Added tests for the skyrmion number calculations in atomistic simulations using different methods and either Square and Hexagonal meshes. Removed the Skyrmion Number calculation for the Table in the LLg code, since it is meaningless for a hexagonal grid at least we specify the new sk number method

Author: davidcorteso

fidimag/atomistic/llg.py

@@ -52,10 +52,10 @@ def __init__(self, mesh, name='unnamed', use_jac=False):
             'get': lambda sim: sim.compute_spin_error(),
             'header': 'm_error'}
 
-        self.saver.entities['skx_num'] = {
-            'unit': '<>',
-            'get': lambda sim: sim.skyrmion_number(),
-            'header': 'skx_num'}
+        # self.saver.entities['skx_num'] = {
+        #     'unit': '<>',
+        #     'get': lambda sim: sim.skyrmion_number(),
+        #     'header': 'skx_num'}
 
         self.saver.update_entity_order()
 

tests/test_skyrmion_number.py

@@ -1,16 +1,22 @@
 from __future__ import print_function
 from fidimag.atomistic import Sim
 from fidimag.common import CuboidMesh
+from fidimag.atomistic.hexagonal_mesh import HexagonalMesh
 from fidimag.atomistic import DMI
 from fidimag.atomistic import UniformExchange
 from fidimag.atomistic import Zeeman
+from fidimag.atomistic import Anisotropy
 
 from fidimag.micro import DMI as microDMI
 from fidimag.micro import UniaxialAnisotropy as microUniaxialAnisotropy
 from fidimag.micro import UniformExchange as microUniformExchange
 from fidimag.micro import Zeeman as microZeeman
 from fidimag.micro import Sim as microSim
 
+import fidimag.common.constant as const
+
+import numpy as np
+
 
 def init_m(pos, x0, y0, r):
     x = pos[0]
@@ -27,6 +33,20 @@ def init_m(pos, x0, y0, r):
         return m2
 
 
+def init_m_multiple_sks(pos, r, sk_pos):
+    # Generate singularities with radius r at the positions in the
+    # sk_pos list, in order to generate multiple skyrmions after
+    # relaxation. Example: sk_pos=[(1, 1), (2, 2)]
+    #                               x  y
+    x, y = pos[0], pos[1]
+
+    for coord in sk_pos:
+        if (x - coord[0]) ** 2 + (y - coord[1]) ** 2 < r ** 2:
+            return (0, 0, 1)
+
+    return (0, 0, -1)
+
+
 def test_skx_num_atomistic():
     """
     Test the *finite spin chirality* or skyrmion number for
@@ -45,6 +65,10 @@ def test_skx_num_atomistic():
     The area of the two triangles cover a unit cell, thus the sum
     cover the whole area of the atomic lattice
 
+    We also test the Berg and Luscher definition for a topological
+    charge (see the hexagonal mesh test for details) in a
+    square lattice.
+
     This test generate a skyrmion pointing down with unrealistic
     paremeters.
 
@@ -79,8 +103,82 @@ def test_skx_num_atomistic():
 
     skn = sim.skyrmion_number()
     print('skx_number', skn)
+
+    skn_BL = sim.skyrmion_number(method='BergLuscher')
+    print('skx_number_BergLuscher', skn_BL)
+
+    # Test the finite chirality method
     assert skn > -1 and skn < -0.99
 
+    # Test the Berg-Luscher method
+    assert np.abs(skn_BL - (-1)) < 1e-4 and np.sign(skn_BL) < 0
+
+
+def test_skx_num_atomistic_hexagonal():
+    """
+
+    Test the topological charge or skyrmion number for a discrete spins
+    simulation in a two dimensional hexagonal lattice, using Berg and Luscher
+    definition in [Nucl Phys B 190, 412 (1981)] and simplified in [PRB 93,
+    174403 (2016)], which maps a triangulated lattice (using triangles of
+    neighbouring spins) area into a unit sphere.
+
+    The areas of two triangles per lattice site cover a unit cell, thus the sum
+    cover the whole area of the atomic lattice
+
+    This test generates a skyrmion pointing down and two skyrmions pointing up
+    in a PdFe sample using magnetic parameters from: PRL 114, 177203 (2015)
+
+    """
+
+    mesh = HexagonalMesh(0.2715, 41, 41, periodicity=(True, True))
+
+    sim = Sim(mesh, name='skx_number_hexagonal')
+    sim.set_tols(rtol=1e-6, atol=1e-6)
+    sim.alpha = 1.0
+    sim.gamma = 1.0
+    sim.mu_s = 3 * const.mu_B
+
+    sim.set_m(lambda pos: init_m(pos, 16.1, 10, 2))
+
+    sim.do_precession = False
+
+    J = 5.881 * const.meV
+    exch = UniformExchange(J)
+    sim.add(exch)
+
+    D = 1.557 * const.meV
+    dmi = DMI(D, dmi_type='interfacial')
+    sim.add(dmi)
+
+    sim.add(Anisotropy(0.406 * const.meV, axis=[0, 0, 1]))
+
+    zeeman = Zeeman([0, 0, 2.5])
+    sim.add(zeeman)
+
+    sim.relax(dt=1e-13, stopping_dmdt=1e-2, max_steps=2000,
+              save_m_steps=None, save_vtk_steps=100)
+
+    skn_single = sim.skyrmion_number(method='BergLuscher')
+    print('skx_number_hexagonal', skn_single)
+
+    # Now we generate two skyrmions pointing up
+    sim.reset_integrator()
+    sim.set_m(lambda pos: init_m_multiple_sks(pos, 1,
+                                              sk_pos=[(9, 6), (18, 12)]
+                                              )
+              )
+    sim.get_interaction('Zeeman').update_field([0, 0, -2.5])
+    sim.relax(dt=1e-13, stopping_dmdt=1e-2, max_steps=2000,
+              save_m_steps=None, save_vtk_steps=None)
+
+    skn_two = sim.skyrmion_number(method='BergLuscher')
+    print('skx_number_hexagonal', skn_two)
+
+    # Check that we get a right sk number
+    assert np.abs(skn_single - (-1)) < 1e-4 and np.sign(skn_single) < 0
+    assert np.abs(skn_two - (2)) < 1e-4 and np.sign(skn_two) > 0
+
 
 def test_skx_num_micromagnetic():
     """
@@ -145,4 +243,5 @@ def test_skx_num_micromagnetic():
 if __name__ == '__main__':
 
     test_skx_num_atomistic()
+    test_skx_num_atomistic_hexagonal()
     test_skx_num_micromagnetic()