Why more K Points give a different magnetic State?

[zongtan_fang1]

Hi,

Just curious, what is the physics behind the relationship between K points and magnetic state?

For the system I am running, if I slowly increase K points, in a small range, the energy converges and the magnetic state remains the same; while there is a magnetic state change of the system with the mesh points over a certain value.

Interestingly, if I reoptimize the relaxed geometry ( with more K points) using less K points, I got the same magnetic state, which is different from the result with a different initial geometry and the same K points;

Thus, there may be two or more close states; why different K points may give different magnetic states ?

Thanks.

Best,

Zongtang

[henrique_miranda]

Hi,

This is not so much a matter of physics but one of numerics.

The magnetization is computed from:
- the difference between the up and down components of the density in the case of a collinear spin calculation
- from the 2x2 density matrix in the case of a non-collinear spin calculation

In either case the density depends on how well you describe the fermi surface of your system, i.e. which electronic states are ocuppied, partially occupied or empty. This depends on how well you are able to describe the electronic structure i.e. how many k-points you choose to sample the BZ.
Changing the type of smearing wiki/index.php/ISMEAR or its value wiki/index.php/SIGMA can also afect the computed magnetic moments. Small values of SIGMA normally require using a denser k-point grid. Increasing SIGMA too much might lead to unphysical results.

The total energy is in general less sensitive to these details and in general converges with less k-points.

Some advices and warnings:
- check that the k-points with respect to the quantity you want to obtain: converged energy does not necessarily mean converged magnetic moments
- the k-point convergence depends on the value of SIGMA (and of course the type of smearing ISMEAR).
- the ionic positions and cell volume/shape change the electronic structure and consequently the magnetic moments

Hope this helps

Kind regards,
Henrique Miranda

[zongtan_fang1]

Hi Henrique,

Thanks for you reply.

by the way, I am having another quick question, for a ferromagnetic system, what does a negative magnetic moment on Oxygen mean? Pretty big, ~ -0.7.

Does it mean AFM is more stable or huge spin delocalization ?

Best,

Zongtang

[henrique_miranda]

Sorry for my late reply.
It does not mean anything in particular.

If you are doing a collinear calculation you might have the spin pointing up or down (positive or negative values respectively).
If its a non-collinear calculation you will get a component which can be positive or negative in each direction.

To know whether you have anti ferromagnetic ordering or not you need to look into the other atoms in your system not to a single one.
Following a line of atoms you will have up down up down and so on...