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«Nanoscale Phenomena in Oxide Heterostructures Joseph A. Sulpizio Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot ...»

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Nanoscale Phenomena in Oxide Heterostructures

Joseph A. Sulpizio

Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

joseph.sulpizio@weizmann.ac.il

Shahal Ilani

Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

shahal.ilani@weizmann.ac.il

Patrick Irvin

Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA

prist2@pitt.edu,

Jeremy Levy

Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA jlevy@pitt.edu Keywords complex oxides, scanning probe microscopy, strongly correlated electrons Abstract Recent advances in creating complex oxide heterostructures, interfaces formed between two different transition metal oxides, have heralded a new era of materials and physics research, enabling a uniquely diverse set of coexisting physical properties to be combined with an everincreasing degree of experimental control. Already, these systems have exhibited such varied phenomena as superconductivity, magnetism, and ferroelasticity, all of which are gate-tunable, demonstrating their promise for fundamental discovery and technological innovation alike. To fully exploit this richness, it is necessary to understand and control the physics on the smallest scales, making the use of nanoscale probes essential. Using the prototypical LaAlO3/SrTiO3 interface as a guide, we explore the exciting developments in the physics of oxide-based heterostructures, with a focus on nanostructures and the nanoscale probes employed to unravel their complex behavior.

Table of Contents Keywords

Abstract

1. Introduction

2. SrTiO3 – The universal substrate

2.1 Broken Symmetries in SrTiO3

2.2 SrTiO3 Electronic Structure

3. LaAlO3/SrTiO3 – A conducting layer between two insulators

3.1 Influence of growth conditions

3.2 Mechanisms for interfacial conduction

4. Device fabrication

4.1 Lithography and LaAlO3 thickness modulation

4.2 Ion beam irradiation

4.3 Conductive AFM lithography

5. Transport at the LaAlO3/SrTiO3 interface

5.1 General transport phenomenology

5.2 Anisotropic magnetoresistance

5.3 A universal Lifshitz transition from single-band to multi-band transport

6. Superconductivity

6.1 Superconducting phase diagram

6.2 Local structure of superconductivity

6.3 Superconductivity and magnetic fields

7. Magnetism

7.1 Experimental manifestations of magnetism at the interface

7.2 Origin of ferromagnetic moments

7.3 Magnetic phase diagram

8. Ferroelasticity – the microscopic structure of domains

8.1 Ferroelastic domains in SrTiO3

8.2 Domain structure and influence on transport

8.3 Toward domain-based nanosystems

9. Functional Devices down to the Nanoscale

9.1 Microscale

9.2 Mesoscale

9.3 Nanoscale

10. Future Directions

10.1 Beating complexity by probing on the nanoscale

10.2 Hybrid systems

10.3 Engineered physics with d-orbital electrons on the nanoscale

Acknowledgements

Literature Cited

1. Introduction For many decades, there has persisted a sharp dichotomy between the study of quantum materials and semiconductor/mesoscopic physics. The major thrust in the field of quantum materials has been the development and study of bulk, 3D correlated systems, where many physical phenomena can be achieved within a single materials family. A particularly fruitful family is that of the complex (transitionmetal) oxides. Varying the composition and arrangement of the metal atoms in these oxides has enabled the synthesis of a diverse array of materials, including high-temperature superconductors, quantum magnets, ferroelectrics, and multiferroics. Meanwhile, the field of semiconductor physics has primarily focused on developing control over the dimensionality, cleanliness, and geometry of functional devices.

Over the last ten years, these formerly independent communities have begun to overlap, beginning with the discovery of a high mobility two-dimensional electron gas living at the interface between strontium titanate (SrTiO3) and lanthanum aluminate (LaAlO3) (1). This emerging field of complex oxide heterostructures, devices made by combining different transition metal oxides, has enabled researchers to apply the experimental flexibility and tools of semiconductor physics to a family of materials that exhibits a multitude of intriguing physical properties.

The target audience for this review consists of researchers in mesoscopic physics, quantum transport, device engineering, and quantum information who are interested in this burgeoning field. Until recently, the main advances in this new field have been made by traditional materials science-based approaches.

However, as complex oxide heterostructures reach an ever higher degree of maturity, researchers employing a broader class of approaches, from fundamental quantum physics to device applications, can find fertile ground for discovery.





To appreciate the potential novelty of oxide heterointerfaces, in Table 1 we highlight a selection of their properties as compared to those in other flagship solid state systems. Clearly, oxide interfaces are not yet as electronically clean as these other systems (although this is rapidly improving). However, their origin in strongly correlated materials endows these interfaces with a large set of properties that are rarely found to coexist in conventional materials systems. These include gate-tunable magnetism that persists to room temperature, intrinsic superconductivity, strong spin-orbit interactions, electron-lattice interactions, and possibly even ferroelectricity. Moreover, these properties have strong interrelationships, which once properly understood can be exploited to realize unique physical systems that have no counterpart in any other material system.

This review aims to provide an overview of the properties of oxide nanostructures, with an emphasis on the important role that local probes can play in gaining insight into this family of materials. Already, nanoscale probes have made important contributions to understanding and controlling the microscopic physics in the oxides. Scanning probes were critical in establishing the two-dimensionality of conducting electronic systems living near the interface (2), identifying the influence of microscopic structural domains on interfacial electrons (3, 4), and creating unique device architectures down to the nanoscale (5, 6). As will become clear over the course of this article, with so many different physical effects simultaneously at play in these systems, it is crucial to visualize and isolate the individual components on microscopic scales. Thus, nanoscale probes serve an increasingly vital role in the study of the oxides.

The prototypical, and most widely-studied, oxide heterostructure is LaAlO3/SrTiO3, and so naturally this particular heterostructure will occupy much of the focus of this review. The knowledge gained, however, is endemic to the growing class of related oxide materials.

Table 1: Comparison between LaAlO3/SrTiO3 and other solid state material systems for nanoscale devices. Although LaAlO3/SrTiO3 is currently more electronically disordered than the other material systems, its broad array of physical properties and potential tunability make it very attractive as a system for studying correlated electron physics in engineered environments.

–  –  –

2. SrTiO3 – The universal substrate Strontium titanate (SrTiO3) serves as the near-universal substrate on which complex oxide structures are built and from which their properties are largely inherited. Thus, before proceeding to our discussions of nanoscale phenomena in complex oxide heterostructures, we first review the relevant physics of SrTiO3, a material that has been extensively and continuously studied since the 1940s due to its remarkable array of properties. These diverse properties are best appreciated by considering how they emerge through the breaking of fundamental symmetries: point group symmetry (ferroelasticity), charge inversion symmetry (ferroelectricity), U(1) gauge symmetry (superconductivity), and spin rotation symmetry (ferromagnetism). We now discuss the specific breaking of each of these symmetries in the context of SrTiO3, guided by the order in which they emerge as a function of decreasing temperature.

Figure 1: SrTiO3 - The universal substrate. (a-e) The physical properties of SrTiO3 emerge through the breaking of various symmetries as the temperature is lowered. (a) At room temperature, the Perovskite unit cell has cubic symmetry, with three orthogonal -axes of equal length. (b) Below = 105 K, a ferroelastic transition to tetragonal crystal symmetry occurs, where the crystal has two short -axes and one long -axis. This transition arises from an increasing “octahedral tilt”, wherein neighboring oxygen octahedra develop a relative rotation (bottom projection, red arrows indicate rotation). (c) A ferroelectric transition occurs for SrTi18O3 at = 23 K, endowing the unit cell with a permanent electric dipole from the displacement of the central titanium atom toward a corner of the distorted oxygen octahedron (dashed arrow). Quantum tunneling suppresses this transition for normal SrTi16O3, making it a “quantum paraelectric”. (d) Near = 300 mK, doped SrTiO3 becomes a superconductor, (16). whose critical temperature exhibits a “dome” structure as a function of carrier density. (e) Rotation symmetry in spin space is always preserved, and therefore bulk SrTiO3 does not exhibit magnetism at any temperature. (f-h) Electronic structure of SrTiO3. (f) The electronic orbitals near the Fermi energy in SrTiO3 are the fivefold-degenerate titanium orbitals. Once the titanium is surrounded by the oxygen octahedron, the -orbitals are split into a higher energy doublet ( states) and a lower energy triplet (2 states). (g) Electrons located in the 2 orbitals (, , ) are coupled to identical orbitals on neighboring lattice sites. Hopping matrix elements are much larger in the plane of an orbital’s lobes than in the perpendicular direction. This is illustrated by the thickness of the arrows which indicates that hopping between orbitals (blue) is stronger along the and directions (light effective mass) than along the direction (heavy effective mass). (h) The corresponding Fermi surface is cigar-shaped, elongated in the direction for the orbitals (solid), and elongated in the and directions for the and orbitals (transparent), respectively.

2.1 Broken Symmetries in SrTiO3 SrTiO3 has a perovskite crystal structure, illustrated in Figure 1a. At room temperature its unit cell is cubic, composed of an outermost arrangement of eight strontium atoms. Centered on each face of the cube is one of six oxygen atoms, which form together the vertices of an octahedral cage. At the center of this cage lies the titanium atom. This cubic structure gives the most energetically favorable packing of the constituent atoms at high temperatures, but as the temperature is reduced, more efficient packing can be achieved. At = 105 K, neighboring oxygen octahedra rotate in opposite directions (antiferrodistortive transition, Figure 1b) in order to reach the optimal bond lengths between both the strontium-oxygen and titanium-oxygen pairs (Goldschmidt tolerance) (7, 8). As a result of these rotations the cubic symmetry is broken and the unit cell becomes a rectangular prism with one long axis and two short axes (labeled c and a accordingly in Figure 1b). This ferroelastic transition naturally leads to the formation of domains within the SrTiO3 with different orthogonal orientations of the tetragonal unit cells (9, 10). The consequences of this domain structure for nanoscale phenomena including the effect on local electronic properties of oxide heterostructures will be discussed in detail in subsequent sections. Further lowering of the crystal symmetry into orthorhombic and triclinic structures may occur at lower temperatures, though the magnitude of these additional perturbations is significantly smaller than the aforementioned transition to tetragonal symmetry. All such structural changes in the crystal symmetry lift the orbital degeneracies of the electronic system and thus have a direct effect on the electronic structure of the material.

After the cubic crystal symmetry of SrTiO3 has been broken, the next symmetry to break is inversion symmetry. At room temperature the Ti atom is centered inside the oxygen cage and only through the application of an external electric field will it displace off-center, making SrTiO3 a paraelectric material at these temperatures. This paraelectric state persists even below the ferroelastic transition. At even lower temperatures, however, the unit cell elongates enough such that a double-well potential develops for the titanium atom, with minima situated near opposite ends of the long axis of the oxygen octahedron (Figure 1c). For SrTi18O3, having the heavier isotope of oxygen, at = 23 K a ferroelectric transition occurs (11), in which the titanium atom spontaneously displaces toward one of these minima, resulting in a non-zero dipole moment within the unit cell. In contrast, the 16O isotope happens to be just light enough such that even at zero temperature it can quantum-mechanically tunnel between the two potential minima, a phenomena termed “quantum paraelectricity” (12). Similar to SrTi18O3, whose dielectric constant diverges at the ferroelectric transition, the dielectric constant of SrTi16O3 also rapidly increases with decreasing temperature, however, this increase is cut off by the quantum tunneling and this constant plateaus at a high value of ~20,000 (13), signifying the highly polarizable nature of this state. By growing thin films of SrTiO3 on tensile-strained substrates, ferroelectricity can be observed as high as room temperature (14, 15).



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