About the order parameter in antiferromagnetism

[Hyla Brook]

Hello everyone,

As is known to all, the order parameter for the ferromagnetic case in the Landau expression is chosen as the magnetization. This is easy to understand. But for the antiferromagnetic case, what is the order parameter? People told me it was magnetic moment on the sublattice. But I think even if it is right, what is the difference in the Landau expansion between ferromagnetism and antiferromagnetism? They can be completely the same in expression. That is not easy to understand since they different kind of systems. So what is the key point of it? are there any references about this?

Thank you!

 

[Vanadium 50]

The order parameter is the staggered magnetization: each site has a sign associated with it. Then a Neel antiferromagnet "maps on" to an ordinary ferromagnet. Alternatively, the ferromagnet is the special case where the sign is +1 everywhere.

 

[Hyla Brook]

The order parameter is the staggered magnetization: each site has a sign associated with it. Then a Neel antiferromagnet "maps on" to an ordinary ferromagnet. Alternatively, the ferromagnet is the special case where the sign is +1 everywhere.

Thank you. Do you mean we need more than one order parameter? But, in the Landau expansion, because of the symmetry, the sign (positive or negative) doesn't bring about any difference.

 

[Vanadium 50]

No, I mean that instead of just being magnetization, it's magnetization * number, where the number depends on the lattice position. In antiferromagnetism, it alternates +1 and -1. In ferromagnetism, it is +1 everywhere.