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All sources NASA NTRS DOE OSTI

DOE OSTI2020

Signatures of a liquid-crystal transition in spin-wave excitations of skyrmions

Abstract Understanding the spin-wave excitations of chiral magnetic order, such as the skyrmion crystal (SkX), is of fundamental interest to confirm such exotic magnetic order. The SkX is realized by competing Dzyaloshinskii-Moriya and ferromagnetic-exchange interactions with a magnetic field or anisotropy. Here, we compute the dynamical spin structure factor, using Monte Carlo and spin dynamics simulations, extracting the spin-wave spectrum in the SkX, in the vicinity of the paramagnet to SkX transition. Inside the SkX, we find six spin-wave modes, which are supplemented by another mode originating from the ferromagnetic background. Above the critical temperature T s for the skyrmion crystallization, we find a diffusive regime, reminiscent of the liquid-to-crystal transition, revealing that topological spin texture of skyrmionic character starts to develop above T s as the precursor of the SkX. We discuss the opportunities for the detection of the spin waves of the SkX using inelastic-neutron-scattering experiments in manganite-iridate heterostructures.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Prediction of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling

The over 60 years old Rashba-Dresselhaus effect predicts spin-orbit coupling (SOC) induced momentum-dependent spin splitting and spin polarization in materials with noncentrosymmetric structures. Strong SOC induced effects usually require high-atomic number (Z) elements such as rare-earth elements. It has recently been pointed out that antiferromagnets could hold SOC-independent spin splitting and spin polarization. In the present work we develop the spatial and magnetic symmetry conditions enabling such antiferromagnet (AFM)-induced spin splitting, dividing the 1651 magnetic space groups into seven different spin splitting prototypes (SST-1 to SST-7). This analysis places the physics of AFM spin splitting (SST-4) within the broader context of symmetry conditions that enable the more familiar forms of spin splitting, such as ferromagnetic Zeeman effect (SST-5), nonmagnetic no spin splitting (SST-6), and the nonmagnetic Rashba and Dresselhaus effects (SST-7). The AFM-induced spin splitting and spin polarization do not necessarily require breaking of inversion symmetry or the presence of SOC, hence can exist even in centrosymmetric, low-Z light element compounds, considerably broadening the material base for spin manipulations. We use the “inverse design” approach of first formulating the target property (here, spin splitting in low-Z compounds not restricted to low symmetry structures), then derive the enabling physical design principles—the magnetic symmetry conditions—to search realizable compounds that satisfy these a priori design principles. This process uncovers 422 magnetic space groups (160 centrosymmetric and 262 noncentrosymmetric) that could hold AFM-induced, SOC-independent spin splitting and spin polarization. We then search for stable compounds following such enabling symmetries. We investigate the electronic and spin structures of some selected prototype compounds by density functional theory (DFT) and find spin textures that are different than the traditional Rashba-Dresselhaus patterns and exist even in the absence of SOC effect. We provide the DFT results for all antiferromagnetic spin splitting prototypes (SST-1, SST-2, SST-3, SST-4), and concentrate on two limits of SST-4 that are particularly unusual: When spin splitting is momentum dependent (just like the Rashba effect) but is enabled in antiferromagnets even in the absence of SOC in the Hamiltonian. This includes examples of (a) centrosymmetric SST-4A compounds (e.g., orthorhombic LaMnO 3 illustrating collinear AFM, as well as cubic NiS 2 illustrating noncollinear AFM) and (b) noncentrosymmetric SST-4B compounds (e.g., rhombohedral MnTiO 3 illustrating collinear AFM and hexagonal ScMnO 3 illustrating noncollinear AFM). The symmetry design principles outlined here, along with their transformation into an inverse design material search approach and DFT verification, could open the way to their experimental examination.

36 MATERIALS SCIENCE↗

NASA NTRS2023

Investigating the Effects of Space Weathering in Ryugu Samples Using Coordinated Microanalyses

Airless planetary surfaces are characterized by a distinct lack of an atmosphere or magnetic field, leading to direct exposure to the effects of hypervelocity micrometeoroid impacts and solar wind ion irradiation [1]. These processes, cumulatively known as space weathering, gradually alter the microstructural and chemical properties of the grains on airless surfaces. Signatures of space weathering include vesiculated textures, amorphous grain rims (upper ~100 nm), solar flare tracks, and Fe-bearing nanoparticles (npFe) [2,3]. The accumulation of these microstructural space weathering characteristics, particularly the presence of npFe, alters the spectral properties of airless regoliths resulting in changes in spectral slope and reflectance of the surfaces, and the attenuation of characteristic absorption bands in the visible to near-infrared (Vis-NIR) wavelengths. These spectral changes complicate our ability to accurately interpret the mineralogy of airless bodies via remote sensing spectroscopy [1,4]. Studies of space weathering have primarily focused on anhydrous silicate minerals, reflecting the main components of the available returned samples from the Moon and S-type asteroid Itokawa [3,5,6]. However, our understanding of space weathering of primitive, organic-rich carbonaceous materials is still a work in progress. The Japan Aerospace Exploration Agency (JAXA)’s Hayabusa2 mission offered the first opportunity to directly investigate carbonaceous asteroids by returning samples from C-type asteroid (162173) Ryugu. Initial studies of Ryugu samples show mineralogical similarities to CI chondrites along with surface modifications consistent with space weathering. These surface modifications are primarily in the form of μm-thick silicate melts, amorphized phyllosilicates, glassy spherules, and burst vesicles [3,7]. Here, we report results from coordinated microanalytical techniques to further our understanding of the mineralogy and space weathering of carbonaceous materials.

L E Melendez↗

DOE OSTI2021

Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic (QHFM) phases with broken spin or valley symmetry. Visualizing atomic-scale electronic wave functions with scanning tunneling spectroscopy (STS), we resolved microscopic signatures of valley ordering in QHFM phases and spectral features of fractional quantum Hall phases of graphene. At charge neutrality, we observed a field-tuned continuous quantum phase transition from a valley-polarized state to an intervalley coherent state, with a Kekulé distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekulé phase, we could visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley-ordered phases and their topological excitations in a wide range of materials.

valley symmetry↗

DOE OSTI2025

Spin Dynamics of Triple-𝐐 Magnetic Orderings in a Triangular Lattice: Implications for Multi-𝐐 Orderings in General Two-Dimensional Lattices

Multi-𝐐 magnetic structures on two-dimensional (2D) lattices provide a key route to realizing topological physics in 2D magnetism. A major experimental challenge is to unambiguously confirm their formation by excluding the possibility of topologically trivial multidomain single- or double-𝐐 magnetic orders, which cannot be distinguished using conventional diffraction techniques. Here, we propose that long-wavelength spin dynamics offers a universal diagnostic for triangular lattices: Triple-𝐐 orders that preserve rotational symmetry and single- or double-𝐐 orders that break it exhibit qualitatively distinct anisotropies in their Goldstone-mode velocities, stemming from fundamental differences in their underlying spin configurations. We validate this concept using the metallic triangular-lattice antiferromagnet Co 0.325 ⁢TaS 2 , which hosts both a stripe-type single-𝐐 state and a triple-𝐐 tetrahedral ordering at different temperatures. Using inelastic neutron-scattering and spin dynamics simulations, we first refine the spin Hamiltonian by fitting the paramagnetic excitation spectra, allowing us to develop an unbiased model independent of magnetic ordering. We then show that the observed velocity profiles of the Goldstone modes agree with the high-temperature model’s predictions: markedly anisotropic for the single-𝐐 phase and near isotropic for the triple-𝐐 phase. Importantly, this contrast persists across various exchange parameters, highlighting its model-independent nature and suggesting potential applicability to other 2D lattice systems. Beyond the long-wavelength regime, we present a substantial discrepancy between the measured and simulated magnon spectra exclusively in the triple-𝐐 phase. We attribute this discrepancy to magnon energy renormalization arising from order-of-magnitude-enhanced magnon-magnon interactions in the triple-𝐐 phase, due to its noncollinear configuration. This work provides universal insight into the dynamical properties of topological multi-𝐐 magnetic orderings in 2D lattice structures, offering a broadly applicable diagnostic to distinguishing them from topologically trivial single- or double-𝐐 counterparts. The unequivocal confirmation of the triple-𝐐 structure in Co 0.325 ⁢TaS 2 further establishes it as a prominent material platform for exploring topological spin textures in the genuine 2D limit.

Park, Pyeongjae [Oak Ridge National Laboratory (OR↗

DOE OSTI2020

The 2020 Skyrmionics Roadmap

The notion of non-trivial topological winding in condensed matter systems represents a major area of present-day theoretical and experimental research. Magnetic materials offer a versatile platform that is particularly amenable for the exploration of topological spin solitons in real space such as skyrmions. First identified in non-centrosymmetric bulk materials, the rapidly growing zoology of materials systems hosting skyrmions and related topological spin solitons includes bulk compounds, surfaces, thin films, heterostructures, nano-wires and nano-dots. This underscores an exceptional potential for major breakthroughs ranging from fundamental questions to applications as driven by an interdisciplinary exchange of ideas between areas in magnetism which traditionally have been pursued rather independently. The skyrmionics roadmap provides a review of the present state of the art and the wide range of research directions and strategies currently under way. These are, for instance, motivated by the identification of the fundamental structural properties of skyrmions and related textures, processes of nucleation and annihilation in the presence of non-trivial topological winding, an exceptionally efficient coupling to spin currents generating spin transfer torques at tiny current densities, as well as the capability to purpose- design broad-band spin dynamic and logic devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Photo-induced non-collinear interlayer RKKY coupling in bulk Rashba semiconductors

Abstract The interplay between light-matter, spin-orbit, and magnetic interactions allows the investigation of light-induced magnetic phenomena that are otherwise absent without irradiation. We present our analysis of light-driven effects on the interlayer exchange coupling mediated by a bulk Rashba semiconductor in a magnetic multilayer. The collinear magnetic exchange coupling mediated by the photon-dressed spin-orbit coupled electrons of BiTeI develops light-induced oscillation periods and displays new decay power laws, both of which are enhanced with an increasing light-matter coupling. For magnetic layers with non-collinear magnetization, we find a non-collinear magnetic exchange coupling uniquely generated by light-driving of the multilayer. As the non-collinear magnetic exchange coupling mediated by the photon-dressed electrons of BiTeI is unique to the irradiated system and it is enhanced with increasing light-matter coupling, this effect offers a promising platform of investigation of light-driven effects on magnetic phenomena in spin-orbit coupled systems. In this platform, light properties, such as its intensity, can serve as external knobs for inducing non-collinear couplings of the interlayer exchange and for modulating the collinear couplings. Both of these effects signify the photo-generated modification in the spin textures of spin-orbit coupled electrons in BiTeI.

Physics↗

DOE OSTI2022

Spin orbit torque in ferromagnet/topological-quantum-material heterostructures

The main objective of this proposal was to investigate the spin-orbital driven phenomena in topological insulator (TI)/ferromagnet (FM) or transition metal (TM) heterostructures. In particularly, we tried to utilize the spin-momentum locking properties on the surface of TIs to achieve ideal spin-orbit torques (SOTs). In practice, we found that the surface properties have been greatly modified, resulting in much more complicated magneto-transport behaviors than what is expected in SOT-driven magnetotransport. Through systematic and extended investigations, we start to unravel that the nonlinear magnetotransport properties, which was, in the past, mainly attributed to SOT-driven phenomena, can be used to infer the modification of the electronic band structures of TIs and spin textures in FMs which are closely related with charge-spin interconversion phenomena. Regarding the band structures In TIs, we find under electrostatic perturbations imposed by deposition of nonmagnetic TMs, the quantum well states formed on the surface of TIs develop substantial Rashba spin-splitting, which is detected as a bilinear magnetoresistance (BMR). Under magnetic perturbations, the nonlinear planar Hall effect (NPHE) in the topological surface states is greatly enhanced, possibly reflecting the modified surface band structure due to time-reversal symmetry breaking. In a double HM/FM heterostructure where the magnetic anisotropy can be robustly tuned, we observed second-harmonic Hall voltage responses corresponding to domain wall structures with fixed chirality, stabilized by interfacial Dzyaloshinskii–Moriya interaction (DMI). In addition, in the linear transport regime, we utilized inverse-SHE-induced anomalous Hall effect in Pt to probe the exchange bias on the surface of a doped magnetic insulator Tm 3 Fe 5 O 12 .

36 MATERIALS SCIENCE↗

DOE OSTI2024

Ultrastrong magnon-magnon coupling and chiral spin-texture control in a dipolar 3D multilayered artificial spin-vortex ice

Strongly-interacting nanomagnetic arrays are ideal systems for exploring reconfigurable magnonics. They provide huge microstate spaces and integrated solutions for storage and neuromorphic computing alongside GHz functionality. These systems may be broadly assessed by their range of reliably accessible states and the strength of magnon coupling phenomena and nonlinearities. Increasingly, nanomagnetic systems are expanding into three-dimensional architectures. This has enhanced the range of available magnetic microstates and functional behaviours, but engineering control over 3D states and dynamics remains challenging. Here, we introduce a 3D magnonic metamaterial composed from multilayered artificial spin ice nanoarrays. Comprising two magnetic layers separated by a non-magnetic spacer, each nanoisland may assume four macrospin or vortex states per magnetic layer. This creates a system with a rich 16 N microstate space and intense static and dynamic dipolar magnetic coupling. The system exhibits a broad range of emergent phenomena driven by the strong inter-layer dipolar interaction, including ultrastrong magnon-magnon coupling with normalised coupling rates of $\frac{Δf}{v}$ = 0.57, GHz mode shifts in zero applied field and chirality-control of magnetic vortex microstates with corresponding magnonic spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Manipulating topological Hall-like signatures by interface engineering in epitaxial ruthenate/manganite heterostructures

Topologically protected non-trivial spin textures (e.g. skyrmions) give rise to a novel phenomenon called the topological Hall effect (THE) and have promising implications in future energy-efficient nanoelectronic and spintronic devices. Here, we have studied the Hall effect in SrRuO 3 /La 0.42 Ca 0.58 MnO 3 (SRO/LCMO) bilayers. Our investigation suggests that pure SRO has hard and soft magnetic characteristics but the anomalous Hall effect (AHE) in SRO is governed by the high coercivity phase. Here, we have shown that the proximity effect of a soft magnetic LCMO on SRO plays a critical role in interfacial magnetic coupling and transport properties in SRO. Upon reducing the SRO thickness in the bilayer, the proximity effect becomes the dominant feature, enhancing the magnitude and temperature range of THE-like signatures. The THE-like features in bilayers can be explained by a diffusive Berry phase transition model in the presence of an emergent magnetic state due to interface coupling. This work provides an alternative understanding of THE-like signatures and their manipulation in SRO-based heterostructures, bilayers and superlattices.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2020

Quantification of MagLIF morphology using the Mallat scattering transformation

The morphology of the stagnated plasma resulting from magnetized liner inertial fusion is measured by imaging the self-emission x rays coming from the multi-keV plasma. Equivalent diagnostic responses can be generated by integrated radiation-magnetohydrodynamic (rad-MHD) simulations from programs such as HYDRA and GORGON. There have been only limited quantitative ways to compare the image morphology, that is the texture, of simulations and experiments. We have developed a metric of image morphology based on the Mallat scattering transformation (MST), a transformation that has proved to be effective at distinguishing textures, sounds, and written characters. This metric is designed, demonstrated, and refined by classifying ensembles (i.e., classes) of synthetic stagnation images and by regressing an ensemble of synthetic stagnation images to the morphology (i.e., model) parameters used to generate the synthetic images. We use this metric to quantitatively compare simulations to experimental images, experimental images to each other, and to estimate the morphological parameters of the experimental images with uncertainty. This coordinate space has proved to be very adept at doing a sophisticated relative background subtraction in the MST space. This was needed to compare the experimental self-emission images to the rad-MHD simulation images.

Glinsky, Michael E. (ORCID:0000000324933326)↗

DOE OSTI2024

Observation of plaid-like spin splitting in a noncoplanar antiferromagnet

Spatial, momentum and energy separation of electronic spins in condensed matter systems guides the development of novel devices where spin-polarized current is generated and manipulated. Recent attention on a set of previously overlooked symmetry operations in magnetic materials leads to the emergence of a new type of spin splitting, enabling giant and momentum-dependent spin polarization of energy bands on selected antiferromagnets. Despite the ever-growing theoretical predictions, the direct spectroscopic proof of such spin splitting is still lacking. Here, we provide solid spectroscopic and computational evidence for the existence of such materials. In the noncoplanar antiferromagnet MnTe 2 , the in-plane components of spin are found to be antisymmetric about the high-symmetry planes of the Brillouin zone, comprising a plaid-like spin texture in the antiferromagnetic (AFM) ground state. Such an unconventional spin pattern, further found to diminish at the high- temperature paramagnetic state, stems from the intrinsic AFM order instead of spin- orbit coupling (SOC). Furthermore, our finding demonstrates a new type of quadratic spin texture induced by time-reversal breaking, placing AFM spintronics on a firm basis and paving the way for studying exotic quantum phenomena in related materials.

Electronic devices↗

DOE OSTI2021

Scale Up of High-Performance REBCO Tapes in a Pilot-Scale Advanced MOCVD Tool With In-Line 2D-XRD System

We have reported the development of an Advanced Metal-Organic Chemical Vapor Deposition (AMOCVD) method featuring ohmic heating of the substrate for REBCO film growth, direct tape temperature monitoring, and laminar precursor flow. This A-MOCVD method has been used to fabricate 4 – 5 m thick film REBCO tapes with record high performance: critical currents exceeding 8700 A/12 mm at 30 K, 3 T; and engineering current density of 5200 A/mm 2 at 4.2 K, 15 T. Recently, we constructed a pilot-scale reel-to-reel A-MOCVD system to scale up the technology to long tapes. Preliminary batches of tapes exhibit consistent performance and good uniformity along the length. An in-line 2D X-ray Diffraction (XRD) system has been integrated into the pilot A-MOCVD tool to monitor the REBCO texture and composition, RE 2 O 3 content, and the dimensions of BaMO 3 (BMO, M=Zr,Hf) nanorods that act as artificial pinning centers. Specifically, the streaking angle between REBCO (103) and BZO (101) has been found to correlate well with (Ba+M)/Cu of the film, lift factor in critical current over a range of temperatures and magnetic fields, and the size of the BMO nanorods. Furthermore, the in-line 2D-XRD is expected to serve as a valuable quality measuring tool supporting realtime feedback control for the process to yield uniform and consistent manufacturing of high performance REBCO tapes by Advanced MOCVD.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Spin skyrmion gaps as signatures of strong-coupling insulators in magic-angle twisted bilayer graphene

Abstract The flat electronic bands in magic-angle twisted bilayer graphene (MATBG) host a variety of correlated insulating ground states, many of which are predicted to support charged excitations with topologically non-trivial spin and/or valley skyrmion textures. However, it has remained challenging to experimentally address their ground state order and excitations, both because some of the proposed states do not couple directly to experimental probes, and because they are highly sensitive to spatial inhomogeneities in real samples. Here, using a scanning single-electron transistor, we observe thermodynamic gaps at even integer moiré filling factors at low magnetic fields. We find evidence of a field-tuned crossover from charged spin skyrmions to bare particle-like excitations, suggesting that the underlying ground state belongs to the manifold of strong-coupling insulators. From the spatial dependence of these states and the chemical potential variation within the flat bands, we infer a link between the stability of the correlated ground states and local twist angle and strain. Our work advances the microscopic understanding of the correlated insulators in MATBG and their unconventional excitations.

36 MATERIALS SCIENCE↗

NASA NTRS1988

Impact and extinction signatures in complete Cretaceous-Tertiary (K-T) boundary sections

The Zumaya, Caravaca and Agost sections in Spain, the El Kef section in Tunisia and the Negev (Nahal Avdat) sections in Israel are among the most continuous, expanded and complete K-T boundary sections. The distribution patterns of the planktic faunas were quantitatively analyzed in closely spaced samples across the K-T boundary in these sections, in conjuction with the geochemistry, stable isotopes, mineralogy and magnetostratigraphy. Three hundred foraminiferal specimens were randomly selected and determined. Reliable estimates for the foraminiferal productivity changes across the K-T boundary and for the 1 to 2 Ma interval preceding the K-T boundary were made from the numbers of individuals/gram of sediment corrected for the sedimentation rates (calculated from magnetic reversals and lithology). No gradual or stepwise extinction is seen below the K-T boundary nor any productivity decrease. Stable isotope analyses show a warming just after deposition of the ejecta layer, not cooling as predicted by nuclear winter scenarios, although the duration of such cooling may be too short to be observed even in these complete sections. Low REE values and cpx spherules with quench textures idential to quench-textures in diagenetically altered spherules, strongly indicate an oceanic site of (one of) the impactor(s).

Smit, J.↗

NASA NTRS1977

Interpretations of optical observations of Mercury and the moon

Optical, thermal and radar remote-sensing measurements indicate that Mercury is covered with a relatively thick layer of soil similar in texture and thickness to lunar regolith. Photometric limb profiles measured by Mariner 10 imply that the small-scale slopes on Mercury are about half those on the moon, probably because of differing gravity. The differential photometric functions of Mercury and the moon have a latitudinal dependence which can be completely accounted for by shadowing in craters. The lack of polar darkening on Mercury in spite of the presence of a magnetic field implies that the dominant soil-darkening process on Mercury, and by extension, on the moon is not dependent on the solar wind, but probably is deposition of material evaporated by meteorite impacts. Recent measurements of Mercury's spectral reflectivity in the IR and vacuum UV are both consistent with the surface rocks of Mercury being lower in FeO than those of the moon. Based on laboratory experiments the average FeO content on the surface of Mercury is estimated to be between 3 and 6%.

Hapke, B.↗

NASA NTRS1993

Primordial lightning: Evidence preserved in chondrites

An increasing body of evidence suggests that transient heating events were important in forming or modifying many constituents of chondritic meteorites. For example, chondrule compositions and textures imply high cooling rates (approximately 5 to greater than 2000 C/hr) with only limited exposure to elevated temperatures (greater than 1200 C). Similarly, experimental studies of CAI's exhibiting igneous textures suggest cooling rates from 0.5 to 1000 C/hr, and thermal pulses as short as milliseconds may be responsible for CAI rim formation. Additionally, the spectrum of organic compounds observed in chondrites suggests that transient heating may also have played an important role in their formation. The exact nature of these transient events is less clear. A variety of mechanisms have been proposed (e.g., shock melting, drag heating, volcanism, electric discharges, and magnetic reconnection). However, a consensus is lacking as to which or what combination of these mechanisms was responsible for the range of features we observe in chondrites today. Much of the difficulty lies in the inability to identify features unique to any given process. Here we discuss electric discharges ('lightning') as a transient heat source and describe its unique signature preserved in chondrites.

Eisenhour, D.↗

DOE OSTI2021

Isotropic nature of the metallic Kagome ferromagnet Fe 3 Sn 2 at high temperatures.

Anisotropy and competing exchange interactions have emerged as two central ingredients needed for centrosymmetric materials to exhibit topological spin textures. Fe 3 Sn 2 is thought to have these ingredients as well, as it has recently been discovered to host room temperature skyrmionic bubbles with an accompanying topological Hall effect. We present small-angle inelastic neutron scattering measurements that unambiguously show that Fe3Sn2 is an isotropic ferromagnet below TC ≈ 660 K to at least 480 K – the lower temperature threshold of our experimental configuration. Fe 3 Sn 2 is known to have competing magnetic exchange interactions, correlated electron behavior, weak magnetocrystalline anisotropy, and lattice anisotropy; all of these features are thought to play a role in stabilizing skyrmions in centrosymmetric systems. Our results reveal that at elevated temperatures, there is an absence of significant magnetocrystalline anisotropy and that the system behaves as a nearly ideal isotropic exchange interaction ferromagnet, with a spin stiffness D(T = 480 K) = 168 meV Å2, which extrapolates to a ground state spin stiffness D(T = 0 K) = 231 meV Å2.

36 MATERIALS SCIENCE↗