Andrew MacFarlane

Professor

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Doctoral Student Supervision

Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.

Charge-neutral muon centers in magnetic and non-magnetic materials: implications and applications (2021)

Spin polarized muons are widely known as extremely sensitive local probes of magnetism. Muon spin rotation (μSR) spectroscopy has made key contributions in the study of complex condensed matter systems such as frustrated and dilute magnetic systems and superconductors. Additionally, positively charged muons implanted into semiconductors and insulators often bind an electron to form muonium (Mu=[μ+e-]), a charge-neutral muon-electron bound state. Muonium has been studied extensively in a wide range of semiconducting and insulating materials, motivated by the fact that its electronic structure inside a material is virtually identical to that of isolated hydrogen defects, one of the most ubiquitous impurities in semiconductors. However, such measurements are thought to be limited to non-magnetic compounds; in magnetic materials, muonium is widely assumed to be unobservable, and charge-neutral muon states are generally not considered relevant.Here, we present strong evidence that charge-neutral muon centers do exist in magnetic compounds. Detailed μSR investigations of the prototypical antiferromagnets Cr2O3, Fe2O3 and MnF2 reveal that charge-neutral muon states can form and take on different shapes, including muon-polaron complexes and interstitial centers with large muon-electron hyperfine coupling. Crucially, we find that in magnetic materials, charge-neutral muon states do not display any signatures conventionally associated with muonium, effectively “hiding” their presence. Despite their inconspicuous signals, charge-neutral centers can significantly change how the muons interact with their host material and thus significantly alter the μSR signals. In addition, we clearly demonstrate for MnF2 that the charge-state of the muon and the magnetic properties measured by μSR are closely related, and both aspects have to be considered when using μSR to determine the intrinsic magnetic properties. These results indicate that μSR may be useful to study not only the electronic impact of hydrogen defects, but also their role as magnetic impurities in non-conductive magnetic compounds.For comparison, we also investigate charge-neutral muon-polaron complexes in non-magnetic TiO2 as well as vacuum-like muonium diffusing through the voids of an amorphous silica aerogel. These examples are used to highlight the differences and similarities between charge-neutral muon states in magnetic and non-magnetic materials.

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The interfacial dynamics of amorphous materials as revealed by beta-NMR measurements and molecular simulations (2021)

The free surface is important for developing a fundamental understanding of dynamical length scales in glasses. We first investigate the relaxation of freestanding atactic polystyrene (aPS) thin films with molecular dynamics simulations. As in previous coarse-grained simulations, the surface modification on the relaxation times for backbone segments and phenyl rings may be expressed as a power law relation, wherein the bulk dynamics fully encapsulate the temperature-dependence. Variation of the coupling exponent with distance from the surface is consistent with depth-dependent activation barriers. We also quantify a reduction of dynamical heterogeneity, transient spatial fluctuations of the dynamics, at the interface which can be interpreted in the framework of cooperative models for glassy dynamics.Capable of depth-resolved measurements near the surface, implanted-ion beta-detected nuclear magnetic resonance (?-NMR) has been a powerful technique for the study of dynamics in aPS thin films. We have completed and commissioned an upgrade to the ?-NMR spectrometer, extending the accessible upper temperature, and enabling a direct comparison between this experimental technique and the molecular dynamics simulations. We demonstrate that the modified spectrometer is now capable of operation to at least 400 K, an improvement of more than 80 K. We also demonstrate the application of ?-NMR as a probe of ionic liquid molecular dynamics through the measurement of ⁸Li⁺ spin-lattice relaxation (SLR) and resonance in 1-ethyl-3-methylimidazolium acetate. The motional narrowing of the resonance, and the local maxima in the SLR rate, 1/T₁, imply a sensitivity to sub-nanosecond Li⁺ solvation dynamics. From an analysis of 1/T₁, we extract an activation energy and Vogel-Fulcher-Tammann constant in agreement with the dynamic viscosity of the bulk solvent. Near the melting point, the lineshape is broad and intense, and the form of the relaxation is non-exponential, reflective of our sensitivity to heterogeneous dynamics near the glass transition. We also employ the depth resolution capabilities of this technique to probe the subsurface dynamics with nanometer resolution. We show modified dynamics near the surface in, and above, the glassy state.

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Diffusion and surface trapping of 8Li in rutile TiO2 and the comparison on 8Li and 9Li spin relaxation using ?-NMR (2020)

It is well established that the properties of many materials change as their thicknessis shrunk to the nanoscale, often yielding novel features at the near-surface regionthat are absent in the bulk. Even though there are several techniques that can studyeither the bulk or the surface of these materials, there are very few that can scanthe near-surface region of crystals and thin films versus depth. Beta-detected NMR(b-NMR) is capable of this and therefore has been established as a powerful toolfor material science. This thesis aims to further develop the capabilities of b-NMR.The first part of this thesis demonstrates that by comparing the spin-lattice relaxationrates (SLR) of two radioactive Li isotopes (⁸,⁹Li) it is possible to distinguishwhether the source of SLR in a given situation is driven by magnetic or electricinteractions. This is an important development for b-NMR, since there are instanceswhere it is problematic to distinguish whether the measured relaxation is due tomagnetic or electric fluctuations. Using this method, it was found that the SLR inPt is (almost) purely magnetic in origin, whereas the spin relaxation in SrTiO₃ isdriven (almost) entirely by electric quadrupolar interactions.The second part of this thesis traces the development of a-radiotracer, that usesthe progeny a-particles from the decay of ⁸Li, in order to directly measure thenanoscale diffusivity of Li⁺ in Li-ion battery materials. To develop this technique,Monte Carlo simulations of the experimental configuration were carried out, a newapparatus and a new a-detector were designed and used for experiments on rutileTiO₂. In rutile, the measurements revealed that Li+ gets trapped at the (001) surface,a result that helps explain the suppressed intercalation of Li⁺ in bulk rutile. Moreover,the diffusion rate of Li⁺ in rutile was found to follow a bi-Arrhenius relationship,with a high-T activation energy in agreement with other reported measurementsand a low-T component of similar magnitude with the theoretically calculateddiffusion barrier as well as the activation energy of the Li-polaron complex foundwith b-NMR below 100 K.

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Microscopic dynamics of isolated lithium in crystalline solids revealed by nuclear magnetic relaxation and resonance of xLi (2020)

This thesis reports measurements on the dynamics of isolated lithium in single crystal materials using ion-implanted ⁸Li β-detected nuclear magnetic resonance. From spin-lattice relaxation and resonance measurements, we identify the kinetic parameters describing the ion’s site-to-site hop rate – the elementary process in long-range solid-state diffusion – and compare the results with theoretical work in the literature, as well as experiments at higher concentration. In addition to these “ionic” details, the nuclear magnetic resonance probe provides information on the electronic properties of the host, whose most intriguing features are also discussed. In the one-dimensional ion conductor rutile TiO₂, we find two sets of thermally activated dynamics: one below 100 K and another at higher temperatures. We suggest the low temperature process is unrelated to lithium motion, but rather a consequence of electron polarons in the vicinity of the implanted ⁸Li⁺. Above 100 K, Li⁺ undergoes diffusion as an isolated uncomplexed cation, characterized by an activation energy and prefactor that are in agreement with macroscopic diffusion measurements, but not with theory. In Bi₂Te₂Se, a topological insulator with layered tetradymite structure, implanted ⁸Li⁺ undergoes ionic diffusion above 150 K, likely in the van der Waals gap between adjacent Te planes. A comparison with structurally related materials reveals the mobility of isolated Li⁺ is exceptional. At lower temperature, we find linear Korringa-like relaxation, but with a field dependent slope and intercept, accompanied by an anomalous field dependence to the resonance shift. We suggest that these may be related to a strong contribution from orbital currents or the magnetic freezeout of charge carriers in this heavily compensated semiconductor. In the doped tetradymite topological insulators Bi₂Se₃:Ca and Bi₂Te₃:Mn, the onset of lithium dynamics is suppressed to above 200 K. At low temperatures, the nuclear magnetic resonance properties are those of a heavily doped semiconductor in the metallic limit, with Korringa relaxation and a small, negative, temperature-dependent Knight shift. From this, we make a detailed comparison with isostructural Bi₂Te₂Se.

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Beta-detected NMR of 8Li+ in spintronic materials (2013)

β-detected Nuclear Magnetic Resonance (βNMR) employs radioactive ⁸Li⁺ , which is optically spin-polarized, as a local probe to study magnetism in materials via β decay. In this thesis, βNMR is applied to spintronic materials, including GaAs, Ga₁₋xMnx Asand Fe/GaAs heterostructures in a depth-controlled manner at TRIUMF. High resolution β-NMR measurements were carried out on GaAs crystals (semi-insulating (SI-GaAs) and heavily doped n-type (n-GaAs)) as a control experiment for β-NMR on Fe/GaAs heterostructures. A small resonance shiftwas observed and found to be dependent on depth, temperature and doping. The depth dependence is only observed in SI-GaAs and not in n-GaAs. The resonance shift below 150 K in both GaAs is ∼ 100 ppm, on the same orderof some Knight shifts of ⁸Li⁺ in noble metals.Ga₁₋xMnxAs is the first βNMR study on a ferromagnetic material through the ferromagnetic transition. Both spin lattice relaxation (SLR) and resonance of ⁸Li⁺ were measured. Two resonances were clearly resolved from the nonmagnetic GaAs substrate and the magnetic Ga₁₋xMnxAs film. The latter one negatively shifts and is linearly proportional to the applied field. The hyperfine coupling constant AHF of ⁸Li⁺ in Ga₁₋xMnxAs is found to be negative. The SLR rate λ does not follow Korringa’s Law and its amplitude shows a weak temperature dependence through TC. The behaviours of AHF and λ suggest that the delocalized holes originate from a Mn derived impurity band. No evidence of magnetic phase separation is found. ⁸Li⁺ provides a new depth-dependent local probe to detect injected spin polarization. We measured the ⁸Li⁺ resonance in Fe/GaAs heterostructures with semi-insulating and heavily doped n-type substrates, with and without injected current. With zero current, no spin polarization at thermal equilibrium is found. A new current injection system was designed and setup to conduct current injection from the thin Fe layer into the n-GaAs substrate. We found effects of local Joule heating and a very small stray field caused by the injected current but no convincing evidence of injected spin polarization.

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Using low-energy 8Li beta-detected NMR to probe the magnetism of transition metals (2012)

Low-energy, beta-radiation-detected nuclear magnetic resonance (β-NMR) is applied to probe the magnetism of Au and Pd. The measurements were carried out at the TRIUMF β-NMR facility using optically spin-polarized ⁸Li⁺ as the probe. The behaviour of ⁸Li⁺+ in Au was investigated using samples in the form of a foil and a 100 nm film evaporated onto a MgO (100) substrate. The results are in overall agreement with those obtained previously in Ag, Cu, and Al. Narrow, temperature-independent resonances are observed and assigned to ions stopping in the octahedral interstitial and substitutional lattice sites; the latter appearing only for temperatures above 150 K which is attributed to a thermally-activated site change. The spin-lattice relaxation rate of substitutional site ions is less than half as fast at ambient temperature as that in the other simple metals. The rate is independent of external field for fields greater than 15 mT. A Korringa analysis for the substitutional ions indicates no significant electron enhancement over that of a free electron gas. For all four metals, the enhancements obtained are smaller than those for the host nuclei. No depth dependence was found for the resonances in Au.The highly exchange-enhanced metal Pd was studied using samples in the form of a foil and a 100 nm film evaporated onto a SrTiO₃ (100) substrate. Strongly temperature-dependent, negative shifts are observed that scale with the temperature dependence of the host susceptibility between room temperature and 110 K. The resonances appear as two partially resolved lines that exhibit similar behaviour with temperature. The linewidths are broad and double upon cooling. The data are indicative of ions stopping in a site of cubic symmetry. The spin-lattice relaxation rate increases linearly with increasing temperature and eventually saturates at higher temperatures, consistent with the prediction from spin fluctuation theory. In contrast to the simple metals, large Korringa enhancements are obtained in this host. Ferromagnetic dynamical scaling is observed to hold above 110 K. Features below this temperature indicate that the Li ions locally induce a further enhancement of the static susceptibility. The temperature dependence of the modified susceptibility is in keeping with the prediction for a weak itinerant ferromagnet just above the Curie temperature; however, there is no evidence of static order.

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Magnetic Properties Near the Surface of Cuprate Superconductors Probed Using Beta Detected NMR (2010)

Beta-detected Nuclear Magnetic Resonance (β-NMR) uses highly spin polarized β-emitting nuclei as a probe. Besides its use in nuclear physics, it hasalso become a powerful and sensitive tool in condensed matter physics and materials science. At TRIUMF, β-NMR of ⁸Li+ has been developed to study materials in a depth-resolved manner, where the implantation depth of ⁸Li+ is controlled via electrostatic deceleration. In this thesis, β-NMR of ⁸Li+ has been used to study high-Tc cuprate superconductors (HTSC). The objectiveof this work is to search for spontaneous magnetic fields generated by a possible time-reversal symmetry breaking (TRSB) superconducting statenear the surface of hole-doped YBa₂Cu₃O₇−d (YBCO), and study the nature of the vortex lattice (VL) in YBCO and electron-doped Pr₂−xCexCuO₄−d(PCCO). For several advantages, our measurements were carried out by implanting ⁸Li+ in thin silver films evaporated on the superconductors.In our TRSB studies, the magnetic field distribution p(B) is measured 8 nm away from the Ag/YBCO interface in magnetic fields B₀ = 5 to 100 G, applied parallel to the interface. p(B) showed significant broadening below the Tc of ab- and c-axis oriented YBCO films. The broadening signals the existence of weak disordered magnetic fields near the surface of YBCO. From the broadening’s temperature and field dependence we draw an upper limit of 0.2 G on the magnitude of spontaneous magnetic fields associated with TRSB.To study the VL, p(B) is measured at average implantation depths ranging from 20 to 90 nm away from the Ag/YBCO or Ag/PCCO interface in B₀ = 0.1 to 33 kG, applied perpendicular to the surface. p(B) showed a dramatic broadening below Tc as expected from the emerging field lines ofthe VL in the superconductor. In YBCO, p(B) is symmetric and the dependence on B0 is much weaker than expected from an ideal VL, indicatingthat the vortex density varies across the face of the sample on a long length scale, likely due to vortex pinning at twin boundaries. In PCCO, a 2D VLis established due to the high anisotropy of the superconductor leading to a nearly symmetric p(B).

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