Title: Magnetization dynamics and thermal stability of spin-chains
Language: English
Authors: Pechhacker, Roman 
Qualification level: Diploma
Keywords: Magnetismus; Magnetisierung; thermische Stabilität; Attempt Frequency
magnetism; magnetization; thermal stability; attempt frequency
Advisor: Süss, Dieter
Issue Date: 2010
Number of Pages: 50
Qualification level: Diploma
The objective of the diploma thesis is to demonstrate dynamics of magnetic systems based on the theory of micromagnetics and find a analytical approach to calculate Omega0 [[Omega] tief 0] for spin-chains. After a basic introduction on thermodynamics, that involves the formulation of an effective magnetic field and stresses its important contributions (e.g. Zeeman-, anisotropy- and exchange-terms), requirements for the minimization of Gibb's Free Energy are given. The dynamics of single- and multi-particle magnetic systems is analyzed using the Landau-Lifschitz-Gilbert Equation. A finite difference scheme is used to solve the Landau-Lifshitz-Gilbert equation numerically for a magnetic spin-chain. At first the relaxation of a magnetic system into its energetic minimum is simulated. Then magnetization reversal processes as a result of externally applied magnetic fields are investigated. Magnetization reversals due to thermal activity is described by use of the Arrhenius-Nèel Equation, which features the attempt frequency. In the following the attempt frequency is given as a product of a dynamic prefactor lambda+ [[lambda] tief +] and a statistical factor Omega0 [[Omega] tief 0. Furthermore the required Hessians for the calculation of Omega0 [[Omega] tief 0] are derived and an analytical solution for the single-spin-system is given. The analytical derivation of the multi-spin-system is given and simulations are carried out, varying total system size and number of spins. The simulation show that the results depend on the total system size. It could be shown, that cell size of the finite difference discretization does not change the results of Omega0 [[Omega] tief 0]. Additionally eigenfunctions of the Hessian are analyzed with respect to a Fourier mode representation of the Gibb's Free Energy and magnetization. Finally the ratio of the eigenvalues of the Hessians for minimum- and saddle-point-configurations are plotted and fitted by an exponential function. The plot shows that not all ratios of eigenvalues need to be taken into account in order to calculate a sufficiently accurate value of Omega0 [[Omega] tief 0].
URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-30276
Library ID: AC07806821
Organisation: E138 - Institut für Festkörperphysik 
Publication Type: Thesis
Appears in Collections:Thesis

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