magnopy.make_supercell

magnopy.make_supercell(spinham: SpinHamiltonian, supercell)

Creates a spin Hamiltonian on the supercell.

Parameters:

spinhamSpinHamiltonian

Original spin Hamiltonian. spinham.cell is interpreted as the original unit cell.

supercell(3, ) tuple or list of int

Repetitions of the unit cell (spinham.cell) along each lattice vector that define the unit cell. If \((i, j, k)\) is given, then the supercell is formally defined as \((i\cdot\boldsymbol{a}_1, j\cdot\boldsymbol{a}_2, k\cdot\boldsymbol{a}_3)\), where \((\boldsymbol{a}_1, \boldsymbol{a}_2, \boldsymbol{a}_3)\) is the original cell (spinham.cell).

Returns:

new_spinhamSpinHamiltonian

Spin Hamiltonian that is defined on a supercell and has the same parameters as the given spinham propagated over the whole supercell.

Examples

First a simple example with only on-site parameters present in the Hamiltonian (i.e p21) and two atoms per unit cell.

>>> import numpy as np
>>> import magnopy
>>> # First create the original spin Hamiltonian
>>> cell = np.eye(3)
>>> atoms = dict(
...     names=["Fe1", "Fe2"],
...     positions=[[0, 0, 0], [0.5, 0.5, 0.5]],
...     spins=[1, 1],
...     g_factors=[2, 2],
... )
>>> convention = magnopy.Convention(
...     spin_normalized=False, multiple_counting=True, c21=1
... )
>>> spinham = magnopy.SpinHamiltonian(
...     cell=cell, atoms=atoms, convention=convention
... )
>>> # Add an on-site parameter for both atoms
>>> spinham.add_21(alpha=0, parameter=np.eye(3))
>>> spinham.add_21(alpha=1, parameter=np.eye(3))
>>> # Now create a spin Hamiltonian on the (2, 2, 2) supercell
>>> new_spinham = magnopy.make_supercell(spinham=spinham, supercell=(2, 2, 2))
>>> # Note that the unit cell of the new Hamiltonian is the supercell of the original one
>>> new_spinham.cell
array([[2., 0., 0.],
       [0., 2., 0.],
       [0., 0., 2.]])
>>> # All the atoms of the supercell are now contained in the unit cell of the
>>> # new Hamiltonian
>>> len(spinham.atoms.names)
2
>>> len(new_spinham.atoms.names)
16
>>> for i in range(2):
...     print(
...         spinham.atoms.names[i],
...         spinham.atoms.positions[i],
...         spinham.atoms.spins[i],
...     )
Fe1 [0, 0, 0] 1
Fe2 [0.5, 0.5, 0.5] 1
>>> for i in range(16):
...     print(
...         new_spinham.atoms.names[i],
...         new_spinham.atoms.positions[i],
...         new_spinham.atoms.spins[i],
...     )
Fe1_0_0_0 [0.0, 0.0, 0.0] 1
Fe2_0_0_0 [0.25, 0.25, 0.25] 1
Fe1_1_0_0 [0.5, 0.0, 0.0] 1
Fe2_1_0_0 [0.75, 0.25, 0.25] 1
Fe1_0_1_0 [0.0, 0.5, 0.0] 1
Fe2_0_1_0 [0.25, 0.75, 0.25] 1
Fe1_1_1_0 [0.5, 0.5, 0.0] 1
Fe2_1_1_0 [0.75, 0.75, 0.25] 1
Fe1_0_0_1 [0.0, 0.0, 0.5] 1
Fe2_0_0_1 [0.25, 0.25, 0.75] 1
Fe1_1_0_1 [0.5, 0.0, 0.5] 1
Fe2_1_0_1 [0.75, 0.25, 0.75] 1
Fe1_0_1_1 [0.0, 0.5, 0.5] 1
Fe2_0_1_1 [0.25, 0.75, 0.75] 1
Fe1_1_1_1 [0.5, 0.5, 0.5] 1
Fe2_1_1_1 [0.75, 0.75, 0.75] 1
>>> # The parameters are updated as well
>>> len(spinham.p21)
2
>>> for alpha, _ in spinham.p21:
...     print(alpha)
0
1
>>> len(new_spinham.p21)
16
>>> for alpha, _ in new_spinham.p21:
...     print(alpha)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Second example with one atom per unit cell, but with the bilinear interaction that connects two different atoms (p22).

>>> import numpy as np
>>> import magnopy
>>> # First create the original spin Hamiltonian
>>> cell = np.eye(3)
>>> atoms = dict(names=["Fe"], positions=[[0, 0, 0]], spins=[1], g_factors=[2])
>>> convention = magnopy.Convention(
...     spin_normalized=False, multiple_counting=True, c22=1
... )
>>> spinham = magnopy.SpinHamiltonian(
...     cell=cell, atoms=atoms, convention=convention
... )
>>> # Add an on-site parameter for both atoms
>>> spinham.add_22(alpha=0, beta=0, nu=(1, 0, 0), parameter=np.eye(3))
>>> # Now create a spin Hamiltonian on the (2, 2, 2) supercell
>>> new_spinham = magnopy.make_supercell(spinham=spinham, supercell=(2, 2, 2))
>>> len(new_spinham.atoms.names)
8
>>> for i in range(8):
...     print(
...         new_spinham.atoms.names[i],
...         new_spinham.atoms.positions[i],
...         new_spinham.atoms.spins[i],
...     )
Fe_0_0_0 [0.0, 0.0, 0.0] 1
Fe_1_0_0 [0.5, 0.0, 0.0] 1
Fe_0_1_0 [0.0, 0.5, 0.0] 1
Fe_1_1_0 [0.5, 0.5, 0.0] 1
Fe_0_0_1 [0.0, 0.0, 0.5] 1
Fe_1_0_1 [0.5, 0.0, 0.5] 1
Fe_0_1_1 [0.0, 0.5, 0.5] 1
Fe_1_1_1 [0.5, 0.5, 0.5] 1
>>> # The bonds were recalculated automatically
>>> for alpha, beta, nu, _ in spinham.p22:
...     print(alpha, beta, nu)
0 0 (1, 0, 0)
0 0 (-1, 0, 0)
>>> for alpha, beta, nu, _ in new_spinham.p22:
...     print(alpha, beta, nu)
0 1 (0, 0, 0)
1 0 (1, 0, 0)
2 3 (0, 0, 0)
3 2 (1, 0, 0)
4 5 (0, 0, 0)
5 4 (1, 0, 0)
6 7 (0, 0, 0)
7 6 (1, 0, 0)
1 0 (0, 0, 0)
0 1 (-1, 0, 0)
3 2 (0, 0, 0)
2 3 (-1, 0, 0)
5 4 (0, 0, 0)
4 5 (-1, 0, 0)
7 6 (0, 0, 0)
6 7 (-1, 0, 0)