GPU accelerated Monte Carlo simulations of pattern forming magnetic systems in two dimensions

Matthew Ambrose

    Research output: ThesisDoctoral Thesis

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    Abstract

    There are a variety of systems which form patterned states, in which one or more of the order parameters describing the system are not uniform. Typically in these systems energies that favor uniformity of the order parameters and those favoring inhomogeneity compete leading to the formation of stripes or bubbles, although more complex patterns have been observed. Examples of pattern forming systems include superconducting and nonsuperconducting phases in type I superconductors; chemical composition in Langmuir Blodgett films; polarization in ferroelectric films; surface reconstruction in semi-conductor surfaces and the magnetization direction in thin films. This thesis examines pattern formation in thin magnetic films using Monte Carlo simulations. These magnetic systems are particularly interesting due to the fine control of composition that is possible allowing for the fabrication of lms that closely match theoretical results obtained from two dimensional models. Using Monte Carlo statistics, the effects of varied temperature on two different pattern forming magnetic systems have been investigated. The first consists of a spiral structure, referred to as a Skyrmion. Under the influence of an external applied field these Skyrmions form a close-packed hexagonal structure. It is shown that that a morphological description of this state in terms of numbers of Skyrmions is more stable against thermal fluctuations than measures of chiral structure. More specifically we have shown that the phase transition out of the ordered hexagonal state is driven first by small fluctuations of the Skyrmion profile and then by long spatial fluctuations. The second spatial structure studied here is stripe formation. In thin films, with strong anisotropy acting perpendicular to film surface, perpendicular magnetization can form a regular series of stripes. In this system the way that domain morphology is affected by changes in higher order anisotropy terms, and by the inclusion of non-magnetic defects, is investigated. It is found that the defects modify details of the phase transition. Specifically, wall fluctuations are strongly modified, and the manner in which spins reorient depend strongly on defect density relative to anisotropy. Monte Carlo solutions can be computationally intensive, particularly for the systems studied here in which there are many degrees of freedom. In order to perform such simulations a high performance implementation was required. Much of this project comprised of creating new algorithms to exploit the parallel execution possible on programmable GPU chips found in modern graphics cards.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Publication statusUnpublished - 2013

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    magnetic forming
    anisotropy
    defects
    simulation
    magnetization
    theses
    magnetic films
    cards
    Langmuir-Blodgett films
    thin films
    two dimensional models
    chemical composition
    inhomogeneity
    bubbles
    conductors
    degrees of freedom
    chips
    statistics
    inclusions
    fabrication

    Cite this

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    title = "GPU accelerated Monte Carlo simulations of pattern forming magnetic systems in two dimensions",
    abstract = "There are a variety of systems which form patterned states, in which one or more of the order parameters describing the system are not uniform. Typically in these systems energies that favor uniformity of the order parameters and those favoring inhomogeneity compete leading to the formation of stripes or bubbles, although more complex patterns have been observed. Examples of pattern forming systems include superconducting and nonsuperconducting phases in type I superconductors; chemical composition in Langmuir Blodgett films; polarization in ferroelectric films; surface reconstruction in semi-conductor surfaces and the magnetization direction in thin films. This thesis examines pattern formation in thin magnetic films using Monte Carlo simulations. These magnetic systems are particularly interesting due to the fine control of composition that is possible allowing for the fabrication of lms that closely match theoretical results obtained from two dimensional models. Using Monte Carlo statistics, the effects of varied temperature on two different pattern forming magnetic systems have been investigated. The first consists of a spiral structure, referred to as a Skyrmion. Under the influence of an external applied field these Skyrmions form a close-packed hexagonal structure. It is shown that that a morphological description of this state in terms of numbers of Skyrmions is more stable against thermal fluctuations than measures of chiral structure. More specifically we have shown that the phase transition out of the ordered hexagonal state is driven first by small fluctuations of the Skyrmion profile and then by long spatial fluctuations. The second spatial structure studied here is stripe formation. In thin films, with strong anisotropy acting perpendicular to film surface, perpendicular magnetization can form a regular series of stripes. In this system the way that domain morphology is affected by changes in higher order anisotropy terms, and by the inclusion of non-magnetic defects, is investigated. It is found that the defects modify details of the phase transition. Specifically, wall fluctuations are strongly modified, and the manner in which spins reorient depend strongly on defect density relative to anisotropy. Monte Carlo solutions can be computationally intensive, particularly for the systems studied here in which there are many degrees of freedom. In order to perform such simulations a high performance implementation was required. Much of this project comprised of creating new algorithms to exploit the parallel execution possible on programmable GPU chips found in modern graphics cards.",
    keywords = "Magnetic, Monte Carlo, Thin film, GPU, Stripe, Melting, Two dimensions, Skyrmions",
    author = "Matthew Ambrose",
    year = "2013",
    language = "English",

    }

    GPU accelerated Monte Carlo simulations of pattern forming magnetic systems in two dimensions. / Ambrose, Matthew.

    2013.

    Research output: ThesisDoctoral Thesis

    TY - THES

    T1 - GPU accelerated Monte Carlo simulations of pattern forming magnetic systems in two dimensions

    AU - Ambrose, Matthew

    PY - 2013

    Y1 - 2013

    N2 - There are a variety of systems which form patterned states, in which one or more of the order parameters describing the system are not uniform. Typically in these systems energies that favor uniformity of the order parameters and those favoring inhomogeneity compete leading to the formation of stripes or bubbles, although more complex patterns have been observed. Examples of pattern forming systems include superconducting and nonsuperconducting phases in type I superconductors; chemical composition in Langmuir Blodgett films; polarization in ferroelectric films; surface reconstruction in semi-conductor surfaces and the magnetization direction in thin films. This thesis examines pattern formation in thin magnetic films using Monte Carlo simulations. These magnetic systems are particularly interesting due to the fine control of composition that is possible allowing for the fabrication of lms that closely match theoretical results obtained from two dimensional models. Using Monte Carlo statistics, the effects of varied temperature on two different pattern forming magnetic systems have been investigated. The first consists of a spiral structure, referred to as a Skyrmion. Under the influence of an external applied field these Skyrmions form a close-packed hexagonal structure. It is shown that that a morphological description of this state in terms of numbers of Skyrmions is more stable against thermal fluctuations than measures of chiral structure. More specifically we have shown that the phase transition out of the ordered hexagonal state is driven first by small fluctuations of the Skyrmion profile and then by long spatial fluctuations. The second spatial structure studied here is stripe formation. In thin films, with strong anisotropy acting perpendicular to film surface, perpendicular magnetization can form a regular series of stripes. In this system the way that domain morphology is affected by changes in higher order anisotropy terms, and by the inclusion of non-magnetic defects, is investigated. It is found that the defects modify details of the phase transition. Specifically, wall fluctuations are strongly modified, and the manner in which spins reorient depend strongly on defect density relative to anisotropy. Monte Carlo solutions can be computationally intensive, particularly for the systems studied here in which there are many degrees of freedom. In order to perform such simulations a high performance implementation was required. Much of this project comprised of creating new algorithms to exploit the parallel execution possible on programmable GPU chips found in modern graphics cards.

    AB - There are a variety of systems which form patterned states, in which one or more of the order parameters describing the system are not uniform. Typically in these systems energies that favor uniformity of the order parameters and those favoring inhomogeneity compete leading to the formation of stripes or bubbles, although more complex patterns have been observed. Examples of pattern forming systems include superconducting and nonsuperconducting phases in type I superconductors; chemical composition in Langmuir Blodgett films; polarization in ferroelectric films; surface reconstruction in semi-conductor surfaces and the magnetization direction in thin films. This thesis examines pattern formation in thin magnetic films using Monte Carlo simulations. These magnetic systems are particularly interesting due to the fine control of composition that is possible allowing for the fabrication of lms that closely match theoretical results obtained from two dimensional models. Using Monte Carlo statistics, the effects of varied temperature on two different pattern forming magnetic systems have been investigated. The first consists of a spiral structure, referred to as a Skyrmion. Under the influence of an external applied field these Skyrmions form a close-packed hexagonal structure. It is shown that that a morphological description of this state in terms of numbers of Skyrmions is more stable against thermal fluctuations than measures of chiral structure. More specifically we have shown that the phase transition out of the ordered hexagonal state is driven first by small fluctuations of the Skyrmion profile and then by long spatial fluctuations. The second spatial structure studied here is stripe formation. In thin films, with strong anisotropy acting perpendicular to film surface, perpendicular magnetization can form a regular series of stripes. In this system the way that domain morphology is affected by changes in higher order anisotropy terms, and by the inclusion of non-magnetic defects, is investigated. It is found that the defects modify details of the phase transition. Specifically, wall fluctuations are strongly modified, and the manner in which spins reorient depend strongly on defect density relative to anisotropy. Monte Carlo solutions can be computationally intensive, particularly for the systems studied here in which there are many degrees of freedom. In order to perform such simulations a high performance implementation was required. Much of this project comprised of creating new algorithms to exploit the parallel execution possible on programmable GPU chips found in modern graphics cards.

    KW - Magnetic

    KW - Monte Carlo

    KW - Thin film

    KW - GPU

    KW - Stripe

    KW - Melting

    KW - Two dimensions

    KW - Skyrmions

    M3 - Doctoral Thesis

    ER -