crystod-mag -c 139_PPOSCAR_La2CuO4 --element Cu --qpoint 0 0 0.5 --conventional

* Structure *
  Space group: I4/mmm (#139)
  Magnetic sites: Cu x 1
    Cu1: [0.0, 0.0, 0.0]

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

* Spin (axial-vector) representation *
  Spin (axial-vector) representation on Cu sites: 3 dimensions
  Decomposition: X3+(1) + X4+(1) + X2+(1)

* Symmetry-adapted spin bases *
  X3+(1): dim 1 [AFM (q != 0)]
  X4+(1): dim 1 [AFM (q != 0)]
  X2+(1): dim 1 [AFM (q != 0)]

* Magnetic cell *
  Magnetic (commensurate) supercell: 1x1x2
  Display cell: conventional (I centring), 2x2x1 cells
  the magnetic space group refers to the real spin field of the magnetic cell (global phase fixed as the VESTA export)

* X3+(1) [AFM (q != 0)] *
  component 1m10:
    Cu1: S = [ 0.7071, -0.7071,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: C_Amca (BNS 64.480, type IV), 64 operations, 32 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) (conventional magnetic cell):
      La1: [0, 0, 0]
      La2: [0, 0, 0]
      Cu3: [0.7071, -0.7071, 0.0000]
      O4: [0, 0, 0]
      O5: [0, 0, 0]
      O6: [0, 0, 0]
      O7: [0, 0, 0]
      La8: [0, 0, 0]
      La9: [0, 0, 0]
      Cu10: [-0.7071, 0.7071, -0.0000]
      O11: [0, 0, 0]
      O12: [0, 0, 0]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      La15: [0, 0, 0]
      La16: [0, 0, 0]
      Cu17: [-0.7071, 0.7071, -0.0000]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      La22: [0, 0, 0]
      La23: [0, 0, 0]
      Cu24: [-0.7071, 0.7071, -0.0000]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      La29: [0, 0, 0]
      La30: [0, 0, 0]
      Cu31: [0.7071, -0.7071, 0.0000]
      O32: [0, 0, 0]
      O33: [0, 0, 0]
      O34: [0, 0, 0]
      O35: [0, 0, 0]
      La36: [0, 0, 0]
      La37: [0, 0, 0]
      Cu38: [0.7071, -0.7071, 0.0000]
      O39: [0, 0, 0]
      O40: [0, 0, 0]
      O41: [0, 0, 0]
      O42: [0, 0, 0]
      La43: [0, 0, 0]
      La44: [0, 0, 0]
      Cu45: [0.7071, -0.7071, 0.0000]
      O46: [0, 0, 0]
      O47: [0, 0, 0]
      O48: [0, 0, 0]
      O49: [0, 0, 0]
      La50: [0, 0, 0]
      La51: [0, 0, 0]
      Cu52: [-0.7071, 0.7071, -0.0000]
      O53: [0, 0, 0]
      O54: [0, 0, 0]
      O55: [0, 0, 0]
      O56: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0.7071 -0.7071 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.7071 0.7071 -0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.7071 0.7071 -0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.7071 0.7071 -0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.7071 -0.7071 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.7071 -0.7071 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.7071 -0.7071 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.7071 0.7071 -0.0000   0 0 0   0 0 0   0 0 0   0 0 0

* X4+(1) [AFM (q != 0)] *
  component 110:
    Cu1: S = [ 0.7071,  0.7071,  0.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: C_Accm (BNS 66.500, type IV), 64 operations, 32 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) (conventional magnetic cell):
      La1: [0, 0, 0]
      La2: [0, 0, 0]
      Cu3: [0.7071, 0.7071, 0.0000]
      O4: [0, 0, 0]
      O5: [0, 0, 0]
      O6: [0, 0, 0]
      O7: [0, 0, 0]
      La8: [0, 0, 0]
      La9: [0, 0, 0]
      Cu10: [-0.7071, -0.7071, -0.0000]
      O11: [0, 0, 0]
      O12: [0, 0, 0]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      La15: [0, 0, 0]
      La16: [0, 0, 0]
      Cu17: [-0.7071, -0.7071, -0.0000]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      La22: [0, 0, 0]
      La23: [0, 0, 0]
      Cu24: [-0.7071, -0.7071, -0.0000]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      La29: [0, 0, 0]
      La30: [0, 0, 0]
      Cu31: [0.7071, 0.7071, 0.0000]
      O32: [0, 0, 0]
      O33: [0, 0, 0]
      O34: [0, 0, 0]
      O35: [0, 0, 0]
      La36: [0, 0, 0]
      La37: [0, 0, 0]
      Cu38: [0.7071, 0.7071, 0.0000]
      O39: [0, 0, 0]
      O40: [0, 0, 0]
      O41: [0, 0, 0]
      O42: [0, 0, 0]
      La43: [0, 0, 0]
      La44: [0, 0, 0]
      Cu45: [0.7071, 0.7071, 0.0000]
      O46: [0, 0, 0]
      O47: [0, 0, 0]
      O48: [0, 0, 0]
      O49: [0, 0, 0]
      La50: [0, 0, 0]
      La51: [0, 0, 0]
      Cu52: [-0.7071, -0.7071, -0.0000]
      O53: [0, 0, 0]
      O54: [0, 0, 0]
      O55: [0, 0, 0]
      O56: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0.7071 0.7071 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.7071 -0.7071 -0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.7071 -0.7071 -0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.7071 -0.7071 -0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.7071 0.7071 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.7071 0.7071 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.7071 0.7071 0.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.7071 -0.7071 -0.0000   0 0 0   0 0 0   0 0 0   0 0 0

* X2+(1) [AFM (q != 0)] *
  component z:
    Cu1: S = [ 0.0000,  0.0000,  1.0000]
    net moment over the magnetic supercell: [0.0, 0.0, 0.0]
    magnetic space group: C_Amca (BNS 64.480, type IV), 64 operations, 32 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) (conventional magnetic cell):
      La1: [0, 0, 0]
      La2: [0, 0, 0]
      Cu3: [0.0000, 0.0000, 1.0000]
      O4: [0, 0, 0]
      O5: [0, 0, 0]
      O6: [0, 0, 0]
      O7: [0, 0, 0]
      La8: [0, 0, 0]
      La9: [0, 0, 0]
      Cu10: [-0.0000, -0.0000, -1.0000]
      O11: [0, 0, 0]
      O12: [0, 0, 0]
      O13: [0, 0, 0]
      O14: [0, 0, 0]
      La15: [0, 0, 0]
      La16: [0, 0, 0]
      Cu17: [-0.0000, -0.0000, -1.0000]
      O18: [0, 0, 0]
      O19: [0, 0, 0]
      O20: [0, 0, 0]
      O21: [0, 0, 0]
      La22: [0, 0, 0]
      La23: [0, 0, 0]
      Cu24: [-0.0000, -0.0000, -1.0000]
      O25: [0, 0, 0]
      O26: [0, 0, 0]
      O27: [0, 0, 0]
      O28: [0, 0, 0]
      La29: [0, 0, 0]
      La30: [0, 0, 0]
      Cu31: [0.0000, 0.0000, 1.0000]
      O32: [0, 0, 0]
      O33: [0, 0, 0]
      O34: [0, 0, 0]
      O35: [0, 0, 0]
      La36: [0, 0, 0]
      La37: [0, 0, 0]
      Cu38: [0.0000, 0.0000, 1.0000]
      O39: [0, 0, 0]
      O40: [0, 0, 0]
      O41: [0, 0, 0]
      O42: [0, 0, 0]
      La43: [0, 0, 0]
      La44: [0, 0, 0]
      Cu45: [0.0000, 0.0000, 1.0000]
      O46: [0, 0, 0]
      O47: [0, 0, 0]
      O48: [0, 0, 0]
      O49: [0, 0, 0]
      La50: [0, 0, 0]
      La51: [0, 0, 0]
      Cu52: [-0.0000, -0.0000, -1.0000]
      O53: [0, 0, 0]
      O54: [0, 0, 0]
      O55: [0, 0, 0]
      O56: [0, 0, 0]
    MAGMOM = 0 0 0   0 0 0   0.0000 0.0000 1.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.0000 -0.0000 -1.0000   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 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.0000 -0.0000 -1.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.0000 0.0000 1.0000   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 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0.0000 0.0000 1.0000   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   0 0 0   -0.0000 -0.0000 -1.0000   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
X3+(1) [AFM (q != 0)]  1m10       C_Amca (64.480)  IV    mmm1'  none               antiferromagnet (T tau)
X4+(1) [AFM (q != 0)]  110        C_Accm (66.500)  IV    mmm1'  none               antiferromagnet (T tau)
X2+(1) [AFM (q != 0)]  z          C_Amca (64.480)  IV    mmm1'  none               antiferromagnet (T tau)

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_La2CuO4_spin_X3+_X_1m10_conv.vesta
  Spin basis written to: POSCAR_La2CuO4_spin_X4+_X_110_conv.vesta
  Spin basis written to: POSCAR_La2CuO4_spin_X2+_X_z_conv.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).
