Magnetic Tight-Binding Simulations of Defects in Iron
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Magnetic Tight-Binding Simulations of Defects in Iron Preetma K. Soin1,2 , Andrew P. Horsfield1 and Duc Nguyen-Manh2 1 Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, UK 2 EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB, UK ABSTRACT We consider a tight binding model for magnetic systems, in which we allow atoms to become charged and to interact via the long ranged Coulomb interaction to a published tight binding model; this is then applied to the study defects in ferromagnetic iron. We encounter several problems with achieving self consistency with existing schemes. To address the issue of instability and slow convergency we developed a robust, efficient scheme for charge and spin self consistency. This is based on minimizing an extended form of the Harris-Foulkes functional which includes spin, leading to a Newton-Raphson iterative procedure. We then apply this to both bulk and defect calculations for iron. INTRODUCTION The possible application of iron to fission and fusion power plants [1,2] places it at the forefront of interest in materials. It is essential that defects in iron resulting from irradiation are investigated carefully as they determine mechanical properties. A balance needs to be struck between modeling a large number of atoms and capturing the correct magnetic state of the atoms. Empirical potentials are at one end of the spectrum and are a natural choice for studying extended defects such as grain boundaries and dislocations [3,4,5]. There have been some efforts to capture the correct magnetic state with potentials [6,7], however, modeling the electronic structure explicitly is likely to be more reliable. There are limits to the number of atoms that can be treated with density functional theory (DFT) and tight binding suggests itself as the obvious solution [8,9]. To employ tight binding we need to determine the charge and spin on atoms self consistently using an iterative procedure. This is technically the most difficult challenge and developing an efficient scheme to do this forms the main focus of our work. We adapt a magnetic Stoner d-band tight binding model [10] to include charge transfer. This is implemented using the computer code PLATO. There is an onsite contribution to the energy from the charge on each atomic site, whilst at long range the interaction between sites becomes Coulomb’s law. To achieve self consistency we choose a variational scheme that reduces the problem to one of energy minimization. For this we use an extended form of the Harris-Foulkes energy functional [11,12] which includes both input and output spin and charge. We present results for various bulk structures and for vacancy and interstitial point defects in iron.
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THEORY Extended Harris-Foulkes functional To describe the energy per computational cell of our tight binding system we used the following extension of the Harris-Foulkes (H-F) energy functional. Double counting terms for both charge and spin are included. E=
1 Nk
¦ f
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