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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Proximity Magnetism in Mn(Bi,Sb) 2 Te 4 –(Bi,Sb) 2 Te 3 /MnTe Natural Heterostructures

Magnetic topological insulators and their heterostructures provide significant opportunities to couple band topology with a nontrivial spin configuration for enhanced spintronic device performance, as well as designing magnetoelectric systems and functionalities. We find that Mn interdiffusion from MnTe when interfaced with (Bi,Sb) 2 Te 3 stabilizes as self-organized Mn(Bi,Sb) 2 Te 4 septuple lamellae among alternating (Bi,Sb) 2 Te 3 quintuple layers, as observed using scanning transmission electron microscopy and depth-sensitive polarized neutron reflectometry. We further demonstrate a valuable combination of magnetic and topological orders in these naturally formed Mn(Bi,Sb) 2 Te 4 –(Bi,Sb) 2 Te 3 heterostructures, which are exchange-coupled with MnTe. Magnetotransport experiments and quantum magnetism simulations reveal that, above its own Néel temperature T N ∼ 20 K, Mn(Bi,Sb) 2 Te 4 mediates the exchange field leading to an anomalous Hall effect at the (Bi,Sb) 2 Te 3 /MnTe interface, with an enhanced interfacial T N exceeding 200 K, approaching that of the bulk MnTe. This magnetic interface, in turn, allows a robust and deterministic spin–orbit torque switching without an external magnetic field at a low critical current density of 3 × 10 5 A cm –2 . The antiferromagnetically coupled architecture of Mn(Bi,Sb) 2 Te 4 –(Bi,Sb) 2 Te 3 /MnTe, featuring magnetic and topological proximity effects across a chalcogenide backbone, is rich in fundamental interface physics and holds the potential for practical applications in spintronics.

magnetic topological insulator↗
DOE OSTI2026

Early Solar Wind and Dynamo Magnetic Field Topology Predictions for (16) Psyche and Other Asteroids

Abstract Asteroid (16) Psyche is a metal‐rich body that might record an ancient coherent magnetization if some relict crust or mantle is preserved. Herein, we use magnetohydrodynamic simulations to predict (16) Psyche's field topology for several distinct pathways: (i) an early solar wind‐induced magnetization imparted after a larger body was impacted, forming the present‐day asteroid, (ii) a core dynamo magnetization imparted in an asteroid that is either presently largely intact or was a rubble pile, and (iii) magnetization in the turbulent solar nebula disk. For pathway (i) we find the field to be predominantly dipolar and spin axis‐aligned. For pathway (ii) we find the field to be either dipolar and spin axis‐misaligned, or highly multipolar. We also find that (iii) a field produced earlier before the solar nebula cleared, would be highly multipolar. In cases (i) and (ii) we also place constraints on the field strength. Simple detection of a magnetic field without constraining its topology and temporal variability would be insufficient to confirm a remanent source, due to the influence of the present‐day solar wind, electromagnetic induction, and (16) Psyche's high obliquity. For sufficiently strong fields however, the field topology and orientation may reveal key observable consequences of the nature and history of (16) Psyche. Our framework is also broadly applicable to the study of magnetic fields from other asteroids.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Spectrally sharp magnetic excitations above the critical temperature in a frustrated Weyl semimetal

The rare-earth α-pyrochlore iridates are a prospective class of conducting frustrated magnets where electronic correlations, large spin-orbit coupling, and geometrical frustration interplay, leading to a rich set of magnetic and electronic phases. Despite their intriguing properties, the magnetic order and excitations in this fundamental class of topological quantum materials remain poorly understood due to challenges in growing large single crystals and insufficient microscopic information on their temperature-dependent phases. Here, by combining state-of-the-art thin-film synthesis, resonant elastic and inelastic X-ray scattering, spin wave analysis, and dynamical spin susceptibility calculations, we unequivocally reveal the presence of spectrally sharp, gapped magnetic excitations in Y 2 Ir 2 O 7 that surprisingly persist well above the Néel transition temperature, signaling the presence of a quasi-universal regime connected to fluctuations on frustrated lattices. This finding implies the existence of a highly unusual cooperative paramagnetic (CP) phase above the ordering temperature and offers an explanation for the puzzling high-temperature magnetic behavior observed across the family of metallic pyrochlore crystals. Understanding such magnetic excitations at technologically relevant temperatures opens up possibilities for novel topological spintronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Connection between f -electron correlations and magnetic excitations in UTe 2

The detailed anisotropic dispersion of the low-temperature, low-energy magnetic excitations of the candidate spin-triplet superconductor UTe 2 is revealed using inelastic neutron scattering. The magnetic excitations emerge from the Brillouin zone boundary at the high symmetry Y and T points and disperse along the crystallographic $\hat{b}$ -axis. In applied magnetic fields to at least μ 0 H = 11 T along the $\hat{c}-{\rm{axis}}$ , the magnetism is found to be field-independent in the (hk0) plane. The scattering intensity is consistent with that expected from U 3+ /U 4+ f-electron spins with preferential orientation along the crystallographic $\hat{a}$ -axis, and a fluctuating magnetic moment of μ eff =1.7(5) μ B . We propose interband spin excitons arising from f-electron hybridization as a possible origin of the magnetic excitations in UTe 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Machine learning assisted search for Fe–Co–C ternary compounds with high magnetic anisotropy

We employ a machine learning (ML)-guided framework to explore rare earth free magnetic materials, specifically focusing on Fe–Co–C ternary compounds for potential use in permanent magnets. Utilizing a specifically trained crystal graph convolutional neural network model, we efficiently screen a vast space of nearly a million substitutional structures to select 620 promising structures for further investigation by first-principles calculation. We predict five low-energy metastable Fe–Co–C compounds with formation energy less than 150 meV/atom above the convex hull. These compounds exhibit high magnetization (Js > 1.0 T) and significant magnetic anisotropy (K1 > 1.0 MJ/m3), making them promising candidates for permanent magnet applications. The phonon calculations indicate these compounds are dynamically stable. Our ML-guided framework demonstrates the utility of rapidly identifying novel materials with tailored magnetic properties.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Diagnosing electric and magnetic fields in laser-driven coil targets

Laser-driven capacitor coils are widely used to generate intense magnetic fields for various applications in high-energy-density (HED) physics research. Accurate measurement of the magnetic fields is essential but challenging, due to the overlapping contributions from magnetic and electric fields in proton radiography, which is the primary tool diagnosing the field generation around the coils. In this study, we systematically analyze proton radiographs obtained from laser-driven capacitor-coil targets along two orthogonal axes under various electromagnetic field conditions, including magnetic field only, electric field only, and combined electromagnetic fields. By analyzing key features in the radiographs, we distinguish and characterize the respective contributions from magnetic and electric fields. Using detailed simulations validated by experimental benchmarks, methods to isolate and quantify the magnetic field and electric field are given. The methods are successfully applied to determine the electric current and charge distribution in a double coil configuration. Our findings provide insights into improving the diagnostic capability of proton radiography, potentially leading to more accurate measurements of electromagnetic fields and enhancing the utility of laser-driven capacitor coils in HED experiments.

electromagnetic field diagnostics↗
DOE OSTI2025

Impact of dynamic Jahn-Teller effect on magnetic excitations, lattice vibration, and thermal conductivity in U 𝑥 ⁢T⁢h 1−𝑥 ⁡O 2 system

Vibrational and magnetic properties of single-crystal uranium-thorium dioxide (U 𝑥 ⁢T⁢h 1−𝑥⁡ O 2 ) with a full range of 0 < 𝑥 < 1 are investigated. Thorium dioxide is a diamagnet whose thermal properties are governed by lattice vibration. The addition of paramagnetic uranium ions leads to the emergence of magnetic effects that alter the thermophysical properties noticeably even at room temperature. The interaction of phonons with magnetic moments of uranium 5⁢𝑓 electrons mediated by magnetoelastic coupling results in an anomalous low-temperature thermal conductivity profile. Analysis of the magnetic susceptibility measurements indicates a departure from the Curie-Weiss relationship characteristic of noninteracting paramagnetic ions, previously associated with the dynamic Jahn-Teller (DJT) effect characterized by coupling between spin and the oxygen sublattice. The T 2⁢g Raman peak position follows a nonlinear trend as a function of uranium concentration and hints that these Raman active optical modes play a role in either DJT or in mediating quadrupole-quadrupole interactions. A first-principle-based thermal transport model is implemented to explain the low-temperature transport measurements, where the anomalous reduction is attributed to phonon-spin resonant scattering. The interplay between spins and phonons is also captured using high-resolution inelastic x-ray scattering (IXS) measurements of phonon linewidths. Our results provide insights into the phonon interactions with the magnetic excitations governing DJT effect and impacting the low-temperature thermal transport processes in this material system. Furthermore, these findings have implications for understanding low-temperature thermal transport and magnetic properties in advanced materials for information processing and energy applications.

36 - MATERIALS SCIENCE↗
DOE OSTI2025

Interfacial alloying contributions to the magnetic proximity effect in Pt/dysprosium iron garnet

The magnetic proximity effect (MPE), a magnetic response from a heavy metal layer induced by an adjacent magnetic layer, plays an important role in the behavior of heavy-metal/ferro- or ferrimagnet thin film heterostructures. However, in the case of heavy-metal/rare earth iron garnet bilayers the presence and magnitude of the MPE has been debated. We previously reported an MPE in a Pt/dysprosium iron garnet (DyIG) heterostructure where the two layers were grown without breaking vacuum, finding that the magnetic moment present in the Pt layer scales with the magnitude of the DyIG moment and varies nonmonotonically through the DyIG compensation temperature. However, the origin of the magnetic signal from the Pt layer was not identified. In contrast, Pt/DyIG grown with a vacuum break did not exhibit an MPE. Here we investigate the origin of the magnetic moment in the Pt layer using x-ray absorption spectroscopy, x-ray circular dichroism, composition mapping and simulations of ion bombardment. In conclusion, the results are consistent with the presence of an intermixed Fe-Dy-Pt interfacial alloy layer formed during the growth of the Pt on the DyIG and resulting in a measurable MPE.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Accurate machine-learning predictions of coercivity in high-performance permanent magnets

Increased demand for high-performance permanent magnets in the electric vehicle and wind-turbine industries has prompted the search for cost-effective alternatives. Discovering magnetic materials with the desired intrinsic and extrinsic permanent magnet properties presents a significant challenge to researchers because of issues with the global supply of rare-earth elements, material stability, and a low maximum magnetic energy product BH max . While first-principles density functional theory (DFT) predicts materials’ magnetic moments, magnetocrystalline anisotropy constants, and exchange interactions, it cannot compute extrinsic properties such as coercivity (H c ). Although it is possible to calculate H c theoretically with micromagnetic simulations, the predicted value is larger than the experiment by almost an order of magnitude due to the Brown paradox. To circumvent these issues, we employ machine-learning (ML) methods on an extensive database obtained from experiments, DFT calculations, and micromagnetic modeling. The use of a large experimental dataset enables realistic H c predictions for materials such as Ce-doped Nd 2 ⁢Fe 14 ⁢B, comparing favorably against micromagnetically simulated coercivities. Remarkably, our ML model accurately identifies uniaxial magneto-crystalline anisotropy as the primary contributor to H c . With DFT calculations, we predict the Nd-site-dependent magnetic anisotropy behavior in Nd 2 ⁢Fe 14 ⁢B, confirming that Nd 4⁢g sites mainly contribute to uniaxial magnetocrystalline anisotropy, and also calculate the Curie temperature (T c ). Finally, both calculated results are in good agreement with the experiments. The coupled experimental dataset and ML modeling with DFT input predict H c with far greater accuracy and speed than was previously possible using micromagnetic modeling. Further, we reverse engineer the grain-boundary and intergrain exchange coupling with micromagnetic simulations by employing the ML predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Linking NH$^+_4$ motion to magnetism in molecular multiferroic (NH 4 ) 2 ⁢[FeCl 5 ⁢(H 2 ⁢O)]: A neutron vibrational spectroscopy study

Here, we present a neutron vibrational spectroscopy study to investigate the influence of NH$^+_4$ motion on the magnetism in [(NH 4 ) 1–x K x ] 2 ⁢[FeCl 5 ⁢(H 2 ⁢O)]. The parent compounds, (NH 4 ) 2 ⁢[FeCl 5 ⁢(H 2 ⁢O)] (x = 0) and K 2 ⁡[FeCl 5 ⁢(H 2 ⁢O)]⁢(x = 1) are isostructural at room temperature, yet displaying drastically different magnetic and multiferroic behavior. K 2 ⁡[FeCl 5 ⁢(H 2 ⁢O)] is nonmultiferroic with type-A collinear antiferromagnetic structure below T N ≈ 14.06 K, whereas (NH 4 ) 2 ⁢[FeCl 5 ⁢(H 2 ⁢O)] is a type-II multiferroic with incommensurate cycloidal spin structure below T FE ≈ 6.8 K. A recent study of the dielectric, structure, and magnetic properties in the mixed [(NH 4 ) 1–x ⁢K x ] 2 ⁢[FeCl 5 ⁢(H 2 ⁢O)] shows that a small amount of potassium substitution to replace NH$^+_4$ transforms the spin structure from incommensurate cycloidal (x ≤ 0.06) into commensurate collinear antiferromagnetic (x ≥ 0.15), indicating NH$^+_4$ is essential to the emergent phenomena observed in this molecular multiferroic compound. Our vibrational spectroscopy study reveals that NH$^+_4$ libration and torsion motion exhibit substantial temperature dependence at low temperatures. The intensity of NH$^+_4$ libration and torsion modes increases slightly at 5 K in comparison with data at 25 K behaving like a magnon, indicating that they are coupled to the magnetism in (NH 4 ) 2 ⁢[FeCl 5 ⁢(H 2 ⁢O)]. Comparing data of x=0, 0.06, 0.09, and 0.15 samples further illustrates that the strength of the increased signal in NH$^+_4$ libration mode is very sensitive to potassium concentration. The signal diminishes quickly with increasing potassium concentration and vanishes in the x = 0.15 sample corresponding to the magnetic structure change for x ≥ 0.15. The results directly link the anomalous behavior in NH$^+_4$ libration motion to the magnetism in [(NH 4 ) 1–x ⁢K x ] 2 ⁢[FeCl 5 ⁢(H 2 ⁢O)], providing new insights into the crucial role NH$^+_4$ plays in the coupled phenomena in (NH 4 ) 2 ⁢[FeCl 5 ⁢(H 2 ⁢O)]. The unique information opens a new door to go through in searching for new multifunctional materials by incorporation of NH 4 via a material-by-design approach.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Reference lattice, sound, stiffness, and magnetic transitions of Ising monolayers

A reference lattice, away from which elastic distortions induced by the spin texturing of two-dimensional (2D) magnets take hold, is motivated from a picture of pairwise Biot-Savart interactions among identical solenoids that either elongate or compress a (“zero-current”) spring lattice. Applied to a paradigmatic CrSiTe 3 monolayer, the reference is given by the average between the atomic positions of ferromagnetic (FM) and Néel antiferromagnetic (AFM) lattices; such an atomic disposition permits understanding structural distortions and elastic energies due to magnetism readily. Furthermore, the anisotropic speed of sound in the magnetic ground state explains an observed anisotropy of vibrational frequencies on similar magnets. Elastic stiffness constants are reported, too. Magnetic energies in four Ising structural configurations were calculated and the strain needed for those 2D magnets to undergo an AFM to FM quantum phase transition was determined as well.

density functional theory↗
DOE OSTI2024

Anomalous proximitized transport in metal/quantum magnet heterostructure Bi 2 Ir 2 O 7 /Yb 2 Ti 2 O 7

Fluctuations of quantum spins play a crucial role in the emergence of exotic magnetic phases and excitations. The lack of the charge degree of freedom in insulating quantum magnets, however, precludes such fluctuations from mediating electronic transport. Here, we show that the quantum fluctuations of a localized frustrated magnet induce strong proximitized charge transport of the conduction electrons in a synthetic heterostructure comprising an epitaxial Bi 2 Ir 2 O 7 ultrathin film on a single crystal of Yb 2 Ti 2 O 7 . The proximity effects are evidenced by the scaling behavior of the Bi 2 Ir 2 O 7 resistance in correspondence with the dynamic scaling of the dynamic spincorrelation function of Yb 2 Ti 2 O 7 , which is a result of quantum fluctuations near a multiphase quantum critical point. The proximitized transport in Bi 2 Ir 2 O 7 can be effectively tuned by a magnetic field through suppressing the quantum spin fluctuations (QSFs) as well as inducing transitions via magnetic anisotropy in Yb 2 Ti 2 O 7 . In this study, we establish a pathway for harnessing QSFs in magnetic insulators with electric transport, offering exciting prospects for potential applications in the realm of quantum spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Topological magnons and topological electronic properties in metallic Kagome magnets

The primary goal of this project is to study metallic Kagome magnets that potentially host topological electronic properties and topological magnetic excitations, aiming to understand the effect of lattice geometry on topological character of magnons and electronic bands and to study the interplay between magnetism and topological electronic properties. Through this DOE-funded research program, we have unraveled novel electronic and thermoelectric properties of RMn 6 Sn 6 (R = Y, Tb, and Er) and Fe 3 Ge Kagome magnets, including anomalous Hall effect and anomalous Nernst effect, which are associated with the Berry curvature contribution from the massive Dirac gaps in the 3D momentum space. In addition, we have also revealed topological Hall effect and topological Nernst effect, and we ascribed these phenomena to the Berry curvature associated with the magnetic field-induced non-zero scalar spin chirality. These features highlight the synergic effects of the Berry phases in both momentum space and real space of Kagome magnets, which render them excellent candidates for room-temperature electronic and thermoelectric applications based on transverse transport. In addition, through this program we have also study novel thermal transport properties of quantum materials by probing the thermal Hall effect, which can provide crucial insights into nontrivial topological character and chirality of quasiparticles like magnons and magnon-polarons. This report provides an overview of some project activities related to these accomplishments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Criticality and Magnetic Phases of Ising Shastry–Sutherland Candidate Holmium Tetraboride

Frustrated magnetic systems arising in geometrically constrained lattices represent rich platforms for exploring unconventional phases of matter, including fractional magnetization plateaus, incommensurate orders and complex domain dynamics. However, determining the microscopic spin configurations that stabilize such phases is a key challenge, especially when in-plane and out-of-plane spin components coexist and compete. Here, we combine neutron scattering and magnetic susceptibility experiments with simulations to investigate the emergence of field-induced fractional plateaus and the related criticality in a frustrated magnet holmium tetraboride (HoB 4 ) that represents the family of rare earth tetraborides that crystalize in a Shastry–Sutherland lattice in the ab plane. We focus on the interplay between classical and quantum criticality near phase boundaries, as well as the role of material defects in the stabilization of the ordered phases. We find that simulations using classical annealing can explain certain observed features in the experimental Laue diffraction and the origin of multiple magnetization plateaus. Our results show that defects and out-of-plane interactions play an important role and can guide the route towards resolving microscopic spin textures in highly frustrated magnets.

Frustration↗
DOE OSTI2024

Proton Acceleration in Low- β Magnetic Reconnection with Energetic Particle Feedback

Magnetic reconnection regions in space and astrophysics are known as active particle acceleration sites. There is ample evidence showing that energetic particles can take a substantial amount of converted energy during magnetic reconnection. However, there has been a lack of studies understanding the backreaction of energetic particles at magnetohydrodynamical scales in magnetic reconnection. To address this, we have developed a new computational method to explore the feedback by nonthermal energetic particles. This approach considers the backreaction from these energetic particles by incorporating their pressure into magnetohydrodynamics (MHD) equations. The pressure of the energetic particles is evaluated from their distribution evolved through Parker's transport equation, solved using stochastic differential equations (SDEs), so we coin the name MHD-SDE. Applying this method to low-β magnetic reconnection simulations, we find that reconnection is capable of accelerating a large fraction of energetic particles that contain a substantial amount of energy. When the feedback from these particles is included, their pressure suppresses the compression structures generated by magnetic reconnection, thereby mediating particle energization. Consequently, the feedback from energetic particles results in a steeper power-law energy spectrum. These findings suggest that feedback from nonthermal energetic particles plays a crucial role in magnetic reconnection and particle acceleration.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Toward Tunable Magnetic Dirac Semimetals: Mn Doping of Cd 3 As 2

Magnetic impurities provide a route toward increasing functionality in electronic materials, often enabling new device concepts and architectures. In the case of topological semimetals, dilute magnetic doping presents a particularly attractive approach for inducing a Dirac to Weyl phase change via time reversal symmetry breaking. However, efforts to realize changes in the electronic structure have been limited by challenges in incorporating magnetic impurities into crystals with sufficiently high electron mobilities to detect them via transport or spectroscopic techniques. Here, we demonstrate incorporation of Mn into Cd 3 ⁢As 2 Dirac semimetal thin films grown by molecular beam epitaxy (MBE). Using As-rich growth conditions and [001] oriented thin films, Mn compositions of >10% are achieved. Films contain uniform distributions of Mn with no evidence of secondary phases and exhibit electron mobilities greater than 10 000–30 000 cm 2 /Vs up to 5% Mn. An evolution in the magnetization behavior along with the emergence of a second quantum oscillation frequency at low Mn concentrations provide preliminary evidence of Mn-induced changes in the electronic structure that are consistent with a Weyl phase. This work demonstrates the potential of magnetically doping topological semimetal thin films and a pathway for synthesizing them.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Magnetic Properties Tuning via Broad Range Site Deficiency in Square Net Material UCu x Bi 2

HfCuSi 2 -type pnictogen compounds have recently been shown to be a versatile platform for designing materials with topologically nontrivial band structures. However, these phases require strict control over the electron count to tune the Fermi level, which can only be achieved in compositions with A 2+ M 2+ Pn 2 and A 3+ M + Pn 2 (A = lanthanides, M = transition metals, Pn = pnictogens P–Bi) charge distribution. While such lanthanide compounds have been thoroughly studied as candidate magnetic topological materials, their heavy element analogs with uranium and bismuth remain largely underexplored. In this report, we present the synthesis of UCu x Bi 2 single crystals and study their magnetic properties. Detailed structural analysis revealed that flux-grown crystals always form as a site-deficient UCu x Bi 2 composition, where x varies between 0.20 and 0.64. Magnetic property measurements revealed a dependence of the magnetic coupling on the Cu site deficiency, linearly changing the Néel temperature from 51 K for UCu 0.60 Bi 2 to 118 K for UCu 0.30 Bi 2 . Moreover, higher Cu concentration promotes a metamagnetic transition in highly magnetically anisotropic UCu 0.60 Bi 2 single crystals. We show that DFT calculations can successfully model site deficiency in the UCu x Sb 2 and UCu x Bi 2 systems. This work paves the way toward using the site deficiency to tune the Fermi level in more ubiquitous A 3+ M 2+ x Pn 2 phases, which previously have not been considered topological candidate materials due to unfavorable electron count.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A practical approach to calculating magnetic Johnson noise for precision measurements

Magnetic Johnson noise is an important consideration for many applications involving precision magnetometry, and its significance will only increase in the future with improvements in measurement sensitivity. The fluctuation–dissipation theorem can be utilized to derive analytic expressions for magnetic Johnson noise in certain situations, but when used in conjunction with finite element analysis tools, the combined approach is particularly powerful as it provides a practical means to calculate the magnetic Johnson noise arising from conductors of arbitrary geometry and permeability. In this paper, we demonstrate this method to be one of the most comprehensive approaches presently available to calculate thermal magnetic noise. In particular, its applicability is shown to not be limited to cases where the noise is evaluated at a point in space but also can be expanded to include cases where the magnetic field detector has a more general shape, such as a finite-size loop, a gradiometer, or a detector that consists of a polarized atomic species trapped in a volume. Furthermore, some physics insights gained through studies made using this method are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗