Why is the dispersion relation of magnons quadratic in k for small wavelengths?

[PLuz]

Hello,

Can anyone explain to me why, concept wise (not from calculations that I get it), is the dispersion relation of magnons (spin waves) quadratic in $k$ for small wavelengths?

Also, can you give me other examples where such behavior appears?

Thank you

 

[DrDu]

See 5.5.Y here:

http://people.ccmr.cornell.edu/~clh/p654/5.5.pdf