the SPIN-POLARIZED orientiation of GNR electrode

[njuxyh]

he SPIN-POLARIZED orientiation of GNR electrode

hi, recently, i have saw a paper appl.phys.lett.96.042104 (2010)
and in the artical, the spin orientation of the two GNR leads are set parallel and anti-parallel, only the two case.
my understanding is: left lead: top edge up,low edge up. right lead： top edge up,low edge up.
the anti-parallel is similar. am i right?
however as i know, aslo zh answered in Re: how can we set the value of " initial_scaled_spin", At least, you should consider two cases: i) the parallel spin configuration (i.e., ferromagnetic state) for the two edges of a graphene nanoribbon; ii) the anti-parallel spin configuration (anti-ferromagnetic state) the two edges of a graphene nanoribbon.   
therefore based upon zh answering, i think the spin orientation configure has much more.
for example left lead is top:up,low:up and right lead is top:up,low:down.
left lead is top:up,low:up and right lead is top:down,low:up.
left lead is top:up,low:down and right lead is top:up,low:down.
left lead is top:up,low:down and right lead is top:down,low:down
.........................
why the paper above only consider two of all configures?

[zh]

In the artical, the spin orientation of the two GNR leads are set parallel and anti-parallel,

Here "parallel" means that the spin configuration of the left electrode is same with that of the right electrode; "anti-parallel" means that the spin configuration of the left electrode is opposite to that of the right electrode.

For zigzag GNR, the antiferromagnetic state is slightly stable than the ferromagnetic state. Therefore, one configuration needs to be considered:

top:up,low:down

, or

top:down,low:up

[njuxyh]

thank you zh. i know it.