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How to determine the Euler angle in Atoms.SpeciesAndCoordinates
Date: 2018/04/27 22:18
Name: lucky   <3033467121@qq.com>

Hi
Recently,I read the manual of OpenMX Ver. 3.8, I want to do Non-collinear DFT calculation , when I read the page of 116, I feel puzzled.
The manual is appeared the Euler angle theta and phi.
8:Euler angle, theta, of the magnetic field for spin magnetic moment
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Re: How to determine the Euler angle in Atoms.SpeciesAndCoordinates ( No.1 )
Date: 2018/04/27 22:29
Name: lucky  <3033467121@qq.com>

I am sorry,I do not complete the question,this is a completed question.

Hi
Recently,I read the manual of OpenMX Ver. 3.8, I want to do Non-collinear DFT calculation , when I read the page of 116, I feel puzzled.
The manual is appeared the Euler angle theta and phi.

8: Euler angle, theta, of the magnetic field for spin magnetic moment
9: Euler angle, phi, of the magnetic field for spin magnetic moment.Also, the 8th and 9th are used to generate the initial non-collinear
spin charge distribution
10. the Euler angle, theta, of the magnetic field for orbital magnetic moment
11. the Euler angle, phi, of the magnetic field for orbital magnetic moment

Now , I want to change to spin of Fe3+ cation,Choose any direction,but how to set up the theta and phi for Fe cation.I am so confused that the theta,which
it is of the magnetic field for spin magnetic moment,but I do not provide a magnetic field,I don't know how to find the angle of magnetic field and spin magnetic moment.
and the angle of magnetic field and spin orbital magnetic moment. I hope that you can help me and give me some suggestions.

Thank you

best wishes

lucky
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Re: How to determine the Euler angle in Atoms.SpeciesAndCoordinates ( No.2 )
Date: 2018/04/29 01:35
Name: Naoya Yamaguchi

Hi,

The parameters of the columns 8-13 are optional, and you can omit them if you don't apply some constraints (e.g. the Zeeman term; See also:
http://www.openmx-square.org/openmx_man3.8/node105.html
http://www.openmx-square.org/openmx_man3.8/node106.html
http://www.openmx-square.org/openmx_man3.8/node108.html
http://www.openmx-square.org/openmx_man3.8/node109.html
).

However, you should give the parameters of the column 8, 9 if you specify the initial directions of spin moments.

Regards,
Naoya Yamaguchi
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Re: How to determine the Euler angle in Atoms.SpeciesAndCoordinates ( No.3 )
Date: 2018/04/30 16:37
Name: lucky  <3033467121@qq.com>

Thank you, Naoya Yamaguchi.
I specify the initial directions of spin moments. But I have some difficulty when I give the parameter of the column 8,9. For instance,
The range of the value of the Euler of the Euler angle theta, phi. How do I change the angle(theta and phi) when I want to set up ferromagnetism(FM)
and antiferromagnetism(AFM) ? I read some document about Euler angle as https://en.wikipedia.org/wiki/Euler_angles .
I hope that you can give me some suggestions , reference or examples about Euler angle, FM and AFM. Thank you

Regards,
lucky
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Re: How to determine the Euler angle in Atoms.SpeciesAndCoordinates ( No.4 )
Date: 2018/04/30 18:19
Name: lucky  <3033467121@qq.com>

Dear all
Hi
I want to set up the spin of angle (theta and phi) for my Non-collinear DFT calculation.
Whether this angle should be measured must be counterclockwise?
Or the angle is just the smaller angle(theta and phi) between the Z axis and the spin magnetic moment?
I am so puzzled so much . I hope that you can help me a lot. Thank you.

Regards,
lucky

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Re: How to determine the Euler angle in Atoms.SpeciesAndCoordinates ( No.5 )
Date: 2018/05/01 12:09
Name: Naoya Yamaguchi

Hi,

The definition of the Euler angle is shown in the bottom of p.2 of a technical note about non-collinear spin density functional as follows:

Then, consider the following two-step rotation of a unit vector (1,0) along the z-axis:
First, rotate $\theta$ on the y-axis $\to \exp\left(-i
\frac{\sigma_2\theta}{2}
\right) $
Second, rotate $\phi$ on the z-axis $\to \exp\left(-i
\frac{\sigma_3\phi}{2}
\right) $

(See also the original technical note:
http://www.openmx-square.org/tech_notes/tech2-1_0/tech2-1_0.html (HTML ver.)
http://www.openmx-square.org/tech_notes/tech2-1_0.pdf (PDF ver.)
)


For your purpose, however, I think that the collinear DFT (i.e. "scf.SpinPolarization=ON") is enough if you don't use the non-collinear DFT (i.e. "scf.SpinPolarization=NC").

And, you can find an example of a FM system as a file "Febcc2.dat" in the directory "work". The parameters of the columns 6, 7 give the number of initial charges for the spin up and the spin down states of each atom, respectively (e.g. 8.0, 6.0 in the following).

<Atoms.SpeciesAndCoordinates
1 Fe 0.0000 0.0000 0.0000 8.0 6.0
2 Fe 0.5000 0.5000 0.5000 8.0 6.0
Atoms.SpeciesAndCoordinates>


In addition, you can get that of a AFM system by modifying as follows:

<Atoms.SpeciesAndCoordinates
1 Fe 0.0000 0.0000 0.0000 6.0 8.0
2 Fe 0.5000 0.5000 0.5000 8.0 6.0
Atoms.SpeciesAndCoordinates>

Regards,
Naoya Yamaguchi
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Re: How to determine the Euler angle in Atoms.SpeciesAndCoordinates ( No.6 )
Date: 2018/05/01 07:00
Name: Chi-Cheng Lee  <cclee.physics@gmail.com>

Dear lucky,

Besides Yamaguchi's information, I have something simple to mention.
I think the theta and phi for the orbital moments are the same as those for the spin moment, which you
already knew how to setup. They are based on the global xyz coordinate that is chosen for your system
when you define the unit cell vectors. The z-direction (magnetic direction) defined by the theta and phi angles
are simply the angle measured from z axis and x axis (counterclockwise), respectively. I guess everyone will
feel dizzy if the angles were more complicated than this.

Cheers,
Chi-Cheng
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Re: How to determine the Euler angle in Atoms.SpeciesAndCoordinates ( No.7 )
Date: 2018/05/05 18:02
Name: lucky  <3033467121@qq.com>

Dear Naoya Yamaguchi ,Chi-Cheng Lee
Thank you for your reply.I realize that Euler angle is similar to the angle1,angle2 of Quantum Espresso.
The range of theta in the range of 0 to 180 degrees. The theta does not need to be valued by counterclockwise.
The range of phi in the range of 0 to 360 degrees.
I agree with Naoya Yamaguchi about the concent of ferromagnetism.
Thank you.
Best wishes.

Lucky
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