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