crystod-mag -c 185_PPOSCAR_LuFeO3 --element Fe --qpoint GM

* Structure *
  Space group: P6_3cm (#185)
  Magnetic sites: Fe x 6
    Fe1: [0.0, 0.333977, 0.998821]
    Fe2: [0.333977, 0.0, 0.998821]
    Fe3: [0.666023, 0.666023, 0.998821]
    Fe4: [0.0, 0.666023, 0.498821]
    Fe5: [0.666023, 0.0, 0.498821]
    Fe6: [0.333977, 0.333977, 0.498821]

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

* Spin (axial-vector) representation *
  Spin (axial-vector) representation on Fe sites: 18 dimensions
  Decomposition: GM1(1) + 2 x GM2(1) + 2 x GM4(1) + GM3(1) + 3 x GM5(2) + 3 x GM6(2)

* Symmetry-adapted spin bases *
  GM1(1): dim 1 [AFM, 64pole]
  GM2(1): dim 1 [FM, dipole]
  GM2(1): dim 1 [AFM, quadrupole]
  GM4(1): dim 1 [AFM, octupole]
  GM4(1): dim 1 [AFM, hexadecapole]
  GM3(1): dim 1 [AFM, octupole]
  GM5(2): dim 2 [AFM, quadrupole]
  GM5(2): dim 2 [AFM, octupole]
  GM5(2): dim 2 [AFM, hexadecapole]
  GM6(2): dim 2 [FM, dipole]
  GM6(2): dim 2 [AFM, quadrupole]
  GM6(2): dim 2 [AFM, octupole]

* GM1(1) [AFM, 64pole] *
  component comp1:
    Fe1: S = [-0.8660, -0.5000,  0.0000]
    Fe2: S = [ 0.0000,  1.0000,  0.0000]
    Fe3: S = [ 0.8660, -0.5000,  0.0000]
    Fe4: S = [ 0.8660,  0.5000,  0.0000]
    Fe5: S = [-0.0000, -1.0000,  0.0000]
    Fe6: S = [-0.8660,  0.5000,  0.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: P6_3cm (BNS 185.197, type I), 12 operations, 0 with time reversal
    magnetic point group: 6mm
    allowed by symmetry: net magnetization none; linear magnetoelectric effect 1 component; piezomagnetism 1 component
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [-0.8660, -0.5000, 0.0000]
      Fe8: [0.0000, 1.0000, 0.0000]
      Fe9: [0.8660, -0.5000, 0.0000]
      Fe10: [0.8660, 0.5000, 0.0000]
      Fe11: [-0.0000, -1.0000, 0.0000]
      Fe12: [-0.8660, 0.5000, 0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.8660 -0.5000 0.0000   0.0000 1.0000 0.0000   0.8660 -0.5000 0.0000   0.8660 0.5000 0.0000   -0.0000 -1.0000 0.0000   -0.8660 0.5000 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM2(1) [FM, dipole] *
  component z:
    Fe1: S = [ 0.0000,  0.0000,  1.0000]
    Fe2: S = [ 0.0000,  0.0000,  1.0000]
    Fe3: S = [ 0.0000,  0.0000,  1.0000]
    Fe4: S = [ 0.0000,  0.0000,  1.0000]
    Fe5: S = [ 0.0000,  0.0000,  1.0000]
    Fe6: S = [ 0.0000,  0.0000,  1.0000]
    net moment: [0.0, 0.0, 6.0]
    magnetic space group: P6_3c'm' (BNS 185.201, type III), 12 operations, 6 with time reversal
    magnetic point group: 6m'm'
    allowed by symmetry: net magnetization along z; linear magnetoelectric effect 2 components; piezomagnetism 3 components
    collinear order: ferromagnet
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [0.0000, 0.0000, 1.0000]
      Fe8: [0.0000, 0.0000, 1.0000]
      Fe9: [0.0000, 0.0000, 1.0000]
      Fe10: [0.0000, 0.0000, 1.0000]
      Fe11: [0.0000, 0.0000, 1.0000]
      Fe12: [0.0000, 0.0000, 1.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.0000 0.0000 1.0000   0.0000 0.0000 1.0000   0.0000 0.0000 1.0000   0.0000 0.0000 1.0000   0.0000 0.0000 1.0000   0.0000 0.0000 1.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM2(1) [AFM, quadrupole] *
  component comp1:
    Fe1: S = [ 0.5000, -0.8660,  0.0000]
    Fe2: S = [-1.0000,  0.0000,  0.0000]
    Fe3: S = [ 0.5000,  0.8660,  0.0000]
    Fe4: S = [-0.5000,  0.8660,  0.0000]
    Fe5: S = [ 1.0000,  0.0000,  0.0000]
    Fe6: S = [-0.5000, -0.8660,  0.0000]
    net moment: [-0.0, 0.0, 0.0]
    magnetic space group: P6_3c'm' (BNS 185.201, type III), 12 operations, 6 with time reversal
    magnetic point group: 6m'm'
    allowed by symmetry: net magnetization along z; linear magnetoelectric effect 2 components; piezomagnetism 3 components
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [0.5000, -0.8660, 0.0000]
      Fe8: [-1.0000, 0.0000, 0.0000]
      Fe9: [0.5000, 0.8660, 0.0000]
      Fe10: [-0.5000, 0.8660, 0.0000]
      Fe11: [1.0000, 0.0000, 0.0000]
      Fe12: [-0.5000, -0.8660, 0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.5000 -0.8660 0.0000   -1.0000 0.0000 0.0000   0.5000 0.8660 0.0000   -0.5000 0.8660 0.0000   1.0000 0.0000 0.0000   -0.5000 -0.8660 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM4(1) [AFM, octupole] *
  component comp1:
    Fe1: S = [-0.5000,  0.8660,  0.0000]
    Fe2: S = [ 1.0000,  0.0000,  0.0000]
    Fe3: S = [-0.5000, -0.8660,  0.0000]
    Fe4: S = [-0.5000,  0.8660,  0.0000]
    Fe5: S = [ 1.0000,  0.0000,  0.0000]
    Fe6: S = [-0.5000, -0.8660,  0.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: P6_3'cm' (BNS 185.200, type III), 12 operations, 6 with time reversal
    magnetic point group: 6'mm'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism 1 component
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [-0.5000, 0.8660, 0.0000]
      Fe8: [1.0000, 0.0000, 0.0000]
      Fe9: [-0.5000, -0.8660, 0.0000]
      Fe10: [-0.5000, 0.8660, 0.0000]
      Fe11: [1.0000, 0.0000, 0.0000]
      Fe12: [-0.5000, -0.8660, 0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.5000 0.8660 0.0000   1.0000 0.0000 0.0000   -0.5000 -0.8660 0.0000   -0.5000 0.8660 0.0000   1.0000 0.0000 0.0000   -0.5000 -0.8660 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM4(1) [AFM, hexadecapole] *
  component z:
    Fe1: S = [ 0.0000,  0.0000,  1.0000]
    Fe2: S = [ 0.0000,  0.0000,  1.0000]
    Fe3: S = [ 0.0000,  0.0000,  1.0000]
    Fe4: S = [ 0.0000,  0.0000, -1.0000]
    Fe5: S = [ 0.0000,  0.0000, -1.0000]
    Fe6: S = [ 0.0000,  0.0000, -1.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: P6_3'cm' (BNS 185.200, type III), 12 operations, 6 with time reversal
    magnetic point group: 6'mm'
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism 1 component
    collinear order: altermagnet (g-wave; spin splitting allowed by symmetry ~ k_x k_z (k_x^2 - 3 k_y^2); spin-degenerate planes perpendicular to [100], [1 sqrt3 0], [1 -sqrt3 0], [001])
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [0.0000, 0.0000, 1.0000]
      Fe8: [0.0000, 0.0000, 1.0000]
      Fe9: [0.0000, 0.0000, 1.0000]
      Fe10: [0.0000, 0.0000, -1.0000]
      Fe11: [0.0000, 0.0000, -1.0000]
      Fe12: [0.0000, 0.0000, -1.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.0000 0.0000 1.0000   0.0000 0.0000 1.0000   0.0000 0.0000 1.0000   0.0000 0.0000 -1.0000   0.0000 0.0000 -1.0000   0.0000 0.0000 -1.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM3(1) [AFM, octupole] *
  component comp1:
    Fe1: S = [-0.8660, -0.5000,  0.0000]
    Fe2: S = [ 0.0000,  1.0000,  0.0000]
    Fe3: S = [ 0.8660, -0.5000,  0.0000]
    Fe4: S = [-0.8660, -0.5000,  0.0000]
    Fe5: S = [ 0.0000,  1.0000,  0.0000]
    Fe6: S = [ 0.8660, -0.5000,  0.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: P6_3'c'm (BNS 185.199, type III), 12 operations, 6 with time reversal
    magnetic point group: 6'm'm
    allowed by symmetry: net magnetization none; linear magnetoelectric effect none; piezomagnetism 1 component
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [-0.8660, -0.5000, 0.0000]
      Fe8: [0.0000, 1.0000, 0.0000]
      Fe9: [0.8660, -0.5000, 0.0000]
      Fe10: [-0.8660, -0.5000, 0.0000]
      Fe11: [0.0000, 1.0000, 0.0000]
      Fe12: [0.8660, -0.5000, 0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.8660 -0.5000 0.0000   0.0000 1.0000 0.0000   0.8660 -0.5000 0.0000   -0.8660 -0.5000 0.0000   0.0000 1.0000 0.0000   0.8660 -0.5000 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM5(2) [AFM, quadrupole] *
  component comp1:
    Fe1: S = [ 0.8660,  0.5000,  0.0000]
    Fe2: S = [-0.0000,  0.0000,  0.0000]
    Fe3: S = [ 0.8660, -0.5000,  0.0000]
    Fe4: S = [-0.8660, -0.5000,  0.0000]
    Fe5: S = [ 0.0000, -0.0000,  0.0000]
    Fe6: S = [-0.8660,  0.5000,  0.0000]
    net moment: [-0.0, 0.0, 0.0]
    magnetic space group: Cm'c'2_1 (BNS 36.176, type III), 4 operations, 2 with time reversal
    magnetic point group: m'm'2
    allowed by symmetry: net magnetization along z; linear magnetoelectric effect 3 components; piezomagnetism 5 components
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [0.8660, 0.5000, 0.0000]
      Fe8: [-0.0000, 0.0000, 0.0000]
      Fe9: [0.8660, -0.5000, 0.0000]
      Fe10: [-0.8660, -0.5000, 0.0000]
      Fe11: [0.0000, -0.0000, 0.0000]
      Fe12: [-0.8660, 0.5000, 0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.8660 0.5000 0.0000   -0.0000 0.0000 0.0000   0.8660 -0.5000 0.0000   -0.8660 -0.5000 0.0000   0.0000 -0.0000 0.0000   -0.8660 0.5000 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0
  component comp2:
    Fe1: S = [ 0.4330,  0.2500,  0.0000]
    Fe2: S = [ 0.0000,  1.0000,  0.0000]
    Fe3: S = [-0.4330,  0.2500,  0.0000]
    Fe4: S = [-0.4330, -0.2500,  0.0000]
    Fe5: S = [-0.0000, -1.0000,  0.0000]
    Fe6: S = [ 0.4330, -0.2500,  0.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: Cmc2_1 (BNS 36.172, type I), 4 operations, 0 with time reversal
    magnetic point group: mm2
    allowed by symmetry: net magnetization none; linear magnetoelectric effect 2 components; piezomagnetism 3 components
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [0.4330, 0.2500, 0.0000]
      Fe8: [0.0000, 1.0000, 0.0000]
      Fe9: [-0.4330, 0.2500, 0.0000]
      Fe10: [-0.4330, -0.2500, 0.0000]
      Fe11: [-0.0000, -1.0000, 0.0000]
      Fe12: [0.4330, -0.2500, 0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.4330 0.2500 0.0000   0.0000 1.0000 0.0000   -0.4330 0.2500 0.0000   -0.4330 -0.2500 0.0000   -0.0000 -1.0000 0.0000   0.4330 -0.2500 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM5(2) [AFM, octupole] *
  component comp1:
    Fe1: S = [ 0.2500, -0.4330,  0.0000]
    Fe2: S = [ 1.0000,  0.0000,  0.0000]
    Fe3: S = [ 0.2500,  0.4330,  0.0000]
    Fe4: S = [-0.2500,  0.4330,  0.0000]
    Fe5: S = [-1.0000, -0.0000,  0.0000]
    Fe6: S = [-0.2500, -0.4330,  0.0000]
    net moment: [-0.0, 0.0, 0.0]
    magnetic space group: Cm'c'2_1 (BNS 36.176, type III), 4 operations, 2 with time reversal
    magnetic point group: m'm'2
    allowed by symmetry: net magnetization along z; linear magnetoelectric effect 3 components; piezomagnetism 5 components
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [0.2500, -0.4330, 0.0000]
      Fe8: [1.0000, 0.0000, 0.0000]
      Fe9: [0.2500, 0.4330, 0.0000]
      Fe10: [-0.2500, 0.4330, 0.0000]
      Fe11: [-1.0000, -0.0000, 0.0000]
      Fe12: [-0.2500, -0.4330, 0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.2500 -0.4330 0.0000   1.0000 0.0000 0.0000   0.2500 0.4330 0.0000   -0.2500 0.4330 0.0000   -1.0000 -0.0000 0.0000   -0.2500 -0.4330 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0
  component comp2:
    Fe1: S = [-0.5000,  0.8660,  0.0000]
    Fe2: S = [ 0.0000, -0.0000,  0.0000]
    Fe3: S = [ 0.5000,  0.8660,  0.0000]
    Fe4: S = [ 0.5000, -0.8660,  0.0000]
    Fe5: S = [-0.0000,  0.0000,  0.0000]
    Fe6: S = [-0.5000, -0.8660,  0.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: Cmc2_1 (BNS 36.172, type I), 4 operations, 0 with time reversal
    magnetic point group: mm2
    allowed by symmetry: net magnetization none; linear magnetoelectric effect 2 components; piezomagnetism 3 components
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [-0.5000, 0.8660, 0.0000]
      Fe8: [0.0000, -0.0000, 0.0000]
      Fe9: [0.5000, 0.8660, 0.0000]
      Fe10: [0.5000, -0.8660, 0.0000]
      Fe11: [-0.0000, 0.0000, 0.0000]
      Fe12: [-0.5000, -0.8660, 0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.5000 0.8660 0.0000   0.0000 -0.0000 0.0000   0.5000 0.8660 0.0000   0.5000 -0.8660 0.0000   -0.0000 0.0000 0.0000   -0.5000 -0.8660 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM5(2) [AFM, hexadecapole] *
  component z:
    Fe1: S = [-0.0000, -0.0000,  0.5000]
    Fe2: S = [-0.0000, -0.0000, -1.0000]
    Fe3: S = [-0.0000, -0.0000,  0.5000]
    Fe4: S = [-0.0000, -0.0000,  0.5000]
    Fe5: S = [-0.0000, -0.0000, -1.0000]
    Fe6: S = [-0.0000, -0.0000,  0.5000]
    net moment: [0.0, 0.0, -0.0]
    magnetic space group: Cm'c'2_1 (BNS 36.176, type III), 4 operations, 2 with time reversal
    magnetic point group: m'm'2
    allowed by symmetry: net magnetization along z; linear magnetoelectric effect 3 components; piezomagnetism 5 components
    collinear order: compensated, sublattices not related by symmetry
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [-0.0000, -0.0000, 0.5000]
      Fe8: [-0.0000, -0.0000, -1.0000]
      Fe9: [-0.0000, -0.0000, 0.5000]
      Fe10: [-0.0000, -0.0000, 0.5000]
      Fe11: [-0.0000, -0.0000, -1.0000]
      Fe12: [-0.0000, -0.0000, 0.5000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.0000 -0.0000 0.5000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 0.5000   -0.0000 -0.0000 0.5000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 0.5000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0
  component z:
    Fe1: S = [ 0.0000,  0.0000,  1.0000]
    Fe2: S = [ 0.0000,  0.0000,  0.0000]
    Fe3: S = [ 0.0000,  0.0000, -1.0000]
    Fe4: S = [ 0.0000,  0.0000,  1.0000]
    Fe5: S = [ 0.0000,  0.0000,  0.0000]
    Fe6: S = [ 0.0000,  0.0000, -1.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: Cmc2_1 (BNS 36.172, type I), 4 operations, 0 with time reversal
    magnetic point group: mm2
    allowed by symmetry: net magnetization none; linear magnetoelectric effect 2 components; piezomagnetism 3 components
    collinear order: altermagnet (d-wave; spin splitting allowed by symmetry ~ k_x k_y; spin-degenerate planes perpendicular to [100], [010])
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [0.0000, 0.0000, 1.0000]
      Fe8: [0.0000, 0.0000, 0.0000]
      Fe9: [0.0000, 0.0000, -1.0000]
      Fe10: [0.0000, 0.0000, 1.0000]
      Fe11: [0.0000, 0.0000, 0.0000]
      Fe12: [0.0000, 0.0000, -1.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0.0000 0.0000 -1.0000   0.0000 0.0000 1.0000   0.0000 0.0000 0.0000   0.0000 0.0000 -1.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM6(2) [FM, dipole] *
  component x:
    Fe1: S = [ 1.0000, -0.0000,  0.0000]
    Fe2: S = [ 1.0000,  0.0000,  0.0000]
    Fe3: S = [ 1.0000, -0.0000,  0.0000]
    Fe4: S = [ 1.0000, -0.0000,  0.0000]
    Fe5: S = [ 1.0000,  0.0000,  0.0000]
    Fe6: S = [ 1.0000, -0.0000,  0.0000]
    net moment: [6.0, -0.0, 0.0]
    magnetic space group: Cm'c2_1' (BNS 36.174, type III), 4 operations, 2 with time reversal
    magnetic point group: m'm2'
    allowed by symmetry: net magnetization along x; linear magnetoelectric effect 2 components; piezomagnetism 5 components
    collinear order: ferromagnet
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [1.0000, -0.0000, 0.0000]
      Fe8: [1.0000, 0.0000, 0.0000]
      Fe9: [1.0000, -0.0000, 0.0000]
      Fe10: [1.0000, -0.0000, 0.0000]
      Fe11: [1.0000, 0.0000, 0.0000]
      Fe12: [1.0000, -0.0000, 0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   1.0000 -0.0000 0.0000   1.0000 0.0000 0.0000   1.0000 -0.0000 0.0000   1.0000 -0.0000 0.0000   1.0000 0.0000 0.0000   1.0000 -0.0000 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0
  component y:
    Fe1: S = [-0.0000,  1.0000, -0.0000]
    Fe2: S = [ 0.0000,  1.0000, -0.0000]
    Fe3: S = [-0.0000,  1.0000, -0.0000]
    Fe4: S = [-0.0000,  1.0000, -0.0000]
    Fe5: S = [ 0.0000,  1.0000, -0.0000]
    Fe6: S = [-0.0000,  1.0000, -0.0000]
    net moment: [-0.0, 6.0, 0.0]
    magnetic space group: Cmc'2_1' (BNS 36.175, type III), 4 operations, 2 with time reversal
    magnetic point group: mm'2'
    allowed by symmetry: net magnetization along y; linear magnetoelectric effect 2 components; piezomagnetism 5 components
    collinear order: ferromagnet
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [-0.0000, 1.0000, -0.0000]
      Fe8: [0.0000, 1.0000, -0.0000]
      Fe9: [-0.0000, 1.0000, -0.0000]
      Fe10: [-0.0000, 1.0000, -0.0000]
      Fe11: [0.0000, 1.0000, -0.0000]
      Fe12: [-0.0000, 1.0000, -0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.0000 1.0000 -0.0000   0.0000 1.0000 -0.0000   -0.0000 1.0000 -0.0000   -0.0000 1.0000 -0.0000   0.0000 1.0000 -0.0000   -0.0000 1.0000 -0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM6(2) [AFM, quadrupole] *
  component comp1:
    Fe1: S = [ 0.5000,  0.8660,  0.0000]
    Fe2: S = [-1.0000, -0.0000,  0.0000]
    Fe3: S = [ 0.5000, -0.8660,  0.0000]
    Fe4: S = [ 0.5000,  0.8660,  0.0000]
    Fe5: S = [-1.0000, -0.0000,  0.0000]
    Fe6: S = [ 0.5000, -0.8660,  0.0000]
    net moment: [-0.0, 0.0, 0.0]
    magnetic space group: Cm'c2_1' (BNS 36.174, type III), 4 operations, 2 with time reversal
    magnetic point group: m'm2'
    allowed by symmetry: net magnetization along x; linear magnetoelectric effect 2 components; piezomagnetism 5 components
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [0.5000, 0.8660, 0.0000]
      Fe8: [-1.0000, -0.0000, 0.0000]
      Fe9: [0.5000, -0.8660, 0.0000]
      Fe10: [0.5000, 0.8660, 0.0000]
      Fe11: [-1.0000, -0.0000, 0.0000]
      Fe12: [0.5000, -0.8660, 0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.5000 0.8660 0.0000   -1.0000 -0.0000 0.0000   0.5000 -0.8660 0.0000   0.5000 0.8660 0.0000   -1.0000 -0.0000 0.0000   0.5000 -0.8660 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0
  component comp2:
    Fe1: S = [ 0.8660, -0.5000, -0.0000]
    Fe2: S = [-0.0000,  1.0000, -0.0000]
    Fe3: S = [-0.8660, -0.5000, -0.0000]
    Fe4: S = [ 0.8660, -0.5000, -0.0000]
    Fe5: S = [-0.0000,  1.0000, -0.0000]
    Fe6: S = [-0.8660, -0.5000, -0.0000]
    net moment: [-0.0, -0.0, 0.0]
    magnetic space group: Cmc'2_1' (BNS 36.175, type III), 4 operations, 2 with time reversal
    magnetic point group: mm'2'
    allowed by symmetry: net magnetization along y; linear magnetoelectric effect 2 components; piezomagnetism 5 components
    collinear order: noncollinear (not classified)
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [0.8660, -0.5000, -0.0000]
      Fe8: [-0.0000, 1.0000, -0.0000]
      Fe9: [-0.8660, -0.5000, -0.0000]
      Fe10: [0.8660, -0.5000, -0.0000]
      Fe11: [-0.0000, 1.0000, -0.0000]
      Fe12: [-0.8660, -0.5000, -0.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.8660 -0.5000 -0.0000   -0.0000 1.0000 -0.0000   -0.8660 -0.5000 -0.0000   0.8660 -0.5000 -0.0000   -0.0000 1.0000 -0.0000   -0.8660 -0.5000 -0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* GM6(2) [AFM, octupole] *
  component z:
    Fe1: S = [-0.0000, -0.0000,  0.5000]
    Fe2: S = [-0.0000, -0.0000, -1.0000]
    Fe3: S = [-0.0000, -0.0000,  0.5000]
    Fe4: S = [-0.0000, -0.0000, -0.5000]
    Fe5: S = [-0.0000, -0.0000,  1.0000]
    Fe6: S = [-0.0000, -0.0000, -0.5000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: Cm'c2_1' (BNS 36.174, type III), 4 operations, 2 with time reversal
    magnetic point group: m'm2'
    allowed by symmetry: net magnetization along x; linear magnetoelectric effect 2 components; piezomagnetism 5 components
    collinear order: altermagnet (d-wave; spin splitting allowed by symmetry ~ k_x k_z; spin-degenerate planes perpendicular to [100], [001])
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [-0.0000, -0.0000, 0.5000]
      Fe8: [-0.0000, -0.0000, -1.0000]
      Fe9: [-0.0000, -0.0000, 0.5000]
      Fe10: [-0.0000, -0.0000, -0.5000]
      Fe11: [-0.0000, -0.0000, 1.0000]
      Fe12: [-0.0000, -0.0000, -0.5000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.0000 -0.0000 0.5000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 0.5000   -0.0000 -0.0000 -0.5000   -0.0000 -0.0000 1.0000   -0.0000 -0.0000 -0.5000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0
  component z:
    Fe1: S = [-0.0000, -0.0000,  1.0000]
    Fe2: S = [-0.0000, -0.0000, -0.0000]
    Fe3: S = [-0.0000, -0.0000, -1.0000]
    Fe4: S = [-0.0000, -0.0000, -1.0000]
    Fe5: S = [-0.0000, -0.0000,  0.0000]
    Fe6: S = [-0.0000, -0.0000,  1.0000]
    net moment: [0.0, 0.0, 0.0]
    magnetic space group: Cmc'2_1' (BNS 36.175, type III), 4 operations, 2 with time reversal
    magnetic point group: mm'2'
    allowed by symmetry: net magnetization along y; linear magnetoelectric effect 2 components; piezomagnetism 5 components
    collinear order: altermagnet (d-wave; spin splitting allowed by symmetry ~ k_y k_z; spin-degenerate planes perpendicular to [010], [001])
    spin directions (all atoms, POSCAR order):
      Lu1: [0, 0, 0]
      Lu2: [0, 0, 0]
      Lu3: [0, 0, 0]
      Lu4: [0, 0, 0]
      Lu5: [0, 0, 0]
      Lu6: [0, 0, 0]
      Fe7: [-0.0000, -0.0000, 1.0000]
      Fe8: [-0.0000, -0.0000, -0.0000]
      Fe9: [-0.0000, -0.0000, -1.0000]
      Fe10: [-0.0000, -0.0000, -1.0000]
      Fe11: [-0.0000, -0.0000, 0.0000]
      Fe12: [-0.0000, -0.0000, 1.0000]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      O15: [0, 0, 0]
      O16: [0, 0, 0]
      O17: [0, 0, 0]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      O22: [0, 0, 0]
      O23: [0, 0, 0]
      O24: [0, 0, 0]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      O29: [0, 0, 0]
      O30: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.0000 -0.0000 1.0000   -0.0000 -0.0000 -0.0000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 -1.0000   -0.0000 -0.0000 0.0000   -0.0000 -0.0000 1.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0

* Magnetic groups and collinear classes *
basis                       component  MSG (BNS)           type  MPG    net magnetization  class
GM1(1) [AFM, 64pole]        comp1      P6_3cm (185.197)    I     6mm    none               noncollinear
GM2(1) [FM, dipole]         z          P6_3c'm' (185.201)  III   6m'm'  along z            ferromagnet
GM2(1) [AFM, quadrupole]    comp1      P6_3c'm' (185.201)  III   6m'm'  along z            noncollinear
GM4(1) [AFM, octupole]      comp1      P6_3'cm' (185.200)  III   6'mm'  none               noncollinear
GM4(1) [AFM, hexadecapole]  z          P6_3'cm' (185.200)  III   6'mm'  none               altermagnet (g-wave)
GM3(1) [AFM, octupole]      comp1      P6_3'c'm (185.199)  III   6'm'm  none               noncollinear
GM5(2) [AFM, quadrupole]    comp1      Cm'c'2_1 (36.176)   III   m'm'2  along z            noncollinear
GM5(2) [AFM, quadrupole]    comp2      Cmc2_1 (36.172)     I     mm2    none               noncollinear
GM5(2) [AFM, octupole]      comp1      Cm'c'2_1 (36.176)   III   m'm'2  along z            noncollinear
GM5(2) [AFM, octupole]      comp2      Cmc2_1 (36.172)     I     mm2    none               noncollinear
GM5(2) [AFM, hexadecapole]  z          Cm'c'2_1 (36.176)   III   m'm'2  along z            compensated (unrelated sublattices)
GM5(2) [AFM, hexadecapole]  z_2        Cmc2_1 (36.172)     I     mm2    none               altermagnet (d-wave)
GM6(2) [FM, dipole]         x          Cm'c2_1' (36.174)   III   m'm2'  along x            ferromagnet
GM6(2) [FM, dipole]         y          Cmc'2_1' (36.175)   III   mm'2'  along y            ferromagnet
GM6(2) [AFM, quadrupole]    comp1      Cm'c2_1' (36.174)   III   m'm2'  along x            noncollinear
GM6(2) [AFM, quadrupole]    comp2      Cmc'2_1' (36.175)   III   mm'2'  along y            noncollinear
GM6(2) [AFM, octupole]      z          Cm'c2_1' (36.174)   III   m'm2'  along x            altermagnet (d-wave)
GM6(2) [AFM, octupole]      z_2        Cmc'2_1' (36.175)   III   mm'2'  along y            altermagnet (d-wave)

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_LuFeO3_spin_GM1_64pole_comp1.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM2_dipole_z.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM2_quadrupole_comp1.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM4_octupole_comp1.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM4_hexadecapole_z.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM3_octupole_comp1.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM5_quadrupole_comp1.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM5_quadrupole_comp2.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM5_octupole_comp1.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM5_octupole_comp2.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM5_hexadecapole_z.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM5_hexadecapole_z_2.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM6_dipole_x.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM6_dipole_y.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM6_quadrupole_comp1.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM6_quadrupole_comp2.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM6_octupole_z.vesta
  Spin basis written to: POSCAR_LuFeO3_spin_GM6_octupole_z_2.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).
