enhance the polar alignment, piezoelectric response, and T_C in ultrathin 2D ferroelectric CIPS flakes. Various emerging device concepts have been discussed, including Mott FeFETs, ferroelectric tunnel junctions, steep slope NC FETs, electron lensing devices, and in operando nonlinear optical filters, highlighting their application potential in high performance, reconfigurable nanoelectronics, optoelectronics, and nano-photonics.

Our discussions showcase the rich functionalities and high application potential of ferroelectric perovskite oxide-based heterostructures. Looking forward, we outline several potential research directions that can broaden the research portfolio based on functional design of ferroelectric oxide heterostructures.

Novel materials synthesis

For technological applications of ferroelectric oxide-gated 2D vdW FETs, it is essential to develop a scalable synthesis method and CMOS-compatible device architectures. In previous studies of 2D FeFETs, ferroelectric oxides are mainly adopted as a global back-gate.⁴ Converting to a top-gate device structure involves dry-transfer of ferroelectric membranes,²⁸ which requires multiple fabrication steps and is not scalable. The recently developed remote epitaxy technique builds on MBE and laser MBE growth of complex oxide thin films (e.g., SrTiO₃¹⁸⁵ and BaTiO₃¹⁸⁶) on substrates buffered with porous graphene, which can be extended to other vdW buffer materials for achieving multifunctional ferroelectric heterointerfaces.

Oxide moiré engineering^29,187 based on stacking and twisting oxide membranes has attracted enormous research interest as it provides a new material platform for exploring functionalities not expected in the single-phase nano-materials, as demonstrated in the van der Waals moiré systems.¹⁸⁸ Unlike the van der Waals materials, which are layered by nature, the transition metal oxides are based on semi-ionic/semi-covalent bonds. This attribute both imposes challenges in materials processing, e.g., for stabilizing small twisting angle phases that are thermodynamically highly unstable, and offers new opportunities capitalizing on the stronger interface interaction and potential modulation for band reconstruction. Experimentally, novel 2D polar vortex patterns have been observed in twisted BaTiO₃.²⁹ It is further conceivable to design novel polar states and magnetism in twisted oxides that are neither polar nor magnetic. The appearance of vortex–antivortex polarization and doping-induced unconventional d⁰ magnetism has been theoretically predicted in twisted SrTiO₃ bilayers,¹⁸⁹ making it promising for realizing a multiferroic state that is controllable via the electric field effect.

Incorporation of binary ferroelectric oxides

Binary ferroelectric oxides such as doped HfO₂ and ZrO₂ are compatible with the mainstream CMOS processing and have high potential for industrial applications.¹⁹⁰ Single crystalline doped HfO₂ has been recently demonstrated,¹⁹¹ and it offers the opportunity to investigate ferroelectricity from a new material perspective. Specifically, this class of ferroelectrics exhibit high sensitivity to surface chemistry,^192,193 possess scale-free DWs,¹⁹⁴ and are potentially immune to the depolarization effect.¹⁹⁵ It is of both fundamental and technological interest to construct HfO₂-based heterostructures and understand how the interfacial electrode would affect the ferroelectric order parameter, polarization switching dynamics, and DW configurations.

Theory-driven material discovery and functionality design

The rapid development of DFT-based computational material search, especially enabled by machine-learning, offers unforeseeable research opportunities to design novel ferroelectric oxides and heterostructures with tailored functionalities. One direction of interest is to design ferroelectric oxide with non-trivial topology properties. It has been theoretically shown that noncentrosymmetric BiInO₃ is ferroelectric and can host persistent spin texture, a momentum-independent spin configuration that can be coupled with the ferroelectric polarization,¹⁹⁶ while the polar phase BiInO₃ remains to be realized experimentally.^197,198 Also of interest is to impose polar symmetry and modulate the electronic and magnetic states in perovskites by designing the oxygen octahedral rotation through epitaxial strain and superlattice engineering.^199,200 This approach has been adopted to stabilize a BiFeO₃-like structure²⁰¹ and anchor room temperature ferroelectricity in CaTiO₃.³⁴

Data availability

There are no new data generated in this work.

Conflicts of interest

The authors have no conflicts to disclose.

Acknowledgements

This work is supported by the National Science Foundation through EPSCoR RII Track-1: Emergent Quantum Materials and Technologies (EQUATE), award no. OIA-2044049 and DMREF award no. DMR-2118828, the UNL Grand Challenges catalyst award entitled Quantum Approaches addressing Global Threats, and the Nebraska Center for Energy Sciences Research.

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