magnopy.converter43.to_biquadratic#

magnopy.converter43.to_biquadratic(parameter, tensor_form=False)[source]#

Computes biquadratic exchange parameter from full tensor form.

\[C_{4,2,2} \sum_{i,j,u,v} J^{ijuv} S_{\mu}^i S_{\mu}^j S_{\nu}^u S_{\nu}^v = C_{4,2,2}B \left( \boldsymbol{S}_{\mu} \cdot \boldsymbol{S}_{\nu} \right)^2 + \dots\]

where \(B\) is defined as

\[B = \dfrac{J^{xxxx} + J^{xyxy} + J^{xzxz} + J^{yxyx} + J^{yyyy} + J^{yzyz} + J^{zxzx} + J^{zyzy} + J^{zzzz}}{9}\]

Parameters:

parameter(3, 3, 3, 3) array-like: Full tensor parameter (\(\boldsymbol{J}\)).
tensor_formbool, default False: Whether to return tensor form of biquadratic exchange parameter instead of the scalar.

Returns:

Bfloat or (3, 3, 3, 3) numpy.ndarray

Biquadratic exchange parameter.

If tensor_form == False, then returns a number \(B\).
If tensor_form == True, then returns an array \(\boldsymbol{J}_B\).

See also

from_biquadratic

Examples

>>> import numpy as np
>>> from magnopy import converter43
>>> parameter = np.ones((3, 3, 3, 3))
>>> B = converter43.to_biquadratic(parameter=parameter)
>>> B
1.0
>>> J_B = converter43.to_biquadratic(parameter=parameter, tensor_form=True)
>>> J_B
array([[[[1., 0., 0.],
         [0., 0., 0.],
         [0., 0., 0.]],

        [[0., 1., 0.],
         [0., 0., 0.],
         [0., 0., 0.]],

        [[0., 0., 1.],
         [0., 0., 0.],
         [0., 0., 0.]]],


       [[[0., 0., 0.],
         [1., 0., 0.],
         [0., 0., 0.]],

        [[0., 0., 0.],
         [0., 1., 0.],
         [0., 0., 0.]],

        [[0., 0., 0.],
         [0., 0., 1.],
         [0., 0., 0.]]],


       [[[0., 0., 0.],
         [0., 0., 0.],
         [1., 0., 0.]],

        [[0., 0., 0.],
         [0., 0., 0.],
         [0., 1., 0.]],

        [[0., 0., 0.],
         [0., 0., 0.],
         [0., 0., 1.]]]])