magpack.vectorop.skyrmion_number#

skyrmion_number(vector_field)#

Calculates the skyrmion topological number.

Parameters:
vector_fieldnp.ndarray

The vector field shape (n, x, y) from which the skyrmion number will be calculated.

Returns:
np.ndarray

The skyrmion topological number.

Notes

The skyrmion topological number for the vector field \(\mathbf{m}\) is given by evaluating integral:

\[\frac{1}{4\pi} \int \mathbf{m} \cdot \left( \frac{\partial \mathbf{m}}{\partial x} \times \frac{\partial \mathbf{m}}{\partial y} \right)\,\text{d}x \text{d}y\]