magnopy.converter22.to_symm_anisotropy

magnopy.converter22.to_symm_anisotropy(parameter)

Extracts traceless, symmetric anisotropic part of the full matrix parameter.

\[C_{2,2} \boldsymbol{S}_{\mu} \boldsymbol{J} \boldsymbol{S}_{\nu} = C_{2,2} J_{iso} \boldsymbol{S}_{\mu} \cdot \boldsymbol{S}_{\nu} + C_{2,2} \boldsymbol{S}_{\mu} \boldsymbol{J}_S \boldsymbol{S}_{\nu} + C_{2,2} \boldsymbol{D} \cdot \left( \boldsymbol{S}_{\mu} \times \boldsymbol{S}_{\nu} \right)\]

where matrix \(\boldsymbol{J}_S\) is defined as

\[\boldsymbol{J}_S = \dfrac{\boldsymbol{J} + \boldsymbol{J}^T}{2}\]

Parameters:

parameter(3, 3) array-like

Full matrix of the exchange parameter (\(\boldsymbol{J}\)).

Returns:

anisofloat or (3, 3) numpy.ndarray

Matrix of a traceless, symmetric anisotropy.

See also

to_iso

to_dmi

Examples

>>> import magnopy
>>> matrix = [[1, 3, 4], [-1, -2, 0], [4, 0, 10]]
>>> magnopy.converter22.to_symm_anisotropy(matrix)
array([[-2.,  1.,  4.],
       [ 1., -5.,  0.],
       [ 4.,  0.,  7.]])