The critical size limit of electric polarization remains a fundamental question in nanoscale ferroelectric research 1 . As such, the viability of ultrathin ferroelectricity greatly impacts emerging low-power logic and nonvolatile memories 2 . Size effects in ferroelectrics have been thoroughly investigated for perovskite oxides -the archetypal ferroelectric system 3 . Perovskites, however, have so far proved unsuitable for thickness-scaling and integration with modern semiconductor processes 4 . Here, we report ultrathin ferroelectricity in doped-HfO2, a fluorite-structure oxide grown by atomic layer deposition on silicon. We demonstrate the persistence of inversion symmetry breaking and spontaneous, switchable polarization down to 1 nm. Our results indicate not only the absence of a ferroelectric critical thickness, but also enhanced polar distortions as film thickness is reduced, contradictory to perovskite ferroelectrics. This work shifts the focus on the fundamental limits of ferroelectricity to simpler transition metal oxide systems -from perovskite-derived complex oxides to fluoritestructure binary oxides -in which 'reverse' size effects counter-intuitively stabilize polar symmetry in the ultrathin regime.Ferroelectric materials exhibit stable states of collectively ordered electrical dipoles whose polarization can be reversed under an applied electric field 5 . Consequently, ultrathin ferroelectrics are of great technological interest for high-density electronics, particularly field-effect transistors and nonvolatile memories 2 . However, ferroelectricity is typically suppressed at the few nanometer scale in the ubiquitous perovskite oxides 6 . First-principles calculations predict six unit cells as the critical thickness in perovskite ferroelectrics 1 due to incomplete screening of depolarization fields 3 . Atomic-scale ferroelectricity in perovskites often fail to demonstrate polarization switching 7,8 , a crucial ingredient for application. Furthermore, attempts to synthesize ferroelectric perovskite films on silicon 9,10 are plagued by chemical incompatibility 4,11 and high temperatures required for epitaxial growth. Since the discovery of ferroelectricity in HfO2-based thin films in 2011 12 , fluorite-structure binary oxides (fluorites) have attracted considerable interest 13 as they enable lowtemperature synthesis and conformal growth in three-dimensional (3D) structures on silicon 14,15 , thereby overcoming many of the issues that restrict its perovskite counterparts in terms of complementary metal-oxide-semiconductor (CMOS) compatibility and thickness scaling 16 .

Epitaxial strain is a proven route to enhancing the properties of complex oxides, however, the details of how the atomic structure accommodates strain are poorly understood due to the difficulty of measuring the oxygen positions in thin films. We present a general methodology for determining the atomic structure of strained oxide films via x-ray diffraction, which we demonstrate using LaNiO3 films. The oxygen octahedral rotations and distortions have been quantified by comparing the intensities of half-order Bragg peaks, arising from the two unit cell periodicity of the octahedral rotations, with the calculated structure factor. Combining ab initio density functional calculations with these experimental results, we determine systematically how strain modifies the atomic structure of this functional oxide.Comment: 23 pages, 11 figure

We investigate structural coupling of the MnO6 octahedra across a film/substrate interface and the resultant changes of the physical properties of ultrathin La2/3Sr1/3MnO3 (LSMO) films. In order to isolate the effect of interfacial MnO6 octahedral behavior from that of epitaxial strain, LSMO films are grown on substrates with different symmetry and similar lattice parameters. Ultrathin LSMO films show an increased magnetization and electrical conductivity on cubic (LaAlO3)0.3(Sr2AlTaO6)0.7 (LSAT) compared to those grown on orthorhombic NdGaO3 (NGO) substrates, an effect that subsides as the thickness of the films is increased. This study demonstrates that interfacial structural coupling can play a critical role in the functional properties of oxide heterostructures.

The disorder inherent to doping by cation substitution in the complex oxides can have profound effects on collective-ordered states. Here, we demonstrate that cation-site ordering achieved through digital-synthesis techniques can dramatically enhance the antiferromagnetic ordering temperatures of manganite films. Cation-ordered (LaMnO3)m/(SrMnO3)2m superlattices show Néel temperatures (TN) that are the highest of any La(1-x)Sr(x)MnO3 compound, approximately 70 K greater than compositionally equivalent randomly doped La(1/3)Sr(2/3)MnO3. The antiferromagnetic order is A-type, consisting of in-plane double-exchange-mediated ferromagnetic sheets coupled antiferromagnetically along the out-of-plane direction. Through synchrotron X-ray scattering, we have discovered an in-plane structural modulation that reduces the charge itinerancy and hence the ordering temperature within the ferromagnetic sheets, thereby limiting TN. This modulation is mitigated and driven to long wavelengths by cation ordering, enabling the higher TN values of the superlattices. These results provide insight into how cation-site ordering can enhance cooperative behaviour in oxides through subtle structural phenomena.

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