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1.
Nature ; 2024 Aug 14.
Artigo em Inglês | MEDLINE | ID: mdl-39143222

RESUMO

Antiferromagnetic spintronics1,2 shows great potential for high-density and ultrafast information devices. Magnetic tunnel junctions (MTJs), a key spintronic memory component that are typically formed from ferromagnetic materials, have seen rapid developments very recently using antiferromagnetic materials3,4. Here we demonstrate a twisting strategy for constructing all-antiferromagnetic tunnel junctions down to the atomic limit. By twisting two bilayers of CrSBr, a 2D antiferromagnet (AFM), a more than 700% nonvolatile tunnelling magnetoresistance (TMR) ratio is shown at zero field (ZF) with the entire twisted stack acting as the tunnel barrier. This is determined by twisting two CrSBr monolayers for which the TMR is shown to be derived from accumulative coherent tunnelling across the individual CrSBr monolayers. The dependence of the TMR on the twist angle is calculated from the electron-parallel momentum-dependent decay across the twisted monolayers. This is in excellent agreement with our experiments that consider twist angles that vary from 0° to 90°. Moreover, we also find that the temperature dependence of the TMR is, surprisingly, much weaker for the twisted as compared with the untwisted junctions, making the twisted junctions even more attractive for applications. Our work shows that it is possible to push nonvolatile magnetic information storage to the atomically thin limit.

2.
Nature ; 613(7945): 656-661, 2023 01.
Artigo em Inglês | MEDLINE | ID: mdl-36653455

RESUMO

Domain-wall nanoelectronics is considered to be a new paradigm for non-volatile memory and logic technologies in which domain walls, rather than domains, serve as an active element. Especially interesting are charged domain walls in ferroelectric structures, which have subnanometre thicknesses and exhibit non-trivial electronic and transport properties that are useful for various nanoelectronics applications1-3. The ability to deterministically create and manipulate charged domain walls is essential to realize their functional properties in electronic devices. Here we report a strategy for the controllable creation and manipulation of in-plane charged domain walls in BiFeO3 ferroelectric films a few nanometres thick. By using an in situ biasing technique within a scanning transmission electron microscope, an unconventional layer-by-layer switching mechanism is detected in which ferroelectric domain growth occurs in the direction parallel to an applied electric field. Based on atomically resolved electron energy-loss spectroscopy, in situ charge mapping by in-line electron holography and theoretical calculations, we show that oxygen vacancies accumulating at the charged domain walls are responsible for the domain-wall stability and motion. Voltage control of the in-plane domain-wall position within a BiFeO3 film gives rise to multiple non-volatile resistance states, thus demonstrating the key functional property of being a memristor a few unit cells thick. These results promote a better understanding of ferroelectric switching behaviour and provide a new strategy for creating unit-cell-scale devices.

3.
Nature ; 570(7759): 87-90, 2019 06.
Artigo em Inglês | MEDLINE | ID: mdl-31168106

RESUMO

Two-dimensional (2D) materials such as graphene and transition-metal dichalcogenides reveal the electronic phases that emerge when a bulk crystal is reduced to a monolayer1-4. Transition-metal oxide perovskites host a variety of correlated electronic phases5-12, so similar behaviour in monolayer materials based on transition-metal oxide perovskites would open the door to a rich spectrum of exotic 2D correlated phases that have not yet been explored. Here we report the fabrication of freestanding perovskite films with high crystalline quality almost down to a single unit cell. Using a recently developed method based on water-soluble Sr3Al2O6 as the sacrificial buffer layer13,14 we synthesize freestanding SrTiO3 and BiFeO3 ultrathin films by reactive molecular beam epitaxy and transfer them to diverse substrates, in particular crystalline silicon wafers and holey carbon films. We find that freestanding BiFeO3 films exhibit unexpected and giant tetragonality and polarization when approaching the 2D limit. Our results demonstrate the absence of a critical thickness for stabilizing the crystalline order in the freestanding ultrathin oxide films. The ability to synthesize and transfer crystalline freestanding perovskite films without any thickness limitation onto any desired substrate creates opportunities for research into 2D correlated phases and interfacial phenomena that have not previously been technically possible.

4.
Nat Mater ; 22(5): 591-598, 2023 May.
Artigo em Inglês | MEDLINE | ID: mdl-37012436

RESUMO

Large spin-orbit torques (SOTs) generated by topological materials and heavy metals interfaced with ferromagnets are promising for next-generation magnetic memory and logic devices. SOTs generated from y spin originating from spin Hall and Edelstein effects can realize field-free magnetization switching only when the magnetization and spin are collinear. Here we circumvent the above limitation by utilizing unconventional spins generated in a MnPd3 thin film grown on an oxidized silicon substrate. We observe conventional SOT due to y spin, and out-of-plane and in-plane anti-damping-like torques originated from z spin and x spin, respectively, in MnPd3/CoFeB heterostructures. Notably, we have demonstrated complete field-free switching of perpendicular cobalt via out-of-plane anti-damping-like SOT. Density functional theory calculations show that the observed unconventional torques are due to the low symmetry of the (114)-oriented MnPd3 films. Altogether our results provide a path toward realization of a practical spin channel in ultrafast magnetic memory and logic devices.

5.
Phys Rev Lett ; 133(3): 036202, 2024 Jul 19.
Artigo em Inglês | MEDLINE | ID: mdl-39094151

RESUMO

Ferroelectric hafnia-based thin films have attracted significant interest due to their compatibility with complementary metal-oxide-semiconductor technology (CMOS). Achieving and stabilizing the metastable ferroelectric phase in these films is crucial for their application in ferroelectric devices. Recent research efforts have concentrated on the stabilization of the ferroelectric phase in hafnia-based films and delving into the mechanisms responsible for this stability. In this study, we experimentally demonstrate that stabilization of the ferroelectric phase in Hf_{0.5}Zr_{0.5}O_{2} (HZO) can be controlled by the interfacial charge transfer and the associated hole doping of HZO. Using the meticulously engineered charge transfer between an La_{1-x}Sr_{x}MnO_{3} buffer layer with variable Sr concentration x and an HZO film, we find the optimal x=0.33 that provides the required hole doping of HZO to most efficiently stabilize its ferroelectric phase. Our theoretical modeling reveals that the competition of the hole distribution between the threefold and fourfold coordinated oxygen sites in HZO controls the enhancement or reduction of the ferroelectric phase. Our findings offer a novel strategy to stabilize the ferroelectric phase of hafnia-based films and provide new insights into the development of ferroelectric devices compatible with CMOS.

6.
Nano Lett ; 23(9): 3781-3787, 2023 May 10.
Artigo em Inglês | MEDLINE | ID: mdl-37115910

RESUMO

van der Waals (vdW) assembly of two-dimensional (2D) materials allows polar layer stacking to realize novel properties switchable by the induced electric polarization. Here, based on symmetry analyses and density-functional calculations, we explore the emergence of the anomalous Hall effect (AHE) in antiferromagnetic MnBi2Te4 films assembled by polar layer stacking. We demonstrate that breaking P̂T̂ symmetry in an MnBi2Te4 bilayer produces a magnetoelectric effect and a spontaneous AHE switchable by electric polarization. We find that reversible polarization at one of the interfaces in a three-layer MnBi2Te4 film drives a metal-insulator transition, as well as switching between the AHE and quantum AHE (QAHE). Finally, we predict that engineering interlayer polarization in a three-layer MnBi2Te4 film allows converting MnBi2Te4 from a trivial insulator to a Chern insulator. Overall, our work emphasizes the topological properties in 2D vdW antiferromagnets induced by polar layer stacking, which do not exist in a bulk material.

7.
Nat Mater ; 21(8): 903-909, 2022 Aug.
Artigo em Inglês | MEDLINE | ID: mdl-35761058

RESUMO

Ferroelectric HfO2-based materials hold great potential for the widespread integration of ferroelectricity into modern electronics due to their compatibility with existing Si technology. Earlier work indicated that a nanometre grain size was crucial for the stabilization of the ferroelectric phase. This constraint, associated with a high density of structural defects, obscures an insight into the intrinsic ferroelectricity of HfO2-based materials. Here we demonstrate that stable and enhanced polarization can be achieved in epitaxial HfO2 films with a high degree of structural order (crystallinity). An out-of-plane polarization value of 50 µC cm-2 has been observed at room temperature in Y-doped HfO2(111) epitaxial thin films, with an estimated full value of intrinsic polarization of 64 µC cm-2, which is in close agreement with density functional theory calculations. The crystal structure of films reveals the Pca21 orthorhombic phase with small rhombohedral distortion, underlining the role of the structural constraint in stabilizing the ferroelectric phase. Our results suggest that it could be possible to exploit the intrinsic ferroelectricity of HfO2-based materials, optimizing their performance in device applications.

8.
Phys Rev Lett ; 131(24): 246301, 2023 Dec 15.
Artigo em Inglês | MEDLINE | ID: mdl-38181146

RESUMO

Valleytronics is a research field utilizing a valley degree of freedom of electrons for information processing and storage. A strong valley polarization is critical for realistic valleytronic applications. Here, we predict a tunneling valley Hall effect (TVHE) driven by tilted Dirac fermions in all-in-one tunnel junctions based on a two-dimensional (2D) valley material. Different doping of the electrode and spacer regions in these tunnel junctions results in momentum filtering of the tunneling Dirac fermions, generating a strong transverse valley Hall current dependent on the Dirac-cone tilting. Using the parameters of an existing 2D valley material, we demonstrate that such a strong TVHE can host a giant valley Hall angle even in the absence of the Berry curvature. Finally, we predict that resonant tunneling can occur in a tunnel junction with properly engineered device parameters such as the spacer width and transport direction, providing significant enhancement of the valley Hall angle. Our work opens a new approach to generate valley polarization in realistic valleytronic systems.

9.
Phys Rev Lett ; 131(22): 226802, 2023 Dec 01.
Artigo em Inglês | MEDLINE | ID: mdl-38101373

RESUMO

HfO_{2}-based ferroelectric thin films are promising for their application in ferroelectric devices. Predicting the ultimate magnitude of polarization and understanding its switching mechanism are critical to realize the optimal performance of these devices. Here, a generalized solid-state variable cell nudged elastic band method is employed to predict the switching pathway associated with domain-wall motion in (Hf,Zr)O_{2} ferroelectrics. It is found that the polarization reversal pathway, where threefold coordinated O atoms pass across the nominal unit-cell boundaries defined by the Hf/Zr atomic planes, is energetically more favorable than the conventional pathway where the O atoms do not pass through these planes. This finding implies that the polarization orientation in the orthorhombic Pca2_{1} phase of HfO_{2} and its derivatives is opposite to that normally assumed, predicts the spontaneous polarization magnitude of about 70 µC/cm^{2} that is nearly 50% larger than the commonly accepted value, signifies a positive intrinsic longitudinal piezoelectric coefficient, and suggests growth of ferroelectric domains, in response to an applied electric field, structurally reversed to those usually anticipated. These results provide important insights into the understanding of ferroelectricity in HfO_{2}-based ferroelectrics.

10.
Phys Rev Lett ; 130(12): 126801, 2023 Mar 24.
Artigo em Inglês | MEDLINE | ID: mdl-37027865

RESUMO

The increasing miniaturization of electronics requires a better understanding of material properties at the nanoscale. Many studies have shown that there is a ferroelectric size limit in oxides, below which the ferroelectricity will be strongly suppressed due to the depolarization field, and whether such a limit still exists in the absence of the depolarization field remains unclear. Here, by applying uniaxial strain, we obtain pure in-plane polarized ferroelectricity in ultrathin SrTiO_{3} membranes, providing a clean system with high tunability to explore ferroelectric size effects especially the thickness-dependent ferroelectric instability with no depolarization field. Surprisingly, the domain size, ferroelectric transition temperature, and critical strain for room-temperature ferroelectricity all exhibit significant thickness dependence. These results indicate that the stability of ferroelectricity is suppressed (enhanced) by increasing the surface or bulk ratio (strain), which can be explained by considering the thickness-dependent dipole-dipole interactions within the transverse Ising model. Our study provides new insights into ferroelectric size effects and sheds light on the applications of ferroelectric thin films in nanoelectronics.

11.
Phys Rev Lett ; 130(21): 216702, 2023 May 26.
Artigo em Inglês | MEDLINE | ID: mdl-37295086

RESUMO

Ferromagnets are known to support spin-polarized currents that control various spin-dependent transport phenomena useful for spintronics. On the contrary, fully compensated antiferromagnets are expected to support only globally spin-neutral currents. Here, we demonstrate that these globally spin-neutral currents can represent the Néel spin currents, i.e., staggered spin currents flowing through different magnetic sublattices. The Néel spin currents emerge in antiferromagnets with strong intrasublattice coupling (hopping) and drive the spin-dependent transport phenomena such as tunneling magnetoresistance (TMR) and spin-transfer torque (STT) in antiferromagnetic tunnel junctions (AFMTJs). Using RuO_{2} and Fe_{4}GeTe_{2} as representative antiferromagnets, we predict that the Néel spin currents with a strong staggered spin polarization produce a sizable fieldlike STT capable of the deterministic switching of the Néel vector in the associated AFMTJs. Our work uncovers the previously unexplored potential of fully compensated antiferromagnets and paves a new route to realize the efficient writing and reading of information for antiferromagnetic spintronics.

12.
Nano Lett ; 22(8): 3349-3355, 2022 Apr 27.
Artigo em Inglês | MEDLINE | ID: mdl-35380845

RESUMO

Magnetic skyrmions are chiral nanoscale spin textures which are usually induced by the Dzyaloshinskii-Moriya interaction (DMI). Recently, magnetic skyrmions have been observed in two-dimensional (2D) van der Waals (vdW) ferromagnetic materials, such as Fe3GeTe2. The electric control of skyrmions is important for their potential application in low-power memory technologies. Here, we predict that DMI and magnetic skyrmions in a Fe3GeTe2 monolayer can be controlled by ferroelectric polarization of an adjacent 2D vdW ferroelectric In2Se3. Based on density functional theory and atomistic spin-dynamics modeling, we find that the interfacial symmetry breaking produces a sizable DMI in a Fe3GeTe2/In2Se3 vdW heterostructure. We show that the magnitude of DMI can be controlled by ferroelectric polarization reversal, leading to creation and annihilation of skyrmions. Furthermore, we find that the sign of DMI in a In2Se3/Fe3GeTe2/In2Se3 heterostructure changes with ferroelectric switching reversing the skyrmion chirality. The predicted electrically controlled skyrmion formation may be interesting for spintronic applications.

13.
Phys Rev Lett ; 128(19): 197201, 2022 May 13.
Artigo em Inglês | MEDLINE | ID: mdl-35622046

RESUMO

Antiferromagnetic (AFM) spintronics has emerged as a subfield of spintronics driven by the advantages of antiferromagnets producing no stray fields and exhibiting ultrafast magnetization dynamics. The efficient method to detect an AFM order parameter, known as the Néel vector, by electric means is critical to realize concepts of AFM spintronics. Here, we demonstrate that noncollinear AFM metals, such as Mn_{3}Sn, exhibit a momentum dependent spin polarization which can be exploited in AFM tunnel junctions to detect the Néel vector. Using first-principles calculations, we predict a tunneling magnetoresistance (TMR) effect as high as 300% in AFM tunnel junctions with Mn_{3}Sn electrodes, where the junction resistance depends on the relative orientation of their Néel vectors and exhibits four nonvolatile resistance states. We argue that the spin-split band structure and the related TMR effect can also be realized in other noncollinear AFM metals like Mn_{3}Ge, Mn_{3}Ga, Mn_{3}Pt, and Mn_{3}GaN. Our work provides a robust method for detecting the Néel vector in noncollinear antiferromagnets via the TMR effect, which may be useful for their application in AFM spintronic devices.

14.
Nano Lett ; 21(1): 175-181, 2021 Jan 13.
Artigo em Inglês | MEDLINE | ID: mdl-33264014

RESUMO

Multiferroic tunnel junctions (MFTJs) have aroused significant interest due to their functional properties useful for nonvolatile memory devices. So far, however, all of the existing MFTJs have been based on perovskite-oxide heterostructures limited by a relatively high resistance-area (RA) product unfavorable for practical applications. Here, using first-principles calculations, we explore spin-dependent transport properties of van der Waals (vdW) MFTJs which consist of two-dimensional (2D) ferromagnetic FenGeTe2 (n = 3, 4, 5) electrodes and 2D ferroelectric In2Se3 barrier layers. We demonstrate that such FemGeTe2/In2Se3/FenGeTe2 (m, n = 3, 4, 5; m ≠ n) MFTJs exhibit multiple nonvolatile resistance states associated with different polarization orientation of the ferroelectric In2Se3 layer and magnetization alignment of the two ferromagnetic FenGeTe2 layers. We find a remarkably low RA product (less than 1 Ω·µm2) which makes the proposed vdW MFTJs superior to the conventional MFTJs in terms of their promise for nonvolatile memory applications.

15.
Phys Rev Lett ; 126(5): 057601, 2021 Feb 05.
Artigo em Inglês | MEDLINE | ID: mdl-33605764

RESUMO

Ferroelectric tunnel junctions (FTJs), which consist of two metal electrodes separated by a thin ferroelectric barrier, have recently aroused significant interest for technological applications as nanoscale resistive switching devices. So far, most existing FTJs have been based on perovskite-oxide barrier layers. The recent discovery of the two-dimensional (2D) van der Waals ferroelectric materials opens a new route to realize tunnel junctions with new functionalities and nm-scale dimensions. Because of the weak coupling between the atomic layers in these materials, the relative dipole alignment between them can be controlled by applied voltage. This allows transitions between ferroelectric and antiferroelectric orderings, resulting in significant changes of the electronic structure. Here, we propose to realize 2D antiferroelectric tunnel junctions (AFTJs), which exploit this new functionality, based on bilayer In_{2}X_{3} (X=S, Se, Te) barriers and different 2D electrodes. Using first-principles density functional theory calculations, we demonstrate that the In_{2}X_{3} bilayers exhibit stable ferroelectric and antiferroelectric states separated by sizable energy barriers, thus supporting a nonvolatile switching between these states. Using quantum-mechanical modeling of the electronic transport, we explore in-plane and out-of-plane tunneling across the In_{2}S_{3} van der Waals bilayers, and predict giant tunneling electroresistance effects and multiple nonvolatile resistance states driven by ferroelectric-antiferroelectric order transitions. Our proposal opens a new route to realize nanoscale memory devices with ultrahigh storage density using 2D AFTJs.

16.
Phys Rev Lett ; 127(13): 136803, 2021 Sep 24.
Artigo em Inglês | MEDLINE | ID: mdl-34623838

RESUMO

The low in-plane symmetry in layered 1T'-ReS_{2} results in strong band anisotropy, while its manifestation in the electronic properties is challenging to resolve due to the lack of effective approaches for controlling the local current path. In this work, we reveal the giant transport anisotropy in monolayer to four-layer ReS_{2} by creating directional conducting paths via nanoscale ferroelectric control. By reversing the polarization of a ferroelectric polymer top layer, we induce a conductivity switching ratio of >1.5×10^{8} in the ReS_{2} channel at 300 K. Characterizing the domain-defined conducting nanowires in an insulating background shows that the conductivity ratio between the directions along and perpendicular to the Re chain can exceed 5.5×10^{4} in monolayer ReS_{2}. Theoretical modeling points to the band origin of the transport anomaly and further reveals the emergence of a flat band in few-layer ReS_{2}. Our work paves the path for implementing highly anisotropic 2D materials for designing novel collective phenomena and electron lensing applications.

17.
Phys Rev Lett ; 124(6): 067203, 2020 Feb 14.
Artigo em Inglês | MEDLINE | ID: mdl-32109084

RESUMO

Antiferromagnetic (AFM) spintronics exploits the Néel vector as a state variable for novel spintronic devices. Recent studies have shown that the fieldlike and antidamping spin-orbit torques (SOTs) can be used to switch the Néel vector in antiferromagnets with proper symmetries. However, the precise detection of the Néel vector remains a challenging problem. In this Letter, we predict that the nonlinear anomalous Hall effect (AHE) can be used to detect the Néel vector in most compensated antiferromagnets supporting the antidamping SOT. We show that the magnetic crystal group symmetry of these antiferromagnets combined with spin-orbit coupling produce a sizable Berry curvature dipole and hence the nonlinear AHE. As a specific example, we consider the half-Heusler alloy CuMnSb, in which the Néel vector can be switched by the antidamping SOT. Based on density-functional theory calculations, we show that the nonlinear AHE in CuMnSb results in a measurable Hall voltage under conventional experimental conditions. The strong dependence of the Berry curvature dipole on the Néel vector orientation provides a new detection scheme of the Néel vector based on the nonlinear AHE. Our predictions enrich the material platform for studying nontrivial phenomena associated with the Berry curvature and broaden the range of materials useful for AFM spintronics.

18.
Nano Lett ; 19(10): 7385-7393, 2019 10 09.
Artigo em Inglês | MEDLINE | ID: mdl-31514498

RESUMO

Ferroelectric tunnel junctions (FTJs) have recently aroused significant interest due to the interesting physics controlling their properties and potential application in nonvolatile memory devices. In this work, we propose a new concept to design high-performance FTJs based on ferroelectric/polar-oxide composite barriers. Using density functional theory calculations, we model electronic and transport properties of LaNiO3/PbTiO3/LaAlO3/LaNiO3 tunnel junctions and demonstrate that an ultrathin polar LaAlO3(001) layer strongly enhances their performance. We predict a tunneling electroresistance (TER) effect in these FTJs with an OFF/ON resistance ratio exceeding a factor of 104 and ON state resistance as low as about 1 kΩµm2. Such an enhanced performance is driven by the ionic charge at the PbTiO3/LaAlO3 interface, which significantly increases transmission across the FTJ when the ferroelectric polarization of PbTiO3 is pointing against the intrinsic electric field produced by this ionic charge. This is due to the formation of a two-dimensional (2D) electron or hole gas, depending on the LaAlO3 termination being (LaO)+ or (AlO2)-, respectively, which is formed to screen the polarization charge of the nonuniform polarization state. This 2D electron (hole) gas can be switched ON and OFF by the reversal of ferroelectric polarization, resulting in the giant TER effect. The proposed design suggests a new direction for creating FTJs with a stable and reversible ferroelectric polarization, a sizable TER effect, and a low-resistance-area product, as required for memory applications.

19.
Nano Lett ; 19(8): 5133-5139, 2019 Aug 14.
Artigo em Inglês | MEDLINE | ID: mdl-31276417

RESUMO

van der Waals (vdW) heterostructures, stacking different two-dimensional materials, have opened up unprecedented opportunities to explore new physics and device concepts. Especially interesting are recently discovered two-dimensional magnetic vdW materials, providing new paradigms for spintronic applications. Here, using density functional theory (DFT) calculations, we investigate the spin-dependent electronic transport across vdW magnetic tunnel junctions (MTJs) composed of Fe3GeTe2 ferromagnetic electrodes and a graphene or hexagonal boron nitride (h-BN) spacer layer. For both types of junctions, we find that the junction resistance changes by thousands of percent when the magnetization of the electrodes is switched from parallel to antiparallel. Such a giant tunneling magnetoresistance (TMR) effect is driven by dissimilar electronic structure of the two spin-conducting channels in Fe3GeTe2, resulting in a mismatch between the incoming and outgoing Bloch states in the electrodes and thus suppressed transmission for an antiparallel-aligned MTJ. The vdW bonding between electrodes and a spacer layer makes this result virtually independent of the type of the spacer layer, making the predicted giant TMR effect robust with respect to strain, interface distance, and other parameters, which may vary in the experiment. We hope that our results will further stimulate experimental studies of vdW MTJs and pave the way for their applications in spintronics.

20.
Nano Lett ; 19(5): 3057-3065, 2019 05 08.
Artigo em Inglês | MEDLINE | ID: mdl-30964306

RESUMO

Complex oxide thin-film heterostructures often exhibit magnetic properties different from those known for bulk constituents. This is due to the altered local structural and electronic environment at the interfaces, which affects the exchange coupling and magnetic ordering. The emergent magnetism at oxide interfaces can be controlled by ferroelectric polarization and has a strong effect on spin-dependent transport properties of oxide heterostructures, including magnetic and ferroelectric tunnel junctions. Here, using prototype La2/3Sr1/3MnO3/BaTiO3 heterostructures, we demonstrate that ferroelectric polarization of BaTiO3 controls the orbital hybridization and magnetism at heterointerfaces. We observe changes in the enhanced orbital occupancy and significant charge redistribution across the heterointerfaces, affecting the spin and orbital magnetic moments of the interfacial Mn and Ti atoms. Importantly, we find that the exchange coupling between Mn and Ti atoms across the interface is tuned by ferroelectric polarization from ferromagnetic to antiferromagnetic. Our findings provide a viable route to electrically control complex magnetic configurations at artificial multiferroic interfaces, taking a step toward low-power spintronics.

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