Expert Answer to "How to derive ferromagnet Lagrangian from the Heisenberg..."

High School
Physics
Electromagnetism
Ferromagnetism

agrejas0hxpx

Answered question

2022-05-18

How to derive ferromagnet Lagrangian from the Heisenberg model:

H = - J_{i j} S_{i} S_{j}

? I understand how to obtain potential energy term, but it is not clear how to get "kinetic energy".

L = \int d^{2} x \frac{ρ}{2} [\frac{(\partial_{t} θ)^{2}}{v^{2}} - (\nabla θ)^{2}]

Answer & Explanation

pomastitxz27r

Beginner2022-05-19Added 16 answers

You only get an equation with a second-order time derivative for an antiferromagnet. If you have feromagnet there is only a first time derivative and you get a Landau-Lifshitz equation rather than a conventional wave equation. Deriving the antiferromagnetic equation is tricky.

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