spin_moment
- sisl.physics.electron.spin_moment(state, S=None, project: bool = False)[source]
Spin magnetic moment (spin texture) and optionally orbitally resolved moments
This calculation only makes sense for non-colinear calculations.
The returned quantities are given in this order:
Spin magnetic moment along \(x\) direction
Spin magnetic moment along \(y\) direction
Spin magnetic moment along \(z\) direction
These are calculated using the Pauli matrices \(\boldsymbol\sigma_x\), \(\boldsymbol\sigma_y\) and \(\boldsymbol\sigma_z\):
\[\begin{split}\mathbf{S}_\alpha^x &= \langle \psi_\alpha | \boldsymbol\sigma_x \mathbf S | \psi_\alpha \rangle \\ \mathbf{S}_\alpha^y &= \langle \psi_\alpha | \boldsymbol\sigma_y \mathbf S | \psi_\alpha \rangle \\ \mathbf{S}_\alpha^z &= \langle \psi_\alpha | \boldsymbol\sigma_z \mathbf S | \psi_\alpha \rangle\end{split}\]If project is true, the above will be the orbitally resolved quantities.
- Parameters:
state (
array_like
) – vectors describing the electronic states, 2nd dimension contains the statesS (
array_like
, optional) – overlap matrix used in the \(\langle\psi|\mathbf S|\psi\rangle\) calculation. If None the identity matrix is assumed. The overlap matrix should correspond to the system and \(\mathbf k\) point the eigenvectors has been evaluated at.project (
bool
, optional) – whether the spin-moments will be orbitally resolved or not
Notes
This routine cannot check whether the input eigenvectors originate from a non-colinear calculation. If a non-polarized eigenvector is passed to this routine, the output will have no physical meaning.
- Returns:
numpy.ndarray
– spin moments per state with final dimension(3, state.shape[0])
, or(3, state.shape[0], state.shape[1]//2)
if project is true