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Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4)(Final Technical Report)

Our work on the CM4 grant focused on new mathematical and computational approaches for stochastic methods for mesoscopic systems. Our work included continuum SPDEs, molecular coarse-grained models, and hybrid particle-continuum approaches. This work was motivated by applications in soft materials, fluidic devices, and interfacial phenomena. Throughout the project we collaborated with several staff researchers, including from Pacific Northwest National Laboratories (PNNL) and Sandia National Laboratory (SNL) as well as other members of the CM4 project. Below we summarize briefly a few specific accomplishments from this work over the funding period. A full list of published papers and software releases supported by the grant are listed at the end.

97 MATHEMATICS AND COMPUTING↗

Scaling and statistics of bottom-up synthesized armchair graphene nanoribbon transistors

Bottom-up assembled nanomaterials and nanostructures allow for the studies of rich and unprecedented quantum-related and mesoscopic transport phenomena. However, it can be difficult to quantify the correlations between the geometrical or structural parameters obtained from advanced microscopy and measured electrical characteristics when they are made into macroscopic devices. Here, we propose a strategy to connect the nanomaterial morphologies and the device performance through a Monte Carlo device model and apply it to understand the scaling trends of bottom-up synthesized armchair graphene nanoribbon (GNR) transistors. A new nanofabrication process is developed for GNR transistors with channel length down to 7 nm. Further, the impacts of the GNR spatial distributions and the device geometries on the device performance are investigated systematically through comparison of experimental data with the model. Through this study, challenges and opportunities of transistor technologies based on bottom-up synthesized GNRs are pinpointed, paving the way to the further improvement of the GNR device performance for future transistor technology nodes.

36 MATERIALS SCIENCE↗

Relevance of anisotropy in the Kondo effect: Lessons from the symplectic case

A Kondo model with symplectic symmetry was recently put forward as the effective low-energy theory of a superconducting-island device coupled to multiple leads. This model, which possesses non-Fermi liquid physics and effective anyons, was argued to belong to the class of topological Kondo effects. Here, we clarify the extent of stability of its exotic fixed point using perturbative and numerical renormalization group in conjunction with bosonization and conformal field theory. In contrast to previous claims, we show that asymmetry in the coupling to the leads destabilizes the non-Fermi liquid. Other destabilizing perturbations include asymmetry in the superconducting pairing or internal energy of the individual quantum dots in the island. Nevertheless, these perturbations all generate the same relevant operators. Thus, only a small number of couplings need to be tuned individually, and these can be selected according to experimental convenience. Our results highlight a common misconception that anisotropy in single-channel Kondo couplings is always irrelevant. As demonstrated, relevant terms will emerge whenever the group generators do not span the full space of impurity operators. This calls for a more detailed inspection of models that exhibit this property, such as large-spin impurities and SO⁡( M ) Kondo models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Emergent Inductance from Chiral Orbital Currents in a Bulk Ferrimagnet

Here, we report the discovery of a new form of inductance in the bulk ferrimagnet Mn 3 ⁢Si 2 ⁢Te 6 , which features strong spin-orbit coupling, large magnetic anisotropy, and pronounced magnetoelastic interactions. Below its Curie temperature (𝑇 𝐶 ≈ 78 K), Mn 3 ⁢Si 2 ⁢Te 6 hosts chiral orbital currents (COC) that circulate within the crystal lattice and give rise to collective electronic behavior [Control of chiral orbital currents in a colossal magnetoresistance material, Nature (London) 611, 467 (2022).]. By applying a magnetic field along the hard 𝑐 axis and driving the system with low-frequency currents, we uncover a giant inductive response up to millhenry scale, originating from first-order reconfigurations of COC domains. These domains act as coherent mesoscopic inductive elements that resist reversal upon current reduction, producing a large electromotive force and sharply increasing voltage. This emergent inductance defies classical models, occurs without superconductivity or engineered nanostructures, and opens a new frontier in orbital-based quantum functionality and device concepts.

complex materials↗

Spin-helical detection in a semiconductor quantum device with ferromagnetic contacts

Spin-helical states, which arise in quasi-one-dimensional (1D) channels with spin-orbital (SO) coupling, underpin efforts to realize topologically protected quantum bits based on Majorana modes in semiconductor nanowires. Detecting helical states is challenging due to non-idealities present in real devices. Past efforts have focused on devices with normal contacts. In contrast, here we show by means of tight-binding calculations that by using ferromagnetic contacts it is possible to detect helical modes with high sensitivity even in the presence of realistic device effects, such as quantum interference. We show that by taking advantage of the spin-selective transmission properties of helical states, new transport signatures become possible. In addition, we show that spin-polarized contacts provide a unique path to investigate the spin-texture and spin-momentum locking properties of helical states. Our results are of interest not only for the ongoing development of Majorana qubits, but also for realizing possible spin-based quantum devices, such as quantum spin modulators and interconnects based on spin-helical channels.

36 MATERIALS SCIENCE↗

Controlling reversible phase transitions in rare-earth nickelates for novel memory devices

Resistive switching in correlated complex oxides is lucrative for emerging applications in neuromorphic computing, and densely scaled non-volatile memory. Electrical conductance of such complex oxides can be controllable switched across multiple orders of magnitude by either (a) electroforming a conduction channel (e.g., in tungsten oxide), or (b) inducing Mott-Hubbard transition (e.g., in rare-earth nickelates)– both via controlled migration of defects (such as oxygen vacancies) under applied bias. Nevertheless, the promise of such defect-driven electronic transitions are far from realized due to a lack of fundamental understanding of the atomic-scale processes that underlie migration and spatiotemporal evolution of oxygen vacancies over nano-to-mesoscopic length/timescales under applied electric field. In this project, we employ a synergistic integration of density functional theory (DFT) calculations, ab initio/classical molecular dynamics (AIMD/CMD) simulations, machine learning (ML), precision synthesis, and multi-modal X-ray imaging experiments to address this knowledge gap. Such an integrated approach offers to elucidate the correlations between subtle structural distortion and oxidation states; treat localized charge carriers; describe defect/ion transport in the presence of electric field; and, in turn, greatly advance the current understanding of microstructural evolution in complex oxides under applied bias. The fundamental knowledge gained from this work will enable precise control over hierarchical defect structures and unravel new routes to manipulate resistance states in complex oxides. This, in turn, will accelerate design of novel devices with desired set of neural functionalities, and high-speed densely-scaled resistive random access memory technologies.

36 MATERIALS SCIENCE↗

Mesoporous Thin Film Architectures: Addressing Material Demands through Molecular Self-Assembly

Mesoporous thin films spark interest across a wide range of disciplines due to their tunable nanostructures, large internal surface areas, and strong compatibility with planar optical, electronic, and microfluidic devices. While attention in the porous materials community has shifted toward macroporous or disordered nanoporous systems, a resurgence in mesoporous thin film research is underway, driven by new molecular self-assembly methods, advanced materials chemistry, and improved characterization techniques. The integration of high-χN block copolymer design, kinetically persistent micelle templating, and postdeposition processing protocols now allows control over structural parameters such as pore size, wall thickness, porosity, and connectivity. These advances have overcome many of the thermodynamic and processing constraints that previously limited widespread adoption. Rather than serving only as high-surface-area supports, mesoporous thin films are engineered as active interfaces where responsive chemistries and nanoscale confinement act in tandem. Embedding switchable ligands, thermoresponsive polymers, redox mediators, or ion-selective groups directly within the pore walls enables real-time control over transport, optical, and electrochemical properties. These capabilities open up new directions in adaptive coatings, gated membranes, and fast-response biosensors. To further expand their functional scope, mesoporous films are integrated into hierarchical and multicomponent architectures. Techniques such as triblock terpolymer templating, crack-directed assembly, and nanoimprint lithography allow for control over spatial organization on the micron and submicron scale and pore system orientation. This enables programmable anisotropy, enhanced molecular diffusion, and wavelength-selective photonic behavior, essential for next-generation sensing, catalysis, and energy applications. Such structural and functional complexity requires equally sophisticated characterization. Multimodal and in situ techniques can track material dynamics under operational conditions. Recent progress includes extended-range ellipsometric porosimetry (EP) for hierarchical architectures, vacuum EP for interface energetics, time-resolved EP for diffusion kinetics, and correlative AFM-SAXS mapping. The introduction of advanced neutron-based spectroscopies, particularly quasielastic neutron scattering (QENS), promises to provide real-time access to ion transport dynamics and segmental motion under nanoscale confinement, offering a path toward deeper mechanistic understanding of structure-performance correlations in mesoporous systems. This Account reflects the technical advances made and the interdisciplinary collaborations that have shaped our collective vision. The particular dimensions of mesopores enable us to subtly tune interactions at the molecular, interfacial, and mesoscopic levels that permit us to harness nanoconfinement. What emerges is a versatile, modular platform capable of chemical gating, energy transduction, and sensing with a level of tunability unmatched by other porous materials. We highlight critical challenges including the need for more robust large-area processing, a deeper understanding of dynamic behavior under cycling, and better integration with device-level architectures. Our strategies support the transition of mesoporous thin films into active high-performance components in next-generation energy, environmental, and biomedical systems.

oxides↗

A Superconducting Micro-Magnetometer for Quantum Vortex in Superconducting Nanoflakes

Superconducting quantum interferometer device (SQUID) plays a key role in understanding electromagnetic properties and emergent phenomena in quantum materials. The technological appeal of SQUID is that its detection accuracy for the electromagnetic signal can precisely reach the quantum level of a single magnetic flux. However, conventional SQUID techniques normally can only be applied to a bulky sample and do not have the capability to probe the magnetic properties of micro-scale samples with small magnetic signals. Here, in this paper, it is demonstrated that, based on a specially designed superconducting nano-hole array, the contactless detection of magnetic properties and quantized vortices in micro-sized superconducting nanoflakes is realized. An anomalous hysteresis loop and a suppression of Little–Parks oscillation are observed in the detected magnetoresistance signal, which originates from the disordered distribution of the pinned vortices in Bi 2 Sr 2 CaCu 2 O 8+δ . Therefore, the density of pinning centers of the quantized vortices on such micro-sized superconducting samples can be quantitatively evaluated, which is technically inaccessible for conventional SQUID detection. The superconducting micro-magnetometer provides a new approach to exploring mesoscopic electromagnetic phenomena of quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Geometric control of magnetic domain morphology in electrodeposited Ni rich NiPt mesoscopic wires

In this paper, we study the electrodeposited Ni—Pt magnetic wires, exploring the mechanisms by which changes in geometry and composition influence the local magnetic structure. The samples were prepared by electrodeposition, their elemental composition was analyzed by energy dispersive X-ray spectroscopy, and phase analysis was carried out by an X-ray diffraction measurement. Magnetic force microscopy measurements, and magnetic force microscopy measurements in magnetic field were carried out to study the domain morphology of the prepared samples. Magnetization characteristics were measured via vibrating sample magnetometry mode of a superconducting quantum interference device. Here, the results were analyzed and compared with micromagnetic simulations. It is shown that a strong perpendicular magnetic anisotropy is responsible for the characteristic checkerboard-like surface magnetization patterns, which can be tuned by geometrical constriction and Ni content. Understanding these relationships provides insights into the design of magnetic materials with tailored properties for advanced applications, like magnetic sensors.

Binary alloy↗

Optical transient grating pumped X-ray diffraction microscopy for studying mesoscale structural dynamics

Abstract A fundamental understanding of materials’ structural dynamics, with fine spatial and temporal control, underpins future developments in electronic and quantum materials. Here, we introduce an optical transient grating pump and focused X-ray diffraction probe technique (TGXD) to examine the structural evolution of materials excited by modulated light with a precisely controlled spatial profile. This method adds spatial resolution and direct structural sensitivity to the established utility of a sinusoidal transient-grating excitation. We demonstrate TGXD using two thin-film samples: epitaxial BiFeO 3 , which exhibits a photoinduced strain (structural grating) with an amplitude proportional to the optical fluence, and FeRh, which undergoes a magnetostructural phase transformation. In BiFeO 3 , structural relaxation is location independent, and the strain persists on the order of microseconds, consistent with the optical excitation of long-lived charge carriers. The strain profile of the structural grating in FeRh, in comparison, deviates from the sinusoidal excitation and exhibits both higher-order spatial frequencies and a location-dependent relaxation. The focused X-ray probe provides spatial resolution within the engineered optical excitation profile, resolving the spatiotemporal flow of heat through FeRh locally heated above the phase transition temperature. TGXD successfully characterizes mesoscopic energy transport in functional materials without relying on a specific transport model.

36 MATERIALS SCIENCE↗

Solid State Quantum Refrigeration Superconducting, Absorption and Measurement Based (Final Technical Report)

During this DOE grant, DE-SC0017890, in place for the past six years, all proposed research was carried out and published in peer-reviewed papers, as well as other projects that emerged during the research. In that effort the research team accomplished all proposed research, as well as many closely related research projects discovered and conceived of during the grant. These works included “Efficient Quantum Measurement Engines”, a work published in Physical Review Letters, giving a theory of quantum measurement-based engines, which uses quantum measurement as a resource. These engines are designed to efficiently convert energy from the stochastic quantum measurement process into useful work. Further publications include “Experimental Realization of a Quantum Dot Energy Harvester”, a joint theory and experimental work in collaboration with the group of Charles Smith in Cambridge, UK, as well as long time theoretical collaborators, Rafael Sánchez and Björn Sothmann. This work, featured as an Editor’s Suggestion in Physical Review Letters, realized an earlier theoretical proposal of ours, whereby two resonant tunneling quantum dots are connected to a central electronic cavity that is heated by a hot energy source. We also published “Superconducting Quantum Refrigerator: Breaking and Rejoining Cooper Pairs with Magnetic Field Cycles” a work done in collaboration with experimentalist Francesco Giazotto from ENS Pisa, Italy, which also resulted in a patent. This paper, published in Phys. Rev. Applied, advanced the concept of a cyclic fridge based on the normal/superconducting phase transition together with layered materials separated by tunnel junctions. We also completed the proposed research on a heat transistor, publishing “Thermal transistor and thermometer based on Coulomb-coupled conductors”, carried out as a collaboration between my group and theorists Splettstoesser (Lund U., Sweden), Sothmann (U. Duisburg-Essen, Germany), and Sánchez (U. Autónoma de Madrid, Spain). We carried out an analysis of a quantum coupled to a quantum point contact as a sensitive thermometer and heat transistor. We found the optimal statistical estimator for the temperature and compared it with experiments on the same type of devices. We also investigated autonomous quantum absorption refrigerators using quantum dots to cool by using a very hot thermal reservoir to drive heat between two other reservoirs. In the article “Quantifying the quantum heat contribution from a driven superconducting circuit”, we demonstrated that for a driven superconducting circuit, we showed heat flow provided by a hot source to the qubit can be switched on and off by varying external parameters, the frequency and the intensity of the driving. In the work “Stochastic thermodynamic cycles of a mesoscopic thermoelectric engine”, we reconsidered the autonomous thermoelectric heat engine in terms of underlying cycles. Rather than periodic behavior, the cycles were stochastic in nature. Nevertheless, by undertaking a graph theoretical analysis of the elementary transport processed, great quantitative and qualitative insight could be found. We also considered the quantum measurement process and showed that a quantum version of Maxwell’s demon could be related to the work extraction of a quantum system, closely related to arrow-of-time measures for quantum measurement, as described in our article “Thermodynamics of quantum measurement and Maxwell's demon's arrow of time”. This work was selected in Phys. Rev. A as an Editor’s Suggestion. A recent preprint titled “Cyclic Superconducting Quantum Refrigerators Using Guided Fluxon Propagation” accomplished an important piece of this grant: to propose a new kind of quantum refrigerator using the dynamics of fluxons in a type II superconductor. This invention envisioned a race-track type geometry where fluxons are confined. By applying a gradient of magnetic field together with electric current in a Corbino geometry, the circulating fluxons can actively cool a cold reservoir, realizing a new type of cyclic superconducting refrigerator. We also investigated the possibility of thermal control from different points of view. The application of quantum measurement to the system gives a new kind of control on the system of interest – we have pioneered this approach and shown that measurement can boost the thermal power of quantum engines as described in “Continuous measurement boosted adiabatic quantum thermal machines”. The ability to have heat flows on demand is an outstanding challenge, and we have provided new solutions to this problem in Thermal control across a chain of electronic nanocavities” for a chain of electron cavities using gating voltage control. The control methods using qubit/qubit coupling to create absorption fridges at their most fundamental level have also been developed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Toroidal polar topology in strained ferroelectric polymer

Polar topological texture has become an emerging research field for exotic phenomena and potential applications in reconfigurable electronic devices. Here, we report toroidal topological texture self-organized in a ferroelectric polymer, poly(vinylidene fluoride-ran-trifluoroethylene) [P(VDF-TrFE)], that exhibits concentric topology with anticoupled chiral domains. The interplay among the elastic, electric, and gradient energies results in continuous rotation and toroidal assembly of the polarization perpendicular to polymer chains, whereas relaxor behavior is induced along polymer chains. Such toroidal polar topology gives rise to periodic absorption of polarized far-infrared (FIR) waves, enabling the manipulation of the terahertz wave on a mesoscopic scale. Our observations should inform design principles for flexible ferroic materials toward complex topologies and provide opportunities for multistimuli conversions in flexible electronics.

36 MATERIALS SCIENCE↗

Nanodiffraction imaging of ionically driven phase separation in cobaltite heterostructures

Controlling the anionic stoichiometry and distribution of perovskite cobaltites presents a powerful method for tailoring the magnetic and electronic properties for magneto-ionic applications. Nevertheless, the influence of nanoscale morphology, including phase separation and defects in cobaltite heterostructures, remains largely unexplored. We used x-ray nanodiffraction to directly image the nanoscale topotactic phase transformation in La 1−x Sr x CoO 3 (LSCO) heterostructures capped with a reactive aluminum (Al) layer (i.e., oxygen “getter”) of varying thicknesses (0.5, 3, and 7 nm). Nanodiffraction images reveal the formation of highly elongated BM filaments extending over mesoscopic lengths (>67 μm), indicating a strong tendency toward oxygen vacancy ordering in both P and BM phases in all heterostructures. Local strain and strain gradient analysis shows a strong correlation between the depletion of the P phase and strain gradients. Our measurements suggest that elongation of the BM filaments is the predominant mechanism for topotactic transformation in LSCO/Al heterostructures, preferred over coarsening, branching, and fractal growth. Our study provides a detailed nanoscale analysis of ionically driven phase transitions in LSCO/Al heterostructures, which is crucial for tailoring the functional properties of cobaltites for magneto-ionic devices.

36 MATERIALS SCIENCE↗

Opto-twistronic Hall effect in a three-dimensional spiral lattice

Studies of moire systems have elucidated the exquisite effect of quantum geometry on the electronic bands and their properties, leading to the discovery of new correlated phases. However, most experimental studies have been confined to a few layers in the 2D limit. The extension of twistronics to its 3D limit, where the twist is extended into the third dimension between adjacent layers, remains underexplored due to the challenges in precisely stacking layers. Here, in this study, we focus on 3D twistronics on a platform of self-assembled spiral superlattice of multilayered WS 2 . Our findings reveal an opto-twistronic Hall effect in the spiral superlattice. This mesoscopic response is an experimental manifestation of the noncommutative geometry that arises when translational symmetry is replaced by a non-symmorphic screw operation. We also discover signatures of altered laws of optical excitation, manifested as an unconventional photon momentum-lattice interaction owing to moire of moire modulations in the 3D twistronic system. Crucially, our findings mark the initial identification of higher-order quantum geometrical tensors in light-matter interactions. This breakthrough opens new avenues for designing quantum materials-based optical lattices with large nonlinearities, paving the way for the development of advanced quantum nanophotonic devices.

Ji, Zhurun↗

Electron-Beam Induced Emergence of Mesoscopic Ordering in Layered MnPS 3

Ordered mesoscale structures in 2D materials induced by small misorientations have allowed for a wide variety of electronic, ferroelectric, and quantum phenomena to be explored. Until now, the only mechanism to induce this periodic ordering was via mechanical rotations between the layers, with the periodicity of the resulting moiré pattern being directly related to twist angle. Here we report a fundamentally distinct mechanism for emergence of mesoscopic periodic patterns in multilayer sulfur-containing metal phosphorus trichalcogenide, MnPS3, induced by the electron beam. The formation under the beam of periodic hexagonal patterns with several characteristic length scales, nucleation and transitions between the phases, and local dynamics are demonstrated. The associated mechanisms are attributed to the relative contraction of the layers caused by beam-induced sulfur vacancy formation with subsequent ordering and lattice parameter change. As a result, the plasmonic response of the system is locally altered, suggesting an element of control over plasmon resonances by electron beam patterning. To conclude, we pose that harnessing this phenomenon provides both insight into fundamental physics of quantum materials and enables device applications by enabling controlled periodic potentials on the atomic scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mesoscopic finite-size effects of unconventional electron transport in PdCoO 2

A wide range of unconventional transport phenomena has recently been observed in single-crystal delafossite metals. Here, we present a theoretical framework to elucidate electron transport using a combination of first-principles calculations and numerical modeling of the anisotropic Boltzmann transport equation. Using PdCoO 2 as a model system, we study different microscopic electron and phonon scattering mechanisms and establish the mean free path hierarchy of quasiparticles at different temperatures. We treat the anisotropic Fermi surface explicitly to numerically obtain experimentally-accessible transport observables, which bridge between the “diffusive,” “ballistic,” and “hydrodynamic” transport regime limits. Further, we illustrate that the distinction between the “quasiballistic” and “quasihydrodynamic” regimes is challenging and often needs to be quantitative in nature. From first-principles calculations, we populate the resulting transport regime plots and demonstrate how the Fermi surface orientation adds complexity to the observed transport signatures in micrometer-scale devices. Our work provides key insights into microscopic interaction mechanisms on open hexagonal Fermi surfaces and establishes their connection to the macroscopic electron transport in finite-size channels.

36 MATERIALS SCIENCE↗

Development of Nanocrystalline Graphite from Lignin Sources

Carbon composites are attractive to a variety of high-impact applications, such as carbon fibers, batteries, and vehicle parts, due to their multifunctional properties. The properties of carbon are highly dependent on the allotrope the carbon takes and the functionality, impurities, and defects contained within the structure. The increase in demand for sustainable carbon sources in energy storage devices motivates interest in understanding synthesis parameters of lignin value-added products. Also, as the dependence on oil for fuel decreases, alternative sources for carbon in many applications will be needed. In this work, the thermochemical conversion of lignin powders from different feedstocks was evaluated via small and wide-angle X-ray scattering techniques to resolve the amorphous, disordered, and crystalline domains present in the lignin carbons. Scattering analyses indicated an evolution of hierarchical structures along with an increase in ordered domains as a function of carbonization temperature. Qualitative and quantitative methods were used to describe isotropic scattering intensity profiles at multiple length scales. The use of power law models in the mesoscopic region served as the basis to describe morphological changes related to structural features, for example, graphene stacking, degree of roughness, and surface fractals. Kraft softwood and switchgrass produced carbon powder with the most crystalline domains and the least surface roughness. Softwoods reached the highest degree of crystallinity followed by switchgrass samples and had less variability in particle sizes. These results suggest lignin carbons extracted from softwoods and switchgrass are viable substitutes for graphite. Interpretation of X-ray scattering data from lignin carbon powders elucidates feedstock- and processing-dependent morphological features across multiple length scales providing a straightforward framework to evaluate the feasibility of leveraging lignin carbons for producing tunable application-specific materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Advanced magnetic X-ray spectro-microscopies to characterize mesoscopic magnetic materials

Here, this article provides a brief overview of advanced magnetic X-ray spectro-microscopies that are widely used in characterizing mesoscopic magnetic materials. Common to those techniques are various X-ray magnetic dichroism effects that are used as magnetic contrast mechanism. A particular interest is to use those techniques to image the underlying microscopic spin structures in magnetic materials with high spatial resolution and to ultimately resolve their full 3D mesoscale characteristics with elemental sensitivity, as well as their ultrafast dynamics upon excitations with field and current pulses. Recent research examples using various magnetic X-ray spectro-microscopies are presented to showcase their specific features with a focus on imaging novel topological spin textures, such as vortices, skyrmions and Hopfions, which are considered as potential building blocks towards low power, high-speed and high-density magnetic devices that could transform information technologies and potentially be used in biomedical applications. Future developments with magnetic X-ray spectro-microscopies harness the full coherence of next generation X-ray sources and could open the path towards single shot imaging with spatial and temporal resolutions down to fundamental magnetic length and time scales.

36 MATERIALS SCIENCE↗