138 research outputs found
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Determination of tip transfer function for quantitative MFM using frequency domain filtering and least squares method
Magnetic force microscopy has unsurpassed capabilities in analysis of nanoscale and microscale magnetic samples and devices. Similar to other Scanning Probe Microscopy techniques, quantitative analysis remains a challenge. Despite large theoretical and practical progress in this area, present methods are seldom used due to their complexity and lack of systematic understanding of related uncertainties and recommended best practice. Use of the Tip Transfer Function (TTF) is a key concept in making Magnetic Force Microscopy measurements quantitative. We present a numerical study of several aspects of TTF reconstruction using multilayer samples with perpendicular magnetisation. We address the choice of numerical approach, impact of non-periodicity and windowing, suitable conventions for data normalisation and units, criteria for choice of regularisation parameter and experimental effects observed in real measurements. We present a simple regularisation parameter selection method based on TTF width and verify this approach via numerical experiments. Examples of TTF estimation are shown on both 2D and 3D experimental datasets. We give recommendations on best practices for robust TTF estimation, including the choice of windowing function, measurement strategy and dealing with experimental error sources. A method for synthetic MFM data generation, suitable for large scale numerical experiments is also presented
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Round robin comparison on quantitative nanometer scale magnetic field measurements by magnetic force microscopy
Magnetic force microscopy (MFM) can be considered as a standard tool for nano-scale investigation of magnetic domain structures by probing the local stray magnetic field landscape of the measured sample. However, this generally provides only qualitative data. To quantify the stray magnetic fields, the MFM system must be calibrated. To that end, a transfer function (TF) approach was proposed, that, unlike point probe models, fully considers the finite extent of the MFM tip. However, albeit being comprehensive, the TF approach is not yet well established, mainly due to the ambiguities concerning the input parameters and the measurement procedure. Additionally, the calibration process represents an ill-posed problem which requires a regularization that introduces further parameters. In this paper we propose a guideline for quantitative stray field measurements by standard MFM tools in ambient conditions. All steps of the measurement and calibration procedure are detailed, including reference sample and sample under test (SUT) measurements and the data analysis. The suitability of the reference sample used in the present work for calibrated measurements on a sub-micron scale is discussed. A specific regularization approach based on a Pseudo-Wiener Filter is applied and combined with criteria for the numerical determination of a unique regularization parameter. To demonstrate the robustness of such a defined approach, a round robin comparison of magnetic field measurements was conducted by four laboratories. The guideline, the reference sample and the results of the round robin are discussed
Hardy's inequality for functions vanishing on a part of the boundary
We develop a geometric framework for Hardy's inequality on a bounded domain
when the functions do vanish only on a closed portion of the boundary.Comment: 26 pages, 2 figures, includes several improvements in Sections 6-8
allowing to relax the assumptions in the main results. Final version
published at http://link.springer.com/article/10.1007%2Fs11118-015-9463-
On Type I singularities of the local axi-symmetric solutions of the Navier-Stokes equations
Local regularity of axially symmetric solutions to the Navier-Stokes
equations is studied. It is shown that under certain natural assumptions there
are no singularities of Type I
First description of a fossil chamaeleonid from Greece and its relevance for the European biogeographic history of the group
The fossil record of Chamaeleonidae is very scarce and any new specimen is therefore considered important for our understanding of the evolutionary and biogeographic history of the group. New specimens from the early Miocene of Aliveri (Evia Island), Greece constitute the only fossils of these lizards from southeastern Europe. Skull roofing material is tentatively attributed to the Czech species Chamaeleo cf. andrusovi, revealing a range extension for this taxon, whereas tooth-bearing elements are described as indeterminate chamaeleonids. The Aliveri fossils rank well among the oldest known reptiles from Greece, provide evidence for the dispersal routes of chameleons out of Africa towards the European continent and, additionally, imply strong affinities with coeval chamaeleonids from Central Europe
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