Artificial spin ice (ASI) based on a square lattice with a topological defect are known to generate orbital angular momentum (OAM) in diffracted X-ray beams. A previous investigation of ASI with even-charge topological defects showed both charge and magnetic X-ray scattering yield photon OAM, but these were confined to integer OAM values. However, the period of the square ASI's antiferromagnetic ground state is twice the period of the structural ground state, which should lead to fractional OAM from magnetic scattering when the topological defect has odd-charge. We employed photoemission electron microscopy to confirm that these ASIs order into antiferromagnetic ground states with protected superdomain walls that provide the phase discontinuity required for fractional OAM. Resonant, coherent X-ray scattering from ASIs with topological defects of charge 1 yields integer-valued X-ray OAM at structural charge peaks and fractional X-ray OAM at magnetic peaks. For thermally active ASIs, the fractional OAM beam exhibits fluctuations in the position of the phase discontinuity and thus dynamic rotation of the beam.

In addition to spin angular momentum, light can carry orbital angular momentum. The orbital angular momentum degree of freedom in the extreme ultraviolet and x-ray regimes enables fundamental studies of light-matter interactions and new methods to study materials. Advances in x-ray optics, as well as undulator radiation and high harmonic generation techniques, lead to the creation of beams with non-trivial phase structure, such as a helical phase structure, creating new possibilities for the use of extreme ultraviolet and x-ray photons with orbital angular momentum in probing complex electronic structures in matter. In this article, we review the generation and applications of orbital angular momentum beams in the x-ray and extreme ultraviolet regime. We discuss several recent works that exploit the orbital angular momentum degree of freedom and showcase the potential advantages of using these beams.

We present experimental evidence that a heavy Fermi surface consisting of itinerant, charge-neutral spinons underpins both heavy-fermion-strange-metal (without f electrons) and quantum-spin-liquid states in the 4d-electron trimer lattice, Ba_{4}Nb_{1-x}Ru_{3+x}O_{12}(|x|<0.20). These two exotic states both exhibit an extraordinarily large entropy, a linear heat capacity extending into the milli-Kelvin regime, a linear thermal conductivity at low temperatures, and separation of charges and spins. Furthermore, the insulating spin liquid is a much better thermal conductor than the heavy-fermion-strange-metal that separately is observed to strongly violate the Wiedemann-Franz law. We propose that at the heart of this 4d system is a universal, heavy spinon Fermi surface that provides a unified framework for explaining the exotic phenomena observed throughout the entire series. The control of such exotic ground states provided by variable Nb concentration offers a new paradigm for studies of correlated quantum matter.

X-ray beams with orbital angular momentum (OAM) are a promising tool for x-ray characterization techniques. Beams with OAM have a helicity--an azimuthally varying phase--which leads to a gradient of the light field. New material properties can be probed by utilizing the helicity of an OAM beam. Here, we demonstrate a novel dichroic effect in resonant diffraction from an artificial antiferromagnet with a topological defect. We found that the scattered OAM beam has circular dichroism at the antiferromagnetic Bragg peak whose sign is coupled to its helicity, which reveals the real-space configuration of the antiferromagnetic ground state. Thermal cycling of the artificial antiferromagnet can change the ground state, as indicated by reversal of the sign of circular dichroism. This result is one of the first demonstrations of a soft x-ray spectroscopy characterization technique utilizing the OAM of x-rays. This helicity-dependent circular dichroism exemplifies the potential to utilize OAM beams to probe matter in a way that is inaccessible using currently available x-ray techniques.

The results of a numerical study of an ordered substitution of a double-segment into the unit cell of square artificial spin ice are presented. Each pattern vertex has three magnetic moment configurations that compete to form a magnetic ground state in zero applied magnetic field, including nearest-neighbor and next-nearest-neighbor interaction contributions to the total magnetostatic energy. The ground state depends on the number of lattice sites considered and the spacing between the two film segments that comprise the double segment. Monte Carlo simulations reveal that the doub le-segment sublattice adopts long-range antiferromagnetic order that can be supplanted by magnetic quadrupole order by applying an in-plane magnetic field perpendicular to the double-segment easy axis. The quadrupole-ordered state consists of a sublattice of weakly correlated chains of double-segments with antiparallel polarizations, which admits many different ground states that reflect a very high degree of frustration.

Detectors with microchannel plates (MCPs) provide unique capabilities to detect single photons with high spatial (<10 µm) and timing (<25 ps) resolution. Although this detection technology was originally developed for applications with low event rates, recent progress in readout electronics has enabled their operation at substantially higher rates by simultaneous detection of multiple particles. In this study, the potential use of MCP detectors with Timepix readout for soft X-ray imaging and spectroscopic applications where the position and time of each photon needs to be recorded is investigated. The proof-of-principle experiments conducted at the Advanced Light Source demonstrate the capabilities of MCP/Timepix detectors to operate at relatively high input counting rates, paving the way for the application of these detectors in resonance inelastic X-ray scattering and X-ray photon correlation spectroscopy (XPCS) applications. Local count rate saturation was investigated for the MCP/Timepix detector, which requires optimization of acquisition parameters for a specific scattering pattern. A single photon cluster analysis algorithm was developed to eliminate the charge spreading effects in the detector and increase the spatial resolution to subpixel values. Results of these experiments will guide the ongoing development of future MCP devices optimized for soft X-ray photon-counting applications, which should enable XPCS dynamics measurements down to sub-microsecond timescales.

Artificial spin ices (ASI) have been widely investigated as magnetic metamaterials with exotic properties governed by their geometries. In parallel, interest in x-ray photon orbital angular momentum (OAM) has been rapidly growing. Here we show that a square ASI with a patterned topological defect, a double edge dislocation, imparts OAM to scattered x rays. Unlike single dislocations, a double dislocation does not introduce magnetic frustration, and the ASI equilibrates to its antiferromagnetic (AFM) ground state. The topological charge of the defect differs with respect to the structural and magnetic order; thus, x-ray diffraction from the ASI produces photons with even and odd OAM quantum numbers at the structural and AFM Bragg conditions, respectively. The magnetic transitions of the ASI allow the AFM OAM beams to be switched on and off by modest variations of temperature and applied magnetic field. These results demonstrate ASIs can serve as metasurfaces for reconfigurable x-ray optics that could enable selective probes of electronic and magnetic properties.

We present experimental and numerical results for the dynamic response of a connected Kagome artificial spin ice. We explicitly consider the effect of the vertex magnetization configuration on the ferromagnetic resonance (FMR) mode characteristics using micromagnetic simulations. We show that the bulk mode frequencies of each single-domain thin-film segment not only depend on the direction of the segment's easy-axes with respect to the applied magnetic field but also depend on the vertex magnetization configurations of nearby vertices. Therefore, the FMR modes can be controlled by altering the vertex magnetization texture. Moreover, we distinguish between vertex center modes (VCMs) and localized domain wall (LDW) modes. We show that the LDW mode evolves during the nucleation process of domain walls and that VCMs and LDW modes can be controlled using specific field protocols, which have important implications for future design of magnonic and spintronic devices.

We have measured the angular dependence of ferromagnetic resonance (FMR) spectra for Fibonacci-distorted, Kagome artificial spin ice (ASI). The number of strong modes in the FMR spectra depend on the orientation of the applied DC magnetic field. In addition, discontinuities observed in the FMR field-frequency dispersion curves also depend on DC field orientation, and signal a multi-step DC magnetization reversal, which is caused by the reduced energy degeneracy of Fibonacci-distorted vertices. The results suggest the orientation of applied magnetic field and severity of Fibonacci distortion constitute control variables for FMR modes and multi-step reversal in future magnonic devices and magnetic switching systems.

The Ruddlesden-Popper phases Srn+1IrnO3n+1 (n = 1, 2, and ∞) have been intensively studied, and exhibit many novel behaviors and ground states driven by a rare interplay between strong spin-orbit and Coulomb interactions. One key empirical trend is that most iridates are antiferromagnetic insulators, contrary to conventional wisdom. The spin-orbit-coupled Mott state does not always closely track the magnetic state in iridates. Often, chemical doping can effectively induce a metallic state. Defying expectations, Sr2IrO4, which is the prototypical spin-orbit-coupled Mott insulator, does not become superconducting upon electron doping, but remains insulating under applied pressures extending into the Mbar range, highlighting the extraordinary susceptibility to the lattice degrees of freedom, which is at the heart of the physics driving the iridates.

We present a new formulation of the dynamical matrix method for computing the magnetic normal modes of a large system, resulting in a highly scalable approach. The motion equation, which takes into account external field, dipolar and ferromagnetic exchange interactions, is rewritten in the form of a generalized eigenvalue problem without any additional approximation. For its numerical implementation several solvers have been explored, along with preconditioning methods. This reformulation was conceived to extend the study of magnetization dynamics to a broader class of finer-mesh systems, such as three-dimensional, irregular or defective structures, which in recent times raised the interest among researchers. To test its effectiveness, we applied the method to investigate the magnetization dynamics of a hexagonal artificial spin-ice as a function of a geometric distortion parameter following the Fibonacci sequence. We found several important features characterizing the low frequency spin modes as the geometric distortion is gradually increased.

Electrical current as a means to control structural and related physical properties has been recognized only recently. The application of small electrical currents in sensitive detector and control applications, and in information technologies, is often preferable to other external stimuli. However, until recently it has not been widely accepted that electrical current can readily couple to the lattice, orbital, and spin degrees of freedom. Mounting experimental evidence has indicated that a combination of strong spin-orbit interactions and a distorted crystal structure in magnetic Mott insulators may be sufficient for electrical current to control structural and related properties. Current control of quantum states in 4d- and 5d-transition metal oxides has therefore rapidly expanded as a key research topic. This chapter presents two model systems, Ca2RuO4 and Sr2IrO4, in which applied current effectively controls the lattice, and thus the physical properties.

We present results of ferromagnetic resonance (FMR) experiments and micromagnetic simulations for a distorted, 2D Kagome artificial spin ice. The distorted structure is created by continuously modulating the 2D primitive lattice translation vectors of a periodic honeycomb lattice, according to an aperiodic Fibonacci sequence used to generate 1D quasicrystals. Experimental data and micromagnetic simulations show the Fibonacci distortion causes broadening and splitting of FMR modes into multiple branches, which accompany the increasing number of segment lengths and orientations that develop with increasing distortion. When the applied field is increased in the opposite direction to the net magnetization of a segment, spin wave modes appear, disappear or suddenly shift, to signal segment magnetization reversal events. These results show the complex behavior of reversal events, as well as well-defined frequencies and frequency-field slopes of FMR modes, can be precisely tuned by varying the severity of the aperiodic lattice distortion. This type of distorted structure could therefore provide a new tool for the design of complicated magnonic systems.

Applications of sensitive vibrating reed magnetometry to a variety of superconducting and magnetic materials are reviewed. The advantages of conducting vibrating reed studies of small single crystals, ceramics, thin films and multilayers with high anisotropy, composition gradients, strain and nonlinear magnetic response are documented. The equilibrium and dynamic properties of magnetic flux in superconductors, and coexistence of magnetic and superconducting states are emphasised. Vibrating reed experiments on Nb, NbSe2, (Ba0.6K0.4)BiO3, HoNi2B2C, {Nb(x)/Ni(y)}(Z) multilayer films, and kappa-(ET)(2)Cu{N(CN)(2)}Br have revealed subtle, exotic superconducting behaviours that remain unexplained. Future prospects for vibrating reed measurements of ferromagnetic thin films with patterned nanostructures are considered.

It is commonly anticipated that an insulating state will collapse in favor of an emergent metallic state at high pressures: The average electron density must increase with pressure, while the electronic bandwidth is expected to broaden and fill the insulating energy band gap. Here we report an unusually stable insulating state that persists up to at least 185 GPa in Sr2IrO4, the archetypical spin-orbit-driven J(eff) = 1/2 insulator. This study shows that the electrical resistance R of single-crystal Sr2IrO4 initially decreases with applied pressure P, reaches a minimum in the range 32-38 GPa, then abruptly rises to recover the insulating state with increasing P up to 185 GPa. However, evidence of a saturation of R below 80 K for P >= 124 GPa GPa raises the possibility of a low-temperature exotic state. Our synchrotron x-ray diffraction and Raman scattering data show the emergence of the rapid increase in R is accompanied by a structural phase transition from the native tetragonal I-41/acd phase to an orthorhombic Pbca phase (with much reduced symmetry) at 40.6 GPa. The clear correspondence of the onset pressures of these two anomalies is key to understanding the stability of the insulating state at megabar pressures: Pressure-induced, structural distortions prevent the expected onset of metallization, despite the sizable volume compression attained at the highest pressure accessed in this study.

We report evidence of spontaneous formation of a heterogeneous network of superdomains in two-dimensional square artificial spin ice nanostructures in externally applied magnetic fields. The magnetic heterogeneity is locally disordered but has a zig-zag texture at longer length scales. Resonant coherent soft-x-ray scattering off such textures give rise to unique internal structure in Bragg peaks. Our result shows that the macroscopic magnetic texture is derived from the microscopic structure of the Dirac strings.

Collective dynamics often play an important role in determining the stability of ground states for both naturally occurring materials and metamaterials. We studied the temperature dependent dynamics of antiferromagnetically ordered superdomains in a square artificial spin lattice using soft x-ray photon correlation spectroscopy. We observed an exponential slowing down of superdomain wall motion below the antiferromagnetic onset temperature, similar to the behavior of typical bulk antiferromagnets. Using a continuous time random walk model we show that these superdomain walls undergo low-temperature ballistic and high-temperature diffusive motions.

It is commonly anticipated that an insulating state collapses in favor of an emergent metallic state at high pressures as the unit cell shrinks and the electronic bandwidth broadens to fill the insulating energy band gap. Here we report a rare insulating state that persists up to at least 185 GPa in the antiferromagnetic iridate Sr2IrO4, which is the archetypical spin-orbit-driven Jeff = 1/2 insulator. This study shows the electrical resistance of single-crystal Sr2IrO4 initially decreases with applied pressure, reaches a minimum in the range, 32 - 38 GPa, then abruptly rises to fully recover the insulating state with further pressure increases up to 185 GPa. Our synchrotron x-ray diffraction and Raman scattering data show the onset of the rapid increase in resistance is accompanied by a structural phase transition from the native tetragonal I41/acd phase to an orthorhombic Pbca phase (with much reduced symmetry) at 40.6 GPa. The clear-cut correspondence of these two anomalies is key to understanding the stability of the insulating state at megabar pressures: Pressure-induced, severe structural distortions prevent the expected metallization, despite the 26% volume compression attained at the highest pressure accessed in this study. Moreover, the resistance of Sr2IrO4 remains stable while the applied pressure is tripled from 61 GPa to 185 GPa. These results suggest that a novel type of electronic Coulomb correlation compensates the anticipated band broadening in strongly spin-orbit-coupled materials at megabar pressures.

Single-crystal x-ray diffraction refinements indicate SrSn2Fe4O11 crystallizes in the hexagonal R-type ferrite structure with non-centrosymmetric space group P63mc and lattice parameters a = 5.9541(2) Å, c = 13.5761(5) Å, Z = 2 (R(F) = 0.034). Octahedrally coordinated sites are randomly occupied by Sn and Fe; whereas tetrahedrally coordinated sites are exclusively occupied by Fe, whose displacement from ideal trigonal-bipyramidal coordination causes the loss of inversion symmetry. DC magnetization data indicate SrSn2Fe4O11 single crystals undergo ferro- or ferri-magnetic order below a transition temperature TC = 630 K with very low coercive fields Hc⊥ = 0.27 Oe and Hc// = 1.5 Oe at 300 K, for applied fields perpendicular and parallel to the c-axis, respectively. The value for TC is exceptionally high, and the coercive fields exceptionally low, among the known R-type ferrites. Enhanced coercivity and thermomagnetic hysteresis suggest the onset of short-range, spin glass order occurs below Tf = 35 K. Optical measurements indicate a band gap of 0.8 eV, consistent with wide-gap semiconducting behavior and a previously established empirical correlation between the semiconducting gap and TC for R-type ferrites based upon Ru.

Triple-layered Sr${}_{4}$Ru${}_{3}$O${}_{10}$ presents a rare case of coexistence of interlayer ($c$-axis) ferromagnetism and intralayer (basal-plane) metamagnetism at ambient pressure. This study reveals the pressure-induced intralayer itinerant antiferromagnetism arising from the interlayer ferromagnetism. The application of modest hydrostatic pressure generates anisotropy that may cause flattening and tilting of RuO${}_{6}$ octahedra. These lattice distortions weaken the $c$-axis ferromagnetism as well as the basal-plane metamagnetism, while inducing a basal-plane, itinerant antiferromagnetic state that is remarkably uncommon. The unusually large magnetoelastic coupling inherent in this ruthenate makes it an ideal model system for studies of itinerant magnetism.