Task 73 - integral value

[Andrew Shyichuk]

Dear Developers,

What should a 3D magnetization plot (task 73) sum up to?

If I have the " total moment" per cell about 1 - I expect the 3D magnetization plot to integrate to (roughly) the same value.

And, I know that for Elk 3D files, the integral over cell equals S * V / N, where S is the sum of values of the 3D file, V is cell volume and N is the number of points in the 3D file.
Or, which is the same, the integral is the sum times the voxel volume.

For my 3D files, I get the value of about 0.15, which coincides with the ratio between cubic Angstrom and cubic Bohr.

Is there any change that the magnetization density is written in the units of Angstrom^-3?

Best regards.
Andrew

[J. K. Dewhurst]

Dear Andrew,

Unless stated explicitly, all of Elk's output units are atomic.

Your formula is correct: if S is the sum of the data from MAG3D.OUT, then the moment in the unit cell should be S * V /N.

However, your sampling grid may not be sufficient for resolving the muffin-tin moment. Try increasing the plot3d grid and this should fix the problem.

Regards,
Kay.

[Andrew Shyichuk]

Dear Kay,

I've made a test on system with a 10.4 Angstrom side lengh and a 108x108x108 g-vector grid.
The integral as a function of the NxNxN 3D plot grid is:

 N   Integrated magnetization 
 20   5.5786380189537965
 27   2.6195550437733353 
 40   1.540586033524166
 54   1.207590381642519
 70   1.0877206831044655
108   1.0073521869283015
135   0.9908741650541215

The best result is obtained without the interpolation (when N_plot = N_g_vector), and the value is what it should be.

The bug was in my integration code: there was a conversion to Angstrom which I was not aware of.

Anyway, I am happy this piece of information is now public :)

Best regards.
Andrew