Hysteresis of Natural Magnetite Ensembles: Micromagnetics of Silicate-Hosted Magnetite Inclusions Based on Focused-Ion-Beam Nanotomography

Three-dimensional geometries of silicate-hosted magnetic inclusions from the Harcus intrusion, South Australia have been determined using focused-ion-beam nanotomography (FIB-nt). By developing an effective workflow, the geometries were reconstructed for magnetic particles in a plagioclase (162) and a pyroxene (282), respectively. For each inclusion, micromagnetic modelling using MERRILL provided averaged hysteresis loops and backfield remanence curves of 20 equidistributed field directions together with average Ms, Mrs, Hc, and Hcr . The micromagnetic structures within each silicate are single-domain, single-vortex, multi-vortex and multi-domain states. They have been analyzed using domain-state diagnostic plots, such as the Day plot and the Néel plot. SD particles can be subdivided into groups with dominant uniaxial anisotropy (Mrs/Ms ∼ 0.5 and 10 < Hc < 100 mT) and mixed uniaxial/multiaxial anisotropy (Mrs/Ms ∼ 0.7 and 10 < Hc < 30 mT). Most single-vortex particles lie on a trend with 0 < Mrs/Ms < 0.1 and 0 < Hc < 10 mT, while others dis- play a broad range of intermediate Mrs/Ms and Hc values. Single-vortex and multi-vortex states do not plot on systematic grain-size trends. Instead, the multi-component mixture of domain states within each silicate spans the entire range of natural variability seen in bulk samples. This questions the interpretation of bulk average hysteresis parameters in terms of grain size alone. FIB-nt combined with large-scale micromagnetic simulations provides a more complete characterization of silicate-hosted carriers of stable magnetic remanence. This approach will improve the understanding of single-crystal paleomagnetism, and enable primary paleomagnetic data to be extracted from ancient rocks

A remark on totally smooth renormings

[EN] E. Oja, T. Viil, andD. Werner showed, in Totally smooth renormings, Archiv der Mathematik, 112, 3, (2019), 269-281, that a weakly compactly generated Banach space ( X, center dot) with the property that every linear functional on X has a unique Hahn-Banach extension to the bidual X ** (the so-called Phelps' property U in X **, also known as the Hahn-Banach smoothness property) can be renormed to have the stronger property that for every subspace Y of X, every linear functional on Y has a unique Hahn-Banach extension to X ** (the so-called total smoothness property of the space). We mention here that this result holds in full generality -without any restriction on the space- and in a stronger form, thanks to a result ofM. Raja, On dual locally uniformly rotund norms, Israel Journal of Mathematics 129 (2002), 77-91.Supported by AEI/FEDER (project MTM2017-83262-C2-2-P of Ministerio de Economia y Competitividad), by Fundacion Seneca, Region de Murcia (Grant 19368/PI/14), and Universitat Politecnica de Valencia (A. J. Guirao). Supported by AEI/FEDER (project MTM2017-83262-C2-1-P of Ministerio de Economia y Competitividad) and Universitat Politecnica de Valencia (V. Montesinos). We thank the referees for their work, that neatly improved the original version of this note to its final form.Cobollo, C.; Guirao Sánchez, AJ.; Montesinos Santalucia, V. (2020). A remark on totally smooth renormings. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-4. https://doi.org/10.1007/s13398-020-00831-5S141142Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach space theory: the basis of linear and nonlinear analysis. Springer, New York (2011)Fabian, M., Montesinos, V., Zizler, V.: Smoothness in Banach spaces. Selected problems. Rev. R. Acad. Cien. Ser. A. Mat. RACSAM. 100(1–2), 101–125 (2006)Ferrari, S., Orihuela, J., Raja, M.: Generalized metric properties of spheres and renorming of Banach spaces. Rev. R. Acad. Cienc. Exactas Fis. Natl. Ser. A Math. RACSAM. 113, 2655–2663 (2019)Foguel, S.R.: On a theorem by A. E. Taylor. Proc. Amer. Math. Soc. 9, 325 (1958)Godefroy, G.: Points de Namioka, espaces normants, applications à la théorie isométrique de la dualité. Israel J. Math. 38, 209–220 (1981)Guirao, A.J., Montesinos, V., Zizler, V.: Open Problems in the geometry and analysis of Banach spaces. Springer International Pub, Switzerland (2016)Harmand, P., Werner, D., Werner, W.: M-ideals in Banach spaces and Banach algebras. Lecture notes in math, vol. 1547. Springer, Berlin (1993)Haydon, R.: Locally uniformly rotund norms in Banach spaces and their duals. J. Funct. Anal. 254, 2023–2039 (2008)Oja, E., Viil, T., Werner, D.: Totally smooth renormings. Archiv. der. Mathematik. 112(3), 269–281 (2019)Phelps, R.R.: Uniqueness of Hahn–Banach extensions and unique best approximation. Trans. Amer. Math. Soc. 95, 238–255 (1960)Raja, M.: On dual locally uniformly rotund norms. Israel J. Math. 129, 77–91 (2002)Smith, R.J., Troyanski, S.L.: Renormings of $$C(K)$$ spaces. Rev. R. Acad. Cienc. Exactas Fís. Natl. Ser. A Math. RACSAM 104(2), 375–412 (2010)Sullivan, F.: Geometrical properties determined by the higher duals of a Banach space. Illinois J. Math. 21, 315–331 (1977)Taylor, A.E.: The extension of linear functionals. Duke Math. J. 5, 538–547 (1939

Multi-scale three-dimensional characterization of iron particles in dusty olivine: Implications for paleomagnetism of chondritic meteorites

Dusty olivine (olivine containing multiple sub-micrometer inclusions of metallic iron) in chondritic meteorites is considered an ideal carrier of paleomagnetic remanence, capable of maintaining a faithful record of pre-accretionary magnetization acquired during chondrule formation. Here we show how the magnetic architecture of a single dusty olivine grain from the Semarkona LL3.0 ordinary chondrite meteorite can be fully characterised in three dimensions, using a combination of Focussed-Ion-Beam nanotomography (FIB-nT), electron tomography and finite-element micromagnetic modelling. We present a three-dimensional (3D) volume reconstruction of a dusty olivine grain, obtained by selective milling through a region of interest in a series of sequential 20 nm slices, which are then imaged using scanning electron microscopy. The data provide a quantitative description of the iron particle ensemble, including the distribution of particle sizes, shapes, interparticle spacings and orientations. Iron particles are predominantly oblate ellipsoids with average radii 242 ± 94 nm by 199 ± 80 nm by 123 ± 58 nm. Using analytical TEM we observe that the particles nucleate on sub-grain boundaries and are loosely arranged in a series of sheets parallel to (001) of the olivine host. This is in agreement with the orientation data collected using the FIB-nT, and highlights how the underlying texture of the dusty olivine is crystallographically constrained by the olivine host. The shortest dimension of the particles is oriented normal to the sheets and their longest dimension is preferentially aligned within the sheets. Individual particle geometries are converted to a finite-element mesh and used to perform micromagnetic simulations. The majority of particles adopt a single vortex state, with ‘bulk’ spins that rotate around a central vortex core. We observed no particles, which are in a true single domain state. The results of the micromagnetic simulations challenge some pre-conceived ideas about the remanence carrying properties of vortex states. There is often not a simple predictive relationship between the major, intermediate and minor axes of the particles and the remanence vector imparted in different fields. Although the orientation of the vortex core is determined largely by the ellipsoidal geometry (i.e., parallel to the major axis for prolate ellipsoids and parallel to the minor axis for oblate ellipsoids), the core and remanence vectors can sometimes lie at very large (tens of degree) angles to the principal axes. The subtle details of the morphology can control the overall remanence state, leading in some cases to a dominant contribution from the bulk spins to the net remanence, with profound implications for predicting the anisotropy of the sample. The particles have very high switching fields (several hundred mT), demonstrating their high stability and suitability for paleointensity studies.The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC grant agreements 291522-3DIMAGE (P.A.M.) and 320750 - Nanopaleomagnetism (J.F.E., R.J.H., and P.A.M.). BPW and RRF were supported by NASA Emerging Worlds program grant #NNX15AH72G, the NASA Solar System Exploration and Research Virtual Institute grant #NNA14AB01A, and a generous gift from Thomas F. Peterson, Jr. The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 320832-Imagine. (W.W . and P.O.C.) W.W. was also supported for this research under NERC grant NE/J020966/1 - Predicting the reliability with which the geomagnetic field can be recorded in igneous rocks.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the Mineralogical Society of America

Deep 230-470 MHz VLA observations of the mini-halo in the Perseus cluster

© 2017 The Authors. We present a low-frequency view of the Perseus cluster with new observations from the Karl G. Jansky Very Large Array (JVLA) at 230-470 MHz. The data reveal a multitude of new structures associated with the mini-halo. The mini-halo seems to be influenced both by the AGN activity and the sloshing motion of the cool core cluster's gas. In addition, it has a filamentary structure similar to that seen in radio relics found in merging clusters. We present a detailed description of the data reduction and imaging process of the dataset. The depth and resolution of the observations allow us to conduct for the first time a detailed comparison of the mini-halo structure with the X-ray structure as seen in the Chandra X-ray images. The resulting image very clearly shows that the mini-halo emission is mostly contained behind the western cold front, similar to that predicted by simulations of gas sloshing in galaxy clusters, but fainter emission is also seen beyond, as if particles are leaking out. However, due to the proximity of the Perseus cluster, as well as the quality of the data at low radio frequencies and at X-ray wavelengths, we also find evidence of fine structure. This structure includes several radial radio filaments extending in different directions, a concave radio structure associated with the southern X-ray bay and sharp radio edges that correlate with X-ray edges. Minihaloes are therefore not simply diffuse, uniform radio sources, but rather have a rich variety of complex structures. These results illustrate the high-quality images that can be obtained with the new JVLA at low radio frequencies, as well as the necessity to obtain deeper, higher fidelity radio images of mini-haloes in clusters to further understand their origin

Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition

In the stability analysis of large-scale interconnected systems it is frequently desirable to be able to determine a decay point of the gain operator, i.e., a point whose image under the monotone operator is strictly smaller than the point itself. The set of such decay points plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system and in the numerical construction of a LISS Lyapunov function. We provide a homotopy algorithm that computes a decay point of a monotone op- erator. For this purpose we use a fixed point algorithm and provide a function whose fixed points correspond to decay points of the monotone operator. The advantage to an earlier algorithm is demonstrated. Furthermore an example is given which shows how to analyze a given perturbed interconnected system.Comment: 30 pages, 7 figures, 4 table

Nanomechanical Detection of Itinerant Electron Spin Flip

Spin is an intrinsically quantum property, characterized by angular momentum. A change in the spin state is equivalent to a change in the angular momentum or mechanical torque. This spin-induced torque has been invoked as the intrinsic mechanism in experiments ranging from the measurements of angular momentum of photons g-factor of metals and magnetic resonance to the magnetization reversal in magnetic multi-layers A spin-polarized current introduced into a nonmagnetic nanowire produces a torque associated with the itinerant electron spin flip. Here, we report direct measurement of this mechanical torque and itinerant electron spin polarization in an integrated nanoscale torsion oscillator, which could yield new information on the itinerancy of the d-band electrons. The unprecedented torque sensitivity of 10^{-22} N m/ \sqrt{Hz} may enable applications for spintronics, precision measurements of CP-violating forces, untwisting of DNA and torque generating molecules.Comment: 14 pages, 4 figures. visit http://nano.bu.edu/ for related paper

Gate-tunable black phosphorus spin valve with nanosecond spin lifetimes

Two-dimensional materials offer new opportunities for both fundamental science and technological applications, by exploiting the electron spin. While graphene is very promising for spin communication due to its extraordinary electron mobility, the lack of a band gap restricts its prospects for semiconducting spin devices such as spin diodes and bipolar spin transistors. The recent emergence of 2D semiconductors could help overcome this basic challenge. In this letter we report the first important step towards making 2D semiconductor spin devices. We have fabricated a spin valve based on ultra-thin (5 nm) semiconducting black phosphorus (bP), and established fundamental spin properties of this spin channel material which supports all electrical spin injection, transport, precession and detection up to room temperature (RT). Inserting a few layers of boron nitride between the ferromagnetic electrodes and bP alleviates the notorious conductivity mismatch problem and allows efficient electrical spin injection into an n-type bP. In the non-local spin valve geometry we measure Hanle spin precession and observe spin relaxation times as high as 4 ns, with spin relaxation lengths exceeding 6 um. Our experimental results are in a very good agreement with first-principles calculations and demonstrate that Elliott-Yafet spin relaxation mechanism is dominant. We also demonstrate that spin transport in ultra-thin bP depends strongly on the charge carrier concentration, and can be manipulated by the electric field effect

Clusters of galaxies : observational properties of the diffuse radio emission

Clusters of galaxies, as the largest virialized systems in the Universe, are ideal laboratories to study the formation and evolution of cosmic structures...(abridged)... Most of the detailed knowledge of galaxy clusters has been obtained in recent years from the study of ICM through X-ray Astronomy. At the same time, radio observations have proved that the ICM is mixed with non-thermal components, i.e. highly relativistic particles and large-scale magnetic fields, detected through their synchrotron emission. The knowledge of the properties of these non-thermal ICM components has increased significantly, owing to sensitive radio images and to the development of theoretical models. Diffuse synchrotron radio emission in the central and peripheral cluster regions has been found in many clusters. Moreover large-scale magnetic fields appear to be present in all galaxy clusters, as derived from Rotation Measure (RM) studies. Non-thermal components are linked to the cluster X-ray properties, and to the cluster evolutionary stage, and are crucial for a comprehensive physical description of the intracluster medium. They play an important role in the cluster formation and evolution. We review here the observational properties of diffuse non-thermal sources detected in galaxy clusters: halos, relics and mini-halos. We discuss their classification and properties. We report published results up to date and obtain and discuss statistical properties. We present the properties of large-scale magnetic fields in clusters and in even larger structures: filaments connecting galaxy clusters. We summarize the current models of the origin of these cluster components, and outline the improvements that are expected in this area from future developments thanks to the new generation of radio telescopes.Comment: Accepted for the publication in The Astronomy and Astrophysics Review. 58 pages, 26 figure

Breast cancer chemoprevention: beyond tamoxifen

A large number of new potential chemoprevention agents are available that target molecular abnormalities found in estrogen receptor (ER)-negative and/or ER-positive precancerous breast tissue and have side effect profiles that differ from tamoxifen. Classes of agents currently undergoing evaluation in clinical prevention trials or those for which testing is planned in the near future include new selective ER modulators, aromatase inactivators/inhibitors, gonadotrophin-releasing hormone agonists, monoterpenes, isoflavones, retinoids, rexinoids, vitamin D derivatives, and inhibitors of tyrosine kinase, cyclooxygenase-2, and polyamine synthesis. New clinical testing models will use morphological and molecular biomarkers to select candidates at highest short-term risk, to predict the response to a particular class of agent, and to assess the response in phase II prevention trials. If validated, morphological and molecular markers could eventually replace cancer incidence as an indicator of efficacy in future phase III trials

Neuroactive steroids in depression and anxiety disorders: Clinical studies

Certain neuroactive steroids modulate ligand-gated ion channels via non-genomic mechanisms. Especially 3 alpha-reduced pregnane steroids are potent positive allosteric modulators of the gamma-aminobutyric acid type A (GABA(A)) receptor. During major depression, there is a disequilibrium of 3 alpha-reduced neuroactive steroids, which is corrected by clinically effective pharmacological treatment. To investigate whether these alterations are a general principle of successful antidepressant treatment, we studied the impact of nonpharmacological treatment options on neuroactive steroid concentrations during major depression. Neither partial sleep deprivation, transcranial magnetic stimulation, nor electroconvulsive therapy affected neuroactive steroid levels irrespectively of the response to these treatments. These studies suggest that the changes in neuroactive steroid concentrations observed after antidepressant pharmacotherapy more likely reflect distinct pharmacological properties of antidepressants rather than the clinical response. In patients with panic disorder, changes in neuroactive steroid composition have been observed opposite to those seen in depression. However, during experimentally induced panic induction either with cholecystokinine-tetrapeptide or sodium lactate, there was a pronounced decline in the concentrations of 3 alpha-reduced neuroactive steroids in patients with panic disorder, which might result in a decreased GABAergic tone. In contrast, no changes in neuroactive steroid concentrations could be observed in healthy controls with the exception of 3 alpha,5 alpha-tetrahydrodeoxycorticosterone. The modulation of GABA(A) receptors by neuroactive steroids might contribute to the pathophysiology of depression and anxiety disorders and might offer new targets for the development of novel anxiolytic compounds. Copyright (c) 2006 S. Karger AG, Basel