# Generate all the possible multipole expansion for magnetic structures at Gamma point
crystod-mag -c 221_PPOSCAR_AlNi3 --element Ni --qpoint 0 0 0 --format vasp

* Structure *
  Space group: Pm-3m (#221)
  Magnetic sites: Ni x 3
    Ni1: [0.5, 0.5, 0.0]
    Ni2: [0.5, 0.0, 0.5]
    Ni3: [0.0, 0.5, 0.5]

* Selected Q point *
  Selected q-point: GAMMA = [0.0, 0.0, 0.0]

* Spin (axial-vector) representation *
  Spin (axial-vector) representation on Ni sites: 9 dimensions
  Decomposition: 2 x GM4+(3) + GM5+(3)

* Symmetry-adapted spin bases *
  GM4+(3): dim 3 [FM, dipole]
  GM4+(3): dim 3 [AFM, octupole]
  GM5+(3): dim 3 [AFM, octupole]

* GM4+(3) [FM, dipole] *
  component z:
    Ni1: S = [ 0.0000,  0.0000,  1.0000]
    Ni2: S = [ 0.0000,  0.0000,  1.0000]
    Ni3: S = [ 0.0000,  0.0000,  1.0000]
    net moment: [0.0, 0.0, 3.0]
    magnetic space group: P4/mm'm' (BNS 123.345, type III), 16 operations, 8 with time reversal
    magnetic point group: 4/mm'm'
    allowed by symmetry: net magnetization along z; linear magnetoelectric effect none; piezomagnetism 3 components
    collinear order: ferromagnet
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 1.0000]
      Ni3: [0.0000, 0.0000, 1.0000]
      Ni4: [0.0000, 0.0000, 1.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 1.0000   0.0000 0.0000 1.0000   0.0000 0.0000 1.0000
  component x:
    Ni1: S = [ 1.0000,  0.0000,  0.0000]
    Ni2: S = [ 1.0000,  0.0000,  0.0000]
    Ni3: S = [ 1.0000,  0.0000,  0.0000]
    net moment: [3.0, 0.0, 0.0]
    magnetic space group: P4/mm'm' (BNS 123.345, type III), 16 operations, 8 with time reversal
    magnetic point group: 4/mm'm'
    allowed by symmetry: net magnetization along x; linear magnetoelectric effect none; piezomagnetism 3 components
    collinear order: ferromagnet
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [1.0000, 0.0000, 0.0000]
      Ni3: [1.0000, 0.0000, 0.0000]
      Ni4: [1.0000, 0.0000, 0.0000]
    MAGMOM = 0 0 0   1.0000 0.0000 0.0000   1.0000 0.0000 0.0000   1.0000 0.0000 0.0000
  component y:
    Ni1: S = [ 0.0000,  1.0000,  0.0000]
    Ni2: S = [ 0.0000,  1.0000,  0.0000]
    Ni3: S = [ 0.0000,  1.0000,  0.0000]
    net moment: [0.0, 3.0, 0.0]
    magnetic space group: P4/mm'm' (BNS 123.345, type III), 16 operations, 8 with time reversal
    magnetic point group: 4/mm'm'
    allowed by symmetry: net magnetization along y; linear magnetoelectric effect none; piezomagnetism 3 components
    collinear order: ferromagnet
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 1.0000, 0.0000]
      Ni3: [0.0000, 1.0000, 0.0000]
      Ni4: [0.0000, 1.0000, 0.0000]
    MAGMOM = 0 0 0   0.0000 1.0000 0.0000   0.0000 1.0000 0.0000   0.0000 1.0000 0.0000
  component 111:
    Ni1: S = [ 0.5774,  0.5774,  0.5774]
    Ni2: S = [ 0.5774,  0.5774,  0.5774]
    Ni3: S = [ 0.5774,  0.5774,  0.5774]
    net moment: [1.732051, 1.732051, 1.732051]
    magnetic space group: R-3m' (BNS 166.101, type III), 12 operations, 6 with time reversal
    magnetic point group: -3m'
    allowed by symmetry: net magnetization along [111]; linear magnetoelectric effect none; piezomagnetism 4 components
    collinear order: ferromagnet
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [0.5774, 0.5774, 0.5774]
      Ni3: [0.5774, 0.5774, 0.5774]
      Ni4: [0.5774, 0.5774, 0.5774]
    MAGMOM = 0 0 0   0.5774 0.5774 0.5774   0.5774 0.5774 0.5774   0.5774 0.5774 0.5774

* GM4+(3) [AFM, octupole] *
  component z:
    Ni1: S = [ 0.0000,  0.0000,  1.0000]
    Ni2: S = [ 0.0000,  0.0000, -0.5000]
    Ni3: S = [ 0.0000,  0.0000, -0.5000]
    net moment: [0.0, 0.0, -0.0]
    magnetic space group: P4/mm'm' (BNS 123.345, type III), 16 operations, 8 with time reversal
    magnetic point group: 4/mm'm'
    allowed by symmetry: net magnetization along z; linear magnetoelectric effect none; piezomagnetism 3 components
    collinear order: compensated, sublattices not related by symmetry
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 1.0000]
      Ni3: [0.0000, 0.0000, -0.5000]
      Ni4: [0.0000, 0.0000, -0.5000]
    MAGMOM = 0 0 0   0.0000 0.0000 1.0000   0.0000 0.0000 -0.5000   0.0000 0.0000 -0.5000
  component x:
    Ni1: S = [ 0.5000, -0.0000, -0.0000]
    Ni2: S = [ 0.5000, -0.0000, -0.0000]
    Ni3: S = [-1.0000, -0.0000, -0.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: P4/mm'm' (BNS 123.345, type III), 16 operations, 8 with time reversal
    magnetic point group: 4/mm'm'
    allowed by symmetry: net magnetization along x; linear magnetoelectric effect none; piezomagnetism 3 components
    collinear order: compensated, sublattices not related by symmetry
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [0.5000, -0.0000, -0.0000]
      Ni3: [0.5000, -0.0000, -0.0000]
      Ni4: [-1.0000, -0.0000, -0.0000]
    MAGMOM = 0 0 0   0.5000 -0.0000 -0.0000   0.5000 -0.0000 -0.0000   -1.0000 -0.0000 -0.0000
  component y:
    Ni1: S = [-0.0000,  0.5000, -0.0000]
    Ni2: S = [-0.0000, -1.0000, -0.0000]
    Ni3: S = [-0.0000,  0.5000, -0.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: P4/mm'm' (BNS 123.345, type III), 16 operations, 8 with time reversal
    magnetic point group: 4/mm'm'
    allowed by symmetry: net magnetization along y; linear magnetoelectric effect none; piezomagnetism 3 components
    collinear order: compensated, sublattices not related by symmetry
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [-0.0000, 0.5000, -0.0000]
      Ni3: [-0.0000, -1.0000, -0.0000]
      Ni4: [-0.0000, 0.5000, -0.0000]
    MAGMOM = 0 0 0   -0.0000 0.5000 -0.0000   -0.0000 -1.0000 -0.0000   -0.0000 0.5000 -0.0000
  component 111:
    Ni1: S = [ 0.4082,  0.4082,  0.8165]
    Ni2: S = [ 0.4082, -0.8165, -0.4082]
    Ni3: S = [-0.8165,  0.4082, -0.4082]
    net moment: [0.0, 0.0, -0.0]
    magnetic space group: R-3m' (BNS 166.101, type III), 12 operations, 6 with time reversal
    magnetic point group: -3m'
    allowed by symmetry: net magnetization along [11-1]; linear magnetoelectric effect none; piezomagnetism 4 components
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [0.4082, 0.4082, 0.8165]
      Ni3: [0.4082, -0.8165, -0.4082]
      Ni4: [-0.8165, 0.4082, -0.4082]
    MAGMOM = 0 0 0   0.4082 0.4082 0.8165   0.4082 -0.8165 -0.4082   -0.8165 0.4082 -0.4082

* GM5+(3) [AFM, octupole] *
  component z:
    Ni1: S = [ 0.0000,  0.0000,  0.0000]
    Ni2: S = [ 0.0000,  0.0000,  1.0000]
    Ni3: S = [ 0.0000,  0.0000, -1.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: P4'/mm'm (BNS 123.342, type III), 16 operations, 8 with time reversal
    magnetic point group: 4'/mm'm
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism 2 components
    collinear order: altermagnet (d-wave; spin splitting allowed by symmetry ~ k_x^2 - k_y^2; spin-degenerate planes perpendicular to [110], [1-10])
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 0.0000]
      Ni3: [0.0000, 0.0000, 1.0000]
      Ni4: [0.0000, 0.0000, -1.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 -1.0000
  component x:
    Ni1: S = [ 1.0000,  0.0000,  0.0000]
    Ni2: S = [-1.0000,  0.0000,  0.0000]
    Ni3: S = [ 0.0000,  0.0000,  0.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: P4'/mm'm (BNS 123.342, type III), 16 operations, 8 with time reversal
    magnetic point group: 4'/mm'm
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism 2 components
    collinear order: altermagnet (d-wave; spin splitting allowed by symmetry ~ k_y^2 - k_z^2; spin-degenerate planes perpendicular to [011], [01-1])
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [1.0000, 0.0000, 0.0000]
      Ni3: [-1.0000, 0.0000, 0.0000]
      Ni4: [0.0000, 0.0000, 0.0000]
    MAGMOM = 0 0 0   1.0000 0.0000 0.0000   -1.0000 0.0000 0.0000   0.0000 0.0000 0.0000
  component y:
    Ni1: S = [ 0.0000,  1.0000,  0.0000]
    Ni2: S = [ 0.0000,  0.0000,  0.0000]
    Ni3: S = [ 0.0000, -1.0000,  0.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: P4'/mm'm (BNS 123.342, type III), 16 operations, 8 with time reversal
    magnetic point group: 4'/mm'm
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism 2 components
    collinear order: altermagnet (d-wave; spin splitting allowed by symmetry ~ k_x^2 - k_z^2; spin-degenerate planes perpendicular to [101], [10-1])
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 1.0000, 0.0000]
      Ni3: [0.0000, 0.0000, 0.0000]
      Ni4: [0.0000, -1.0000, 0.0000]
    MAGMOM = 0 0 0   0.0000 1.0000 0.0000   0.0000 0.0000 0.0000   0.0000 -1.0000 0.0000
  component 111:
    Ni1: S = [ 0.7071,  0.7071,  0.0000]
    Ni2: S = [-0.7071,  0.0000,  0.7071]
    Ni3: S = [ 0.0000, -0.7071, -0.7071]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: R-3m (BNS 166.97, type I), 12 operations, 0 with time reversal
    magnetic point group: -3m
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism 2 components
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Al1: [0, 0, 0]
      Ni2: [0.7071, 0.7071, 0.0000]
      Ni3: [-0.7071, 0.0000, 0.7071]
      Ni4: [0.0000, -0.7071, -0.7071]
    MAGMOM = 0 0 0   0.7071 0.7071 0.0000   -0.7071 0.0000 0.7071   0.0000 -0.7071 -0.7071

* Magnetic groups and collinear classes *
basis                    component  MSG (BNS)           type  MPG      net magnetization  class
GM4+(3) [FM, dipole]     z          P4/mm'm' (123.345)  III   4/mm'm'  along z            ferromagnet
GM4+(3) [FM, dipole]     x          P4/mm'm' (123.345)  III   4/mm'm'  along x            ferromagnet
GM4+(3) [FM, dipole]     y          P4/mm'm' (123.345)  III   4/mm'm'  along y            ferromagnet
GM4+(3) [FM, dipole]     111        R-3m' (166.101)     III   -3m'     along [111]        ferromagnet
GM4+(3) [AFM, octupole]  z          P4/mm'm' (123.345)  III   4/mm'm'  along z            compensated (unrelated sublattices)
GM4+(3) [AFM, octupole]  x          P4/mm'm' (123.345)  III   4/mm'm'  along x            compensated (unrelated sublattices)
GM4+(3) [AFM, octupole]  y          P4/mm'm' (123.345)  III   4/mm'm'  along y            compensated (unrelated sublattices)
GM4+(3) [AFM, octupole]  111        R-3m' (166.101)     III   -3m'     along [11-1]       noncollinear
GM5+(3) [AFM, octupole]  z          P4'/mm'm (123.342)  III   4'/mm'm  none               altermagnet (d-wave)
GM5+(3) [AFM, octupole]  x          P4'/mm'm (123.342)  III   4'/mm'm  none               altermagnet (d-wave)
GM5+(3) [AFM, octupole]  y          P4'/mm'm (123.342)  III   4'/mm'm  none               altermagnet (d-wave)
GM5+(3) [AFM, octupole]  111        R-3m (166.97)       I     -3m      none               noncollinear

MSG: magnetic space group from the moment directions (BNS number, type I-IV);
MPG: magnetic point group; net magnetization: the direction allowed by symmetry;
class: from the signs of the moments along their common axis only (nonrelativistic).
MSG and MPG symbols are in the standard BNS setting; directions are in the Cartesian axes of the input cell.

* Output files *
  Spin basis written to: POSCAR_AlNi3_spin_GM4+_dipole_z.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM4+_dipole_x.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM4+_dipole_y.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM4+_dipole_111.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM4+_octupole_z.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM4+_octupole_x.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM4+_octupole_y.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM4+_octupole_111.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM5+_octupole_z.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM5+_octupole_x.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM5+_octupole_y.vesta
  Spin basis written to: POSCAR_AlNi3_spin_GM5+_octupole_111.vesta

All AFM bases satisfy sum_i S_i = 0; FM entries carry the cluster dipole moment.
Reference: M.-T. Suzuki et al., PRB 95, 094406 (2017); PRB 99, 174407 (2019).
Reference (collinear classes): L. Smejkal, J. Sinova and T. Jungwirth, Phys. Rev. X 12, 031042 (2022).







# Generate all the possible multipole expansion for magnetic structures at R point
crystod-mag -c 221_PPOSCAR_AlNi3 --element Ni --qpoint 0.5 0.5 0.5 --format vasp

* Structure *
  Space group: Pm-3m (#221)
  Magnetic sites: Ni x 3
    Ni1: [0.5, 0.5, 0.0]
    Ni2: [0.5, 0.0, 0.5]
    Ni3: [0.0, 0.5, 0.5]

* Selected Q point *
  Selected q-point: R = [0.5, 0.5, 0.5]

* Spin (axial-vector) representation *
  Spin (axial-vector) representation on Ni sites: 9 dimensions
  Decomposition: R2+(1) + R3+(2) + R4+(3) + R5+(3)

* Symmetry-adapted spin bases *
  R2+(1): dim 1 [AFM (q != 0)]
  R3+(2): dim 2 [AFM (q != 0)]
  R4+(3): dim 3 [AFM (q != 0)]
  R5+(3): dim 3 [AFM (q != 0)]

* Magnetic cell *
  Magnetic (commensurate) supercell: 2x2x2
  the magnetic space group refers to the real spin field of the magnetic cell (global phase fixed as the VESTA export)

* R2+(1) [AFM (q != 0)] *
  component comp1:
    Ni1: S = [ 0.0000,  0.0000,  1.0000]
    Ni2: S = [ 0.0000,  1.0000,  0.0000]
    Ni3: S = [ 1.0000,  0.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: F_Sm-3c (BNS 226.127, type IV), 384 operations, 192 with time reversal
    magnetic point group: m-3m1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 2] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 1.0000]
      Ni3: [0.0000, 1.0000, 0.0000]
      Ni4: [1.0000, 0.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -0.0000, -1.0000]
      Ni7: [-0.0000, -1.0000, -0.0000]
      Ni8: [-1.0000, -0.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -0.0000, -1.0000]
      Ni11: [-0.0000, -1.0000, -0.0000]
      Ni12: [-1.0000, -0.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, 1.0000]
      Ni15: [0.0000, 1.0000, 0.0000]
      Ni16: [1.0000, 0.0000, 0.0000]
      Al17: [0, 0, 0]
      Ni18: [-0.0000, -0.0000, -1.0000]
      Ni19: [-0.0000, -1.0000, -0.0000]
      Ni20: [-1.0000, -0.0000, -0.0000]
      Al21: [0, 0, 0]
      Ni22: [0.0000, 0.0000, 1.0000]
      Ni23: [0.0000, 1.0000, 0.0000]
      Ni24: [1.0000, 0.0000, 0.0000]
      Al25: [0, 0, 0]
      Ni26: [0.0000, 0.0000, 1.0000]
      Ni27: [0.0000, 1.0000, 0.0000]
      Ni28: [1.0000, 0.0000, 0.0000]
      Al29: [0, 0, 0]
      Ni30: [-0.0000, -0.0000, -1.0000]
      Ni31: [-0.0000, -1.0000, -0.0000]
      Ni32: [-1.0000, -0.0000, -0.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 1.0000   0.0000 1.0000 0.0000   1.0000 0.0000 0.0000   0 0 0   -0.0000 -0.0000 -1.0000   -0.0000 -1.0000 -0.0000   -1.0000 -0.0000 -0.0000   0 0 0   -0.0000 -0.0000 -1.0000   -0.0000 -1.0000 -0.0000   -1.0000 -0.0000 -0.0000   0 0 0   0.0000 0.0000 1.0000   0.0000 1.0000 0.0000   1.0000 0.0000 0.0000   0 0 0   -0.0000 -0.0000 -1.0000   -0.0000 -1.0000 -0.0000   -1.0000 -0.0000 -0.0000   0 0 0   0.0000 0.0000 1.0000   0.0000 1.0000 0.0000   1.0000 0.0000 0.0000   0 0 0   0.0000 0.0000 1.0000   0.0000 1.0000 0.0000   1.0000 0.0000 0.0000   0 0 0   -0.0000 -0.0000 -1.0000   -0.0000 -1.0000 -0.0000   -1.0000 -0.0000 -0.0000

* R3+(2) [AFM (q != 0)] *
  component comp1:
    Ni1: S = [-0.0000, -0.0000, -1.0000]
    Ni2: S = [-0.0000,  0.5000, -0.0000]
    Ni3: S = [ 0.5000, -0.0000, -0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: I_c4/mcm (BNS 140.550, type IV), 128 operations, 64 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 2] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [-0.0000, -0.0000, -1.0000]
      Ni3: [-0.0000, 0.5000, -0.0000]
      Ni4: [0.5000, -0.0000, -0.0000]
      Al5: [0, 0, 0]
      Ni6: [0.0000, 0.0000, 1.0000]
      Ni7: [0.0000, -0.5000, 0.0000]
      Ni8: [-0.5000, 0.0000, 0.0000]
      Al9: [0, 0, 0]
      Ni10: [0.0000, 0.0000, 1.0000]
      Ni11: [0.0000, -0.5000, 0.0000]
      Ni12: [-0.5000, 0.0000, 0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, -1.0000]
      Ni15: [0.0000, 0.5000, 0.0000]
      Ni16: [0.5000, 0.0000, 0.0000]
      Al17: [0, 0, 0]
      Ni18: [0.0000, 0.0000, 1.0000]
      Ni19: [0.0000, -0.5000, 0.0000]
      Ni20: [-0.5000, 0.0000, 0.0000]
      Al21: [0, 0, 0]
      Ni22: [0.0000, 0.0000, -1.0000]
      Ni23: [0.0000, 0.5000, 0.0000]
      Ni24: [0.5000, 0.0000, 0.0000]
      Al25: [0, 0, 0]
      Ni26: [0.0000, 0.0000, -1.0000]
      Ni27: [0.0000, 0.5000, 0.0000]
      Ni28: [0.5000, 0.0000, 0.0000]
      Al29: [0, 0, 0]
      Ni30: [0.0000, 0.0000, 1.0000]
      Ni31: [0.0000, -0.5000, 0.0000]
      Ni32: [-0.5000, 0.0000, 0.0000]
    MAGMOM = 0 0 0   -0.0000 -0.0000 -1.0000   -0.0000 0.5000 -0.0000   0.5000 -0.0000 -0.0000   0 0 0   0.0000 0.0000 1.0000   0.0000 -0.5000 0.0000   -0.5000 0.0000 0.0000   0 0 0   0.0000 0.0000 1.0000   0.0000 -0.5000 0.0000   -0.5000 0.0000 0.0000   0 0 0   0.0000 0.0000 -1.0000   0.0000 0.5000 0.0000   0.5000 0.0000 0.0000   0 0 0   0.0000 0.0000 1.0000   0.0000 -0.5000 0.0000   -0.5000 0.0000 0.0000   0 0 0   0.0000 0.0000 -1.0000   0.0000 0.5000 0.0000   0.5000 0.0000 0.0000   0 0 0   0.0000 0.0000 -1.0000   0.0000 0.5000 0.0000   0.5000 0.0000 0.0000   0 0 0   0.0000 0.0000 1.0000   0.0000 -0.5000 0.0000   -0.5000 0.0000 0.0000
  component comp2:
    Ni1: S = [ 0.0000,  0.0000, -0.0000]
    Ni2: S = [ 0.0000,  1.0000,  0.0000]
    Ni3: S = [-1.0000,  0.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: I_c4/mmm (BNS 139.540, type IV), 128 operations, 64 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 2] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, -0.0000]
      Ni3: [0.0000, 1.0000, 0.0000]
      Ni4: [-1.0000, 0.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -0.0000, 0.0000]
      Ni7: [-0.0000, -1.0000, -0.0000]
      Ni8: [1.0000, -0.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -0.0000, 0.0000]
      Ni11: [-0.0000, -1.0000, -0.0000]
      Ni12: [1.0000, -0.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, -0.0000]
      Ni15: [0.0000, 1.0000, 0.0000]
      Ni16: [-1.0000, 0.0000, 0.0000]
      Al17: [0, 0, 0]
      Ni18: [-0.0000, -0.0000, 0.0000]
      Ni19: [-0.0000, -1.0000, -0.0000]
      Ni20: [1.0000, -0.0000, -0.0000]
      Al21: [0, 0, 0]
      Ni22: [0.0000, 0.0000, -0.0000]
      Ni23: [0.0000, 1.0000, 0.0000]
      Ni24: [-1.0000, 0.0000, 0.0000]
      Al25: [0, 0, 0]
      Ni26: [0.0000, 0.0000, -0.0000]
      Ni27: [0.0000, 1.0000, 0.0000]
      Ni28: [-1.0000, 0.0000, 0.0000]
      Al29: [0, 0, 0]
      Ni30: [-0.0000, -0.0000, 0.0000]
      Ni31: [-0.0000, -1.0000, -0.0000]
      Ni32: [1.0000, -0.0000, -0.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 -0.0000   0.0000 1.0000 0.0000   -1.0000 0.0000 0.0000   0 0 0   -0.0000 -0.0000 0.0000   -0.0000 -1.0000 -0.0000   1.0000 -0.0000 -0.0000   0 0 0   -0.0000 -0.0000 0.0000   -0.0000 -1.0000 -0.0000   1.0000 -0.0000 -0.0000   0 0 0   0.0000 0.0000 -0.0000   0.0000 1.0000 0.0000   -1.0000 0.0000 0.0000   0 0 0   -0.0000 -0.0000 0.0000   -0.0000 -1.0000 -0.0000   1.0000 -0.0000 -0.0000   0 0 0   0.0000 0.0000 -0.0000   0.0000 1.0000 0.0000   -1.0000 0.0000 0.0000   0 0 0   0.0000 0.0000 -0.0000   0.0000 1.0000 0.0000   -1.0000 0.0000 0.0000   0 0 0   -0.0000 -0.0000 0.0000   -0.0000 -1.0000 -0.0000   1.0000 -0.0000 -0.0000

* R4+(3) [AFM (q != 0)] *
  component comp1:
    Ni1: S = [ 0.0000,  0.0000,  0.0000]
    Ni2: S = [ 1.0000,  0.0000,  0.0000]
    Ni3: S = [ 0.0000,  1.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: I_c4/mcm (BNS 140.550, type IV), 128 operations, 64 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 2] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 0.0000]
      Ni3: [1.0000, 0.0000, 0.0000]
      Ni4: [0.0000, 1.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -0.0000, -0.0000]
      Ni7: [-1.0000, -0.0000, -0.0000]
      Ni8: [-0.0000, -1.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -0.0000, -0.0000]
      Ni11: [-1.0000, -0.0000, -0.0000]
      Ni12: [-0.0000, -1.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, 0.0000]
      Ni15: [1.0000, 0.0000, 0.0000]
      Ni16: [0.0000, 1.0000, 0.0000]
      Al17: [0, 0, 0]
      Ni18: [-0.0000, -0.0000, -0.0000]
      Ni19: [-1.0000, -0.0000, -0.0000]
      Ni20: [-0.0000, -1.0000, -0.0000]
      Al21: [0, 0, 0]
      Ni22: [0.0000, 0.0000, 0.0000]
      Ni23: [1.0000, 0.0000, 0.0000]
      Ni24: [0.0000, 1.0000, 0.0000]
      Al25: [0, 0, 0]
      Ni26: [0.0000, 0.0000, 0.0000]
      Ni27: [1.0000, 0.0000, 0.0000]
      Ni28: [0.0000, 1.0000, 0.0000]
      Al29: [0, 0, 0]
      Ni30: [-0.0000, -0.0000, -0.0000]
      Ni31: [-1.0000, -0.0000, -0.0000]
      Ni32: [-0.0000, -1.0000, -0.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 1.0000 0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -1.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -1.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000   0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 1.0000 0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -1.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000   0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 1.0000 0.0000   0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 1.0000 0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -1.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000
  component comp2:
    Ni1: S = [ 0.0000,  1.0000,  0.0000]
    Ni2: S = [ 0.0000,  0.0000,  1.0000]
    Ni3: S = [ 0.0000,  0.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: I_c4/mcm (BNS 140.550, type IV), 128 operations, 64 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 2] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 1.0000, 0.0000]
      Ni3: [0.0000, 0.0000, 1.0000]
      Ni4: [0.0000, 0.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -1.0000, -0.0000]
      Ni7: [-0.0000, -0.0000, -1.0000]
      Ni8: [-0.0000, -0.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -1.0000, -0.0000]
      Ni11: [-0.0000, -0.0000, -1.0000]
      Ni12: [-0.0000, -0.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 1.0000, 0.0000]
      Ni15: [0.0000, 0.0000, 1.0000]
      Ni16: [0.0000, 0.0000, 0.0000]
      Al17: [0, 0, 0]
      Ni18: [-0.0000, -1.0000, -0.0000]
      Ni19: [-0.0000, -0.0000, -1.0000]
      Ni20: [-0.0000, -0.0000, -0.0000]
      Al21: [0, 0, 0]
      Ni22: [0.0000, 1.0000, 0.0000]
      Ni23: [0.0000, 0.0000, 1.0000]
      Ni24: [0.0000, 0.0000, 0.0000]
      Al25: [0, 0, 0]
      Ni26: [0.0000, 1.0000, 0.0000]
      Ni27: [0.0000, 0.0000, 1.0000]
      Ni28: [0.0000, 0.0000, 0.0000]
      Al29: [0, 0, 0]
      Ni30: [-0.0000, -1.0000, -0.0000]
      Ni31: [-0.0000, -0.0000, -1.0000]
      Ni32: [-0.0000, -0.0000, -0.0000]
    MAGMOM = 0 0 0   0.0000 1.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0 0 0   -0.0000 -1.0000 -0.0000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 -0.0000   0 0 0   -0.0000 -1.0000 -0.0000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 -0.0000   0 0 0   0.0000 1.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0 0 0   -0.0000 -1.0000 -0.0000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 -0.0000   0 0 0   0.0000 1.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0 0 0   0.0000 1.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0 0 0   -0.0000 -1.0000 -0.0000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 -0.0000
  component comp3:
    Ni1: S = [ 1.0000,  0.0000,  0.0000]
    Ni2: S = [ 0.0000,  0.0000,  0.0000]
    Ni3: S = [ 0.0000,  0.0000,  1.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: I_c4/mcm (BNS 140.550, type IV), 128 operations, 64 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 2] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [1.0000, 0.0000, 0.0000]
      Ni3: [0.0000, 0.0000, 0.0000]
      Ni4: [0.0000, 0.0000, 1.0000]
      Al5: [0, 0, 0]
      Ni6: [-1.0000, -0.0000, -0.0000]
      Ni7: [-0.0000, -0.0000, -0.0000]
      Ni8: [-0.0000, -0.0000, -1.0000]
      Al9: [0, 0, 0]
      Ni10: [-1.0000, -0.0000, -0.0000]
      Ni11: [-0.0000, -0.0000, -0.0000]
      Ni12: [-0.0000, -0.0000, -1.0000]
      Al13: [0, 0, 0]
      Ni14: [1.0000, 0.0000, 0.0000]
      Ni15: [0.0000, 0.0000, 0.0000]
      Ni16: [0.0000, 0.0000, 1.0000]
      Al17: [0, 0, 0]
      Ni18: [-1.0000, -0.0000, -0.0000]
      Ni19: [-0.0000, -0.0000, -0.0000]
      Ni20: [-0.0000, -0.0000, -1.0000]
      Al21: [0, 0, 0]
      Ni22: [1.0000, 0.0000, 0.0000]
      Ni23: [0.0000, 0.0000, 0.0000]
      Ni24: [0.0000, 0.0000, 1.0000]
      Al25: [0, 0, 0]
      Ni26: [1.0000, 0.0000, 0.0000]
      Ni27: [0.0000, 0.0000, 0.0000]
      Ni28: [0.0000, 0.0000, 1.0000]
      Al29: [0, 0, 0]
      Ni30: [-1.0000, -0.0000, -0.0000]
      Ni31: [-0.0000, -0.0000, -0.0000]
      Ni32: [-0.0000, -0.0000, -1.0000]
    MAGMOM = 0 0 0   1.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 1.0000   0 0 0   -1.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -1.0000   0 0 0   -1.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -1.0000   0 0 0   1.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 1.0000   0 0 0   -1.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -1.0000   0 0 0   1.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 1.0000   0 0 0   1.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 1.0000   0 0 0   -1.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -1.0000

* R5+(3) [AFM (q != 0)] *
  component comp1:
    Ni1: S = [-0.0000, -0.0000, -0.0000]
    Ni2: S = [ 1.0000, -0.0000, -0.0000]
    Ni3: S = [-0.0000, -1.0000, -0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: I_c4/mmm (BNS 139.540, type IV), 128 operations, 64 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 2] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [-0.0000, -0.0000, -0.0000]
      Ni3: [1.0000, -0.0000, -0.0000]
      Ni4: [-0.0000, -1.0000, -0.0000]
      Al5: [0, 0, 0]
      Ni6: [0.0000, 0.0000, 0.0000]
      Ni7: [-1.0000, 0.0000, 0.0000]
      Ni8: [0.0000, 1.0000, 0.0000]
      Al9: [0, 0, 0]
      Ni10: [0.0000, 0.0000, 0.0000]
      Ni11: [-1.0000, 0.0000, 0.0000]
      Ni12: [0.0000, 1.0000, 0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, 0.0000]
      Ni15: [1.0000, 0.0000, 0.0000]
      Ni16: [0.0000, -1.0000, 0.0000]
      Al17: [0, 0, 0]
      Ni18: [0.0000, 0.0000, 0.0000]
      Ni19: [-1.0000, 0.0000, 0.0000]
      Ni20: [0.0000, 1.0000, 0.0000]
      Al21: [0, 0, 0]
      Ni22: [0.0000, 0.0000, 0.0000]
      Ni23: [1.0000, 0.0000, 0.0000]
      Ni24: [0.0000, -1.0000, 0.0000]
      Al25: [0, 0, 0]
      Ni26: [0.0000, 0.0000, 0.0000]
      Ni27: [1.0000, 0.0000, 0.0000]
      Ni28: [0.0000, -1.0000, 0.0000]
      Al29: [0, 0, 0]
      Ni30: [0.0000, 0.0000, 0.0000]
      Ni31: [-1.0000, 0.0000, 0.0000]
      Ni32: [0.0000, 1.0000, 0.0000]
    MAGMOM = 0 0 0   -0.0000 -0.0000 -0.0000   1.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000   0 0 0   0.0000 0.0000 0.0000   -1.0000 0.0000 0.0000   0.0000 1.0000 0.0000   0 0 0   0.0000 0.0000 0.0000   -1.0000 0.0000 0.0000   0.0000 1.0000 0.0000   0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 -1.0000 0.0000   0 0 0   0.0000 0.0000 0.0000   -1.0000 0.0000 0.0000   0.0000 1.0000 0.0000   0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 -1.0000 0.0000   0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 -1.0000 0.0000   0 0 0   0.0000 0.0000 0.0000   -1.0000 0.0000 0.0000   0.0000 1.0000 0.0000
  component comp2:
    Ni1: S = [-0.0000,  1.0000, -0.0000]
    Ni2: S = [-0.0000, -0.0000, -1.0000]
    Ni3: S = [-0.0000, -0.0000, -0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: I_c4/mmm (BNS 139.540, type IV), 128 operations, 64 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 2] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [-0.0000, 1.0000, -0.0000]
      Ni3: [-0.0000, -0.0000, -1.0000]
      Ni4: [-0.0000, -0.0000, -0.0000]
      Al5: [0, 0, 0]
      Ni6: [0.0000, -1.0000, 0.0000]
      Ni7: [0.0000, 0.0000, 1.0000]
      Ni8: [0.0000, 0.0000, 0.0000]
      Al9: [0, 0, 0]
      Ni10: [0.0000, -1.0000, 0.0000]
      Ni11: [0.0000, 0.0000, 1.0000]
      Ni12: [0.0000, 0.0000, 0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 1.0000, 0.0000]
      Ni15: [0.0000, 0.0000, -1.0000]
      Ni16: [0.0000, 0.0000, 0.0000]
      Al17: [0, 0, 0]
      Ni18: [0.0000, -1.0000, 0.0000]
      Ni19: [0.0000, 0.0000, 1.0000]
      Ni20: [0.0000, 0.0000, 0.0000]
      Al21: [0, 0, 0]
      Ni22: [0.0000, 1.0000, 0.0000]
      Ni23: [0.0000, 0.0000, -1.0000]
      Ni24: [0.0000, 0.0000, 0.0000]
      Al25: [0, 0, 0]
      Ni26: [0.0000, 1.0000, 0.0000]
      Ni27: [0.0000, 0.0000, -1.0000]
      Ni28: [0.0000, 0.0000, 0.0000]
      Al29: [0, 0, 0]
      Ni30: [0.0000, -1.0000, 0.0000]
      Ni31: [0.0000, 0.0000, 1.0000]
      Ni32: [0.0000, 0.0000, 0.0000]
    MAGMOM = 0 0 0   -0.0000 1.0000 -0.0000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 -0.0000   0 0 0   0.0000 -1.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0 0 0   0.0000 -1.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0 0 0   0.0000 1.0000 0.0000   0.0000 0.0000 -1.0000   0.0000 0.0000 0.0000   0 0 0   0.0000 -1.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0 0 0   0.0000 1.0000 0.0000   0.0000 0.0000 -1.0000   0.0000 0.0000 0.0000   0 0 0   0.0000 1.0000 0.0000   0.0000 0.0000 -1.0000   0.0000 0.0000 0.0000   0 0 0   0.0000 -1.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000
  component comp3:
    Ni1: S = [ 1.0000,  0.0000,  0.0000]
    Ni2: S = [ 0.0000,  0.0000,  0.0000]
    Ni3: S = [ 0.0000,  0.0000, -1.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: I_c4/mmm (BNS 139.540, type IV), 128 operations, 64 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 2] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [1.0000, 0.0000, 0.0000]
      Ni3: [0.0000, 0.0000, 0.0000]
      Ni4: [0.0000, 0.0000, -1.0000]
      Al5: [0, 0, 0]
      Ni6: [-1.0000, -0.0000, -0.0000]
      Ni7: [-0.0000, -0.0000, -0.0000]
      Ni8: [-0.0000, -0.0000, 1.0000]
      Al9: [0, 0, 0]
      Ni10: [-1.0000, -0.0000, -0.0000]
      Ni11: [-0.0000, -0.0000, -0.0000]
      Ni12: [-0.0000, -0.0000, 1.0000]
      Al13: [0, 0, 0]
      Ni14: [1.0000, 0.0000, 0.0000]
      Ni15: [0.0000, 0.0000, 0.0000]
      Ni16: [0.0000, 0.0000, -1.0000]
      Al17: [0, 0, 0]
      Ni18: [-1.0000, -0.0000, -0.0000]
      Ni19: [-0.0000, -0.0000, -0.0000]
      Ni20: [-0.0000, -0.0000, 1.0000]
      Al21: [0, 0, 0]
      Ni22: [1.0000, 0.0000, 0.0000]
      Ni23: [0.0000, 0.0000, 0.0000]
      Ni24: [0.0000, 0.0000, -1.0000]
      Al25: [0, 0, 0]
      Ni26: [1.0000, 0.0000, 0.0000]
      Ni27: [0.0000, 0.0000, 0.0000]
      Ni28: [0.0000, 0.0000, -1.0000]
      Al29: [0, 0, 0]
      Ni30: [-1.0000, -0.0000, -0.0000]
      Ni31: [-0.0000, -0.0000, -0.0000]
      Ni32: [-0.0000, -0.0000, 1.0000]
    MAGMOM = 0 0 0   1.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 -1.0000   0 0 0   -1.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 1.0000   0 0 0   -1.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 1.0000   0 0 0   1.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 -1.0000   0 0 0   -1.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 1.0000   0 0 0   1.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 -1.0000   0 0 0   1.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 -1.0000   0 0 0   -1.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 1.0000

* Magnetic groups and collinear classes *
basis                  component  MSG (BNS)           type  MPG      net magnetization  class
R2+(1) [AFM (q != 0)]  comp1      F_Sm-3c (226.127)   IV    m-3m1'   none               noncollinear
R3+(2) [AFM (q != 0)]  comp1      I_c4/mcm (140.550)  IV    4/mmm1'  none               noncollinear
R3+(2) [AFM (q != 0)]  comp2      I_c4/mmm (139.540)  IV    4/mmm1'  none               noncollinear
R4+(3) [AFM (q != 0)]  comp1      I_c4/mcm (140.550)  IV    4/mmm1'  none               noncollinear
R4+(3) [AFM (q != 0)]  comp2      I_c4/mcm (140.550)  IV    4/mmm1'  none               noncollinear
R4+(3) [AFM (q != 0)]  comp3      I_c4/mcm (140.550)  IV    4/mmm1'  none               noncollinear
R5+(3) [AFM (q != 0)]  comp1      I_c4/mmm (139.540)  IV    4/mmm1'  none               noncollinear
R5+(3) [AFM (q != 0)]  comp2      I_c4/mmm (139.540)  IV    4/mmm1'  none               noncollinear
R5+(3) [AFM (q != 0)]  comp3      I_c4/mmm (139.540)  IV    4/mmm1'  none               noncollinear

MSG: magnetic space group from the moment directions (BNS number, type I-IV);
MPG: magnetic point group; net magnetization: the direction allowed by symmetry;
class: from the signs of the moments along their common axis only (nonrelativistic).
MSG and MPG symbols are in the standard BNS setting; directions are in the Cartesian axes of the input cell.
component: the tag of the listing and of the VESTA file name (comp<N>: the N-th basis vector of its space).

* Output files *
  Spin basis written to: POSCAR_AlNi3_spin_R2+_R_comp1.vesta
  Spin basis written to: POSCAR_AlNi3_spin_R3+_R_comp1.vesta
  Spin basis written to: POSCAR_AlNi3_spin_R3+_R_comp2.vesta
  Spin basis written to: POSCAR_AlNi3_spin_R4+_R_comp1.vesta
  Spin basis written to: POSCAR_AlNi3_spin_R4+_R_comp2.vesta
  Spin basis written to: POSCAR_AlNi3_spin_R4+_R_comp3.vesta
  Spin basis written to: POSCAR_AlNi3_spin_R5+_R_comp1.vesta
  Spin basis written to: POSCAR_AlNi3_spin_R5+_R_comp2.vesta
  Spin basis written to: POSCAR_AlNi3_spin_R5+_R_comp3.vesta

Reference: M.-T. Suzuki et al., PRB 95, 094406 (2017); PRB 99, 174407 (2019).
Reference (collinear classes): L. Smejkal, J. Sinova and T. Jungwirth, Phys. Rev. X 12, 031042 (2022).




# All irreducible representations for multipoles
crystod-mag -c 221_PPOSCAR_AlNi3 --element Ni  

* Structure *
  Space group: Pm-3m (#221)
  Magnetic sites: Ni x 3
    Ni1: [0.5, 0.5, 0.0]
    Ni2: [0.5, 0.0, 0.5]
    Ni3: [0.0, 0.5, 0.5]

* Spin (axial-vector) Irreducible Representations of Ni sites *
  k point (primitive): GM [0.0, 0.0, 0.0]
    2.0 [GM4+(3)] + 1.0 [GM5+(3)]
  k point (primitive): R [0.5, 0.5, 0.5]
    1.0 [R2+(1)] + 1.0 [R3+(2)] + 1.0 [R4+(3)] + 1.0 [R5+(3)]
  k point (primitive): X [0.0, 0.5, 0.0]
    1.0 [X1-(1)] + 1.0 [X3+(1)] + 1.0 [X5+(2)] + 2.0 [X5-(2)] + 1.0 [X2-(1)]
  k point (primitive): M [0.5, 0.5, 0.0]
    1.0 [M1-(1)] + 1.0 [M3-(1)] + 1.0 [M5+(2)] + 1.0 [M5-(2)] + 1.0 [M2+(1)] + 1.0 [M2-(1)] + 1.0 [M4-(1)]

Use --qpoint to obtain the symmetry-adapted spin bases, MAGMOM lines, and VESTA files at one k point.


# Generate all the possible multipole expansion for magnetic structures at M point
crystod-mag -c 221_PPOSCAR_AlNi3 --element Ni --qpoint M --format vasp

* Structure *
  Space group: Pm-3m (#221)
  Magnetic sites: Ni x 3
    Ni1: [0.5, 0.5, 0.0]
    Ni2: [0.5, 0.0, 0.5]
    Ni3: [0.0, 0.5, 0.5]

* Selected Q point *
  Selected q-point: M = [0.5, 0.5, 0.0]

* Spin (axial-vector) representation *
  Spin (axial-vector) representation on Ni sites: 9 dimensions
  Decomposition: M1-(1) + M3-(1) + M5+(2) + M5-(2) + M2+(1) + M2-(1) + M4-(1)

* Symmetry-adapted spin bases *
  M1-(1): dim 1 [AFM (q != 0)]
  M3-(1): dim 1 [AFM (q != 0)]
  M5+(2): dim 2 [AFM (q != 0)]
  M5-(2): dim 2 [AFM (q != 0)]
  M2+(1): dim 1 [AFM (q != 0)]
  M2-(1): dim 1 [AFM (q != 0)]
  M4-(1): dim 1 [AFM (q != 0)]

* Magnetic cell *
  Magnetic (commensurate) supercell: 2x2x1
  the magnetic space group refers to the real spin field of the magnetic cell (global phase fixed as the VESTA export)

* M1-(1) [AFM (q != 0)] *
  component comp1:
    Ni1: S = [ 0.0000,  0.0000,  0.0000]
    Ni2: S = [ 1.0000,  0.0000,  0.0000]
    Ni3: S = [ 0.0000,  1.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: P_C4/nbm (BNS 125.373, type IV), 64 operations, 32 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 1] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 0.0000]
      Ni3: [1.0000, 0.0000, 0.0000]
      Ni4: [0.0000, 1.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -0.0000, -0.0000]
      Ni7: [-1.0000, -0.0000, -0.0000]
      Ni8: [-0.0000, -1.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -0.0000, -0.0000]
      Ni11: [-1.0000, -0.0000, -0.0000]
      Ni12: [-0.0000, -1.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, 0.0000]
      Ni15: [1.0000, 0.0000, 0.0000]
      Ni16: [0.0000, 1.0000, 0.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 1.0000 0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -1.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -1.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000   0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 1.0000 0.0000

* M3-(1) [AFM (q != 0)] *
  component comp1:
    Ni1: S = [ 0.0000,  0.0000,  0.0000]
    Ni2: S = [ 0.0000,  1.0000,  0.0000]
    Ni3: S = [-1.0000,  0.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: P_C4/nmm (BNS 129.421, type IV), 64 operations, 32 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 1] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 0.0000]
      Ni3: [0.0000, 1.0000, 0.0000]
      Ni4: [-1.0000, 0.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -0.0000, -0.0000]
      Ni7: [-0.0000, -1.0000, -0.0000]
      Ni8: [1.0000, -0.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -0.0000, -0.0000]
      Ni11: [-0.0000, -1.0000, -0.0000]
      Ni12: [1.0000, -0.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, 0.0000]
      Ni15: [0.0000, 1.0000, 0.0000]
      Ni16: [-1.0000, 0.0000, 0.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 0.0000   0.0000 1.0000 0.0000   -1.0000 0.0000 0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000   1.0000 -0.0000 -0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000   1.0000 -0.0000 -0.0000   0 0 0   0.0000 0.0000 0.0000   0.0000 1.0000 0.0000   -1.0000 0.0000 0.0000

* M5+(2) [AFM (q != 0)] *
  component x:
    Ni1: S = [ 1.0000, -0.0000,  0.0000]
    Ni2: S = [-0.0000, -0.0000, -0.0000]
    Ni3: S = [-0.0000, -0.0000, -0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: C_amma (BNS 67.509, type IV), 32 operations, 16 with time reversal
    magnetic point group: mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: antiferromagnet (conventional: a translation exchanges the sublattices, T tau)
    spin directions (all atoms, POSCAR order) ([2, 2, 1] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [1.0000, -0.0000, 0.0000]
      Ni3: [-0.0000, -0.0000, -0.0000]
      Ni4: [-0.0000, -0.0000, -0.0000]
      Al5: [0, 0, 0]
      Ni6: [-1.0000, 0.0000, -0.0000]
      Ni7: [0.0000, 0.0000, 0.0000]
      Ni8: [0.0000, 0.0000, 0.0000]
      Al9: [0, 0, 0]
      Ni10: [-1.0000, 0.0000, -0.0000]
      Ni11: [0.0000, 0.0000, 0.0000]
      Ni12: [0.0000, 0.0000, 0.0000]
      Al13: [0, 0, 0]
      Ni14: [1.0000, 0.0000, 0.0000]
      Ni15: [0.0000, 0.0000, 0.0000]
      Ni16: [0.0000, 0.0000, 0.0000]
    MAGMOM = 0 0 0   1.0000 -0.0000 0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   0 0 0   -1.0000 0.0000 -0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0 0 0   -1.0000 0.0000 -0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0 0 0   1.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 0.0000
  component y:
    Ni1: S = [ 0.0000,  1.0000,  0.0000]
    Ni2: S = [ 0.0000,  0.0000,  0.0000]
    Ni3: S = [ 0.0000,  0.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: C_amma (BNS 67.509, type IV), 32 operations, 16 with time reversal
    magnetic point group: mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: antiferromagnet (conventional: a translation exchanges the sublattices, T tau)
    spin directions (all atoms, POSCAR order) ([2, 2, 1] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 1.0000, 0.0000]
      Ni3: [0.0000, 0.0000, 0.0000]
      Ni4: [0.0000, 0.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -1.0000, -0.0000]
      Ni7: [-0.0000, -0.0000, -0.0000]
      Ni8: [-0.0000, -0.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -1.0000, -0.0000]
      Ni11: [-0.0000, -0.0000, -0.0000]
      Ni12: [-0.0000, -0.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 1.0000, 0.0000]
      Ni15: [0.0000, 0.0000, 0.0000]
      Ni16: [0.0000, 0.0000, 0.0000]
    MAGMOM = 0 0 0   0.0000 1.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0 0 0   -0.0000 -1.0000 -0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   0 0 0   -0.0000 -1.0000 -0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   0 0 0   0.0000 1.0000 0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 0.0000

* M5-(2) [AFM (q != 0)] *
  component z:
    Ni1: S = [ 0.0000,  0.0000,  0.0000]
    Ni2: S = [-0.0000, -0.0000, -0.0000]
    Ni3: S = [-0.0000, -0.0000,  1.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: C_ammm (BNS 65.489, type IV), 32 operations, 16 with time reversal
    magnetic point group: mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: antiferromagnet (conventional: a translation exchanges the sublattices, T tau)
    spin directions (all atoms, POSCAR order) ([2, 2, 1] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 0.0000]
      Ni3: [-0.0000, -0.0000, -0.0000]
      Ni4: [-0.0000, -0.0000, 1.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -0.0000, -0.0000]
      Ni7: [0.0000, 0.0000, 0.0000]
      Ni8: [0.0000, 0.0000, -1.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -0.0000, -0.0000]
      Ni11: [0.0000, 0.0000, 0.0000]
      Ni12: [0.0000, 0.0000, -1.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, 0.0000]
      Ni15: [0.0000, 0.0000, -0.0000]
      Ni16: [0.0000, 0.0000, 1.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 0.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 1.0000   0 0 0   -0.0000 -0.0000 -0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 -1.0000   0 0 0   -0.0000 -0.0000 -0.0000   0.0000 0.0000 0.0000   0.0000 0.0000 -1.0000   0 0 0   0.0000 0.0000 0.0000   0.0000 0.0000 -0.0000   0.0000 0.0000 1.0000
  component z:
    Ni1: S = [ 0.0000,  0.0000,  0.0000]
    Ni2: S = [ 0.0000,  0.0000,  1.0000]
    Ni3: S = [ 0.0000,  0.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: C_ammm (BNS 65.489, type IV), 32 operations, 16 with time reversal
    magnetic point group: mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: antiferromagnet (conventional: a translation exchanges the sublattices, T tau)
    spin directions (all atoms, POSCAR order) ([2, 2, 1] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 0.0000]
      Ni3: [0.0000, 0.0000, 1.0000]
      Ni4: [0.0000, 0.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -0.0000, -0.0000]
      Ni7: [-0.0000, -0.0000, -1.0000]
      Ni8: [-0.0000, -0.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -0.0000, -0.0000]
      Ni11: [-0.0000, -0.0000, -1.0000]
      Ni12: [-0.0000, -0.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, 0.0000]
      Ni15: [0.0000, 0.0000, 1.0000]
      Ni16: [0.0000, 0.0000, 0.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 -0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 -0.0000   0 0 0   0.0000 0.0000 0.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000

* M2+(1) [AFM (q != 0)] *
  component z:
    Ni1: S = [ 0.0000,  0.0000,  1.0000]
    Ni2: S = [ 0.0000,  0.0000,  0.0000]
    Ni3: S = [ 0.0000,  0.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: P_C4/mbm (BNS 127.397, type IV), 64 operations, 32 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: antiferromagnet (conventional: a translation exchanges the sublattices, T tau)
    spin directions (all atoms, POSCAR order) ([2, 2, 1] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 1.0000]
      Ni3: [0.0000, 0.0000, 0.0000]
      Ni4: [0.0000, 0.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -0.0000, -1.0000]
      Ni7: [-0.0000, -0.0000, -0.0000]
      Ni8: [-0.0000, -0.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -0.0000, -1.0000]
      Ni11: [-0.0000, -0.0000, -0.0000]
      Ni12: [-0.0000, -0.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, 1.0000]
      Ni15: [0.0000, 0.0000, 0.0000]
      Ni16: [0.0000, 0.0000, 0.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0.0000 0.0000 0.0000   0 0 0   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   0 0 0   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -0.0000   0 0 0   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0.0000 0.0000 0.0000

* M2-(1) [AFM (q != 0)] *
  component comp1:
    Ni1: S = [ 0.0000,  0.0000,  0.0000]
    Ni2: S = [ 1.0000,  0.0000,  0.0000]
    Ni3: S = [ 0.0000, -1.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: P_C4/nmm (BNS 129.421, type IV), 64 operations, 32 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 1] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 0.0000]
      Ni3: [1.0000, 0.0000, 0.0000]
      Ni4: [0.0000, -1.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -0.0000, -0.0000]
      Ni7: [-1.0000, -0.0000, -0.0000]
      Ni8: [-0.0000, 1.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -0.0000, -0.0000]
      Ni11: [-1.0000, -0.0000, -0.0000]
      Ni12: [-0.0000, 1.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, 0.0000]
      Ni15: [1.0000, 0.0000, 0.0000]
      Ni16: [0.0000, -1.0000, 0.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 -1.0000 0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -1.0000 -0.0000 -0.0000   -0.0000 1.0000 -0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -1.0000 -0.0000 -0.0000   -0.0000 1.0000 -0.0000   0 0 0   0.0000 0.0000 0.0000   1.0000 0.0000 0.0000   0.0000 -1.0000 0.0000

* M4-(1) [AFM (q != 0)] *
  component comp1:
    Ni1: S = [ 0.0000,  0.0000,  0.0000]
    Ni2: S = [ 0.0000,  1.0000,  0.0000]
    Ni3: S = [ 1.0000,  0.0000,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: P_C4/nbm (BNS 125.373, type IV), 64 operations, 32 with time reversal
    magnetic point group: 4/mmm1'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism none
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order) ([2, 2, 1] magnetic supercell):
      Al1: [0, 0, 0]
      Ni2: [0.0000, 0.0000, 0.0000]
      Ni3: [0.0000, 1.0000, 0.0000]
      Ni4: [1.0000, 0.0000, 0.0000]
      Al5: [0, 0, 0]
      Ni6: [-0.0000, -0.0000, -0.0000]
      Ni7: [-0.0000, -1.0000, -0.0000]
      Ni8: [-1.0000, -0.0000, -0.0000]
      Al9: [0, 0, 0]
      Ni10: [-0.0000, -0.0000, -0.0000]
      Ni11: [-0.0000, -1.0000, -0.0000]
      Ni12: [-1.0000, -0.0000, -0.0000]
      Al13: [0, 0, 0]
      Ni14: [0.0000, 0.0000, 0.0000]
      Ni15: [0.0000, 1.0000, 0.0000]
      Ni16: [1.0000, 0.0000, 0.0000]
    MAGMOM = 0 0 0   0.0000 0.0000 0.0000   0.0000 1.0000 0.0000   1.0000 0.0000 0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000   -1.0000 -0.0000 -0.0000   0 0 0   -0.0000 -0.0000 -0.0000   -0.0000 -1.0000 -0.0000   -1.0000 -0.0000 -0.0000   0 0 0   0.0000 0.0000 0.0000   0.0000 1.0000 0.0000   1.0000 0.0000 0.0000

* Magnetic groups and collinear classes *
basis                  component  MSG (BNS)           type  MPG      net magnetization  class
M1-(1) [AFM (q != 0)]  comp1      P_C4/nbm (125.373)  IV    4/mmm1'  none               noncollinear
M3-(1) [AFM (q != 0)]  comp1      P_C4/nmm (129.421)  IV    4/mmm1'  none               noncollinear
M5+(2) [AFM (q != 0)]  x          C_amma (67.509)     IV    mmm1'    none               antiferromagnet (T tau)
M5+(2) [AFM (q != 0)]  y          C_amma (67.509)     IV    mmm1'    none               antiferromagnet (T tau)
M5-(2) [AFM (q != 0)]  z          C_ammm (65.489)     IV    mmm1'    none               antiferromagnet (T tau)
M5-(2) [AFM (q != 0)]  z_2        C_ammm (65.489)     IV    mmm1'    none               antiferromagnet (T tau)
M2+(1) [AFM (q != 0)]  z          P_C4/mbm (127.397)  IV    4/mmm1'  none               antiferromagnet (T tau)
M2-(1) [AFM (q != 0)]  comp1      P_C4/nmm (129.421)  IV    4/mmm1'  none               noncollinear
M4-(1) [AFM (q != 0)]  comp1      P_C4/nbm (125.373)  IV    4/mmm1'  none               noncollinear

MSG: magnetic space group from the moment directions (BNS number, type I-IV);
MPG: magnetic point group; net magnetization: the direction allowed by symmetry;
class: from the signs of the moments along their common axis only (nonrelativistic).
MSG and MPG symbols are in the standard BNS setting; directions are in the Cartesian axes of the input cell.
component: the tag of the listing and of the VESTA file name (comp<N>: the N-th basis vector of its space).

* Output files *
  Spin basis written to: POSCAR_AlNi3_spin_M1-_M_comp1.vesta
  Spin basis written to: POSCAR_AlNi3_spin_M3-_M_comp1.vesta
  Spin basis written to: POSCAR_AlNi3_spin_M5+_M_x.vesta
  Spin basis written to: POSCAR_AlNi3_spin_M5+_M_y.vesta
  Spin basis written to: POSCAR_AlNi3_spin_M5-_M_z.vesta
  Spin basis written to: POSCAR_AlNi3_spin_M5-_M_z_2.vesta
  Spin basis written to: POSCAR_AlNi3_spin_M2+_M_z.vesta
  Spin basis written to: POSCAR_AlNi3_spin_M2-_M_comp1.vesta
  Spin basis written to: POSCAR_AlNi3_spin_M4-_M_comp1.vesta

Reference: M.-T. Suzuki et al., PRB 95, 094406 (2017); PRB 99, 174407 (2019).
Reference (collinear classes): L. Smejkal, J. Sinova and T. Jungwirth, Phys. Rev. X 12, 031042 (2022).
