[Pw_forum] Non-collinear magnetism and the parameter angle1(i)

[Juan Manuel Ramírez de Arellano]

Dear all:

We are trying to make a calculation on a hypothetical Gd system consisting
of connected Gd tetrahedra, which, as units, would have the diamond
structure. This structure would have the 3D version of the Kagomé lattice.
The Gd-Gd interaction is antiferromagnetic. One possible arrangement is
having all the magnetic moments pointing either towards the center or away
of the center, so the crystal would have one tetrahedron with the moments
pointing to the center and the next one pointing out, making an 'in-out'
arrangement.

For this magnetic structure we tried a non-collinear calculation using a
unit cell of four Gd atoms, with the magnetic moment of the top atom
pointing up and that of the other three atoms pointing down. We expected
that the down pointing moments would eventually end out pointing away from
the center of the tetrahedron, in which case the magnetic moments would
make an angle of 109 degrees between them.

But we have tried different initial values for the angle with respect to
the z axis for these three atoms, and our problem is that the angles barely
move at the end of the calculation. We've considered initial angles of
angle1(i) = 100, 120 and 160° relative to the up-pointing moment but in
each case the final value of that angle changes only slightly. Maybe the
program is not optimizing this parameter?

We have read different posts in this forum concerning non-collinear
magnetism, and we tried different values for the "degauss" and "k-points"
parameters too, as indicated there. Our results are the same, though. So,
is our non-collinear magnetic calculation working? Are we using the correct
parameters?

Thanks in advance. Hopefully you can give us a piece of advice about our
problem, which will be greatly appreciated. We're using Quantum Espresso
version 5.0.2-d-mpi and below we included one of our input files using
angle1(i) = 120°:

*&control
    calculation='scf',
    pseudo_dir = './',
    outdir='./tmp'
    !verbosity = 'high',
    prefix='Gd-piro-scf-noncol-v4',
/
 &system
    ibrav=  5, celldm(1)=9.44863,
    celldm(4)=0.5,
    nat=  4, ntyp= 4,
    ecutwfc = 30.0,
    occupations='smearing', smearing='mp', degauss=0.02,
    nosym=.TRUE.,
    starting_magnetization(1)= 0.6
    starting_magnetization(2)= 0.6
    starting_magnetization(3)= 0.6
    starting_magnetization(4)= 0.6
    angle1(1)=0.0
    angle2(1)=0.0
    angle1(2)=120.0
    angle2(2)=0.0
    angle1(3)=120.0
    angle2(3)=120.0
    angle1(4)=120.0
    angle2(4)=240.0
    noncolin=.true.,
    nbnd = 56,
 /
 &electrons
    mixing_beta = 0.5
    conv_thr = 1.0e-4,
 /
ATOMIC_SPECIES
 Gd1  1.  Gd.pbe-mt_fhi.UPF
 Gd2  1.  Gd.pbe-mt_fhi.UPF
 Gd3  1.  Gd.pbe-mt_fhi.UPF
 Gd4  1.  Gd.pbe-mt_fhi.UPF
 ATOMIC_POSITIONS crystal
 Gd1 0.5  0.5  0.5
 Gd2 0.0  0.5  0.5
 Gd3 0.5  0.0  0.5
 Gd4 0.5  0.5  0.0
K_POINTS automatic
12 12 12 1 1 1*

And here's part of the output file, giving the final polar coordinates of
the magnetic moments:

*
 ==============================================================================
     atom number    1 relative position :    0.0000  -0.0000   1.2247
     charge :     7.543134
     magnetization :          0.000653   -0.001747    6.294888
     magnetization/charge:    0.000087   -0.000232    0.834519
     polar coord.: r, theta, phi [deg] :     6.294889    0.016974
 -69.491031

 ==============================================================================

 ==============================================================================
     atom number    2 relative position :   -0.2500   0.1443   0.8165
     charge :     7.538805
     magnetization :          5.399085   -0.003164   -3.202229
     magnetization/charge:    0.716173   -0.000420   -0.424766
     polar coord.: r, theta, phi [deg] :     6.277292  120.672421
-0.033581

 ==============================================================================

 ==============================================================================
     atom number    3 relative position :    0.0000  -0.2887   0.8165
     charge :     7.535512
     magnetization :         -2.699082    4.673208   -3.200589
     magnetization/charge:   -0.358182    0.620158   -0.424734
     polar coord.: r, theta, phi [deg] :     6.274368  120.670857
 120.009226

 ==============================================================================

 ==============================================================================
     atom number    4 relative position :    0.2500   0.1443   0.8165
     charge :     7.533559
     magnetization :         -2.695245   -4.673544   -3.200622
     magnetization/charge:   -0.357765   -0.620363   -0.424849
     polar coord.: r, theta, phi [deg] :     6.272985  120.678693
-119.972156

 ==============================================================================
*

-- 
Dr. Juan Manuel Ramirez de Arellano
email: radear82 at gmail.com
Facultad de Ciencias, Taller de Estado Sólido Computacional,
Universidad Nacional Autónoma de México,
04510, Ciudad Universitaria, D.F., México.
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