The space group generators are stored in the symmetry.dat file, and spinw.lattice.sym stores all symmetry operators of the space group

All 230 standard spacegroups are supported.

You can add your own symmetry to the symmetry.dat file or supply it directly.

Form of symmetry string:

symStr = '-z, y+3/4, x+3/4; z+3/4, -y, x+3/4; z+3/4, y+3/4, -x; y+3/4, x+3/4, -z; x+3/4, -z, y+3/4; -z, x+3/4, y+3/4';

Applying the symmetry:

s.genlattice('lat_const', [3 3 3], 'angled', [90 90 90], 'spgr', symStr, 'label', 'F d -3 m Z')

Interaction symmetries

• Point group at bond center determines $J_{i,j}$
• Few rules:
  • Inversion symmetry $\rightarrow J_A = 0$
  • Mirror plane $\rightarrow D_\perp = 0$
  • 2-fold rotation $\rightarrow D \parallel C_2$
• Transformation under $(R, \mathbf{t})$ symmetry operators:

We have three types of tensor variable: polar vector, axial vector, 2d tensors.

The respective transformation rules using orthogonal matrices are:

Where $\nu$ is a column vector.

To generate transformation matrices use:

Rotation:

 R = sw_rotmat(rotAxis, rotAngle);

Mirroring:

[~, R] = sw_mirror(normalAxis);

Determine the symmetry allowed elements of the matrices with spinw.getmatrix or spinw.setmatrix.
Most common usage settings:

Text output of the possible matrix elements.

spinw.getmatrix('mat', 'J1');

Which for example gives the following output:

The symmetry analysis of the coupling between atom 1 and atom 2:
lattice translation vector: [0,0,0]
distance: 3.546 Angstrom
center of bond (in lattice units): [0.500,0.375,0.375]
label of the assigned matrix: 'J1'
allowed elements in the symmetric matrix:
  S = | C| 0| 0|
      | 0| A| B|
      | 0| B| A|

allowed components of the Dzyaloshinskii-Moriya vector:
  D = [ 0 , D1,-D1]

Matrix output of the possible modes, D: [3 3 nModes].

normModes = spinw.getmatrix('mat', 'J1');

Assigning pre-factors for the calculated modes and save them into the J1 matrix

A = 1; B = 2; C = 3;
spinw.setmatrix('mat', 'J1', 'pref', [A, B, C]);