Linear Spin Wave theory

Tutorial tasks

• Use one of the spin Hamiltonians from the previous tutorial and compute all terms of the magnon Hamiltonian.

• Compute magnon dispersion of a simple ferromagnet.

• Compute magnon dispersion of a simple antiferromagnet.

All methods of linear spin-wave theory are grouped under the magnopy.LSWT class.

Two objects are required to create it

• Spin Hamiltonian

• Directions of spins in the ground state

import numpy as np
import magnopy

spinham = magnopy.examples.cubic_ferro_nn(S=1, J_21=(0, 0, -0.5))

lswt = magnopy.LSWT(spinham=spinham, spin_directions=[[0, 0, 1]])

Once created it can be used to compute terms of the magnon Hamiltonian

Correction to the classical energy

print(lswt.E_2)

-3.5

Coefficients of the one-operator terms

print(lswt.O)

[0.+0.j]

Magnon energies

print(lswt.omega(k=[0, 0, 0]))

[1.+0.j]

Parallelization

Typically one wants to compute magnon energies for a set of k-points. Often for a rather large set of k-points. Magnopy offers simple interface to parallelize the calculations over the k-points using multiprocessing. See magnopy.multiprocess_over_k() for details. For example, to compute magnon energies for the set of k-points (that are given as absolute coordinates in reciprocal space) utilizing two processes use

kpoints = np.linspace([0, 0, 0], [1, 0, 0], 1000)

results = magnopy.multiprocess_over_k(
    kpoints=kpoints,
    relative=False,
    function=lswt.omega,
    number_processors=2,
)

Note that results[i] is equivalent to lswt.omega(k=kpoints[i], relative=False).

print(results[42])

print(lswt.omega(k=kpoints[42], relative=False))

[1.00176727+0.j]
[1.00176727+0.j]