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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Applied physics 16 (1978), S. 279-287 
    ISSN: 1432-0630
    Keywords: 42.80 ; 85.30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Optical projection of masks is a very troublesome task if dimensions are in the submicron range. It is difficult to get an undistorted image in the resist. This problem can be overcome by introducing corrections in the penultimate mask. Till now this has been done by a trial and error method in which an acceptable pattern is made only after a time consuming iterative process. In this paper a description will be given of the image forming process in which diffraction at the penultimate mask and at the aperture of the lens are the critical features. Based upon this theory correction formulas are derived for the direct design of penultimate masks. Rules for maximum edge sharpness are given, so that the tolerance demands on the production process can be relaxed. Extensive experimental measurements are in good agreement with theory. It will be shown theoretically as well as practically that by asymmetrical arrangement of the optical system images of gratings with 0.2–0.3 μm linewidth can be obtained.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Applied physics 2 (1973), S. 137-142 
    ISSN: 1432-0630
    Keywords: Thin MnBi films ; Coercive force ; Rayleigh curve
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Statistical Rayleigh-curve theory is applied to thin evaporated MnBi films in order to obtain information concerning the density of wall pinning centra. The treatment results in a prediction of the coercive forceH c and the average distance between adjacent wall pinning centra, 2L 0. The coercive forceH cis also measured experimentally. The results of the two methods are in good agreement with each other. The influence of dislocations on the coercive force is discussed briefly.
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  • 3
    Electronic Resource
    Electronic Resource
    [s.l.] : Macmillian Magazines Ltd.
    Nature 418 (2002), S. 509-512 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Since the invention of the first magnetic memory disk in 1954, much effort has been put into enhancing the speed, bit density and reliability of magnetic memory devices. In the case of magnetic random access memory (MRAM) devices, fast coherent magnetization rotation by precession of the entire ...
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 79 (1996), S. 2601-2608 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A magnetization model is presented that is used to cover trilayers containing two magnetic layers that are exchange coupled via an intermediate nonmagnetic layer and that have different crystalline anisotropies. The interfaces are coupled to the bulk by a twisted magnetization configuration which is evaluated using the Ritz method. By minimizing the total energy, experimental magnetization curves of strongly coupled Co/Ru sandwiches can be reproduced with a good precision and with the same set of parameters in two perpendicular field directions. These physical parameters can be determined with a good reliability and are in agreement with the literature except for the bulk anisotropy of the Co layer first deposited, which is twice as large as the known bulk value. This originates in the magnetoelastic contributions due to lattice misfit and interface roughness. It is shown that the interlayer exchange coupling forces the magnetization of both layers to be along the same axis in the low-field range notwithstanding the opposite sign of the anisotropy constants in most stacks. It is also demonstrated that the differences in the orientations of the moments in one Co layer are modest and depend on the various parameters. In particular, the bulk exchange constant is a decisive parameter that makes the calculated curves close to the experimental ones. © 1996 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 76 (1994), S. 6559-6559 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A significant loss in the giant magnetoresistive signal of magnetic stacks with antiferromagnetic coupling across nonmagnetic intermediate layers is caused by regions with a ferro- rather than an antiferromagnetic coupling. The impact of these ferromagnetic coupling regions extends itself into the lateral direction due to the bulk exchange coupling. The present micromagnetic model provides a tool by which a detailed quantitative evaluation of the impact of periodic arrays of parallel line defects is possible. These defects have deviating exchange-coupling constants, and/or anisotropy constants or directions, bulk exchange constants, saturation magnetization, etc., in specific regions. Previously, we developed a phenomenological model of trilayers with two magnetic films separated by a nonmagnetic interlayer that contains one such defect. This model, with a relatively small number of free parameters, allows one to trace complete hysteresis curves. A large number of mode branches reveal themselves and jumpwise transitions between these modes frequently occur along the hysteresis loops. The present micromagnetic model requires a sufficiently accurate assessment of the starting magnetization configuration in order to get a convergence of the code. In general, the micromagnetic code is not capable of overcoming the above irreversible mode conversions. The mode branches evaluated by the phenomenological model are applied to provide the micromagnetic model with appropriate starting configurations after meeting a situation of nonstability.The micromagnetic theory of Brown constitutes the basis of the present approach. The micromagnetic effective field is calculated at grid points and the torque exerted by it on the magnetic dipole is made zero at each grid side by an iteration scheme. The long ranging magnetostatic fields are given by convolution integrals and are evaluated in the Fourier space by using two-dimensional fast Fourier transforms. The single defect is micromagnetically studied by zero padding techniques. Depending on the course of the external field, two different wall regions reveal themselves, to wit, the wall core and the so-called Néel tails. These tails were not incorporated into the phenomenological model. Provided that the defects are sufficiently wide spaced, the agreement between both models is rather good in the core regions. The impact on the GMR signal, in particular of the Néel tails, will be discussed with emphasis on systems with weak interlayer coupling, e.g., the decoupled systems.
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 62 (1987), S. 1952-1959 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The self-consistent domain theory, based on micromagnetic principles, is further developed in order to incorporate all possible solenoidal two-dimensional magnetization distributions in plane-parallel thin-film objects with arbitrary lateral shape. A decomposition of the object into a number of disjunct plane-parallel subregions that completely cover the object's area is put forward. In each subregion, a solenoidal M distribution is defined with the M vector parallel to the subregion's boundary, so that the M distributions in adjacent subregions properly link either via a continuous transition, or via a 180° wall at the intermediate boundary. Two types of subregions are distinguished; namely, the simple connected regions and the so-called parallel regions, being a special type of multiple connected region. In the first category, the basic structures as defined in the preceding paper on this subject are present. The parallel regions are closed ringlike configurations that are built of simpler units—the parallel segments. A parallel segment is a region bounded by two orthogonal trajectories of the same set of straight lines, while two of these straight lines close the segment at either end. No points of intersection of members of this family of lines are found inside the segment. In a specific parallel region, the distance between the orthogonal trajectories is the same for all segments. Adjacent segments in a parallel region are separated by a domain wall which is the locus of centers inside the cross section of the segments of circles that touch at corresponding orthogonal edges of both of the segments involved. A systematic procedure is developed for constructing the parallel subregions, and it is shown that, with this, all possible two-dimensional solenoidal M distributions can be recovered.
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 60 (1986), S. 1104-1113 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A construction method for determining the domain structure in ideally soft-ferromagnetic cylindrical objects with plane-parallel top and bottom surfaces of arbitrary shape is presented. The self-consistent theory is confined to two-dimensional solenoidal dipole distributions in which the dipoles are parallel to the top and bottom surfaces. It is proved that the basic domain structure is uniquely defined in simply connected objects, while an extra criterion has to be added in order to guarantee the uniqueness in the multiply connected ones. The treatment is based on differential geometrical principles. The object edge is partitioned into segments, in which each segment is situated in between two adjacent edge points where the radii of curvature of convex edge segments are locally minimal. To each edge segment, a region is attributed, in which M is uniquely specified by the course of M along that edge segment. In the cross section of regions corresponding to different edge segments, domain walls provide an adequate separation of the dipole distribution imposed by these segments. The extremities of these domain walls are found in the singular points of the evolute corresponding to the extremities of the edge segments and in the points where a number of walls meet. It is proved that the basic domain structure is the locus of centers of all circles inside the object that touch the object edge at at least two points. A number of experimentally observed basic structures are given, and the relevance of the definition of basic structures in multiply connected objects is examined. OFF
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 57 (1985), S. 2168-2173 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The basic concepts of a self-consistent domain theory for the class of ideal soft ferromagnetic media is unfolded. The treatment is based on micromagnetic equilibrium and stability equations which are simplified by removing the contributions due to the intrinsic anisotropy and the spatial variation term in the exchange energy density. Only the solenoidal magnetization distributions in thin film objects are investigated. This limitation makes confinement to two-dimensional dipole distributions possible. Cauchy's method of characteristics is employed to derive dipole distributions that satisfy the relation ∇⋅M=0, where M is the magnetization, and the constitutive equation. It is proved that the characteristic base curves are straight lines perpendicular to the magnetization vector. In an ellipse, four different characteristic base curves that do not coincide intersect at one single point in certain regions, thus generating ambiguities in the magnetization direction. It is demonstrated that these ambiguities originate in the incompatibility of the magnetization distribution that is imposed by the various segments of the edge of the ellipse. Based on differential geometrical principles, a partitioning of the edge into segments is introduced, and along with it two adjoining regions in which the magnetization direction is uniquely determined are defined. It is proved that a domain wall is required in the cross section of both regions to accomplish a dipole configuration in stable equilibrium. Experimental confirmation is given by means of the ferrofluid pattern of a 3500-A(ring)-thick Permalloy layer with elliptical geometry.
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 61 (1987), S. 4194-4199 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A self-consistent domain theory, based on micromagnetic principles, is unfolded for two-dimensional solenoidal M distributions present in ideally soft-magnetic plane-parallel thin-film objects at zero external field and in the absence of conduction currents. Two types of domain configurations are distinguished: the basic structures in simply connected regions and the parallel configurations in special types of multiply connected regions—the parallel regions. A decomposition of the objects's area into disjunct subregions, either simply connected or of the parallel type, whose union completely covers the object, is put forward. A procedure for constructing all feasible parallel regions is presented. In each region, the appropriate solenoidal M distribution is specified with which M is taken parallel to the subregion's boundary. Thus, all the domain structures possible in thin-film objects with arbitrary lateral shapes can be constructed. Experimental examples are provided.
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  • 10
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 63 (1988), S. 4330-4332 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A method for constructing three-dimensional solenoidal magnetization distributions, with invariant magnitude of m, in arbitrarily shaped objects is presented. The formalism harks back to the theory developed by van den Berg for two-dimensional m distributions. The space within a general object Ω is partitioned into i subspaces Ωi, described by a family of surfaces to which the magnetization is tangent. A characteristic equation which defines the course of m at each of the surfaces is derived. A boundary condition for m arises naturally, or can be chosen to determine m at the surface. Within the above framework an infinite number of solutions are generated that, in general, exhibit singularities. Special attention, also from the topological point of view, is paid to the m distributions having point defects only.
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