# A Can't crystal of simple lattice be antiferromagnetic?

1. Apr 11, 2016

### 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.

2. Apr 11, 2016

### 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.

3. Apr 11, 2016

### M Quack

4. Apr 14, 2016

### 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.

5. Apr 15, 2016

### DrDu

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

6. Apr 15, 2016

### 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?

7. Apr 15, 2016

### 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.

8. Apr 15, 2016