Topological Structures in Ferroic Materials

  • Jennifer Mackel

Student thesis: Doctoral ThesisDoctor of Philosophy

Abstract

The study of topological defects in condensed matter involves those regions in which the chosen order parameter ceases to vary continuously, such as points, lines, and surfaces. In ferroic materials, these defects include planar domain walls, which separate regions of uniform orientation of the order parameter, as well as more complex structures such as vortices and skyrmions, which are spiralling configurations of the order parameter. This thesis investigates topological structures arising in both magnetic and ferroelectric structures, highlighting both the similarities and the differences in these material systems.

The first experiment outlined in this thesis is the growth and characterisation of thin films of CoxZnyMnz alloys. Previous work by Tokunaga et al has shown that alloys of CoxZnyMnz (x+y+z=20) crystallise in the -Mn structure, which is non-centrosymmetric and analogous to the B20 structure of common skyrmion-hosting materials such as MnSi. These alloys were shown to exhibit a skyrmion phase at moderate fields just below their Curie temperature, which for some compositions was close to room temperature; an essential feature for potential skyrmion-based devices. Results in the literature also provide evidence that the reduced dimensionality of thin plates or films of skyrmion-hosting materials can increase the range of the skyrmion phase across the field-temperature phase diagram. Consequently, growing thin films of these CoxZnyMnz alloys could prove advantageous. In this thesis, the successful growth of polycrystalline CoxZnyMnz thin films using magnetron sputtering on a lattice-matched BaF2 single-crystal substrate is demonstrated. Crystal structure was confirmed to be the -Mn structure in polycrystalline form by x-ray diffraction (XRD) and electron diffraction performed by transmission electron microscopy (TEM). In addition, the stoichiometry of the alloys was confirmed to be the required ratios using energy dispersive x-ray spectroscopy (EDX) via both scanning and transmission electron microscopy.

Having attained the correct crystal structure and chemical properties, the magnetic properties of the CoxZnyMnz thin films were investigated using several techniques. Vibrating sample magnetometry (VSM) and superconducting quantum interference (SQUID) were used to measure hysteresis loops from films of different composition as well as the variation of the magnetisation in the samples with applied temperature and field. These results enabled the determination of the Curie temperature, which was found to vary significantly with film composition. Interestingly, above the Curie temperature of the film some magnetic character remains, although at a much smaller magnitude. It is believed this is due to a separated cobalt-rich phase in the film, but is expected to account for a very small percentage of the film volume; spectral mapping of the films using EDX shows a homogeneous distribution of all three elements, so any cobalt-rich regions must be very small. Atomic-scale spectral mapping could provide more insight into this phenomenon.

The magnetic domain patterns were also mapped directly using Lorentz-mode TEM at low temperatures, showing an unusual Lichtenberg-like pattern of domains extending throughout the sample. These domain patterns were found to change direction as the direction of the applied field was changed and vanish completely at higher fields and temperatures.

Further analysis of data from VSM and SQUID allowed the production of a partial phase diagram for the CoxZnyMnz films, showing a rapid change to a ferromagnetic phase as the applied field is increased. Further detailed investigation of the region just below the Curie temperature could show interesting features and the potential presence of a skyrmion phase.

Analysis of different heating and cooling data, both in zero field and applied field, identified a thermal hysteresis in the films. Thermal hysteresis is a signature of a first-order phase transition, leading to the likely designation of the phase transition in these films as first order. Thermal hysteresis is also an indicator of spin-glass character; such disordered magnetic structure could be possible in polycrystalline films such as these where long-range magnetic order is disrupted.

Following the magnetic chapters of this thesis, an investigation into ferroelectric lead titanate is described. While magnetic and ferroelectric structures may be quite different in some regards, in terms of topological structures they are similar; both exhibit structures such as domain walls, and recent research shows the existence of polar skyrmion bubbles in ferroelectric thin films which are analogous to magnetic skyrmions in terms of their topological properties. In this investigation, essential groundwork is laid to further the goal of observing in-wall polarisation within the 180 domain walls of lead titanate, as predicted by Wojdeł and Íñiguez. Simulations of these 180 DWs show them to have Bloch-type character, with a polarisation developing within the domain walls perpendicular to that of the domains. Further work by Gonçalves et al demonstrated how nanodomains in lead titanate separated from the bulk material by 180 DWs with in-wall polarisation form polar skyrmion bubbles; i.e. topologically stable objects analogous to the well-established magnetic skyrmions.

In this thesis, the domain patterns in bulk lead titanate are mapped using piezoresponse force microscopy (PFM) to search for 180 domain walls. When cutting a lamella from these regions proved to change the domain patterns, a different approach was followed; lamellae were cut from bulk crystal lead titanate, repaired using thermal annealing and acid washing, and their domain patterns mapped using PFM. Following this, 180 domains were written in the lamella using a voltage applied through the PFM tip, creating the appropriate 180 DW required for this project. This written domain remained stable after a number of weeks and even spread through a larger area of the lamella, showing it is stable against back-switching. The next step will be to analyse the written domains using high-resolution TEM, by which the dipole shifts occurring due to polarisation development within the wall can be mapped and hence provide experimental confirmation of this phenomenon.

During the investigation of lamellae of lead titanate, it was found that a charged domain wall junction had formed within the lamella to balance stresses within the system. Using HRTEM, the polarisation direction in the visible domains was mapped using Fourier masking and dipole shift mapping and determined to be of head-to-head character. Such a charged domain junction has never before been observed in a lead titanate lamella. In addition, the scanning electron beam was observed to change the domain pattern in the lamella during the experiment, demonstrating in-situ switching.

The work presented here provides an essential starting point for two very promising topological systems. With further work to refine sputtering parameters and film growth properties, as well as more detailed magnetic measurements, the thin films of CoxZnyMnz alloys could demonstrate even more interesting magnetic properties and potentially produce a skyrmion phase. By changing the chemical properties, it is possible to tailor the Curie temperature to required values and hence could prove invaluable to potential skyrmion-based devices. Similarly, the investigation into the properties of the domain walls of lead titanate is a promising starting point for further work; it has been demonstrated that 180 domains can be written in repaired lamellae and that the domains remain stable after a long period of time without back-switching. Further investigation using HRTEM will demonstrate the possible existence of the predicted in-wall polarisation, paving the way for the realisation of polar skyrmion bubbles in single-crystal lead titanate.
Date of AwardJul 2020
Original languageEnglish
Awarding Institution
  • Queen's University Belfast
SupervisorMarty Gregg (Supervisor) & Dr David McKee (Supervisor)

Cite this

Topological Structures in Ferroic Materials
Mackel, J. (Author). Jul 2020

Student thesis: Doctoral ThesisDoctor of Philosophy