Theses

Here I compile a (short) list of theses based around the μSR technique. Nowadays, the use μSR is widespread enough that a comprehensive compilation is impractical. Instead, this list mainly reflects works that I’ve read (or at least skimmed).

So far, this collection contains 6 theses. They are listed below in reverse chronological order.

2021

Title: Charge-neutral muon centers in magnetic and non-magnetic materials: implications and applications
Author: M. H. Dehn
Degree: PhD
School: University of British Columbia
Address: Vancouver
Year: 2021
Abstract: 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, ₂O₃ 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.
: 10.14288/1.0402625
: https://hdl.handle.net/2429/80070

Title: Doping and interface effects in topological materials
Author: J. A. Krieger
Degree: PhD
School: ETH Zürich
Address: Zürich
Year: 2021
Abstract: Topological materials are characterized by their exotic electronic bulk and boundary states. This rich phenomenology can be further extended by introducing novel properties into these materialsvia doping or via proximity effects at interfaces. This thesis presents a detailed investigation of these systems, establishing low energy muon spin spectroscopy (LE-μSR) and soft X-ray angle resolved photoemission spectroscopy (SX-ARPES) as complementary probes of their magnetic and electronic properties. We show that these techniques are suited both to further our fundamental understanding of the physics in topological materials and to reveal tuning parameters that can be subsequently used in designing devices.
First, we applied this approach to investigate the role of magnetic and superconducting doping intopological insulators. We were able to show that Cr and V doping in the topological insulation (Bi,Sb)2Te3 can generate long range magnetic order, but we found that this approach inherently suffers from a broad magnetic transition where the magnetism appears gradually in parts of the sample. We identified the critical dopant concentration, below which the topological insulatorremains only partially magnetically ordered even at the lowest temperature. Furthermore, we discovered the presence of a non-dispersive V impurity band in the vicinity of the Fermi level. We identify these factors as main contributors to the low temperature limits on establishing a quantum anomalous Hall effect in these systems.
We then studied proximity induced magnetism and superconductivity in topological insulators. We compared the magnetic proximity between EuS and the topological insulator Bi2Se3 with proximityof EuS to the topologically trivial metal titanium and show that the local magnetic fields behave similarly in both systems, implying that their origin is mostly independent of the topological properties of the interface electronic states. In addition, we revealed the band structure of the buried topological insulator.
At the interface between the Bi2Se3 and the conventional superconductor Nb, we discovered an odd-frequency superconducting state that is proximity induced into the topological insulator. This manifests itself as an intrinsic paramagnetic Meissner effect in Bi2Se3, which we detected in depth-resolved measurements of the local magnetic field.
Finally we presented first attempts at introducing magnetism into Weyl semimetals. For this we have identified 2H-MoTe2 as an intrinsic semiconducting antiferromagnet. Such a component could be invaluable for various spintronics and topotronics devices, especially due to its layered structure which allows it to be easily integrated into heterostructures.
The results of this thesis emphasize the importance of a thorough microscopic understanding ofdoping and interface effects and demonstrate that using a combination of LE-μSR and SX-ARPES offers a more generally applicable experimental route towards this goal.
: 10.3929/ethz-b-000460760
: https://hdl.handle.net/20.500.11850/460760

2012

Title: Absolute value of the magnetic penetration depth and field profile in the Meissner state of exotic superconductors Yttrium barium copper oxide and Co-doped pnictide
Author: M. M. Hossain
Degree: PhD
School: University of British Columbia
Address: Vancouver
Year: 2012
Abstract: One of the fundamental quantities of a superconductor is the magnetic penetration depth, λ, which is the characteristic length scale that a magnetic field penetrates into the surface of a super-conductor while in the Meissner state. In the clean limit the absolute value of λ is directly related to the superfluid density n_s via 1/λ² = μ₀e²n_s/m^*, where m^* is the effective mass. Consequently, its variation as a function of temperature, doping and orientation are of central importance intesting microscopic theories of exotic superconductors.
A low energy beam of spin polarized muons has recently been developed, at the Paul Scherrer Institute, to directly measure λ in a superconductor. When a muon (μ⁺) decays, it emits a fast decay positron preferentially along the direction of its spin due to the parity violating decay. The time evolution of statistical average direction of the spin polarization of the muon ensemble depends sensitively on the local magnetic field which can be monitored as a function of the mean depth of implantation. In this way it is possible to measure the field profile near the surface ofa superconductor and extract the magnetic penetration depth in a direct manner which is not otherwise possible with conventional bulk methods.
In this thesis, accurate measurements of λ and its anisotropy (︀≡ λ_a/λ_b)︀ have been made for three different oxygen (x = 6.52, 6.92 and 6.998) contents of YBa₂Cu₃O_6+x as well as in Ba(Co_0.074Fe_0.926)₂As₂. The measured values of λ and the in-plane anisotropies are considerably different from that reported in the literature, using less direct methods. The a–b anisotropy is surprisingly insensitive to x in YBa₂Cu₃O_6+x. We observe an exponential decay of the magnetic field and corresponding supercurrent density deep inside the crystals. Small deviationsfrom the London model are observed which indicate there is a suppression of the supercurrent density close to the surface. The measured (λ) values are also found to depart substantially from the Uemura relation (︀T_c ∝ 1/λ²)︀.
: 10.14288/1.0073321
: https://hdl.handle.net/2429/43479

Title: Superconductivity and magnetism in cuprate single crystals and thin-film heterostructures
Author: B. M. Wojek
Degree: PhD
School: Universität Zürich
Address: Zürich
Year: 2012
Abstract: The work at hand is concerned with the study of elementary properties of cupra-te high-temperature superconductors by means of low-energy muon-spin rotation(LE-μSR). One of the elementary quantities of a superconductor isits magne-tic penetration depthλwhich is the characteristic length on which the magneticinduction decays into the material and which is a measure of the superfluid den-sity. In anisotropic superconductorsλdepends on the direction of the screeningcurrents—in the cupratesλabis the relevant screening length if the currents flowparallel to the CuO2planes of the structure whileλcdetermines the decay ofthe magnetic field for currents perpendicular to the planes.In YBa2Cu3O7−δtheexistence of one-dimensional CuO chains parallel to the planes implies an ortho-rhombic structure on the material which gives rise to an anisotropy in the in-planepenetration depth and therefore differentλaandλb. Here, the LE-μSR techniquewith an effective background-suppression method has been employed to determineλaband its in-plane anisotropy in the most direct way by measuring the magneticfield profile and its temperature dependence in the Meissner state of optimallydoped detwinned YBa2Cu3O7−δsingle crystals (Tc≈94 K). The field profileshave been found to be exponential on the scale ofλabbut there are deviationsclose to the crystal surface. These can partially be related to surface-flux-trappingeffects, however, a full explanation remains elusive. The obtained average valuesofλaband the in-plane anisotropy agree overall well with resultsof studies withless direct methods.
The further parts of this work report on studies of cuprate thin-film heterostructu-res. Such structures consisting of thin layers of materialswith different electronicproperties are ideally suited to study the interplay between them. First, trilayerand bilayer samples of superconducting YBa2Cu3O7−δ(Tc≈88 K) and isostructu-ral antiferromagnetically ordered “semiconducting” PrBa2Cu3O7−δ(TN≈280 K)have been investigated. Through the observation of the Meissner effect it is foundthat superconductivity can be induced in PrBa2Cu3O7−δlayers by the proximityto YBa2Cu3O7−δlayers while the intrinsic antiferromagnetic ordering of the pla-nar Cu moments in about 90 % of the volume of the PrBa2Cu3O7−δis hardlydisturbed by the Cooper-pair transport through the material. The reason for thatmight be that the transport in fact is mainly governed by tunneling through lo-calized states in the CuO chains or it is probably found in thedelicate electronicstructure of PrBa2Cu3O7−δitself, whose insulating state is close to superconduc-tivity and where therefore, small changes in the electronicproperties might causethe appearance of a superconducting phase at least in parts of the samples.
In a second thin-film-heterostructure study the coupling between optimally do-ped La1.84Sr0.16CuO4(Tc≈32 K) through a barrier layer of strongly underdopedLa1.94Sr0.06CuO4(T′c.5 K) in the “pseudogap state” has been investigated. Inthese structures superconducting screening throughout all layers is observed in theMeissner state up to temperatures of about 4T′cindicating an induced superfluiddensity in the barrier layer above its own transition temperature. However, theinduced superfluid density is suppressed more effectively bythermal excitationsthan in intrinsic superconductors and vanishes at a temperature smaller thanTc.On the premise of proximity effects based on a leaking of Cooper pairs from asuperconductor into a normal metal these effects are not expected over such atemperature range.
: 10.5167/uzh-57024
: https://www.zora.uzh.ch/id/eprint/57024/

1998

Title: The magnetic penetration depth and the vortex core radius in type-II superconductors
Author: J. E. Sonier
Degree: PhD
School: University of British Columbia
Address: Vancouver
Year: 1998
Abstract: In this thesis, muon spin rotation (μSR) measurements of the internal magnetic field distribution in the vortex state of the high-T[sub c] superconductor YBa₂Cu₃O₇_[sub ⍴] and the conventional type-II superconductor NbSe₂ are presented. From the measured field distributions, the "characteristic length scales of superconductivity" are extracted. It is found that both the a-b plane magnetic penetration depth λ[sub ab] and the vortex-core radius r[sub o] (which is closely related to the coherence length Ɛ[sub ab] vary as functions of temperature and magnetic field in both materials.
The behaviour of λ[sub ab](H, T) and r[sub 0](H, T) at low temperatures is found to be substantially different in YBa₂Cu₃0₇_⍴ from what is observed in NbSe₂. This reflects the unconventional nature of the pairing mechanism in this compound. The temperature dependence of λ[sub ab] in the vortex state of YBa₂Cu₃0₇_⍴ agrees well with microwave cavity measurements in the Meissner state. The magnetic field dependence of λ[sub ab], in YBa₂Cu₃0₇_⍴ is found to be considerably stronger than in NbSe₂. This is likely due to both the nonlinear and the nonlocal effects associated with nodes in the superconducting energy gap. However, in NbSe₂ (where nonlocal effects are negligible), it is not clear whether the field dependence of can be explained solely in terms of the nonlinear effects associated with an isotropic s-wave energy gap.
The vortex-core radius r[sub 0] is found to decrease with increasing magnetic field in both superconductors. The reduction in the vortex-core size appears to be due to the increased strength of the vortex-vortex interactions. An important consequence of this variation with field is that Ɛ[sub ab] in the vortex state, which is generally regarded to be extremely small i n the high-T[sub c] compounds, is comparatively large at low magnetic fields.
The vortex-core radius is also found to increase with increasing temperature. The strength of this variation is considerably weaker in YBa₂Cu₃0₇_⍴ than in NbSe₂. One possible interpretation is that the quantum limit is realized at much higher temperatures in the high-T[sub c] compound. The measured temperature dependence of r[sub 0] in both superconductors is weaker than current theoretical predictions for an isolated vortex.
Finally, the effects of vortex pinning and thermal fluctuations of the vortex lines are considered. It is found that the vortex lattice is strongly pinned in YBa₂Cu₃0₇_⍴. The vortex lattice in the underdoped compound YBa₂Cu₃O₆.₆₀ is found to exhibit quasi-2D behaviour. In particular, a field-induced transition of the 3D-vortex lattice to a 2Dvortex lattice is observed—which appears to be due to the small c-axis coherence length and vortex pinning in the Cu0₂ layers of this material. Also, the 3D-solid vortex lattice in YBa₂Cu₃O₆.₆₀ at low temperatures is found to melt and/or undergo a transition to a 2D-vortex lattice as the temperature is increased.
: 10.14288/1.0085673
: https://hdl.handle.net/2429/8608

1997

Title: μSR studies of the metallic alkali fullerides
Author: W. A. MacFarlane
Degree: PhD
School: University of British Columbia
Address: Vancouver
Year: 1997
Abstract: Results of muon spin rotation (μ-SR) in the metallic intercalated C₆₀ compounds (AnC₆₀, where An are n alkali metal atoms) are presented. Except for the case of K₁C₆₀, the metallic state of these systems is unstable at low temperature (to a superconducting transition in A₃C₆₀ and a magnetic metal insulator transition in A₁C₆₀).
In A₃C₆₀, the properties of the metallic and superconducting states are investigated using i) diamagnetic muons to probe the distribution of internal magnetic field and ii) paramagnetic muonium (Mu) trapped within the C₆₀ cage to probe the electronic excitations. Mu is found to exhibit strong T₁ relaxation due to its interaction with the conduction electrons. In the superconducting state this relaxation rate exhibits a small enhancement (Hebel-Slichter coherence peak) which possesses an anomalously strong magnetic field supression. Exponential temperature dependence of the relaxation rate at low reduced temperature is observed, and from this estimates of the superconducting energy gap are obtained. At very low reduced temperature, deviations from this behaviour are found. Estimates of the magnetic penetration depth from broadening of the diamagnetic precession signal in the vortex state are also presented and discussed.
In A₁C₆₀ (A = Rb and Cs), the magnetic state is investigated with zero field μ-SR. Observation of a small rapidly damped oscillation below 2K in Cs₁C₆₀ is the first evidence from μ-SR of magnetic order in these materials. The relaxation at higher temperature indicates that the internal fields are static and possess a broad distribution, indicating a highly disordered static magnetic structure. From the magnitude of the zero field relaxation rates, estimates of the magnitude of the internal field are made.
: 10.14288/1.0085447
: https://hdl.handle.net/2429/8562