Constraint DFT for non-collinear spin orientation

To calculate an electronic structure with an arbitrary spin orientation in the non-collinear DFT, OpenMX Ver. 3.6 provides a constraint functional which gives a penalty unless the difference between the calculated spin orientation and the initial one is zero [11]. The constraint DFT for the non-collinear spin orientation is available by the following keywords:

     scf.Constraint.NC.Spin       on      # on|off, default=off
     scf.Constraint.NC.Spin.v    0.5      # default=0.0(eV)

You can switch on the keyword 'scf.Constraint.NC.Spin' and give a magnitude by 'scf.Constraint.NC.Spin.v' which determines the strength of constraint, when the constraint for the spin orientation is introduced. The constraint is applied on each atom by specifying a switch as follows:

  <Atoms.SpeciesAndCoordinates           
     1   Cr    0.00000   0.00000   0.00000  7.0  5.0 -20.0 0.0  1  off
     2   Cr    0.00000   2.00000   0.00000  7.0  5.0  20.0 0.0  1  off
  Atoms.SpeciesAndCoordinates>

The '1' in the 10th column means that the constraint is applied, and '0' no constraint. The method constrains only the spin orientation. Therefore, the magnitude of spin can vary. Also the constraint scheme is compatible with the LDA+U calculation explained in the Section 'LDA+U'. As an illustration of this method, the dependence of the total energy and magnetic moment in a chromium dimer on the relative angle between two local spins is shown in Fig. 28. You can trace the calculation using an input file Cr2_CNC.dat in the directory 'work'.

Figure 28: The total energy and magnetic moment of Cr atom for a chromium dimer of which bond length is 2.0 Å. The input file is Cr2_CNC.dat in the directory 'work'.