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Outline. Introduction Density Functional Theory (DFT) Approach Constrained local moment (CLM) Method for Spin-Dynamics Using VASP for Amorphous Structure Modeling Using LSMS method for Electronic and Non-collinear Magnetic Structure Calculations

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Outline

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  1. Outline • Introduction • Density Functional Theory (DFT) Approach • Constrained local moment (CLM) Method for Spin-Dynamics • Using VASP for Amorphous Structure Modeling • Using LSMS method for Electronic and Non-collinear Magnetic Structure Calculations • Calculated Results for Fe0.8-xMnx-B0.2 Bulk Amorphous Metals

  2. Electron: Nucleus: Quantum Mechanical Solution of Materials Science Problems Many-electron problem One-electron problem Density Functional Theory electron-electron interaction electron-nucleus interaction many-electron Schrödinger equation non-interacting electrons move in the potential: V[r] one-electron Schrödinger equation Local (Spin) Density Approximation Calculation of V[r] becomes feasible:

  3. Self-consistent Process Schrödinger Equation LDA Potential

  4. Magnetic Structures T = 0 K Ferromagnetic structure T = 0 K Anti-Ferromagnetic structure T = ? Non-collinear magnetic structure

  5. Constrained Local Moment • A local constraining transverse field is applied to each magnetic moment • Each constrained local moment points along a specific pre-defined direction • This model allows density functional theory approach to non-collinear magnetic structures • Instantaneous constrained local moment states, which are obtained self-consistently, form a proper basis for first principles spin dynamics

  6. Locally Self-consistent Multiple Scattering (LSMS) Method • Real space multiple scattering approach • Solve the multiple scattering equations associated with each atom to compute the Green’s function G • Order-N scaling in time and space complexity

  7. Atom Node j 1 2 3 Node i Input: Compute: Receive: Send: Result: j k n n i k m N-1 N m Parallel Implementation N-atom Unit Cell Local Interaction Zone (LIZ)

  8. Theoretical Approach • 100-atom unit cell samples are generated by VASP to simulate the Fe0.8B0.2 bulk amorphous metals • Randomly chosen Fe atoms are replaced with Mn atoms without relaxing the structure • Spin-polarized and spin-canted LSMS calculations are applied to the unit cell sample to determine the magnetic structure of the alloys

  9. Magnetic Moment Orientation

  10. Magnetic Moment Orientation

  11. Magnetic Moment Orientation

  12. Summary • Fe0.8B0.2 has collinear magnetic structure, in which Fe is ferromagnetic and carries moment ranging from 1.5mB to 2.8mB, and B carries a small moment less than 0.2mBand is in opposite direction of Fe moments. • Replacing Fe with Mn introduces non-collinearity to the magnetic structure.

  13. Summary (continue) • As Mn content increases, the average moment decreases, and the spread of the magnetic moments in both orientation and magnitude becomes broader. • Mn0.8B0.2 shows strongly non-collinear magnetic structure. The Mn atom is paramagnetic and carries moment ranging from 0.15mB to 2.7mB, and The moment on B is less than 0.08mB.

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