spin_moment

sisl.physics.electron.spin_moment(state, S=None, projection='diagonal')

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 ${\mathit{\sigma }}_x$, ${\mathit{\sigma }}_y$ and ${\mathit{\sigma }}_z$:

$$\begin{array}{rl}{\mathbf{S}}_{\alpha }^x& =⟨{\psi }_{\alpha }|{\mathit{\sigma }}_x\mathbf{S}|{\psi }_{\alpha }⟩\\ {\mathbf{S}}_{\alpha }^y& =⟨{\psi }_{\alpha }|{\mathit{\sigma }}_y\mathbf{S}|{\psi }_{\alpha }⟩\\ {\mathbf{S}}_{\alpha }^z& =⟨{\psi }_{\alpha }|{\mathit{\sigma }}_z\mathbf{S}|{\psi }_{\alpha }⟩\end{array}$$

If projection is orbitals/basis/true, the above will be the orbitally resolved quantities.

Parameters:

• state (ndarray) – vectors describing the electronic states, 2nd dimension contains the states

• S (ndarray, optional) – overlap matrix used in the $⟨\psi |\mathbf{S}|\psi ⟩$ 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.

• projection (Union[ProjectionTypeTrace, ProjectionTypeDiag, ProjectionTypeHadamard, True, False]) – how the projection should be done

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.

See also

DOS

total DOS

PDOS

projected DOS

COP

calculate COOP or COHP curves

Returns:

spin moments per state with final dimension (3, state.shape[0]), or (3, state.shape[0], state.shape[1]//2) if projection is orbitals/basis/true

Return type:

numpy.ndarray

Parameters:

projection (Union[ProjectionTypeTrace, ProjectionTypeDiag, ProjectionTypeHadamard, True, False])