Can Spin Waves Explain Magnetization?

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Magnetization is defined as the magnetic dipole moment per unit volume, with spin magnetic moments playing a crucial role in ferromagnetic materials. Spin waves, or magnons, are believed to influence the total magnetization by causing fluctuations. The discussion seeks further resources for studying the relationship between magnetization and magnons. Recommended readings include "Introduction to Magnetism and Magnetic Materials" by David Jiles and "Spin Waves: Theory and Applications" by Helmut Schultheiss and Burkard Hillebrands. Understanding these concepts is essential for deeper insights into magnetization dynamics.
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Homework Statement
There is a question on effect of magnons on magnetization M of a ferromagnet material

How magnons affect magnetization in a ferromagnet -
(A) increase magnetization
(B) decrease magnetization
(C) Stabilize the magnetization
(D) Cause critical magnetic fluctuation
Relevant Equations
Magnons in ferromagnets are spin waves.
As per my understanding, magnetization is magnetic dipole moment per unit volume and spin magnetic moment contributes to magnetization of the ferromagnetic material under consideration.

Magnons, aka Spin Waves, according to this understanding will fluctuate the total magnetization of the materialz is it correct ?

More generally speaking, I would be very thankful if someone can point out/suggest detailed topic or resource recommendation for study of magnetization during magnons.

Thank you.
 
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Some good resources to begin with include:

  1. "Introduction to Magnetism and Magnetic Materials" by David Jiles
  2. "Spin Waves: Theory and Applications" by Helmut Schultheiss and Burkard Hillebrands
  3. "Spin Dynamics: Basics of Nuclear Magnetic Resonance" by Malcolm Levitt
 
I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW

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