Spinors with Quantum Espresso

Note that c2x 2.41 or later is required for this example.

This example closely follows the Mn₃Sn Castep example, with just the differences highlighted.

Input Files

Mn3Sn.in

Note that QE describes the initial spins in terms of spherical co-ordinates r,θ,φ whereas Castep uses Cartesians x,y,z. Also QE regards atoms with different initials spins as being different species, albeit sharing pseudopotentials. C2x can convert between the .cell and .in formats.

I am generally confused by the wide choice of QE pseudopotentials. The ones below seem to work, although they may not be optimal for this problem.

$ curl -o Mn.UPF http://pseudopotentials.quantum-espresso.org/upf_files/Mn.rel-pbe-spn-kjpaw_psl.0.3.1.UPF
$ curl -o Sn.UPF http://pseudopotentials.quantum-espresso.org/upf_files/Sn.rel-pbe-dn-kjpaw_psl.1.0.0.UPF

Output

QE may then be run as usual.

  $ pw.x -n Mn3Sn.in > Mn3Sn.log &

It will take around a core-hour. Unlike Castep, QE will use symmetry for this calculation.

It reports total magnetisation

     total magnetization       =    -0.01     0.00    -0.00 Bohr mag/cell
     absolute magnetization    =    19.30 Bohr mag/cell

and also magnetisation per atom after some form of population analysis in a block containing text such as

     atom number    3 relative position :    0.4920   0.5727   0.1997
     charge :    13.692039
     magnetization :          3.038704    0.001398   -0.000000
     magnetization/charge:    0.221932    0.000102   -0.000000
     polar coord.: r, theta, phi [deg] :     3.038704   90.000000    0.026358

If both pwscf.xml and pwscf.save/charge-density are present, then one can run c2x as

$ c2x -sv --vec2force=Mn:1.37i pwscf.xml Mn3Sn.xsf

It reports

Data contain 3 components. Per component analysis:
  min=-2.70618 max=5.41896 sum=-6.61295 int=-0.011441 int|s|=12.8391
  min=-4.63401 max=4.69038 sum=1.60634 int=0.00277911 int|s|=11.4669
  min=-0.00648757 max=0.00648757 sum=-3.6533e-17 int=-6.32051e-20 int|s|=0.0223973
  with s as vector, min(|s|)=0.000040, max(|s|)=5.418967, int|s|=19.302143
  (integral is e per cell for charge and spin densities)
Sampling of vector data integrating over 1.370000A using 22 points radially
Mn at (0.8227,0.6613,0.2500) vector ( 3.1000, 0.0014,-0.0000) modulus 3.1000
Mn at (0.3387,0.6613,0.2500) vector (-1.5544,-2.6815, 0.0000) modulus 3.0994
Mn at (0.3387,0.1773,0.2500) vector (-1.5515, 2.6814, 0.0000) modulus 3.0979
Mn at (0.6613,0.8227,0.7500) vector (-1.5514, 2.6813, 0.0000) modulus 3.0978
Mn at (0.6613,0.3387,0.7500) vector (-1.5544,-2.6816, 0.0000) modulus 3.0996
Mn at (0.1773,0.3387,0.7500) vector ( 3.1001, 0.0014, 0.0000) modulus 3.1001

The total magnetisation of (-0.01, 0.00, 0.00) reported by QE corresponds to the integrals of (-0.011, 0.003, -6e-20) reported by c2x. The absolute magnetisation of 19.30 Bohr/cell corresponds to the c2x report of 19.302.

Mn3Sn with vector spin in Vesta

Above is show the resulting XSF file viewed in Vesta.