How to optimize AFM and FM materials?

[wot19920302]

Dear Quantumwise staffs:
        I have some questions about calculating AFM or FM zigzag nanoribbon(mono H-passivated).
        I find that many papers calculate FM, AFM and NM sates total energy and compare their stabilities, but they all don't mention these three states structure optimizations. So I want to know how to optimize AFM, FM states zigzag nanoribbon?
I think there may be three ways:
       a)  relax unit cell using LDA and no initial spin state setting to get NM optimizd structure-->when we get optimized structure, select LSDA and set initial spin states(AFM, FM) to calculat total energy.  In this way, we don't particularly optimize structure using LSDA anfd initial spin state, just use NM structrues to calculate FM, AFM total energy.
       b)  relax unit cell using LSDA and setting initial spin state(AFM, FM)-->when we get optimized structure, select LSDA and set initial spin states(AFM, FM) to calculate total energy.  In this way, we first optimize structure using LSDA anfd initial spin state.
       c) relax unite cell using LDA  and no initial spin state setting to get NM optimizd structure--> relax unit cell  again using LSDA and setting initial spin state(AFM, FM)-->when we get optimized structures, select LSDA and set initial spin states(AFM, FM) to calculate total energy . In this way, we first get NM structure and use this structure to optimize FM and AFM structures then use second optimized structures to calculate total ernergy.
       Which one is correct?
     

     What's more, For FM zigzag nanoribbon,  we should set C atoms in 1st ,Mth row as 1, others as  0, or 1st,2nd, (M-1)th and Mth row as 1, others as 0?
                                For AFM zigzag nanoribbon, we should set C atoms in 1st, Mth row as 1, 2nd and (M-1)th row as -1, others as 0, is that ture?
       Attachment fig1 is zigzag nanoribbon     
       Hope for your guides 

[Ulrik G. Vej-Hansen]

I would say that both b) and c) are correct, and a) is probably a very good approximation. Personally, I would first do b) and then consider the other options if needed.

I am not familiar enough with magnetic properties of graphene to answer your second question decisively, but in general, the final spin-state in a spin-polarized calculations can depend on the initial state. So one option is to simply do both initial states and look at the results.

[wot19920302]

Dear Ulrik G. Vej-Hansen
       thanks for your help , so you think spin states have a little  influence on structure relaxtion-but not much, right?   

[Petr Khomyakov]

As a general recommendation, it is not a bad idea of first doing non-spin polarized calculation for a spin-polarized system, and then use it for further spin-polarized calculations.

[wot19920302]

Dear Petr Khomyakov ：
      sorry... I am confused 
       you said that we can use non-spin polarized  calculation first then  for a spin-polarized system.....       
     so you think plan a) maybe a pretty good way to perform  spin-dependent calculation?  because plan a)  frist  relax NM structure and then use NM state directly calculate spin-polarized system?
      or you think paln c) maybe  a good way ? because plan c) first optimize NM structure,then use it to relax AFM(FM) state and finally calculate spin-polarized system?
       two ways above both first use NM structure, I don't exactlly understand which one you prefer?
       Best

[zh]

For ziagzag graphene nanoribbon (ZGNR), its electronic structure is quite special because of the edge states.  The edge states are mostly localized at edge carbon (i.e., the first row carbon).

My experience for the setup of initial magnetic moment of ZGNR:
Set a maximal value (e.g., 1.0) for the spin polarization of the edge carbon (i.e., the first row carbon) at one edge, and the specify a negative value (e.g, -1.0) for the spin polarization of the edge carbon at the opposite edge.  This setup is enough to get the AFM spin configuration of ZGNR.

For the FM spin configuration, you can set the same maximal value the spin polarization of the edge carbon at both edges.

If you do the non-spin polarization calculations of ZGNR and plot the local DOS for states at the Fermi level, you can see the distribution of edge states on the carbon atoms. The weight of edge states on the 2nd row carbons (if noted as B site) is very small because the 2nd row carbon are the lattice sites different to the 1st row carbon atoms (noted as A site). The edge states extend to the same lattice carbon atom (A site) into the interior region of ribbon with a certain range.   

[wot19920302]

thanks for your explains, dear zh! very detailed and clearly!