Constant for different types of lattices

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Discussion Overview

The discussion revolves around a constant related to exchange integrals in different types of lattices, specifically focusing on its value for simple cubic lattices and the implications of these integrals on magnetic properties. The context includes theoretical considerations regarding the dependence of exchange integrals on band structure and lattice characteristics.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant presents a formula for a constant C related to exchange integrals in k-space and provides a specific value for simple cubic lattices.
  • Another participant expresses surprise at the existence of a universal constant for simple cubic lattices, questioning the independence of this constant from lattice parameters and atomic types.
  • The same participant notes that J(0) favors ferromagnetism, while J(k) for k ≠ 0 suggests antiferromagnetism with a modulation wave vector k.
  • Additional participants reference external papers for further context or information.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there are differing views on the universality of the constant and its dependence on various factors related to the lattice structure.

Contextual Notes

The discussion highlights potential limitations regarding the assumptions made about the exchange integrals and their dependence on specific lattice characteristics, which remain unresolved.

LagrangeEuler
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##C=\frac{1}{N}\sum_{\vec{k}} \frac{J(0)}{J(0)-J(\vec{k})} ##
##J(\vec{k})## is exchange integral in ##\vec{k}## space. What is the name of this constant and where I can find more about it?

For simple cubic lattice
##C_{SC}=1.516##
 
Last edited:
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Can you provide a bit more context?

Exchange integrals usually depend on details of the band structure, so I am surprised that you can get a universal constant for all simple cubic lattices irrespective of lattice constant, atomic flavor etc.

J(0) would favor ferromagnetism

J(k) with k != 0 would favor antiferromagnetism with a modulation wave vector k.
 
See this paper.
 

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Or here.
 

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