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NASA NTRS1993

Reconnection of vorticity lines and magnetic lines

Magnetic field and fluid vorticity share many features. First, as divergence-free vector fields they are conveniently visualized in terms of their field lines, curves that are everywhere tangent to the field. The lines indicate direction and their density indicates field strength. The question arises of the extent to which the evolution of the fields can be treated in terms of the evolution of their field lines. Newcomb (1958) derived the general conditions on the evolution of vector fields that permit the identification of field lines from one instant to the next. The equations of evolution of the vorticity field and the magnetic field fall within Newcomb's analysis. The dynamics of the flows differ between these two systems, so that geometrically similar phenomena happen in different ways in the two systems. In this paper the geometrical similarities are emphasized. Reconnection will be defined here as evolution in which it is not possible to preserve the global identification of some field lines. There is a close relation between reconnection and the topology of the vector field lines. Nontrivial topology occurs where the field has null points or there are field lines that are closed loops.

Greene, John M.↗

DOE OSTI2026

Braiding of Majorana zero modes in vortex cores

Here, we demonstrate the successful simulation of $\sqrt{𝑍-}$, $\sqrt{𝑋-}$, and 𝑋-quantum gates using Majorana zero modes (MZMs) that emerge in magnetic vortices located in topological superconductors. We compute the transition probabilities and geometric phase differences accounting for the full many-body dynamics and show that qubit states can be read out by fusing the vortex core MZMs and measuring the resulting charge density. We visualize the gate processes using the time- and energy-dependent nonequilibrium local density of states. Our results demonstrate the feasibility of employing vortex core MZMs for the realization of fault-tolerant topological quantum computing.

Majorana bound states↗

DOE OSTI2024

Towards revealing intrinsic vortex-core states in Fe-based superconductors through statistical discovery

Abstract In type-II superconductors, electronic states within magnetic vortices hold crucial information about the paring mechanism and can reveal non-trivial topology. While scanning tunneling microscopy/spectroscopy (STM/S) is a powerful tool for imaging superconducting vortices, it is challenging to isolate the intrinsic electronic properties from extrinsic effects like subsurface defects and disorders. Here we combine STM/STS with basic machine learning to develop a method for screening out the vortices pinned by embedded disorder in iron-based superconductors. Through a principal component analysis of large STS data within vortices, we find that the vortex-core states in Ba(Fe 0.96 Ni 0.04 ) 2 As 2 start to split into two categories at certain magnetic field strengths, reflecting vortices with and without pinning by subsurface defects or disorders. Our machine-learning analysis provides an unbiased approach to reveal intrinsic vortex-core states in novel superconductors and shed light on ongoing puzzles in the possible emergence of a Majorana zero mode.

Guo, Yueming↗

DOE OSTI2023

Evidence for current suppression in superconductor–superconductor bilayers

Superconducting radio frequency (SRF) cavities, which are critical components in many particle accelerators, need to be operated in the Meissner state to avoid strong dissipation from magnetic vortices. For a defect-free superconductor, the maximum attainable magnetic field for operation is set by the superheating field, B sh , which directly depends on the surface current. In heterostructures composed of different superconductors, the current in each layer depends not only on the properties of the individual material, but also on the electromagnetic response of the adjacent layers through boundary conditions at the interfaces. Three prototypical bilayers [Nb 1–x Ti x N (50 nm)/Nb, Nb 1–x Ti x N (80 nm)/Nb, and, Nb 1–x Ti x N (160 nm)/Nb] are investigated here by depth-resolved measurements of their Meissner screening profiles using low energy muon spin rotation (LE-µSR). From fits to a model based on London theory (with appropriate boundary and continuity conditions), a magnetic penetration depth for the thin Nb 1–x Ti x N layers of λ Nb 1–x Ti x N = 182.5(31) nm is found, in good agreement with literature values for the bulk alloy. Using the measured λ Nb 1–x Ti x N , the maximum vortex-free field, B max , of the superconductor-superconductor (SS) bilayer structure was estimated to be 610(40) mT. The strong suppression of the surface current in the Nb 1–x Ti x N layer suggests an optimal thickness of ~ 1.4λ Nb 1–x Ti x N = 261(14) nm.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Observation of magnetic adatom-induced Majorana vortex and its hybridization with field-induced Majorana vortex in an iron-based superconductor

Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe 0.55 Se 0.45 . We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Direct measurement of reduced exchange stiffness and its impact on magnetic vortex behavior in PyGd alloys

Thin films composed of sputtered transition metal/rare earth (TM/RE) ferrimagnets have emerged as promising building blocks for future spintronic devices, offering tunable magnetic properties critical for data storage, memory, and logic applications. However, understanding how the combination of TM and RE elements influences effective magnetic properties, such as exchange stiffness (Aex), remains challenging. Magnetic vortices provide a versatile tool for probing these properties in thin film systems. By combining magnetic imaging via soft x-ray microscopy and micromagnetic modeling, we quantify the effective exchange stiffness in PyGd ferrimagnetic disks with varying Gd concentrations. Our results indicate a reduction in Aex to below 3 pJ/m for a 20% Gd concentration when compared to reference Py, and values below 2 pJ/m for 30% Gd, reflecting weak Ni–Gd exchange coupling. These findings highlight the critical role of rare earth content in tuning the exchange stiffness. The reduced exchange stiffness facilitates a linear field response of the magnetization up to the edge of the disk, as well as significant deformations in the vortex core itself when compared to films with larger Aex. Our results are in line with, albeit lower than, recent measurements of the exchange stiffness in intermixed PyGd. This reduced exchange stiffness has implications for the development of spintronic devices based on ferrimagnetic skyrmions.

Jacob, Liyan↗

DOE OSTI2022

Unusual Magnetic Hysteresis and Transition between Vortex and Double Pole States Arising from Interlayer Coupling in Diamond-Shaped Nanostructures

Controlling the magnetic ground states at the nanoscale is a long-standing basic research problem and an important issue in magnetic storage technologies. Here, we designed a nanostructured material that exhibits very unusual hysteresis loops due to a transition between vortex and double pole states. Arrays of 700 nm diamond-shaped nanodots consisting of Py(30 nm)/Ru(t Ru )/Py(30 nm) (Py, permalloy (Ni 80 Fe 20 )) trilayers were fabricated by interference lithography and e-beam evaporation. We show that varying the Ru interlayer spacer thickness (t Ru ) governs the interaction between the Py layers. We found this interaction mainly mediated by two mechanisms: magnetostatic interaction that favors antiparallel (antiferromagnetic, AFM) alignment of the Py layers and exchange interaction that oscillates between ferromagnetic (FM) and AFM couplings. For a certain range of Ru thicknesses, FM coupling dominates and forms magnetic vortices in the upper and lower Py layers. For Ru thicknesses at which AFM coupling dominates, the magnetic state in remanence is a double pole structure. Our results showed that the interlayer exchange coupling interaction remains finite even at 4 nm Ru thickness. Furthermore, the magnetic states in remanence, observed by magnetic force microscopy (MFM), are in good agreement with corresponding hysteresis loops obtained by the magneto-optic Kerr effect (MOKE) and micromagnetic simulations.

interlayer exchange interaction↗

DOE OSTI2025

Quantifying trapped magnetic vortex losses in niobium resonators at mK temperatures

Trapped magnetic vortices in niobium introduce microwave losses that degrade the performance of superconducting resonators. While such losses have been extensively studied above 1 K, we report here their direct quantification in the millikelvin and low-photon regime relevant to quantum devices. Using a high-quality factor 3D niobium cavity cooled through its superconducting transition in controlled magnetic fields, we isolate vortex-induced losses and find the resistive component of the sensitivity to trapped flux S to be approximately 2 n Ω/mG at 10 mK and 6 GHz. The decay rate is initially dominated by two-level system (TLS) losses from the native niobium pentoxide, with vortex-induced degradation of T 1 occurring above B trap ∼ 50 mG. In the absence of the oxide, even 10 mG of trapped flux limits performance, Q 0 ∼ 10 10 , or T 1 ∼ 350 ms, underscoring the need for stringent magnetic shielding. The resistive sensitivity, S, decreases with temperature and remains largely field-independent, whereas the reactive component, S′, exhibits a maximum near 0.8 K. These behaviors are well modeled within the Coffey–Clem framework in the zero-creep limit, under the assumption that vortex pinning is enhanced by thermally activated processes. Our results suggest that niobium-based transmon qubits can tolerate vortex-induced dissipation at trapped field levels up to several hundred mG, but achieving long coherence times still requires careful magnetic shielding to suppress lower-field losses from other mechanisms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Quantifying Trapped Magnetic Vortex Losses in Niobium Resonators at mK Temperatures

Trapped magnetic vortices in niobium introduce microwave losses that degrade the performance of superconducting resonators. While such losses have been extensively studied above 1 K, we report here their direct quantification in the millikelvin and low-photon regime relevant to quantum devices. Using a high-quality factor 3D niobium cavity cooled through its superconducting transition in controlled magnetic fields, we isolate vortex-induced losses and find the resistive component of the sensitivity to trapped flux S to be approximately 2 nOhm/mG at 10 mK and 6 GHz. The decay rate is initially dominated by two-level system (TLS) losses from the native niobium pentoxide, with vortex-induced degradation of T1 occurring above Btrap~50 mG. In the absence of the oxide, even 10 mG of trapped flux limits performance, Q0 ~ 1010, or T1 ~350 ms, underscoring the need for stringent magnetic shielding. The resistive sensitivity, S, decreases with temperature and remains largely field-independent, whereas the reactive component, S , exhibits a maximum near 0.8 K. These behaviors are well modeled within the Coffey Clem framework in the zero-creep limit, under the assumption that vortex pinning is enhanced by thermally activated processes. Our results suggest that niobium-based transmon qubits can tolerate vortex-induced dissipation at trapped field levels up to several hundred mG, but achieving long coherence times still requires careful magnetic shielding to suppress lower-field losses from other mechanisms

Bafia, Daniel P. [Fermilab]↗

DOE OSTI2024

Enhancement of magnetic domain wall velocity via resonant dissipation of standing wave modes of domain wall structure with perpendicular magnetic anisotropy

The dynamic behaviors of magnetic domain walls have significant implications for developing advanced spintronic devices. In this study, we investigate the intriguing resonance phenomenon within the magnetic domain wall structure, focusing on the dissipation mechanism and its impact on domain wall dynamic motion. By applying a static external magnetic field, we observe a remarkable amplification of domain wall velocity through the resonant excitations of the flexure modes. The resonance of the flexure mode exerts an indirect influence on the domain wall velocity through energy dissipation, leading to a significant enhancement from the predictions of the one-dimensional Walker model. We establish a robust model platform rooted in energy dissipation allows comprehensive understanding the dramatic enhancement of domain wall velocity observed during width-directional flexure mode resonance. By directly quantifying energy dissipation, our approach provides highly effective and accurate estimates of domain wall velocity, surpassing previous methods that focus solely on the instantaneous dynamics of the domain wall structure. These findings offer crucial insights into the fundamental mechanisms governing the dynamics of domain walls and other magnetic systems, such as magnetic skyrmions, bubbles, and magnetic vortices, paving the way for development and optimization of next-generation spintronic devices.

Collective dynamics↗

DOE OSTI2023

Large ordered moment with strong easy-plane anisotropy and vortex-domain pattern in the kagome ferromagnet Fe 3 Sn

We report the magnetic anisotropy of kagome bilayer ferromagnet Fe 3 Sn probed by the bulk magnetometry and magnetic force microscopy (MFM) on high-quality single crystals. The dependence of magnetization on the orientation of the external magnetic field reveals strong easyplane magnetocrystalline anisotropy and anisotropy of the saturation magnetization. The leading magnetocrystalline anisotropy constant shows a monotonous increase from $\mathrm{K_1$≈ –1.0 \times 10^6 J/m^3}$ at 300 K to $\mathrm{–1.3 \times 10^6 J/m^3}$ at 2 K. Our ab initio electronic structure calculations yield the value of total magnetic moment of 7.1$μ_Β$/$f.u.$ and a magnetocrystalline anisotropy energy density of –0.57 $\mathrm{meV/}$$f.u.$ $\mathrm{(–1.62 \times 10^6J/m^3)}$ both being in reasonable agreement with the experimental values. The MFM imaging reveals micrometer-scale magnetic vortices with weakly pinned cores that vanish at the saturation field of ~3T applied perpendicular to the kagome plane. The observed vortex-domain structure is well reproduced by the micromagnetic simulations, using the experimentally determined value of the anisotropy and exchange stiffness.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Magnetic and Optical Properties of Au–Co Solid Solution and Phase-Separated Thin Films and Nanoparticles

The chemical composition and morphology of Au x Co 1–x thin films and nanoparticles are controlled via a combination of cosputtering, pulsed laser-induced dewetting (PLiD), and annealing, leading to tunable magnetic and optical properties. Regardless of chemical composition, the as-deposited thin films and as-PLiD nanoparticles are found to possess a face-centered cubic (FCC) Au x Co 1–x solid-solution crystal structure. Annealing results in large phase-separated grains of Au and Co in both the thin films and nanostructures for all chemical compositions. The magnetic and optical properties are characterized via vibrating sample magnetometry (VSM), ellipsometry, optical transmission spectroscopy, and electron energy loss spectroscopy (EELS). Despite the exceptionally high magnetic anisotropy inherent to Co, the presence of sufficient Au (72 atom %) in the Au x Co 1–x solid solution results in superparamagnetic thin films. Among the as-PLiD nanoparticle samples, an increased Co composition leads to a departure from traditional ferromagnetism in favor of wasp-waisted hysteresis caused by magnetic vortices. Phase separation resulting from annealing leads to ferromagnetism for all compositions in both the thin films and nanoparticles. The optical properties of Au x Co 1–x nanostructures are also largely influenced by the chemical morphology, where the Au x Co 1–x intermixed solid solution has significantly damped plasmonic performance relative to pure Au and comparable to pure Co. Phase separation greatly enhances the quality factor, optical absorption, and electron energy loss spectroscopy (EELS) signatures. The enhancement of the localized surface plasmon resonances (LSPRs) scales with the reduction in Co composition, despite EELS evidence that excitation of the Co portions of a nanoparticle can provide a similar, and in some instances enhanced, LSPR resonance compared to Au. This behavior, however, is seemingly limited to the LSPR dipole mode, while higher-order modes are greatly damped by a Co aloof position. As a result, this observed magneto-plasmonic functionality and tunability could be applicable in biomedicine, namely, cancer therapeutics.

annealing (metallurgy)↗

DOE OSTI2020

Control of spin dynamics in artificial honeycomb spin-ice-based nanodisks

In this paper, we report the experimental and theoretical characterization of the angular-dependent spin dynamics in arrays of ferromagnetic nanodisks arranged on a honeycomb lattice. The magnetic field and microwave frequency dependence, measured by broadband ferromagnetic resonance, reveal a rich spectrum of modes that is strongly affected by the microstate of the network. Based on symmetry arguments with respect to the external field, we show that certain parts of the ferromagnetic network contribute to the detected signal. A comparison of the experimental data with micromagnetic simulations reveals that different subsections of the lattice predominantly contribute to the high-frequency response of the array. This is confirmed by optical characterizations using microfocused Brillouin light scattering. Furthermore, we find indications that nucleation and annihilation of vortexlike magnetization configurations in the low-field range affect the dynamics, which is different from clusters of ferromagnetic nanoellipses. Our work opens up new perspectives for designing magnonic devices that combine geometric frustration in gyrotropic vortex crystals at low frequencies with magnonic crystals at high frequencies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Controllable vortex shedding from dissipative exchange flows in ferromagnetic channels

Ferromagnetic channels subject to spin injection at one extremum sustain long-range coherent textures that carry spin currents known as dissipative exchange flows (DEFs). In the weak injection regime, spin currents carried by DEFs decay algebraically and extend through the length of the channel, a regime known as spin superfluidity. Similar to fluids, these structures are prone to phase slips that manifest as vortex-antivortex pairs. In this work, we numerically study vortex shedding from DEFs excited in a magnetic nanowire with a physical obstacle. Using micromagnetic simulations, we find regimes of laminar flow and vortex shedding as a function of obstacle position tunable by the spin injection sign and magnitude. Vortex-antivortex pairs translate forward (VF regime) or backward (VB regime) with respect to the detector's extremum, resulting in well-defined spectral features. Qualitatively similar results are obtained when temperature, anisotropy, and weak nonlocal dipole fields are included in the simulations. These results provide clear features associated with DEFs that may be detected experimentally in devices with nominally identical boundary conditions. Furthermore, our results suggest that obstacles can be considered as DEF control gates, opening an avenue to manipulate DEFs via physical defects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Robustness of vortex-bound Majorana zero modes against correlated disorder

Here, we investigate the effect of correlated disorder on Majorana zero modes (MZMs) bound to magnetic vortices in two-dimensional topological superconductors. By starting from a lattice model of interacting fermions with a p x ±ip y superconducting ground state in the disorder-free limit, we use perturbation theory to describe the enhancement of the Majorana localization length at weak disorder and a self-consistent numerical solution to understand the breakdown of the MZMs at strong disorder. We find that correlated disorder has a much stronger effect on the MZMs than uncorrelated disorder and that it is most detrimental if the disorder correlation length ℓ is on the same order as the superconducting coherence length ξ. In contrast, MZMs can survive stronger disorder for ℓ $\ll$ξ as random variations cancel each other within the length scale of ξ, while an MZM may survive up to very strong disorder for ℓ$\gg$ξ if it is located in a favorable domain of the given disorder realization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Field-Driven Dynamics of Magnetic Hopfions

Herein, we present micromagnetic simulations on resonant spin wave modes of magnetic Hopfions up to 15 GHz driven by external magnetic fields. A sharp transition is found around 32 mT coinciding with a transition from Hopfions to magnetic torons. Furthermore, the modes exhibit characteristic amplitudes in frequency space accompanied by unique localization patterns in real space, and are found to be robust to damping around topological features, particularly vortex lines in Hopfions and Bloch points in torons. The marked differences in spin wave spectra between Hopfions, torons and target skyrmions can serve as fingerprints in future experimental validation studies of these novel 3d topological spin textures.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Special Issue: To Commemorate the Legacy of Malcolm J. Andrews—Scientist, Educator, and Leader

This special issue celebrates the scientific legacy of Dr. Malcolm J. Andrews, former Editor of the ASME Journal of Fluids Engineering (2010–2018). Malcolm devoted his career to the development and applications of computational, experimental, and analytical tools to investigate and solve diverse, complex fluid dynamics, and heat transfer problems. Malcolm’s most notable research accomplishments include: (i) contributions to innovative experiments, simulations, and theory to understand buoyancydriven turbulent mixing due to Rayleigh–Taylor instability; (ii) development of the multiphase particle-in-cell method for understanding fragmentation in spray jets, coal-water slurry, and other dense particulate flows; (iii) mixing in nano- and biomaterials in applications ranging from protein glues to carbon nanotube composites; (iv) determining dispersion in proteins to improve therapeutic drug delivery via micro-encapsulation; (v) innovative methods for storing information using nanopinned dipole magnetic vortices in superconducting materials; and (vi) modeling and design modifications for shell-and-tube heat exchangers, as well as heat transfer in rotating systems such as turbine blades. The results of his research have been published in a long series of trend-setting journal and conference papers, book chapters, and patents.

42 ENGINEERING↗

DOE OSTI2022

Non-Equilibrium relaxation, aging scaling, and critical depinning dynamics of skyrmions in disordered magnetic films. Final Report

Technical applications of type-II superconductors, especially high-Tc compounds, in external magnetic fields require an effective flux pinning mechanism to reduce Ohmic losses due to flux creep and flow. Naturally abundant point defects, dislocations, and twin boundaries as well as artificially introduced disorder may serve as effective pinning centers for magnetic vortices. The properties of interacting flux lines subject to strong thermal fluctuations and point-like or extended pinning centers have therefore been a major research focus in condensed matter physics, and considerable progress has been achieved in the characterization and mathematical description of the equilibrium phases and non-equilibrium steady states of vortex matter. Detailed studies of the rich phase diagrams that reveal novel glassy states as well as the associated complex dynamical phenomena have in turn enriched the theoretical understanding of condensed matter systems, elucidating specifically the kinetics of elastic objects driven through disordered media and the important role of topological defects such as vortices and dislocations in various materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗