Towards the Development of Computational Techniques and Methodologies for the Analysis of Experimental Positron Annihilation and Angle-Resolved Photo-Emission Spectroscopy

Abstract

In the last century, the study of materials and their constituents has been responsible for the largest technological advances in human history. It is through understanding the properties of these materials and their classes that the emergence of new technology is made possible. Such classes are the Heusler alloys, magnetic alloys made from non-magnetic elements that are useful in the field of spintronics; and perovskites, a unique subset of crystals whose variance in centrosymmetry can give rise to ferroelectric effects which are useful in the production of microelectronics and solar cells. Therefore, it is essential that for technological advancements to be made, not only does the theory of material physics need to advance, but so must the tools and methods used to analyse them. This thesis focuses on advancing theoretical and computational approaches for using and analysing experimental spin-polarised angular correlated electron-positron annihilation radiation (ACAR) and angle-resolved photoemission spectroscopy (ARPES) data in order to obtain physical values which provide a deeper insight into the material. These methods were benchmarked against independently measured Ni, Cu2MnAl and La0.7Sr0.3MnO3 ACAR spectra and experimentally measured Ag ARPES data.

The lifetime of the positron before annihilating with an electron can be predicted using theoretical electronic structure techniques such as density functional theory (DFT). These predicted lifetimes can vary depending on the approximations of the electron exchange-correlation functional and electron-positron enhancement factor (which describes the electron-positron correlations) used. Here, the lifetime for several elements across the Periodic Table was predicted using different combinations of these approximations and compared with the experimentally measured values to determine which configuration gives the most consistently accurate lifetimes overall. Alongside this, a new approximation of the electron-positron enhancement factor was derived using the meta-generalised gradient approximation (meta-GGA) framework and was included.

Arguably, the most essential component of an ACAR experiment is a positron source, often sodium-22 (22Na) undergoing β+ decay. The weak force mediates this process and, as such, violates parity, emitting positrons with preferential polarisation in the direction of propagation. This positron polarisation has been successfully extracted by fitting DFT two-photon momentum density (TPMD) calculations to the experimental ACAR data.

Positrons are statistically more likely to annihilate with electrons of the opposite spin, but occasionally, parallel spins will annihilate, often resulting in the emission of 3 photons, known as 3γ annihilation. Consequently, 3γ annihilations are related to the spin polarisation of the positron. Often, any and all
3γ contributions to experimental TPMDs are ignored due to their low probability. Nevertheless, in this thesis, the impact of 3γ annihilations is evaluated by extracting the value of the 3γ polarisation, P3γ. This contribution was determined safe to ignore on the basis that it was small enough, however, its contribution did provide minor adjustments to quantities related to a variety of physically meaningful variables such as the positron lifetimes.

The total lifetime of a thermalised positron in a material is measured by positron annihilation lifetime spectroscopy (PALS), but this experimental technique is unable to measure the lifetimes of the positron annihilating with each electron spin within a magnetic material. This thesis provides a method to extract the positron lifetimes for the annihilation with each electron spin from individual spin channels measured by ACAR and compares these extracted results with the total lifetimes measured by PALS which yield a good agreement.

Finally, an approach to generate the full three-dimensional (3D) Fermi surface from several two-dimensional (2D) contours is presented. The aim is to be able to construct the full 3D Fermi surface from as few measured APRES spectra as possible. This technique was benchmarked with the Fermi surface of
Ag which it successfully reconstructs from three contours. The applicability of this technique was shown by using different ARPES Fermi surface contours from the surface of a polycrystalline Ag sample measured at the University of Bristol’s NanoESCA facility. A very good 3D Fermi surface from the ARPES data
can be reconstructed from only three different contours. To ensure the universality of this technique, it was applied to a small number of predicted Fermi surface contours of V and (in a blind test) Pb which successfully reconstructed the full 3D Fermi surface.

Date of Award	18 Jun 2024
Original language	English
Awarding Institution	University of Bristol
Supervisor	Chris Bell (Supervisor) & Stephen B Dugdale (Supervisor)