[Wien] Optimization of an spinel structure

Wed Nov 3 09:46:51 CET 2021

Hi Pablo,
You repeat about the structure what I already told (maybe too short), if you check the intenational tables of crystallography you will find that there are two set-ups of the origin possible (0,0,0) or (1/8,1/8,1/8) in space group 227.
Therfore, it is not unique if you give only the  numbers (x,y,z) but you need to give the Wyckoff position and/or which origin setup you use. This you do now.

x is already a free parameter of the structure in your case with origin at  (1/8,1/8,1/8), therefore the -min should find whether x is 1/4 or 1/4+delta, so far the non magnetic case.

My main concern, however, was not the structure but the antiferromagnetic set up and its symmetry assignment.

a) if the spin arrangement is known from experiment then you should use it, (Neutron diffraction, XMCD, etc.) 
b) Is it true that only one species carries a magnetic moment or contibute both, Fe and Mn (and eventually with small part also O) ?
c) was the measurement for the ground state or any excited state, if it was with any magnetic fields at non Zero temperature then it might be very different from your calculation.
d) for magnetic systems one cannot just use the "non-magnetic" space groups but one has to use the magnetic ones.
    ... as Laurence already told "If you have constructed the AFM correctly the structure will have the symmetry of the Coulomb field, not the magnetism."  The important thing is the end of the sentence: "not the magnetism" !!!

You assume a very fixed symmetry which may be far off from reality, in your case, the Mn atoms can not beome antiferromagnetically alligned as you have only 1 distinguished side.

One thing that you can do is to create the cubic cell using supercell, then you fill find that there are much mor possibillities to have an antiferromagnetic arrangement.
Note, the direction of the magnetic moments must not be a long a cube axis [001] but may be along the space diagonal [111], which will result in different symmetry, too.

You tell the problem how it has to look like (tetragonal) and then you wonder that it does not agree with you (cubic) because it takes you serious.
... are you sure it is cubic or was this just an interpretation of experimental data that used a cubic model to explain the data where the atoms (not the magnetic moments) are sitting ?
again:     ... as Laurence already told "If you have constructed the AFM correctly the structure will have the symmetry of the Coulomb field, not the magnetism." !!!

Anyway, if the actual magnetic order is different from that what you use in the calculation, what do you like to learn ?
That was my question.

My other doubt is, that you select different x parameters but I would say if you have differnt results, then it's numerics or something is wrong with Wien2k
(I did many structure optimizations starting from different position parameters but the result for the relaxed structure was always the same within numerics, if I did not make the mistake).
... or do you try to use the result that you like most and forget about which is the relaxed one.

Youre misunderstanding is probably that you try to tell the system what it has to be, instead of asking what it is. 

Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Physics
Johannes Gutenberg - University
55099 Mainz
________________________________________
Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von delamora [delamora at unam.mx]
Gesendet: Mittwoch, 3. November 2021 04:40
An: A Mailing list for WIEN2k users
Betreff: Re: [Wien] Optimization of an spinel structure

Trying to answer your comments;
SG227 is FCC, that is, the conventional cell has 4 primitive cells
the first wyckoff positions are;
8a  1/8,1/8,1/8
8b  3/8,3/8,3/8

16c  0,0,0
16d  1/2,1/2,1/2

32e  x,x,x

8a and 8b have 2 atoms in the primitive cell
16c and 16d have 4
32e has 8

MnFe2O4 is a spinel
Mn; 8a
Fe; 16d
O; 32e  x=0.2639
The primitive cell has 2 formula units while the conventional cel has 8 formula units

then the atomic positions in  MnFe2O4.struct are;
F   LATTICE,NONEQUIV.ATOMS:  3 227_Fd-3m

 16.059466 16.059466 16.059466 90.000000 90.000000 90.000000

ATOM   1: X=0.12500000 Y=0.12500000 Z=0.12500000
ATOM   1:X= 0.87500000 Y=0.87500000 Z=0.87500000
Mn         NPT=  781  R0=0.00005000 RMT=    1.8600   Z: 25.000

ATOM  -2: X=0.50000000 Y=0.50000000 Z=0.50000000
ATOM  -2:X= 0.50000000 Y=0.75000000 Z=0.75000000
ATOM  -2:X= 0.75000000 Y=0.75000000 Z=0.50000000
ATOM  -2:X= 0.75000000 Y=0.50000000 Z=0.75000000
Fe         NPT=  781  R0=0.00005000 RMT=    2.1500   Z: 26.000

ATOM  -3: X=0.26390000 Y=0.26390000 Z=0.26390000
ATOM  -3:X= 0.73610000 Y=0.73610000 Z=0.73610000
ATOM  -3:X= 0.73610000 Y=0.51390000 Z=0.51390000
ATOM  -3:X= 0.26390000 Y=0.98610000 Z=0.98610000
ATOM  -3:X= 0.98610000 Y=0.98610000 Z=0.26390000
ATOM  -3:X= 0.51390000 Y=0.51390000 Z=0.73610000
ATOM  -3:X= 0.51390000 Y=0.73610000 Z=0.51390000
ATOM  -3:X= 0.98610000 Y=0.26390000 Z=0.98610000
O          NPT=  781  R0=0.00010000 RMT=    1.6000   Z:  8.000

Now, if one wants to make it antiferro then one posibility is to take two Fe 'up' and two 'dn', and the system becomes;

B   LATTICE,NONEQUIV.ATOMS:  5 74_Imma

 11.355757 11.355757 16.059466 90.000000 90.000000 90.000000

ATOM   1: X=0.00000000 Y=0.25000000 Z=0.12500000
ATOM   1:X= 0.00000000 Y=0.75000000 Z=0.87500000
Mn         NPT=  781  R0=0.00005000 RMT=    1.8600   Z: 25.000

ATOM   2: X=0.25000000 Y=0.75000000 Z=0.25000000
ATOM   2:X= 0.25000000 Y=0.25000000 Z=0.75000000
Fe1        NPT=  781  R0=0.00005000 RMT=    2.1500   Z: 26.000

ATOM   3: X=0.00000000 Y=0.52780000 Z=0.26390000
ATOM   3:X= 0.00000000 Y=0.47220000 Z=0.73610000
ATOM   3:X= 0.00000000 Y=0.02780000 Z=0.73610000
ATOM   3:X= 0.00000000 Y=0.97220000 Z=0.26390000
O 1        NPT=  781  R0=0.00010000 RMT=    1.6000   Z:  8.000

ATOM   4: X=0.77780000 Y=0.75000000 Z=0.48610000
ATOM   4:X= 0.22220000 Y=0.25000000 Z=0.51390000
ATOM   4:X= 0.77780000 Y=0.25000000 Z=0.51390000
ATOM   4:X= 0.22220000 Y=0.75000000 Z=0.48610000
O 2        NPT=  781  R0=0.00010000 RMT=    1.6000   Z:  8.000

ATOM   5: X=0.00000000 Y=0.00000000 Z=0.50000000
ATOM   5:X= 0.00000000 Y=0.50000000 Z=0.50000000
Fe2        NPT=  781  R0=0.00005000 RMT=    2.1500   Z: 26.000

As it can be seen the 8 O atoms in 32e position are now in two groups of 4 O atoms
and as I mentioned before the 'runsp -min' will move them in a way that it would break the cubic FCC crystal symmetry.
The problem is that Fe in this system has the kagome arangement and antiferro ordering is just a simplification, but the system should be cubic with the SG 227.

Saludos

Pablo
________________________________
De: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> en nombre de Fecher, Gerhard <fecher at uni-mainz.de>
Enviado: martes, 2 de noviembre de 2021 05:07 a. m.
Para: A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
Asunto: Re: [Wien] Optimization of an spinel structure

Sorry,
it depends on the setting for space group 227 whether X=1/4 results in a  8- or 32-fold degenerate position, I did not check which one Wien2k uses (unfortunately one can not use crystallographic Wykoff positions directly).
if you have already the 32-fold degenerate site  (I guess wien2k reports a smaller cell with 8 sites)  then min should find the correct positions by minimizing the forces.

The remarks on the magnetic order are not touched by that.

Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Physics
Johannes Gutenberg - University
55099 Mainz
________________________________________
Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von delamora [delamora at unam.mx]
Gesendet: Dienstag, 2. November 2021 04:49
An: wien at zeus.theochem.tuwien.ac.at
Betreff: [Wien] Optimization of an spinel structure

Dear WIEN community,
I am trying to optimize a spinel structure.
The normal spinel AB2X4 is FCC with SG 227
A: 1/8,1/8,1/8
B: 1/2,1/2,1/2
X: x,x,x  x~1/4
so it has 2 free parameters; 'volume' and 'x,x,x'
but in my cases B is magnetic and it has antiferromagnetic coupling, B also forms the 3D Kagome structure so it is geometrically frustrated.
The volume optimization can be easily done with option 'optimize'
but for the 'x' parameter there is a problem;
To treat the magnetism the best option, in my opinion, is to put half of the B atoms 'up' and the other half 'dn', there are 4 in the primitive cell, so 2 are 'up' and 2 'dn'.
With this, then the FCC cell becomes BCC (SG 74 Imma) and the 8 'X' atoms that were in one wyckoff position are now in two wyckoff positions with 4 atoms in each.
So, if the forces are minimized, 'runsp -min', will move these two 'X' groups in directions that will break the original cubic symmetry.
One posibility is to make 4 'struct' files, in the original SG 227, with slightly different 'x' positions, for example, the initial x,x,x is;
x= 0.254, so I make 4 struct files with; 0.251, 0.253, 0.255, 0.257
after this one should make them antiferromagnetic (SG 74 Imma) then run them separatelly, then one can obtain the optimum 'x' parameter.

I tried to use a modified 'optimize.job' but it did not work.
I also tried to run these 4 'struct' files in the same directory but I found that when I put the next case.struct into the directory, I had to initiate the system in order to be able to run them.

In other words, if I run the system with 1-struct, then for the next 2-struct I cannot just change 1-struct for 2-struct and run.
For the case of changes of volume then the optimize.job works fine, but for small changes in 'x' it does not work.

I anybody has an idea that would make this case simpler I would apreciate.
Thank you anyway

Pablo

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