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Microwave Microscopy and Its Applications

Understanding the nanoscale electrodynamic properties of a material at microwave frequencies is of great interest for materials science, condensed matter physics, device engineering, and biology. With specialized probes, sensitive detection electronics, and improved scanning platforms, microwave microscopy has become an important tool for cutting-edge materials research in the past decade. In this article, we review the basic components and data interpretation of microwave imaging and its broad range of applications. In addition to the general-purpose mapping of permittivity and conductivity, microwave microscopy is now exploited to perform quantitative measurements on semiconductor devices, photosensitive materials, ferroelectric domains and domain walls, and acoustic-wave systems. Implementation of the technique in low-temperature and high-magnetic-field chambers has also led to major discoveries in quantum materials with strong correlation and topological order. We conclude the review with an outlook of the ultimate resolution, operation frequency, and future industrial and academic applications of near-field microwave microscopy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach

A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. It is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic case, the integrand is known explicitly. For the transverse electric case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples are ka = 5 and ka = 10. The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger than ka = 1. Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC.

Kriegsmann, Gregory A.↗

Strain-induced majority carrier inversion in ferromagnetic epitaxial LaCo O 3 - δ thin films

Tensile-strained LaCoO 3-δ thin films are ferromagnetic, in sharp contrast to the zero-spin bulk, although no clear consensus has emerged as to the origin of this phenomenon. While magnetism has been heavily studied, relatively little attention has been paid to electronic transport, due to the insulating nature of the strain-stabilized ferromagnetic state. Here, structure, magnetism, and transport are studied in epitaxial LaCoO 3-δ films (10–22-nm thick) on various substrates (from 1.4% compressive to 2.5% tensile strain), using synchrotron x-ray diffraction, scanning probe and transmission electron microscopy, magnetometry, polarized neutron reflectometry, resistivity, and Hall effect. High quality, smooth films are obtained, exhibiting superstructures associated with both oxygen vacancy ordering and periodic in-plane ferroelastic domains. Consistent with prior work, ferromagnetism with an approximately 80–85 K Curie temperature is observed under tension; polarized neutron reflectometry confirms a relatively uniform magnetization depth profile, albeit with interfacial dead layer formation. Electrical transport is found to have similar semiconducting nature to bulk, but with reduced resistivity and activation energy. Hall effect measurements, however, reveal a striking inversion of the majority carrier type, from p-type in the bulk and under compression to n-type under tension. While thus far overlooked, ferromagnetism in epitaxial LaCoO 3-δ films is thus directly correlated with n-type behavior, providing important insight into the ferromagnetic state in this system. Here, aided by density functional theory calculations, these results are interpreted in terms of tensile-strain-induced orbital occupation and band structure changes, including a rapid decrease in effective mass at the e g -derived conduction band minimum, and corresponding increase at the valence band maximum.

36 MATERIALS SCIENCE↗

Antiferromagnet thickness dependence and rotatable spins in exchange biased CoO/Fe films

The emergence of exchange bias and coercivity enhancement has been investigated in epitaxial CoO/Fe films with varied antiferromagnet (AF) thicknesses, even smaller than the critical value where the frozen CoO spins are detectable. Vector magnetometry and first-order reversal curve (FORC) measurements reveal different CoO thickness dependence of the exchange bias and coercivity enhancement, including the evolution of magnetization reversal from a high coercivity, low bias phase due to rotatable CoO moments to a high bias, low coercivity phase due to frozen CoO moments. Furthermore, the AF domain state is found to be metastable, which can be reoriented by external and exchange fields prior to the appearance of frozen spins, pointing to a generic origin of the training effect. Monte Carlo simulations show that the AF anisotropy energy barrier and the rotatable spins induced by magnetic field and exchange interaction at the interface are responsible for the observed effects.

36 MATERIALS SCIENCE↗

Epitaxial Growth of Large-Scale 2D CrTe 2 Films on Amorphous Silicon Wafers With Low Thermal Budget

2D van der Waals (vdW) magnets open landmark horizons in the development of innovative spintronic device architectures. However, their fabrication with large scale poses challenges due to high synthesis temperatures (>500 °C) and difficulties in integrating them with standard complementary metal-oxide semiconductor (CMOS) technology on amorphous substrates such as silicon oxide (SiO 2 ) and silicon nitride (SiN x ). Here, a seeded growth technique for crystallizing CrTe 2 films on amorphous SiN x /Si and SiO 2 /Si substrates with a low thermal budget is presented. This fabrication process optimizes large-scale, granular atomic layers on amorphous substrates, yielding a substantial coercivity of 11.5 kilo-oersted, attributed to weak intergranular exchange coupling. Field-driven Néel-type stripe domain dynamics explain the amplified coercivity. Moreover, the granular CrTe 2 devices on Si wafers display significantly enhanced magnetoresistance, more than doubling that of single-crystalline counterparts. Current-assisted magnetization switching, enabled by a substantial spin–orbit torque with a large spin Hall angle (85) and spin Hall conductivity (1.02 × 10 7 ℏ/2e Ω -1 m -1 ), is also demonstrated. These observations underscore the proficiency in manipulating crystallinity within integrated 2D magnetic films on Si wafers, paving the way for large-scale batch manufacturing of practical magnetoelectronic and spintronic devices, heralding a new era of technological innovation.

2D magnetic thin films↗

Combined Dimensional and Topology Optimization of Interior Permanent Magnet Synchronous Machine Rotors Using a Permanent Magnet Function Interpolation Method

This paper presents a magneto-structural combined dimensional and topology optimization technique for interior permanent magnet synchronous machine (IPMSM) rotors. Dimensional changes to the permanent magnet (PM) location or size are accomplished by interpolating or projecting a smoothed Heaviside rectangular function representing the presence of PM material onto the IPMSM rotor design domain mesh. A density based Solid Isotropic with Material Penalization (SIMP) topology optimization approach is then used to vary the presence of electrical steel in mesh elements to form flux barriers around the PM. The proposed method enforces a defined shape for the PM without requiring the mesh in the design domain to be deformed. Three examples are presented to demonstrate the technique: two flat bar IPMSM and one V-shaped IPMSM.

33 ADVANCED PROPULSION SYSTEMS↗

Easy axis anisotropy creating high contrast magnetic zones on magnetic tunnel junctions based molecular spintronics devices (MTJMSD)

Abstract Magnetic tunnel junction-based molecular spintronics device (MTJMSD) may enable novel magnetic metamaterials by chemically bonding magnetic molecules and ferromagnets (FM) with a vast range of magnetic anisotropy. MTJMSD have experimentally shown intriguing microscopic phenomenon such as the development of highly contrasting magnetic phases on a ferromagnetic electrode at room temperature. This paper focuses on Monte Carlo Simulations (MCS) on MTJMSD to understand the potential mechanism and explore fundamental knowledge about the impact of magnetic anisotropy. The selection of MCS is based on our prior study showing the potential of MCS in explaining experimental results (Tyagi et al. in Nanotechnology 26:305602, 2015). In this paper, MCS is carried out on the 3D Heisenberg model of cross-junction-shaped MTJMSDs. Our research represents the experimentally studied cross-junction-shaped MTJMSD where paramagnetic molecules are covalently bonded between two FM electrodes along the exposed side edges of the magnetic tunnel junction (MTJ). We have studied atomistic MTJMSDs properties by simulating a wide range of easy-axis anisotropy for the case of experimentally observed predominant molecule-induced strong antiferromagnetic coupling. Our study focused on understanding the effect of anisotropy of the FM electrodes on the overall MTJMSDs at various temperatures. This study shows that the multiple domains of opposite spins start to appear on an FM electrode as the easy-axis anisotropy increases. Interestingly, MCS results resembled the experimentally observed highly contrasted magnetic zones on the ferromagnetic electrodes of MTJMSD. The magnetic phases with starkly different spins were observed around the molecular junction on the FM electrode with high anisotropy.

36 MATERIALS SCIENCE↗

Nanoscale Superconducting States in the Fe-Based Filamentary Superconductor of Pr-Doped CaFe 2 As 2

The low-temperature scanning tunneling microscope and spectroscopy (STM/STS) are used to visualize superconducting states in the cleaved single crystal of 9% praseodymium-doped CaFe 2 As 2 (Pr-Ca122) with Tc ≈ 30 K. The spectroscopy shows strong spatial variations in the density of states (DOS), and the superconducting map constructed from spectroscopy discloses a localized superconducting phase, as small as a single unit cell. The comparison of the spectra taken at 4.2 K and 22 K (below vs. close to the bulk superconducting transition temperature) from the exact same area confirms the superconducting behavior. Nanoscale superconducting states have been found near Pr dopants, which can be identified using dI/dV conductance maps at +300 mV. There is no correlation of the local superconductivity to the surface reconstruction domain and surface defects, which reflects its intrinsic bulk behavior. We, therefore, suggest that the local strain of Pr dopants is competing with defects induced local magnetic moments; this competition is responsible for the local superconducting states observed in this Fe-based filamentary superconductor.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Understanding Space Weather Part III: the Sun's Domain

The Sun exports a continuous outflow of plasma into interplanetary space: the solar wind. The solar wind primarily comprises two components: high- and slow-speed flows. These move with velocities ranging from 200 to 800 km/s depending on the source of the particular flow. As well as its speed, the density, temperature, and even the composition of the solar wind change. Adding to its intrinsic variability, there are embedded transients resulting from flares and coronal mass ejections that further complicate its dynamics and space weather impacts. The solar wind interacts differently with each of the solar system objects it encounters based on their magnetic and atmospheric properties. Even more complex processes occur as the solar wind encounters the interstellar medium, at the outer boundaries of the Sun's domain. The solar wind stretches to beyond 100 au (where 1 au defined to be equal to 149 597 870 700 m) from the Sun, which means that Earth is essentially immersed in the very hot solar atmosphere, and that leads to many space weather impacts on life and society. The specific space weather impacts on Earth will be discussed in detail in the next two papers in this series.

Strong, Keith↗

A Nonlocal Magneto-curvature Instability in a Differentially Rotating Disk

A global mode is shown to be unstable to nonaxisymmetric perturbations in a differentially rotating Keplerian disk containing either vertical or azimuthal magnetic fields. In an unstratified cylindrical disk model, using both global eigenvalue stability analysis and linear global initial-value simulations, it is demonstrated that this instability dominates at strong magnetic fields where local standard magnetorotational instability (MRI) becomes stable. Unlike the standard MRI mode, which is concentrated in the high flow shear region, these distinct global modes (with low azimuthal mode numbers) are extended in the global domain and are Alfvén-continuum-driven unstable modes. As its mode structure and relative dominance over MRI are inherently determined by the global spatial curvature as well as the flow shear in the presence of a magnetic field, we call it the magneto-curvature (magneto-spatial-curvature) instability. Consistent with the linear analysis, as the field strength is increased in the nonlinear simulations, a transition from MRI-driven turbulence to a state dominated by global nonaxisymmetric modes is obtained. This global instability could therefore be a source of nonlinear transport in accretion disks at a higher magnetic field than predicted by local models.

79 ASTRONOMY AND ASTROPHYSICS↗

Waves in Radial Gravity Using Magnetic Fluid

Terrestrial laboratory experiments studying various fluid dynamical processes are constrained, by being in an Earth laboratory, to have a gravitational body force which is uniform and unidirectional. Therefore fluid free-surfaces are horizontal and flat. Such free surfaces must have a vertical solid boundary to keep the fluid from spreading horizontally along a gravitational potential surface. In atmospheric, oceanic, or stellar fluid flows that have a horizontal scale of about one-tenth the body radius or larger, sphericity is important in the dynamics. Further, fluids in spherical geometry can cover an entire domain without any sidewall effects, i.e. have truly periodic boundary conditions. We describe spherical body-force laboratory experiments using ferrofluid. Ferrofluids are dilute suspensions of magnetic dipoles, for example magnetite particles of order 10 nm diameter, suspended in a carrier fluid. Ferrofluids are subject to an additional body force in the presence of an applied magnetic field gradient. We use this body force to conduct laboratory experiments in spherical geometry. The present study is a laboratory technique improvement. The apparatus is cylindrically axisymmetric. A cylindrical ceramic magnet is embedded in a smooth, solid, spherical PVC ball. The geopotential field and its gradient, the body force, were made nearly spherical by careful choice of magnet height-to-diameter ratio and magnet size relative to the PVC ball size. Terrestrial gravity is eliminated from the dynamics by immersing the "planet" and its ferrofluid "ocean" in an immiscible silicone oil/freon mixture of the same density. Thus the earth gravity is removed from the dynamics of the ferrofluid/oil interface and the only dynamically active force there is the radial magnetic gravity. The entire apparatus can rotate, and waves are forced on the ferrofluid surface by exterior magnets. The biggest improvement in technique is in the wave visualization. Fluorescing dye is added to the oil/freon mixture and an argon ion laser generates a horizontal light that can be scanned vertically. Viewed from above, the experiment is a black circle with wave deformations surrounded by a light background. A contour of the image intensity at any light sheet position gives the surface of the ferrofluid "ocean" at that "latitude". Radial displacements of the waves as a function of longitude are obtained by subtracting the contour line positions from a no-motion contour at that laser sheet latitude. The experiments are run by traversing the forcing magnet with the laser sheet height fixed and images are frame grabbed to obtain a time-series at one latitude. The experiment is then re-run with another laser-sheet height to generate a full picture of the three-dimensional wave structure in the upper hemisphere of the ball as a function of time. We concentrate here on results of laboratory studies of waves that are important in Earth's atmosphere and especially the ocean. To get oceanic scaling in the laboratory, the experiment must rotate rapidly (4-second rotation period) so that the wave speed is slow compared to the planetary rotation speed as in the ocean. In the Pacific Ocean, eastward propagating Kelvin waves eventually run into the South American coast. Theory predicts that some of the wave energy should scatter into coastal-trapped Kelvin waves that propagate north and south along the coast. Some of this coastal wave energy might then scatter into mid-latitude Rossby waves that propagate back westward. Satellite observations of the Pacific Ocean sea-surface temperature and height seem to show signatures of westward propagating mid-latitude Rossby waves, 5 to 10 years after the 1982-83 El Nino. The observational data is difficult to interpret unambiguously owing to the large range of motions that fill the ocean at shorter timescales. This series of reflections giving eastward, north- ward, and then westward traveling waves is observed cleanly in the laboratory experiments, confirming the theoretical expectations.

Ohlsen, D. R.↗

Space-Charge-Limited van der Waals Spin Transistor

Integrating semiconducting and magnetic materials could combine transistorlike operation with nonvolatility and enable architectures such as logic in memory. Here, in this work, we employ correlated electrical transport and scanning nitrogen-vacancy center magnetic imaging to elucidate a spin transistor concept that amalgamates vertical and lateral hopping transport inside a 2D antiferromagnetic semiconductor, mechanistically distinct from vertical tunneling devices. Our device, based on a monolayer-bilayer junction in CrSBr, displays giant, gate-tunable magnetoresistance driven by the dual action of electrostatic doping on space-charge-limited lateral conduction and interlayer exchange coupling. Moreover, we visualize a field-trainable, layer-sharing effect that selects between coherent or domain-wall reversal at the spin-flip transition, enabling multilevel, memristive conductance states. Our layer-dependent space charge mechanism for convergent electrical and magnetic control opens opportunities to address limitations in contemporary computing.

2-dimensional systems↗

Topological Magnetic-Spin Textures in Two-Dimensional van der Waals Cr 2 Ge 2 Te 6

Two-dimensional (2D) van der Waals (vdW) materials show a range of profound physical properties that can be tailored through their incorporation in heterostructures and manipulated with external forces. The recent discovery of long-range ferromagnetic order down to atomic layers provides an additional degree of freedom in engineering 2D materials and their heterostructure devices for spintronics, valleytronics, and magnetic tunnel junction switches. In this work, using direct imaging by cryo-Lorentz transmission electron microscopy we show that topologically nontrivial magnetic-spin states, skyrmionic bubbles, can be realized in exfoliated insulating 2D vdW Cr 2 Ge 2 Te 6 . Due to the competition between dipolar interactions and uniaxial magnetic anisotropy, hexagonally packed nanoscale bubble lattices emerge by field cooling with magnetic field applied along the out-of-plane direction. Despite a range of topological spin textures in stripe domains arising due to pair formation and annihilation of Bloch lines, bubble lattices with single chirality are prevalent. In conclusion, our observation of topologically nontrivial homochiral skyrmionic bubbles in exfoliated vdW materials provides a new avenue for novel quantum states in atomically thin insulators for magneto-electronic and quantum devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Simulating a pulsed-power-driven plasma with ideal MHD

We describe a simple practical numerical method for simulating plasma driven within a vacuum chamber by a pulsed power generator. Typically, in this type of simulation, the vacuum region adjacent to the plasma is approximated as a highly resistive, light fluid; this involves computationally expensive solvers describing the diffusion of the magnetic field through this fluid. Instead, we provide a recipe for coupling pulsed power generators to the magnetohydrodynamics (MHD) domain by approximating the perfectly insulating vacuum as a light, perfectly conducting, inviscid MHD fluid and discuss the applicability of this counter-intuitive technique. This much more affordable ideal MHD representation is particularly useful in situations where a plasma exhibits interesting three-dimensional phenomena, either due to the design of the experiment or due to developing instabilities. We verified that this coupling recipe works by modeling an exactly solvable flux compression generator as well as a self-similar Noh-like solution and demonstrated convergence to the theoretical solution. We also showed examples of simulating complex three-dimensional pulsed power devices with this technique. We release our code implementation to the public.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Inverse design of plasma metamaterial devices with realistic elements

In an expansion of a previous study, we apply inverse design methods to produce two-dimensional plasma metamaterial devices with realistic plasma elements which incorporate quartz envelopes, collisionality (loss), non-uniform density profiles, and resistance to experimental error/perturbation. Finite difference frequency domain simulations are used along with forward-mode differentiation to design waveguides and demultiplexers operating under the transverse magnetic polarization. Additionally, optimal devices with realistic elements are compared to previous devices with idealized elements, and several parameter initialization schemes for the optimization algorithm are explored, yielding a robust procedure for producing such devices. Demultiplexing and waveguiding are demonstrated for microwave-regime devices composed of plasma elements with reasonable space-averaged plasma frequencies ~10GHz and a collision frequency ~1 GHz, allowing for future in-situ training and experimental realization of these designs.

42 ENGINEERING↗

Oscillating paramagnetic Meissner effect and Berezinskii-Kosterlitz-Thouless transition in underdoped Bi2Sr2CaCu2O8+δ

ABSTRACT Superconducting phase transitions in two dimensions lie beyond the description of the Ginzburg-Landau symmetry-breaking paradigm for three-dimensional superconductors. They are Berezinskii-Kosterlitz-Thouless (BKT) transitions of paired-electron condensate driven by the unbinding of topological excitations, i.e. vortices. The recently discovered monolayers of layered high-transition-temperature (${{{T}}}_{{\rm C}}$) cuprate superconductor Bi2Sr2CaCu2O8+δ (Bi2212) meant that this 2D superconductor promised to be ideal for the study of unconventional superconductivity. But inhomogeneity posed challenges for distinguishing BKT physics from charge correlations in this material. Here, we utilize the phase sensitivity of scanning superconducting quantum interference device microscopy susceptometry to image the local magnetic response of underdoped Bi2212 from the monolayer to the bulk throughout its phase transition. The monolayer segregates into domains with independent phases at elevated temperatures below ${{{T}}}_{{\rm C}}$. Within a single domain, we find that the susceptibility oscillates with flux between diamagnetism and paramagnetism in a Fraunhofer-like pattern up to ${{{T}}}_{{\rm C}}$. The finite modulation period, as well as the broadening of the peaks when approaching ${{{T}}}_{{\rm C}}$ from below, suggests well-defined vortices that are increasingly screened by the dissociation of vortex-antivortex plasma through a BKT transition. In the multilayers, the susceptibility oscillation differs in a small temperature regime below ${{{T}}}_{{\rm C}}$, consistent with a dimensional crossover led by interlayer coupling. Serving as strong evidence for BKT transition in the bulk, we observe a sharp jump in phase stiffness and paramagnetism at small fields just below ${{{T}}}_{{\rm C}}$. These results unify the superconducting phase transitions from the monolayer to the bulk underdoped Bi2212, and can be collectively referred to as the BKT transition with interlayer coupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic Eddy Viscosity of Mean Sheared Flows in Two-Dimensional Magnetohydrodynamics

Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number (Rm) less than 1 has long been known to cause magnetic drag. Here we show that when Rm $\gg 1$ and the fluid is in a hydrodynamic-dominated regime in which the magnetic energy is much smaller than the kinetic energy, induction due to a mean shear flow leads to a magnetic eddy viscosity. The magnetic viscosity is derived from simple physical arguments, where a coherent response due to shear flow builds up in the magnetic field until decorrelated by turbulent motion. The dynamic viscosity coefficient is approximately $(B^2_p/2_{μ_0}) τ_{corr}$, the poloidal magnetic energy density multiplied by the correlation time. We confirm the magnetic eddy viscosity through numerical simulations of two-dimensional incompressible magnetohydrodynamics. We also consider the three-dimensional case, and in cylindrical or spherical geometry, theoretical considerations similarly point to a nonzero viscosity whenever there is differential rotation. Hence, these results serve as a dynamical generalization of Ferraro's law of isorotation. The magnetic eddy viscosity leads to transport of angular momentum and may be of importance to zonal flows in astrophysical domains such as the interior of some gas giants.

79 ASTRONOMY AND ASTROPHYSICS↗