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Spin order in correlated electron systems Yukawa Institute for Theoretical Physics Zhi Li

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Outline 1.Variety of spin order in condensed matter 1.1 Collinear spin order 1.2 Non-collinear spin order 2.Theory and calculation 2.1 The form of wave function 2.2 Introduction about DFT calculation 2.3 Helical spin order in BaFeO 3 3. Summary

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1. Variety of spin order 1.1 Collinear spin order Ferromagnetism Such as, Fe Anti-ferromagnetism Such as, NiO Ferrimagnetism Such as, Fe 3 O 4, yttrium iron garnet Spin density wave state in Cr

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1. Variety of spin order 1.2 Non-collinear spin order Example: Spiral spin (fcc Fe) The position dependent spin moment could be written as Vector q is the wave vector of the spiral spin order

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2.1 The form of wave function If the electronic system is spin ordered, the form of the wave function has a constraint. A concrete example: Spiral spin n, l : lattice and orbital index Basis function could be plane wave, or Wannier function, or atomic orbital wave function.

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2.1 The form of wave function Check the spin moment in this from of wave function:

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2.1 The form of wave function Many-body Hamiltonian: Total energy note: 1. The wave vector q is coupled to the momentum 2. Generally speaking, the interacting term should be in form of matrix 3. It is almost impossible to get the wave vector q by analytical method

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2.2 Introduction about DFT Calculation The first-principles calculation based on density functional theory (DFT) The total energy of system is in the functional of density matrix expressed in single electronic state Single electron equation

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2.3 Helical spin order in BaFeO 3 Wave vector dependent total energy

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Summary This is a simple introduction about the spin order in correlated electron system. 1. The form of the wave function 2. DFT calculation

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