Can't crystal of simple lattice be antiferromagnetic?

[zhanhai]

Is it correct that a crystall of simple lattice (lattice with primitive cells each having only one atom) cannot be antiferromagnetic? In other words, the antiparallelism must occur between atoms within each primitive cell.

Thanks.

 

[DrDu]

I don't think so, if not, the whole buzz about magnetic space groups would be useless. But this may also be a matter of pure definition: I.e., you may insist in that a translation which maps an atom with spin up onto an atom with spin down is not a true symmetry operation of the ordinary space group. In fact, you have to combine a unitary translation with a time inversion to convert spin up into spin down, so this is not an element of an ordinary space group. Hence if you are only admitting unitary operators as symmetry elements, as in ordinary space groups, then you have to consider a larger basis, while if you use magnetic space groups, which also include non-unitary group elements, then you can use a smaller basis with atoms with different spins being in different unit cells.

 

[M Quack]

BCC Chromium?

http://www.fys.ku.dk/~jjensen/Book/fawcett.pdf

 

[HeavyMetal]

Please correct me if I'm wrong, but isn't BCC not considered in this scenario? Its not a simple (primitive) cubic lattice...BCC is, by definition, two interpenetrating simple cubic lattices. I believe the original question dealt with the primitive cubic lattice (one atom per unit cell), in which case DrDu gave the same answer I would give.

 

[DrDu]

Please correct me if I'm wrong, but isn't BCC not considered in this scenario? Its not a simple (primitive) cubic lattice...BCC is, by definition, two interpenetrating simple cubic lattices. I believe the original question dealt with the primitive cubic lattice (one atom per unit cell), in which case DrDu gave the same answer I would give.

The BCC lattice is a Bravais lattice. Hence in Chromium, there is only one atom per primitive unit cell. So I am with M Quack, here.
https://commons.wikimedia.org/wiki/File:Cubic_cI_and_primitive_cell.png

 

[HeavyMetal]

Just to clarify: are you saying that its Bravais lattice is BCC with a two-atom basis, but that there still exists a [rhombohedron] primitive cell which contains only one atom?

 

[DrDu]

I am saying that the cubic cell which contains two atoms is not primitive.
You can generate a chromium crystal as either a primitive cubic lattice spanned by translation of the non-primitive two-atom basis, or as a bcc lattice obtained by translating the primitive one-atom basis.

 

[M Quack]

Same reply as in another thread:
The reason the non-primitive cubic unit cell is used in BCC and FCC is that this makes the (cubic) symmetry of the system totally obvious. This is not the case for the primitive unit cells - the symmetry is of course the same, but it is not quite as easy to see.