Heisenberg ferromagnet ferromagnet Heisenberg model : - - PowerPoint PPT Presentation

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Heisenberg ferromagnet ferromagnet Heisenberg model : - - PowerPoint PPT Presentation

Jan 14, 2024 208 likes •292 views

Heisenberg ferromagnet ferromagnet Heisenberg model : nearest-neighbor ferromagnetic coupling conserved quantity mean field T c periodic boundary conditions Heisenberg ferromagnet ferromagnet Heisenberg equation of motion Tyablikov

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SLIDE 1

Heisenberg Heisenberg ferromagnet ferromagnet

model: nearest-neighbor ferromagnetic coupling conserved quantity

mean field Tc

periodic boundary conditions

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SLIDE 2

Heisenberg Heisenberg ferromagnet ferromagnet

equation of motion Tyablikov decoupling

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SLIDE 3

Heisenberg Heisenberg ferromagnet ferromagnet

decoupled equation of motion Fourier transformation:

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SLIDE 4

Heisenberg Heisenberg ferromagnet ferromagnet

spectrum of excitations

dynamical structure factor

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SLIDE 5

Heisenberg Heisenberg ferromagnet ferromagnet instability condition

instability condition

mean field

  • nsite equal-spin correlation function

fluctuation-dissipation theorem instability d=3 d= 1,2

Hohenberg Mermin-Wagner

fluctuation renormiert determine m(T)

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SLIDE 6

spin wave spin wave in in ferromagnet ferromagnet -

  • magnon

magnon

Heisenberg ferromagnet

ground state: excited state:

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SLIDE 7

spin wave spin wave in in ferromagnet ferromagnet -

  • magnon

magnon

excited state:

nearest neighbors of i

Fourier transformation

"spin hopping"

"moving particle"

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SLIDE 8

spin wave spin wave in in ferromagnet ferromagnet -

  • magnon

magnon

flip up probe flip down measurement

magnon