On the Krein–Milman Property and the Bade Property

AbstractThroughout this paper a study on the Krein–Milmam Property and the Bade Property is entailed reaching the following conclusions: If a real topological vector space satisfies the Krein–Milmam Property, then it is Hausdorff; if a real topological vector space satisfies the Krein–Milmam Property and is locally convex and metrizable, then all of its closed infinite dimensional vector subspaces have uncountable dimension; if a real pseudo-normed space has the Bade Property, then it is Hausdorff as well but could allow closed infinite dimensional vector subspaces with countable dimension. On other hand, we show the existence of infinite dimensional closed subspaces of ℓ∞ with the Bade Property that are not the space of convergence associated to any series in a real topological vector space. Finally, we characterize unconditionally convergent series in real Banach spaces by means of a new concept called uniform convergence of series

Chemical and structural analysis of sub-20 nm graphene patterns generated by scanning probe lithography

Sub-20 nm patterns have been fabricated by using oxidation scanning probe lithography on epitaxial graphene. The structural and chemical properties of these nanopatterns have been characterized by high resolution transmission electron microscopy, energy dispersive X-ray spectroscopy and electron energy loss spectroscopy. The electron microscopy images reveal that the nanolithography process modifies the graphene monolayer and a thin region of the SiC substrate (1 nm thick). Spatially-resolved electron spectroscopies show that the nanopatterns are made of graphene oxide. The combination of spatially-resolved structural and chemical analysis of graphene nanopatterns will enable the development of high-performance graphene devices

Sputter grown Fe and Fe/Cr multilayers with fourfold magnetic anisotropy on GaAs

Thin films of Fe have been epitaxially sputtered on GaAs substrates with native oxide removal prior to the deposition carried out by an Ar ion milling. Films grown at substrate temperatures above 100 °C show well-defined fourfold anisotropies. The onset of epitaxial growth is accompanied by an increase in the surface roughness with growth occurring in a distinct island-like pattern. The Fe layers show significantly reduced moments, which decrease with increasing temperature. Antiferromagnetic coupling between Fe layers with Cr spacers was measured in a multilayer with a Cr thickness of 2.7 nm, around the second antiferromagnetic peak. The magnetic properties of the films are discussed in the context of multilayer storage applications

Superconducting density of states at the border of an amorphous thin film grown by focused-ion-beam

We present very low temperature Scanning Tunneling Microscopy and Spectroscopy (STM/S) measurements of a W based amorphous thin film grown with focused-ion-beam. In particular, we address the superconducting properties close to the border, where the thickness of the superconducting film decreases, and the Au substrate emerges. When approaching the Au substrate, the superconducting tunneling conductance strongly increases around the Fermi level, and the quasiparticle peaks do not significantly change its position. Under magnetic fields, the vortex lattice is observed, with vortices positioned very close to the Au substrate.Comment: To appear in Journal of Physics: Conference serie

A robust soliton ratchet using combined antiferromagnetic and ferromagnetic interlayer couplings

A sharp magnetic soliton can be created and propagated in a vertical ratchet structure based on magnetic layers with out-of-plane anisotropy using a combination of antiferromagnetic and ferromagnetic interlayer couplings. This allows the use of identical magnetic layers in the stack, which simplifies the implementation of the ratchet compared to schemes which use alternating layer thicknesses. The ratchet behavior is analyzed using an Ising-macrospin approximation and conditions are derived for the propagation of a soliton, which is demonstrated experimentally. Values extracted from the experimental data for the coercivities and interlayer couplings show significant variation, which demonstrates the robustness of the soliton propagation.This research was funded by the European Community under the Seventh Framework Program ERC Contract No. 247368: 3SPIN. R.L. acknowledges support from the Netherlands Organization for Scientific Research (VENI 68047428). A.F.-P. acknowledges an EPSRC Early Career fellowship and support from the Winton Programme for the Physics of Sustainability.This is the author accepted manuscript. The final version is available from AIP via http://dx.doi.org/10.1063/1.491401

Dynamic selective switching in antiferromagnetically-coupled bilayers close to the spin reorientation transition

We have designed a bilayer synthetic antiferromagnet where the order of layer reversal can be selected by varying the sweep rate of the applied magnetic field. The system is formed by two ultra-thin ferromagnetic layers with different proximities to the spin reorientation transition, coupled antiferromagnetically using Ruderman-Kittel-Kasuya-Yosida interactions. The different dynamic magnetic reversal behavior of both layers produces a crossover in their switching fields for field rates in the kOe/s range. This effect is due to the different effective anisotropy of both layers, added to an appropriate asymmetric antiferromagnetic coupling between them. Field-rate controlled selective switching of perpendicular magnetic anisotropy layers as shown here can be exploited in sensing and memory applications.Copyright (2014) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Applied Physics Letters (volume 105: 092408) and may be found at http://scitation.aip.org/content/aip/journal/apl/105/9/10.1063/1.4895032

Review of magnetic nanostructures grown by focused electron beam induced deposition (FEBID)

We review the current status of the use of focused electron beam induced deposition (FEBID) for the growth of magnetic nanostructures. This technique relies on the local dissociation of a precursor gas by means of an electron beam. The most promising results have been obtained using the Co₂(CO)₈ precursor, where the Co content in the grown nanodeposited material can be tailored up to more than 95%. Functional behaviour of these Co nanodeposits has been observed in applications such as arrays of magnetic dots for information storage and catalytic growth, magnetic tips for scanning probe microscopes, nano-Hall sensors for bead detection, nano-actuated magnetomechanical systems and nanowires for domain-wall manipulation. The review also covers interesting results observed in Fe-based and alloyed nanodeposits. Advantages and disadvantages of FEBID for the growth of magnetic nanostructures are discussed in the article as well as possible future directions in this field.Financial support by several projects is acknowledged: MAT2014-51982-C2-1-R, MAT2014-51982-C2-2-R and MAT2015-69725-REDT from MINECO (including FEDER funding), CELINA COST Action CM1301, Aragón Regional Government through project E26, FP7 Marie Curie Fellowship 3DMAGNANOW, EPSRC Early Career Fellowship EP/M008517/1 and Winton Fellowship

Nanoscale chemical and structural study of Co-based FEBID structures by STEM-EELS and HRTEM

Nanolithography techniques in a scanning electron microscope/focused ion beam are very attractive tools for a number of synthetic processes, including the fabrication of ferromagnetic nano-objects, with potential applications in magnetic storage or magnetic sensing. One of the most versatile techniques is the focused electron beam induced deposition, an efficient method for the production of magnetic structures highly resolved at the nanometric scale. In this work, this method has been applied to the controlled growth of magnetic nanostructures using Co₂(CO)₈. The chemical and structural properties of these deposits have been studied by electron energy loss spectroscopy and high-resolution transmission electron microscopy at the nanometric scale. The obtained results allow us to correlate the chemical and structural properties with the functionality of these magnetic nanostructures.The authors acknowledge the Spanish Ministry of Science for the financial support through Project No. MAT2008-06567-C02, including FEDER funding, the Aragon Regional Government Grant No. E26. RFP acknowledges F. De la Peña, K. March, and R. Arenal for the scientific discussions. RFP also acknowledges the Spanish Ministry of Science for the funding through a postdoctoral contract

Block copolymer based novel magnetic mixed matrix membranes-magnetic modulation of water permeation by irreversible structural changes

This contribution focuses on understanding the effect of magnetic field intensity on the performance of novel hydrophilic and hydrophobic mixed matrix membranes (MMMs). The hydrophilic MMMs were made up of polymeric nanoparticles (PNPs) that were synthesized through polymerization-induced self-assembly (PISA) and iron oxide nanoparticles prepared in presence of poly (methacrylic acid)-b-poly quaternized (2-dimethylamino)ethyl methacrylate. The hydrophobic MMMs were prepared by the addition of iron oxide nanoparticles with different surface properties to a linear poly (methacrylic acid)-b-poly (methylmethacrylate) diblock copolymer dissolved in tetrahydrofuran (THF). Three different types of hydrophilic membranes were prepared with polymeric nanoparticles of different morphologies (spherical, vermicular and vesicular). In case of the hydrophobic membranes, six different membranes containing different iron oxide core coated with different stabilizers such as poly (methacrylic acid), quaternized poly(2-dimethylamino)ethyl methacrylate and meso-2, 3-dimercaptosuccinic acid were prepared. An external magnetic field with intensity values up to 1.15 T was used for the permeation studies and the results were compared with those obtained in the absence of magnetic field. The collected data indicate an increase in the water flux of up to 16% and 29% under the magnetic field for hydrophobic and hydrophilic membranes, respectively. The STEM analyses suggest that the magnetic nanoparticles move within the membrane structure during the application of the magnetic field. This displacement/rearrangement causes constant changes in the membrane structure (structure of the active layer) and consequently on the membrane permeability. These results suggest that the application of the magnetic field could be used as a pretreatment step to obtain high flux membranes