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More than two decades after the discovery of superconductivity in Sr$_2$RuO$_4$, it is still unclear whether the order parameter has a single component or two degenerate components. For any two-component scenario, application of uniaxial strain is expected to lift the degeneracy, generating two distinct phase transitions. The presence of a second (lower-temperature) transition may be observable by probes that are sensitive to changes in the London penetration depth, $\lambda$, as a function of temperature, $T$. Here, we use scanning SQUID microscopy combined with a uniaxial strain device to test for a second transition under strain. We only observe a single transition. Within the temperature range where a second transition has been suggested by $\mu$SR measurements, we further place a tight upper bound of less than 1% on the change in the zero temperature superfluid density $n_s\propto\lambda^{-2}(0)$ due to a second transition, suggesting that such a transition does not occur. These results constrain theories of the order parameter in Sr$_2$RuO$_4$.

Strontium ruthenate Sr$_2$RuO$_4$ is an unconventional superconductor whose pairing symmetry has not been fully clarified, despite more than two decades of intensive research. Recent NMR Knight shift experiments have rekindled the Sr$_2$RuO$_4$ pairing debate by giving strong evidence against all odd-parity pairing states, including chiral $p$-wave pairing that was for a long time the leading pairing candidate. Here, we exclude additional pairing states by analyzing recent elastocaloric measurements [YS. Li et al., Nature 607, 276--280 (2022)]. To be able to explain the elastocaloric experiment, we find that unconventional even-parity pairings must include either large $d_{x^2 - y^2}$-wave or large $\{d_{xz} \mid d_{yz}\}$-wave admixtures, where the latter possibility arises because of the body-centered point group symmetry. These $\{d_{xz} \mid d_{yz}\}$-wave admixtures take the form of distinctively body-centered-periodic harmonics that have horizontal line nodes. Hence $g_{xy(x^2-y^2)}$-wave and $d_{xy}$-wave pairings are excluded as possible dominant even pairing states., 20 pages, 8 figures

We report $^{139}$La nuclear magnetic resonance measurements on a single-crystal sample of La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ under uniaxial stress. The spin order is shown to be more robust than at $x = 0.115$ doping, however, for magnetic field $H$ in the $c$ direction and the stress applied along the [110] direction ($\sigma_{[110]}$) the spin order transition temperature $T_{\text{SO}}$ is rapidly suppressed. This is in stark contrast to the behavior with stress in [100] direction ($\sigma_{[100]}$), which has virtually no effect on $T_{\text{SO}}$. For $H \parallel [1\overline{1}0]$, $\sigma_{[110]}$ stress has a weakened effect, and the rate $d T_\text{SO}/d \sigma_\text{[110]}$ is drastically reduced. Thus, $H\parallel [1\overline{1}0]$ acts as a stabilizing factor for spin-stripe order. Also, the onset temperature of the low-temperature tetragonal crystal structure $T_{\text{LTT}}$ is essentially unaffected by [110] stress, while it decreases slowly under compression along [100]. We develop a Landau free energy model and interpret our findings as an interplay of symmetry-breaking terms driven by the orientation of spins. These findings put constraints on the applicability of theoretical models for the development of spin-stripe order., Comment: 25 pages, 10 figures

Funding: We gratefully acknowledge support from the Engineering and Physical Sciences Research Council (Grant Nos. EP/T02108X/1 and EP/R031924/1), the European Research Council (through the QUESTDO project, 714193), and the Leverhulme Trust (Grant No. RL-2016-006). E.A.M., A.Z., and I.M. gratefully acknowledge studentship support from the International Max-Planck Research School for Chemistry and Physics of Quantum Materials. N.K. is supported by a KAKENHI Grants-in-Aids for Scientific Research (Grant Nos.18K04715, and 21H01033), and Core-to-Core Program (No. JPJSCCA20170002) from the Japan Society for the Promotion of Science (JSPS) and by a JST-Mirai Program (Grant No. JPMJMI18A3). APM and CWH acknowledge support from the Deutsche Forschungsgemeinschaft - TRR 435 288 - 422213477 (project A10). We thank Diamond Light Source for access to Beamline I05 (Proposals SI27471 and SI28412), which contributed to the results presented here. We report the evolution of the electronic structure at the surface of the layered perovskite Sr2RuO4 under large in-plane uniaxial compression, leading to anisotropic B1g strains of εxx − εyy = −0.9 ± 0.1%. From angle-resolved photoemission, we show how this drives a sequence of Lifshitz transitions, reshaping the low-energy electronic structure and the rich spectrum of van Hove singularities that the surface layer of Sr2RuO4 hosts. From comparison to tight-binding modelling, we find that the strain is accommodated predominantly by bond-length changes rather than modifications of octahedral tilt and rotation angles. Our study sheds new light on the nature of structural distortions at oxide surfaces, and how targeted control of these can be used to tune density of states singularities to the Fermi level, in turn paving the way to the possible realisation of rich collective states at the Sr2RuO4 surface. Postprint

Muon spin rotation/relaxation ($\mu$SR) and polar Kerr effect measurements provide evidence for a time-reversal symmetry breaking (TRSB) superconducting state in Sr$_2$RuO$_4$. However, the absence of a cusp in the superconducting transition temperature ($T_{\rm c}$) vs. stress and the absence of a resolvable specific heat anomaly at TRSB transition temperature ($T_{\rm TRSB}$) under uniaxial stress challenge a hypothesis of TRSB superconductivity. Recent $\mu$SR studies under pressure and with disorder indicate that the splitting between $T_{\rm c}$ and $T_{\rm TRSB}$ occurs only when the structural tetragonal symmetry is broken. To further test such behavior, we measured $T_\text{c}$ through susceptibility measurements, and $T_\text{TRSB}$ through $\mu$SR, under uniaxial stress applied along a $\langle 110 \rangle$ lattice direction. We have obtained preliminary evidence for suppression of $T_\text{TRSB}$ below $T_\text{c}$, at a rate much higher than the suppression rate of $T_\text{c}$., Comment: 9 pages, 4 figures and Appendix, accepted for publication in PRB

We report the evolution of the electronic structure at the surface of the layered perovskite Sr$_2$RuO$_4$ under large in-plane uniaxial compression, leading to anisotropic $B_{1g}$ strains of ${\varepsilon_{xx}-\varepsilon_{yy}=-0.9\pm0.1\%}$. From angle-resolved photoemission, we show how this drives a sequence of Lifshitz transitions, reshaping the low-energy electronic structure and the rich spectrum of van Hove singularities that the surface layer of Sr$_2$RuO$_4$ hosts. From comparison to tight-binding modelling, we find that the strain is accommodated predominantly by bond-length changes rather than modifications of octahedral tilt and rotation angles. Our study sheds new light on the nature of structural distortions at oxide surfaces, and how targeted control of these can be used to tune density of states singularities to the Fermi level, in turn paving the way to the possible realisation of rich collective states at the Sr$_2$RuO$_4$ surface.

The interplay of electronic and structural degrees of freedom in solids is a topic of intense research. Experience and intuition suggest that structural changes drive conduction electron behavior, because the large number of valence electrons dominate the structural properties. As part of a seminal paper written over sixty years ago, Lifshitz discussed an alternative possibility: lattice softening driven by conduction electrons at topological Fermi surface transitions. The effect he predicted, however, was small, and has not been convincingly observed. Using measurements of the stress-strain relationship in the ultra-clean metal Sr$_{2}$RuO$_{4}$, we reveal a huge softening of the Young's modulus at a Lifshitz transition of a two-dimensional Fermi surface, and show that it is indeed entirely driven by the conduction electrons of the relevant energy band., Comment: 42 pages, 16 figures (including supplementary information)

Muon spin rotation/relaxation ($μ$SR) and polar Kerr effect measurements provide evidence for a time-reversal symmetry breaking (TRSB) superconducting state in Sr$_2$RuO$_4$. However, the absence of a cusp in the superconducting transition temperature ($T_{\rm c}$) vs. stress and the absence of a resolvable specific heat anomaly at TRSB transition temperature ($T_{\rm TRSB}$) under uniaxial stress challenge a hypothesis of TRSB superconductivity. Recent $μ$SR studies under pressure and with disorder indicate that the splitting between $T_{\rm c}$ and $T_{\rm TRSB}$ occurs only when the structural tetragonal symmetry is broken. To further test such behavior, we measured $T_\text{c}$ through susceptibility measurements, and $T_\text{TRSB}$ through $μ$SR, under uniaxial stress applied along a $\langle 110 \rangle$ lattice direction. We have obtained preliminary evidence for suppression of $T_\text{TRSB}$ below $T_\text{c}$, at a rate much higher than the suppression rate of $T_\text{c}$., 9 pages, 4 figures and Appendix, accepted for publication in PRB

Under in-plane uniaxial stress, the largest Fermi surface sheet of the correlated metal Sr$_2$RuO$_4$ undergoes a Lifshitz transition from an electron-like to an open geometry. We investigate the effects of this transition on transport through measurement of the longitudinal resistivity $\rho_{xx}$ and the Hall coefficient $R_\text{H}$. At temperatures where scattering is dominated by electron-electron scattering, $R_\text{H}$ becomes more negative across the Lifshitz transition, opposite to expectations from the change in Fermi surface topology. We show that this change in $R_\text{H}$ is explainable only if scattering changes throughout the Brillouin zone, not just at the point in $k$-space where the Lifshitz transition occurs. In a model of orbital-dependent scattering, the electron-electron scattering rate on sections of Fermi surface with $xy$ orbital weight decreases dramatically. On the other hand, at temperatures where defect scattering dominates $\rho_{xx}$ and $R_\text{H}$ are essentially constant across the Lifshitz transition., Comment: 9 pages, 10 figures

In-plane uniaxial pressure has been shown to strongly tune the superconducting state of Sr2RuO4 by approaching a Lifshitz transition and associated Van Hove singularity (VHS) in the density of states. At the VHS, $T_c$ and the in- and out-of-plane upper critical fields are all strongly enhanced, and the latter has changed its curvature as a function of temperature from convex to concave. However, due to strain inhomogeneity it has not been possible so far to determine how the upper critical fields change with strain. Here, we show the strain dependence of both upper critical fields, which was achieved due to an improved sample preparation. We find that the in-plane upper critical field is mostly linear in $T_c$. On the other hand, the out-of-plane upper critical field varies with a higher power in $T_c$, and peaks strongly at the VHS. The strong increase in magnitude and the change in form of $H_\mathrm{c2||c}$ occur very close to the Van Hove strain, and points to a strong enhancement of both the density of states and the gap magnitude at the Lifshitz transition.

The possibility of direct air capture of CO$_2$ in Antarctica is discussed. Because the concentration of H$_2$O in the atmosphere during the Antarctic winter is extremely low, an installation for direct air capture could employ a physisorption-based process, allowing, in principle, a very short adsorption/desorption cycle time. The lower required binding allows more options for materials for the sorbent. With a shorter cycle time, more resource could be spent on structuring the sorbent to improve energy efficiency, for example by improving its mass efficiency if desorption is driven thermally., Comment: This paper is built around a hypothesis that a one-second adsorption/desorption cycle time is possible. A justification for this hypothesis is not provided, and without it this paper should not be used as a basis for further work. I have been working to describe how such a cycle time might be achieved, and find that it is a difficult problem. This paper was posted prematurely

Conductive domain walls (CDWs) in insulating ferroelectrics have recently attracted considerable attention due to their unique topological, optical, and electronic properties, and offer potential applications such as in memory devices or re-writable circuitry. The electronic properties of domain walls (DWs) can be tuned by the application of strain, hence controlling the charge carrier density at DWs. In this work, we study the influence of uniaxial stress on the conductivity of DWs in the bulk single crystal lithium niobate (LiNbO$_3$). Using conductive atomic force microscopy (cAFM), we observe a large asymmetry in the conductivity of DWs, where only negatively screened walls, so called head-to-head DWs, are becoming increasingly conductive, while positively screened, tail-to-tails DWs, show a decrease in conductivity. This asymmetry of DW conductivity agrees with our theoretical model based on the piezoelectric effect. In addition, we observed that the current in the DW increases up to an order of magnitude for smaller compressive stresses of 100 MPa. This response of DWs remained intact for multiple stress cycles over 2 months, opening a path for future applications.

We probe the effect on $T_c$ of in-plane uniaxial stress applied to the high-temperature superconductor $YBa_2Cu_3O_{6.67}$. We find a highly anisotropic response. Under compression along the $b$ axis, which reduces the orthorhombicity of the $CuO_2$ planes, $T_c$ is broadly flat for stresses up to at least 1.7 GPa. Under compression along the $a$ axis, $T_c$ decreases steeply. For stresses beyond $≈1$ GPa the decrease is quasilinear. We hypothesize that superconductivity is suppressed by competition with uniaxial charge density wave order, which has been found to onset at $≈1$ GPa.

We perform nuclear magnetic resonance (NMR) measurements of the oxygen-17 Knight shifts for Sr$_2$RuO$_4$, while subjected to uniaxial stress applied along [100] direction. The resulting strain is associated with a strong variation of the temperature and magnetic field dependence of the inferred magnetic response. A quasi-particle description based on density-functional theory calculations, supplemented by many-body renormalizations, is found to reproduce our experimental results, and highlights the key role of a van-Hove singularity. The Fermi liquid coherence scale is shown to be tunable by strain, and driven to low values as the associated Lifshitz transition is approached.

Hole-doped cuprate superconductors show a ubiquitous tendency towards charge order. Although onset of superconductivity is known to suppress charge order, there has not so far been a decisive demonstration of the reverse process, namely, the effect of charge order on superconductivity. To gain such information, we report here the dependence of the critical temperature $T_{\mathrm{c}}$ of YBa$_2$Cu$_3$O$_{6.67}$ on in-plane uniaxial stress up to 2 GPa. At a compression of about 1 GPa along the $a$ axis, 3D-correlated charge density wave (3D CDW) order appears. We find that $T_{\mathrm{c}}$ decreases steeply as the applied stress crosses 1 GPa, showing that the appearance of 3D CDW order strongly suppresses superconductivity. Through the elastocaloric effect we resolve the heat capacity anomaly at $T_{\mathrm{c}}$, and find that it does not change drastically as the 3D CDW onsets, which shows that the condensation energy of the 3D CDW is considerably less than that of the superconductivity.

Among unconventional superconductors, Sr$_2$RuO$_4$ has become a benchmark for experimentation and theoretical analysis because its normal-state electronic structure is known with exceptional precision, and because of experimental evidence that its superconductivity has, very unusually, a spontaneous angular momentum, i.e. a chiral state. This hypothesis of chirality is however difficult to reconcile with recent evidence on the spin part of the order parameter. Measurements under uniaxial stress offer an ideal way to test for chirality, because under uniaxial stress the superconducting and chiral transitions are predicted to split, allowing the empirical signatures of each to be identified separately. Here, we report zerofield muon spin relaxation (ZF-$\mu$SR) measurements on crystals placed under uniaxial stresses of up to 1.05 GPa. We report a clear stress-induced splitting between the onset temperatures of superconductivity and time-reversal symmetry breaking, consistent with qualitative expectations for chiral superconductivity. We also report the appearance of unexpected bulk magnetic order under a uniaxial stress of ~ 1.0 GPa in clean Sr$_2$RuO$_4$., Comment: 28 pages, 12 figures

Evidence of nematic effects in the mixed superconducting phase of slightly underdoped Ba(Fe1-xCox)2As2 is reported. We have found strong in-plane resistivity anisotropy for crystals in different strain conditions. For these compositions, there is no magnetic long-range order, so the description may be ascribed to the interplay between the superconducting and nematic order parameters. A piezoelectric-based apparatus is used to apply tensile or compressive strain to tune nematic domain orientation in order to examine intrinsic nematicity. Measurements are done under a rotating magnetic field, and the analysis of the angular dependence of physical quantities identifies the cases in which the sample is detwinned. Furthermore, the angular dependence of the data allows us to evaluate the effects of nematicity on the in-plane superconductor stiffness. Our results show that although nematicity contributes in a decisive way to the conduction properties, its contributions to the anisotropy properties of the stiffness of the superconducting order parameter is not as significant in these samples., Instituto de Física de Líquidos y Sistemas Biológicos

Uniaxial pressure applied along an Ru-Ru bond direction induces an elliptical distortion of the largest Fermi surface of Sr$_2$RuO$_4$, eventually causing a Fermi surface topological transition, also known as a Lifshitz transition, into an open Fermi surface. There are various anomalies in low-temperature properties associated with this transition, including maxima in the superconducting critical temperature and in resistivity. In the present paper, we report new measurements, employing new uniaxial stress apparatus and new measurements of the low-temperature elastic moduli, of the strain at which this Lifshitz transition occurs: a longitudinal strain $\varepsilon_{xx}$ of $(-0.44\pm0.06)\cdot10^{-2}$, which corresponds to a B$_{1g}$ strain $\varepsilon_{xx} - \varepsilon_{yy}$ of $(-0.66\pm0.09)\cdot10^{-2}$. This is considerably smaller than the strain corresponding to a Lifshitz transition in density functional theory calculations, even if the spin-orbit coupling is taken into account. Using dynamical mean-field theory we show that electronic correlations reduce the critical strain. It turns out that the orbital anisotropy of the local Coulomb interaction on the Ru site is furthermore important to bring this critical strain close to the experimental number, and thus well into the experimentally accessible range of strains.

Strontium ruthenate (Sr$_2$RuO$_4$) is a multiband superconductor that displays evidence of topological superconductivity, although a model of the order parameter that is consistent with all experiments remains elusive. We integrated a piezoelectric-based strain apparatus with a scanning superconducting quantum interference device (SQUID) microscope to map the diamagnetic response of single-crystal Sr$_2$RuO$_4$ as a function of temperature, uniaxial pressure, and position with micron-scale spatial resolution. We thereby obtained local measurements of the superconducting transition temperature $T_c$ vs. anisotropic strain $\epsilon$ with sufficient sensitivity for comparison to theoretical models that assume a uniform $p_x\pm ip_y$ order parameter. We found that $T_c$ varies with position and that the locally measured $T_c$ vs. $\epsilon$ curves are quadratic ($T_c\propto\epsilon^2$), as allowed by the C$_4$ symmetry of the crystal lattice. We did not observe the low-strain linear cusp ($T_c\propto \left| \epsilon \right|$) that would be expected for a two-component order parameter such as $p_x\pm ip_y$. These results provide new input for models of the order parameter of Sr$_2$RuO$_4$., Comment: 18 pages, 6 figures, 2 tables

We present a design for a piezoelectric-driven uniaxial stress cell suitable for use at ambient and cryogenic temperatures, and that incorporates both a displacement and a force sensor. The cell has a diameter of 46 mm and a height of 13 mm. It can apply a zero-load displacement of up to ~45 $\mu$m, and a zero-displacement force of up to ~245 N. With combined knowledge of the displacement and force applied to the sample, it can quickly be determined whether the sample and its mounts remain within their elastic limits. In tests on the oxide metal Sr$_2$RuO$_4$, we found that at room temperature serious plastic deformation of the sample onset at a uniaxial stress of ~0.2 GPa, while at 5 K the sample deformation remained elastic up to almost 2 GPa. This result highlights the usefulness of in situ tuning, in which the force can be applied after cooling samples to cryogenic temperatures.

We report the results of a combined study of the normal state resistivity and superconducting transition temperature $T_c$ of the unconventional superconductor Sr$_2$RuO$_4$ under uniaxial pressure. There is strong evidence that as well as driving $T_c$ through a maximum at $\sim$3.5 K, compressive strains $\varepsilon$ of nearly 1 % along the crystallographic [100] axis drive the $\gamma$ Fermi surface sheet through a Van Hove singularity, changing the temperature dependence of the resistivity from $T^2$ above and below the transition region to $T^{1.5}$ within it. This occurs in extremely pure single crystals in which the impurity contribution to the resistivity is $

Symmetry is a basic paradigm for analysis of problems in solid state physics, and to controllably break point-group symmetries is a powerful probe of novel forms of order. In this work, we apply two methods, controlled lattice strain and vector magnetic field, to study a well-known correlated electron phase that appears at low temperatures in the layered material Sr3Ru2O7. This phase responds strongly to C4-symmetry-breaking fields, suggesting spontaneous C4 symmetry breaking. However, in this work we find that the data are more easily explained with microscopic coexistence of two orthogonal order parameter components than spontaneous symmetry breaking. The techniques presented in this work will be relevant for other systems where spontaneous C4 symmetry breaking is suspected., 30 pages, 9 figures

We measure the penetration depth λab(T) in Ba(Fe1-xCox)2As2 using local techniques that do not average over the sample. The superfluid density ρs(T)≡1/λab(T)2 has three main features. First, ρs(T=0) falls sharply on the underdoped side of the dome. Second, λab(T) is flat at low T at optimal doping, indicating fully gapped superconductivity, but varies more strongly in underdoped and overdoped samples, consistent with either a power law or a small second gap. Third, ρs(T) varies steeply near Tc for optimal and underdoping. These observations are consistent with an interplay between magnetic and superconducting phases. Publisher PDF

We present scanning SQUID microscopy data on the superconductors Sr2RuO4 (Tc = 1.5 K) and PrOs$_4$Sb$_{12}$ (Tc = 1.8 K). In both of these materials, superconductivity-related time-reversal symmetry-breaking fields have been observed by muon spin rotation; our aim was to visualize the structure of these fields. However in neither Sr$_2$RuO$_4$ nor PrOs$_4$Sb$_{12}$ do we observe spontaneous superconductivity-related magnetization. In Sr$_2$RuO$_4$, many experimental results have been interpreted on the basis of a $px \pm ipy$ superconducting order parameter. This order parameter is expected to give spontaneous magnetic induction at sample edges and order parameter domain walls. Supposing large domains, our data restrict domain wall and edge fields to no more than ~0.1% and ~0.2% of the expected magnitude, respectively. Alternatively, if the magnetization is of the expected order, the typical domain size is limited to ~30 nm for random domains, or ~500 nm for periodic domains., 8 pages, 7 figures. Submitted to Phys. Rev. B

We measure the penetration depth $\lambda_{ab}(T)$ in Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$ using local techniques that do not average over the sample. The superfluid density $\rho_s(T)\equiv1/\lambda_{ab}(T)^2$ has three main features. First, $\rho_s(T=0)$ falls sharply on the underdoped side of the dome. Second, $\lambda_{ab}(T)$ is flat at low $T$ at optimal doping, indicating fully gapped superconductivity, but varies more strongly in underdoped and overdoped samples, consistent with either a power law or a small second gap. Third, $\rho_s(T)$ varies steeply near $T_c$ for optimal and underdoping. These observations are consistent with an interplay between magnetic and superconducting phases.

We measure changes in the penetration depth $\lambda$ of the $T_c \approx 6$ K superconductor LaFePO. In the process scanning SQUID susceptometry is demonstrated as a technique for accurately measuring {\it local} temperature-dependent changes in $\lambda$, making it ideal for studying early or difficult-to-grow materials. $\lambda$ of LaFePO is found to vary linearly with temperature from 0.36 to $\sim$2 K, with a slope of 143$\pm$15 \AA/K, suggesting line nodes in the superconducting order parameter. The linear dependence up to $\sim T_c/3$ is similar to the cuprate superconductors, indicating well-developed nodes., Comment: 4 pages, 5 figures

Uniaxial stress is a powerful technique to tune the electronic structure of very pure materials. The novel piezoelectric-based techniques developed by our group, which allow application of large and homogeneous uniaxial pressure in a continuously-tunable manner, make uniaxial pressure an independent axis in the parameter space for the study of quantum materials. Many exciting experiments have been performed that combine different measurement methods with this uniaxial stress technique in the past few years. In this thesis, I demonstrate the first electrical transport measurement under uniaxial pressure of a free-standing microstructure single-crystalline sample patterned by focused ion beam (FIB) milling. With the microstructuring technique that I developed, the transport properties transverse to the force direction can be more accurately probed. The ability to resolve the anisotropy introduced by the uniaxial pressure lets us have a better understanding of how the electronic structure of Sr₂RuO₄ changes under uniaxial stress. Moreover, the microstructure technique opens new roads for smaller crystals (∼ 100 µm) to be studied under uniaxial pressure. In addition, higher stresses and better sample homogeneity could be achieved by working with smaller samples. For Sr₂RuO₄, one of the three Fermi-surface sheets can be driven through a Lifshitz transition by applying uniaxial stress along the [100] direction. Superconductivity and resistivity have been observed to be strongly enhanced at the singularity. In addition, a spin-density wave (SDW) has been observed at stresses beyond the Lifshitz transition. Measurement of the Hall effect under uniaxial stress allows us to probe Hund’s metal physics in Sr₂RuO₄. The Hall coefficient of unstressed Sr₂RuO₄ goes through two sign reversals, at 30 K and 120 K. Under the Hund’s metal scenario, this temperature dependence has been proposed to result from orbital differentiation of the inelastic scattering rate, which is a key property expected of Hund’s metals. In the present study, it is shown that at a temperature where electron-electron scattering dominates (≳ 5 K), the Hall coefficient becomes less electron-like while approaching the VHS, which is consistent with increased scattering in the d_xy band. Beyond the transition, the Hall coefficient becomes much more electron-like, which is opposite to expectations from the change in Fermi surface topology, but can be explained by a combination of Hund’s metal physics and strong suppression in the d_xy scattering rate. At very low temperature (0.5 K), the Hall coefficient is essentially unchanged across the Lifshitz transition, despite the change in the Fermi-surface topology. In contrast to the longitudinal resistivity that has a strong peak at the VHS but does not respond to the SDW, the resistance transverse to the force direction shows a strong response to the SDW, but only a small response at the VHS. In addition, I obtain ρ(T) at the Lifshitz transition below Tc by subtracting off the magnetoresistance and find that T² ln(1/T) fits better than T^3/2, which suggests a saddle point rather than an extended saddle point at the VHS.:1. Introduction to Sr2RuO4 1.1. Normal-State Properties Van Hove Singularity and Lifshitz Transition in Sr2RuO4 1.2. Hall Effect in Sr2RuO4 Weak-field Hall Coefficient Experimental Hall Coefficient in Sr2RuO4 and Related Systems 1.3. Hund’s Metal Scenario Dynamical Mean-Field Theory Experimental Evidence for Orbital Differentiation in Sr2RuO4 Hall Coefficient of Sr2RuO4 within Hund’s Metal Scenario 1.4 Uniaxial-Pressure Projects on Sr2RuO4 2. Experimental Setup 2.1. Stress and Strain 2.2. Uniaxial Stress Technique Uniaxial-Stress Cell Sample Carrier 2.3. Imperfections of the Stress Cells 2.4. Sample Preparation Needle Sample Preparation Microstructure Sample Preparation Comparison of the Two Samples 2.5. Measurement Setup 3He Cryostat Transport Measurement Setup 3. Hall Coefficient and Resistivity Measurements 3.1. Basics of Resistivity Measurement Stress Ramps 3.2. Basics of Hall Measurement Setup Field Dependence of Hall Resistivity Temperature Dependence of Hall Coefficient 3.3. Stress Ramps under Constant Magnetic Field 3.4. Stress Dependence of Hall Coefficient and Resistivity 3.5. Resistivity Measurements below Tc 3.6. Field Sweeps within the Magnetic Phase 3.7. Summary 4. Measurements Transverse to the Stress Axis 4.1. Setup for Transport Measurements Transverse to the Uniaxial Stress 4.2. Simulations Based on Finite Element Method 4.3. Resistance Measurements Transverse to Applied Stress 4.4. Summary 5. Data Analysis and Discussion 5.1. A Tight-Binding Model under Uniaxial Pressure 5.2. Analysis of Hall Coefficient across the Lifshitz Transition Hall Coefficient Analysis under the Isotropic-l or Isotropic-τ Approximations Hall Coefficient Analysis under Hund’s Metal Scenario 5.3. Magnetoresistance Subtraction in Temperature Ramps 5.4. Transport Properties at 5 K 5.5. Summary 6. Conclusions and Outlook Appendices A. Si-Gap-Platform Microstructure Project A.1. Si-Gap Platform A.2. Sample Preparation with PFIB-Microstructuring A.3. Microstructure Stress Cells B. Other results B.1. Hall Effect from the Hall Pair 2 B.2. Magnetoresistance in Longitudinal and Transverse Configurations B.3. Toward -1.5 GPa B.4. Comparison of RH(T) in Sr2RuO4 Compressed along [100] Direction and YBa2Cu3O6.67 Compressed along the b-axis Bibliography

Magnetic materials are of great research interest because of their potential applications. Most Mn-based compounds exhibit magnetic ordering, being antiferromagnetic or ferromagnetic depending on their crystal structure. Many of these compounds have complex non-collinear magnetic structures that can give rise to exotic and robust phenomena. The scope of this thesis encompasses two independent projects on exploring single-crystalline Mn-based compounds with magnetic properties: (i) the study of the thickness-dependent magnetic textures in ferromagnetic Mn1.4PtSn by means of Focused Ion Beam (FIB) for sample shaping and Magnetic Force Microscopy (MFM) for imaging, and (ii) the experimental demonstration of an anomalous Hall effect in non-collinear antiferromagnetic Mn3Pt, revealed with the aid of uniaxial pressure tuned in-situ. The first chapter motivates the study of magnetic materials and introduces the theoretical framework on which they are understood. In particular, refers to the energy contributions of magnetic origin and gives an overview of the Hall effect and how it is used to probe magnetic properties, from ferromagnetism to non-collinear antiferromagnetism and non-coplanar spin textures (such as the so-called skyrmions). The second chapter is dedicated to the ferromagnetic compound Mn1.4PtSn. It starts by introducing concepts important in the context of magnetic domains. A variety of magnetic textures are discussed, in particular antiskyrmions which differ from regular skyrmions by their internal structure. A material-specific introduction is given, starting by its discovery as the first antiskyrmion-hosting compound (when in thin-plate shape) and including recent literature showing by means of neutron scattering how magnetic domains in bulk single crystals are best described as anisotropic fractals. This study complements our first observations in real-space MFM images of the magnetic texture in this material. The detailed study of the dependence of the magnetic domains as a function of sample thickness is presented and analyzed. The third and final chapter focuses on antiferromagnetic Mn3Pt. To motivate the experiment, the theoretical study that predicts the presence of an intrinsic zero-field anomalous contribution to the Hall effect for this material is introduced. Next, the experimental investigation of single crystals of Mn3Pt is presented, where a Hall effect dominated by the ordinary contribution in the temperature range from 10 to 300 K is found. Thereafter, the response of the Hall effect to uniaxial pressure tuned in-situ is explored. When the sample is compressed, a hysteresis is observed to open up. The magnitude of this anomalous Hall conductivity (when compressing the sample by ∼0.2 GPa) is estimated to be at least ∼ 10 Ω-1cm-1 at room temperature and ∼ 40 Ω-1cm-1 at 100 K, and it is demonstrated that the measured value originates in the antiferromagnetic structure, rather than in a stress-induced ferromagnetism.:1 Introduction 1 1.1 Overview of elemental properties . . . . . . . . . . . . . . . . 1 1.1.1 Notes on Mn . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Notes on Pt . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Notes on Sn . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Magnetic Interactions . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Zeeman interaction . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Magnetostatic energy . . . . . . . . . . . . . . . . . . . 5 1.2.3 Magnetic anisotropy . . . . . . . . . . . . . . . . . . . 6 1.2.4 Magnetoelastic coupling . . . . . . . . . . . . . . . . . 7 1.2.5 Exchange interaction . . . . . . . . . . . . . . . . . . . 8 1.2.6 Antisymmetric exchange . . . . . . . . . . . . . . . . . 10 1.3 Antiferro-, ferri- and helimagnets . . . . . . . . . . . . . . . . 11 1.4 Hall effect in magnetism . . . . . . . . . . . . . . . . . . . . . 14 1.4.1 Geometrical phase in quantum mechanics . . . . . . . 14 In the context of the anomalous Hall effect . . . . . . 16 1.4.2 Complementary anomalous Hall theories . . . . . . . . 18 Skew scattering . . . . . . . . . . . . . . . . . . . . . . 18 Inelastic scattering . . . . . . . . . . . . . . . . . . . . 18 Side jump . . . . . . . . . . . . . . . . . . . . . . . . . 18 Spin chirality mechanism . . . . . . . . . . . . . . . . 19 I The uniaxial ferromagnet Mn1.4PtSn 21 2 Mn1.4PtSn 23 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Background physics . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.1 Topology in magnetism . . . . . . . . . . . . . . . . . 27 2.2.2 Domain theory . . . . . . . . . . . . . . . . . . . . . . 29 Domain refinement . . . . . . . . . . . . . . . . . . . . 31 2.2.3 Literature overview . . . . . . . . . . . . . . . . . . . . 32 SANS studies on bulk Mn1.4PtSn . . . . . . . . . . . . 34 2.3 Experimental methods . . . . . . . . . . . . . . . . . . . . . . 37 2.3.1 Sample preparation . . . . . . . . . . . . . . . . . . . . 37 2.3.2 Lamellae fabrication . . . . . . . . . . . . . . . . . . . 37 2.3.3 Magnetic Force Microscopy . . . . . . . . . . . . . . . 38 History . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Operating principle . . . . . . . . . . . . . . . . . . . . 39 Specifications for our experiments . . . . . . . . . . . . 40 2.4 Results and discussions . . . . . . . . . . . . . . . . . . . . . . 40 2.4.1 Bulk samples characterization . . . . . . . . . . . . . . 40 Mn1.4Pt0.9Pd0.1Sn polycrystal . . . . . . . . . . . . . . 40 Mn1.4PtSn single crystal . . . . . . . . . . . . . . . . . 43 Mn1.4PtSn single crystal in applied field . . . . . . . . 45 Mn1.4PtSn single crystal below TSR . . . . . . . . . . . 46 2.4.2 Lamellae characterization . . . . . . . . . . . . . . . . 48 Thickness dependence . . . . . . . . . . . . . . . . . . 48 Temperature dependence . . . . . . . . . . . . . . . . 54 Magnetic field dependence . . . . . . . . . . . . . . . . 56 2.5 Conclusions and outlook . . . . . . . . . . . . . . . . . . . . . 63 II The non-collinear antiferromagnet Mn3Pt under strain 65 3 Mn3Pt 67 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2 Background physics . . . . . . . . . . . . . . . . . . . . . . . . 69 3.2.1 Thin film study of Mn3Pt . . . . . . . . . . . . . . . . 71 3.2.2 Our contribution . . . . . . . . . . . . . . . . . . . . . 73 3.3 Experimental methods . . . . . . . . . . . . . . . . . . . . . . 74 3.4 Results and discussions . . . . . . . . . . . . . . . . . . . . . . 75 3.4.1 Characterization of unstrained crystals . . . . . . . . . 75 3.4.2 Elastic response of Mn3Pt single crystals . . . . . . . . 79 Electrical transport response to strain . . . . . . . . . 81 3.4.3 Onset of AHE in single crystals under uniaxial pressure 84 Sample III4 . . . . . . . . . . . . . . . . . . . . . . . . 84 Sample IV1 . . . . . . . . . . . . . . . . . . . . . . . . 89 Sample IV2 . . . . . . . . . . . . . . . . . . . . . . . . 91 3.4.4 Temperature dependence of the AHE . . . . . . . . . . 94 3.4.5 Elastic limit of Mn3Pt . . . . . . . . . . . . . . . . . . 98 3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 A On Mn3Pt resistivity 101 B On Mn3Pt sample mounting 103