## About the Magnetic Anisotropy Energy

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jctung

### About the Magnetic Anisotropy Energy

Hi,
Following with the user's guide of how to calculate the anisotropy energy, the resulting spin moment does not rotate with different setting of SAXIS. Why ?
In detail, I, first, do a spin-polarized calculation to get a CHGCAR. Then I have a noncollinear calculations with ICHARG = 11 and all those that needed. While I
analyse the OUTCAR, I found that the spin moment was kept in the z direction, merely the orbital moments changes with diferent SAXIS settings.
Last edited by jctung on Wed Aug 29, 2007 6:55 am, edited 1 time in total.

Posts: 2922
Joined: Tue Aug 03, 2004 8:18 am

### About the Magnetic Anisotropy Energy

most probably, the system converged into the magnetically stable solution in all cases. Please make use of the possibility to explicitely constrain the direction of the magnetic moments (corresponding INCAR-tags: I_CONSTRAINED_M, LAMBDA, M_CONSTR, RWIGS)
Last edited by admin on Thu Aug 30, 2007 7:31 am, edited 1 time in total.

jctung

### About the Magnetic Anisotropy Energy

Maybe I did not post my question clearly. Here I will talk about it in detail.
First, I have a charge density of my systems in spin-polarized calculations. Then, according to the user's manual, I must use the following settings to have the magnetic anisotropy energy.
MAGMOM: 0 0 X( spin moments here)
NBANDS = 2*(valuse from SP claculation)
SAXIS = 0 0 1
ICHARGE = 11
LSORBIT = .TRUE.
LNONCOLLINEAR = .TRUE.
Then perform a noncollinear calculations. After that, we can only change the setting of SAXIS to 100 and do a noncollinear calculation again. The total energy differences in these two calculations will gives us a MAE.
The question is, the resulting spin moments is always pointed in z directions no matter what SAXIS (001, or 100) are. We check every Iteration in OUTCAR, in both SAXIS = 001 or SAXIS = 100.
It is strange, we are comparing the energy differences in different magnetic orientations, and the programs have the same directions of magnetic moment. Furthermore, the resulting orbital moments is different. When the SAXIS = 0 0 1, the resulting orbital moment might be pointed in z direction. And when SAXIS = 1 0 0, the resulting orbital moment might be pointed in x direction.
Or I should constrain the magnetic moment is such a calculation ?
Last edited by jctung on Thu Aug 30, 2007 9:08 am, edited 1 time in total.

vasp16888
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Posts: 44
Joined: Fri Apr 23, 2010 3:09 am

### About the Magnetic Anisotropy Energy

NBANDS = 2*(valuse from SP claculation)
SAXIS = 0 0 1
ICHARGE = 11
LSORBIT = .TRUE.
LNONCOLLINEAR = .TRUE.
Then perform a noncollinear calculations. After that, we can only change the setting of SAXIS to 100 and do a noncollinear calculation again. The total energy differences in these two calculations will gives us a MAE.
The question is, the resulting spin moments is always pointed in z directions no matter what SAXIS (001, or 100) are. We check every Iteration in OUTCAR, in both SAXIS = 001 or SAXIS = 100.
It is strange, we are comparing the energy differences in different magnetic orientations, and the programs have the same directions of magnetic moment. Furthermore, the resulting orbital moments is different. When the SAXIS = 0 0 1, the resulting orbital moment might be pointed in z direction. And when SAXIS = 1 0 0, the resulting orbital moment might be pointed in x direction.
Or I should constrain the magnetic moment is such a calculation ?
same magnetizaion direction as you said after the two non-scf(ICHARG =11, SAXIS=001 and SAXIS=111), and the total energy E001 and E111 are exactly same. I am confused:(
And I don't think this way really works for MAE. Hope 'admin' can give us some clues, thanks:)
Last edited by vasp16888 on Tue May 25, 2010 6:41 pm, edited 1 time in total.
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kdmiller
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Joined: Tue Aug 04, 2020 6:45 pm

### Re: About the Magnetic Anisotropy Energy

Sorry to revive a long-dead post but I just had this exact same issue. My magnetic moments are also ending up pointing strictly in z-direction regardless of my SAXIS initialization.
Does this indicate that any SAXIS other than 001 is unstable?
Did anyone find a fix for this?
Did you end up constraining the direction?

henrique_miranda
Global Moderator
Posts: 234
Joined: Mon Nov 04, 2019 12:41 pm
Contact:

### Re: About the Magnetic Anisotropy Energy

Hi,

This is indeed an old post but no problem!
Without constraining the magnetic moments the SCF cycle might converge to the lowest energy configuration.
You might need to force the different magnetic moment alignements with a contrained magnetic moments calculation to obtain the different total energies and then compute MCA.

For details about how to proceed with these calculation refer to out wiki tutorial:
https://www.vasp.at/wiki/wiki/index.php ... Anisotropy

For a contrained magnetic moments calculation refer to these VASP variables:
https://www.vasp.at/wiki/index.php/I_CONSTRAINED_M
https://www.vasp.at/wiki/index.php/LAMBDA
https://www.vasp.at/wiki/index.php/M_CONSTR
https://www.vasp.at/wiki/index.php/RWIGS

PS: Note that a bug related to the constrained magnetic calculations was present in vasp 6.1.0 and vasp 6.1.1
This bug is not present in vasp 5.X.X

boyoungzheng
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Posts: 2
Joined: Mon Nov 18, 2019 3:35 pm

### Re: About the Magnetic Anisotropy Energy

Wait, isn't the "z-direction" here means the SAXIS direction? Therefore, the "z-direction" for SAXIS=1 0 0 is actually the x-direction in Cartesian coordinates.

henrique_miranda
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Posts: 234
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Contact:

### Re: About the Magnetic Anisotropy Energy

Sorry for my late reply but I am not sure I understand you last post.
The SAXIS defines a basis of vectors and the transformations to and from cartesian coordinates are documented here:
wiki/index.php/SAXIS

Changing SAXIS means you change how you measure your magnetization.
This applies to both the initial magnetic moments set by MAGMOM but also the final results.
If you are changing only SAXIS you might also start from a different intial magnetic moment in cartesian coordinates.
This might lead to a different final magnetic moment in cartesian coordinates that has the same component in the SAXIS basis.

boyoungzheng
Newbie
Posts: 2
Joined: Mon Nov 18, 2019 3:35 pm

### Re: About the Magnetic Anisotropy Energy

Thanks for the reply. And sorry for this late replay (For some reason, I don't get any notifications for updates in this thread...).
What I mean 'the "z-direction" here means the SAXIS direction' is my understanding of 'the spin is assumed to be parallel to SAXIS (hence VASP will initially report a magnetic moment in the z-direction only)' in https://www.vasp.at/wiki/index.php/SAXIS. Essentially, 'a magnetic moment in the z-direction only' <==> 'spin parallel to SAXIS'.

To reply to what you said on Aug 18, the most confusing part is that
https://www.vasp.at/wiki/index.php/Dete ... Anisotropy
this tutorial does not mention "contrained magnetic moments calculation" at all.

Should it be updated?

henrique_miranda
Global Moderator
Posts: 234
Joined: Mon Nov 04, 2019 12:41 pm
Contact:

### Re: About the Magnetic Anisotropy Energy

What I mean 'the "z-direction" here means the SAXIS direction' is my understanding of 'the spin is assumed to be parallel to SAXIS (hence VASP will initially report a magnetic moment in the z-direction only)' in https://www.vasp.at/wiki/index.php/SAXIS. Essentially, 'a magnetic moment in the z-direction only' <==> 'spin parallel to SAXIS'.
Yes, this is correct
To reply to what you said on Aug 18, the most confusing part is that
https://www.vasp.at/wiki/index.php/Dete ... Anisotropy
this tutorial does not mention "constrained magnetic moments calculation" at all.

Should it be updated?
Yes, it should definitely be updated.
We will work on a new tutorial specific to the computation of MAE.

To expand a bit on my previous answer.
There are two approaches to compute the MAE:

1. non-self consistent calculation described here:
https://www.vasp.at/wiki/wiki/index.php ... Anisotropy
In this case, you perform a computation of charge in the collinear version of VASP and then compute the energy in the non-collinear version in a non-self-consistent way for different orientations of the spin.

2. self-consistent calculation described here:
https://www.vasp.at/wiki/wiki/index.php ... t_Coupling
In this case, you perform the computation self-consistently for different spin orientations.
This is the approach you were likely using. In this case, and without constraining the magnetic moments the SCF cycle might converge to the spin configuration that yields the lowest energy. This makes these results unusable to compute MAE since you would like to have the energies for different spin configurations.
That's where the advice of constraining the magnetic moments comes into play.
Here is a tutorial about how to do that: https://www.vasp.at/wiki/index.php/Cons ... ic_moments

But when using this approach be careful!
To constrain the magnetization you are effectively adding an energy penalty proportional to https://www.vasp.at/wiki/index.php/LAMBDA to configurations where the magnetic moment is not aligned to your constrain.
You should make sure that the difference in energy from the different magnetic configurations does not stem from this LAMBDA value, i.e. it should be made small.
The details are explained here: https://www.vasp.at/wiki/index.php/I_CONSTRAINED_M

Hope this helps