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**Spin order in correlated electron systems**

Yukawa Institute for Theoretical Physics Zhi Li

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**Outline Variety of spin order in condensed matter**

1.1 Collinear spin order 1.2 Non-collinear spin order Theory and calculation 2.1 The form of wave function 2.2 Introduction about DFT calculation 2.3 Helical spin order in BaFeO3 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, Fe3O4, 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 BaFeO3**

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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