Theory of Disordered Magnets
Abstract: Studying magnetic properties of disordered alloys is important both for the understanding of phase transformations in alloys and from the point of view of fundamental issues of magnetism in solids. Disorder in a magnetic system can result in unconventional magnetic structures, such as spin glass, which have rather peculiar features.In this Thesis, a rather general approach to studying disordered magnetic alloys from first principles is presented. Phase transformations and magnetic behavior of crystalline substitutional alloys are considered. This approach is exemplified by calculations of an archetypical spin-glass material: the CuMn alloy.First, a general theoretical framework for the description of the thermodynamics of disordered magnetic alloys is given. It is shown that under certain conditions, a complex magnetic system can be reduced to an effective system containing no magnetic degrees of freedom. This substantially simplifies the investigation of phase transformations in magnetic alloys. The effective model is described in terms of material-specific interaction parameters.It is shown that interaction parameters can be obtained from the ground-state property of a disordered alloy which are in turn calculated from first principles by means of highly accurate up-to-date numerical techniques based on the Green's function method. The interaction parameters can subsequently be used in thermodynamic Monte-Carlo simulations to produce the atomic and magnetic structures of an alloy. An example of calculations for the Cu-rich CuMn alloy is given. It is demonstrated that the atomic and magnetic structure of the alloy obtained by the presented approach agrees very well with the results of neutron-scattering experiments for this system. Moreover, numerical simulations enable one to predict the ground state structure of the alloy, which is difficult to observe in experiment due to large atomic diffusion barriers at temperatures close to the temperature of the phase transformation.A general description of a spin glass is given, and difficulties of modeling this type of magnetic systems are discussed. To overcome the difficulties, improved Monte-Carlo methods, such as parallel tempering, overrelaxation technique, and finite-size scaling method of analysis, are introduced. The results for the CuMn alloy are presented.
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