Scanning Probe Microscopy Investigation of Topological Defects

Abstract

Symmetry lowering phase transitions in ferroelectrics, magnets, and materials with various other forms of inherent order lead to the formation of topological defects. Their non-trivial real-space topology is characterized by a topological charge, which represents the topological invariant. The study of topological defects in such materials has seen increased interest over the last decade. Among the methods used for their study, scanning probe microscopy (SPM) with its many variants has provided valuable new insight into these structures at the nanoscale. In this perspective, various approaches are discussed, and different techniques are compared with regard to their ability to investigate topological defect properties.

1. Introduction

Topological defect formation at the symmetry lowering phase transitions in solids with various forms of intrinsic order is a phenomenon widely studied in materials science and solid-state physics [1]. A prototypical example is a magnetic material cooled through its Curie temperature (see Figure 1), leading to the formation of magnetic domains and associated domain walls, which are a type of topological defect. From a general perspective, such nanoscale structures can have different intrinsic properties from the bulk material itself [2,3], making them interesting nanoscale objects with altered and additional functionality. These different properties are brought about by changes in local crystal structure, sometimes involving large structural gradients. In addition, local symmetry changes allow for the existence of properties forbidden in the higher symmetry bulk phase, again leading to changes from macroscopic materials properties.

These considerations have led to proposals of utilizing these altered properties at topological defects for enhanced material functionality, including for example domain wall nanoelectronics [4] and spintronic devices [5], which have been discussed in various contexts.

The structural width and size of such topological defects typical is found to be in the nanoscale range, down to atomic length scales. This small size requires high resolution characterization methods, involving electron microscopy, nanoscale spectroscopy methods, and in various forms, scanning probe microscopy, the latter being the focus of this article.

2. Types of Topological Defects

The types of topological defects found in solids [6,7] range from domain walls [4], skyrmions [8,9] and associated structures, vortices [10], to dislocations. These structures can be formed in various types of ‘order background’, involving magnetism (magnetic spins), ferroelectricty (electric dipoles), ferroelasticity (spontaneous strain), ferrotoroidicity, and crystal structure defects (dislocations). Their non-trivial real-space topology is characterized by a topological charge, which represents the topological invariant [11].

Domain walls in ferroelectric and multiferroic materials are a prominent example and have been investigated in more detail in the last decade. They have a very small size, on the order of a unit cell, as for example shown in Figure 2a for the case of a 109° domain wall in BiFeO₃. The colors in the image represent tilt angles of the perovskite unit cell overlaid on an atomic structure high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image. At the wall the unit cell tilt reaches ~3°, which is considerable if one takes into account its impact on bond lengths and orbital overlap in the ionic solid. These in turn lead to changes in electronic structure, and, hence the intrinsic properties are altered directly at the domain wall on the same atomic length scale.

3. Scanning Probe Methods

Several different scanning probe methods have been used to study topological defects in solid materials, including their structural, electrical, magnetic, and other functional properties. Some methods are more suitable than others and the measured properties vary, as outlined in

Table 1. Comparison of scanning probe methods used for the study of topological defects in various solid materials. Literature references point to relevant reviews of the technique, and examples of topological defect research, if applicable. Technique acronyms are explained in the text below.

Method	Lateral Resolution	Measured Quantity	Materials	Examples
AFM	atomic	surface morphology; mechanical properties	many, few restrictions	[12,13]
PFM	~5 nm	piezoresponse	ferro-/piezoelectrics	[14,15]
STM	atomic	tunnelling current	semiconductors, metals	[16,17]
KPFM	atomic	surface potential difference	semiconductors, metals	[18]
c-AFM	~5 nm	electrical conductivity	semiconductors, metals	[19,20]
Nano-IR	~10 nm	infrared optical properties	many with IR bands between 600–4500 cm−1	[21]
NSOM	~10 nm	optical properties	many, few restrictions	[22,23]
MFM	~10 nm	magnetic field gradient	ferro-/ferrimagnets; superconductors	[24,25]
scanning SQUID	~100 nm	magnetic flux	antiferro-, ferro-/ferrimagnets; superconductors	[26]
scanning NV	~20 nm	magnetic field strength	antiferro-, ferro-/ferrimagnets; superconductors	[27,28]
sMIM	~50 nm	impedance	many, few restrictions	[29,30]
CGM	~5 nm	charge	ferro-/piezoelectrics	[31,32]

.

Application to Imaging and Manipulating Topological Defects

One feature that is common to all SPM methods is the acquisition of topographical information of measured sample surfaces, depicting their morphology. Even this basic atomic force microscopy (AFM) feature can be used for example to study twinning angles in ferroelastic twin domain walls [33] and to locate their position with sufficient accuracy for other local probing investigations, such as mechanical probing at the nanoscale [34].

Other techniques such as magnetic force microscopy (MFM) can be used to directly image magnetic domain structure, in magnetic materials. This method has also been used to directly visualize skyrmions [23] (Figure 3). Magnetic field dependent measurements show the ‘melting’ of the hexagonal skyrmion crystal lattice through the formation of magnetic monopoles. Other techniques to study magnetic properties include scanning SQUID microscopy [25], and scanning diamond color centre (scanning NV) microscopy [26,27]. The latter also allow for the study of antiferromagnets.

Polar order in ferroelectrics can be visualized by piezoresponse force microscopy (PFM) and charge gradient microscopy (CGM), among others. This technique is often used in conjunction with other SPM modes for the investigation of topological defects, for example conductive AFM (c-AFM) to measure conductivity at domain walls in various ferroelectric and multiferroic oxides. The resolution in this case is given by the contact area of the SPM probe with the material surface (as is the case with several other techniques listed), and can be used to study domain wall devices as well as intrinsic material properties such as carrier properties, sometimes in conjunction with theoretical models. An example is shown in Figure 4, which shows a study of orthorhombic-rhombohedral phase boundaries (hybrid domain walls) in strained BiFeO₃ [35].

Electronic properties of materials have been studied by scanning tunnelling microscopy and spectroscopy (STM), Kelvin probe force microscopy (KPFM), and scanning microwave impedance microscopy (sMIM). This includes domain walls, for example the variation of electronic band structure at individual walls [16]. Local changes of dielectric constant at structural domain walls have been studied in vanadium oxide by sMIM [28], which are especially pronounced for metal insulator transitions, but can also be used for variations in carrier density in semiconducting materials.

Among the SPM techniques available for the study of optical materials are near-field scanning optical microscopy (NSOM), and nanoscale infrared spectroscopy (nano-IR). They have been used to study strain induced variations of optical constants around domain walls [21], and the local variation of phonons around engineered domain walls in van der Waals heterostructure materials [20]. Various other SPM modes can also be combined with optical illumination to study the impact of light on topological defects, for example the displacement of domain walls in ferroelectrics [36,37,38] or optically driven vertex formation [39,40,41].

In addition to the imaging of various properties, SPM techniques can also be used to manipulate topological defects through the application of local stimuli, such as mechanical stress [42], electric and magnetic fields, and the study of topological defects in prototype device structures. One example is the demonstration and investigation of information storage in ferroelectric domain wall non-volatile memory cells [43,44] (Figure 5). Here the conduction paths of individual conductive domain walls can be followed, and polarization orientation can be studied simultaneously, providing information on polarization orientation across individual walls in memory device prototypes.

4. Concluding Remarks and Outlook

The study of materials surfaces and cross sections [45] with physical SPM probes enables the study of various properties associated with topological defects in solid state material systems, from fundamental material properties, to application relevant properties [46] and prototype devices [40,41]. The achieved lateral resolution is in many cases associated with the probe size (tip radius, contact area), which is sufficient to study mesoscopic nanoscale systems just above atomic resolution, or for measurements in UHV, at atomic resolution. It can also be used in correlative microscopy studies that involve other imaging and spectroscopy techniques, where SPM is used to localize features of interest or study corresponding properties.