magnopy.Energy

class magnopy.Energy(spinham)

Ground state energy of the given spin Hamiltonian.

This class is optimized for the computation of the energy for any spin directions for the given Hamiltonian.

If the spin Hamiltonian is modified, then a new instance of the energy class should be created from it.

Parameters:

spinhamSpinHamiltonian

Spin Hamiltonian for the calculation of energy.

Examples

First, one need to create some spin Hamiltonian

>>> import numpy as np
>>> import magnopy
>>> cell = np.eye(3)
>>> atoms = dict(
...     names=["Fe"], spins=[1.5], g_factors=[2], positions=[[0, 0, 0]]
... )
>>> convention = magnopy.Convention(
...     multiple_counting=True, spin_normalized=False, c21=1, c22=-1
... )
>>> spinham = magnopy.SpinHamiltonian(
...     cell=cell, atoms=atoms, convention=convention
... )

Then, add some parameters to the Hamiltonian

>>> spinham.add_21(alpha=0, parameter=np.diag([0, 0, -1]))
>>> spinham.add_22(
...     alpha=0,
...     beta=0,
...     nu=(1, 0, 0),
...     parameter=magnopy.converter22.from_iso(iso=1),
... )

Now everything is ready to create an instance of the Energy class

>>> energy = magnopy.Energy(spinham)

Finally, energy an be used to compute classical energy of the Hamiltonian, its gradient, torque or search for the local minima.

>>> sd1 = [[1, 0, 0]]
>>> sd2 = [[0, 1, 0]]
>>> sd3 = [[0, 0, 1]]
>>> # Default units are meV
>>> energy(sd1), energy(sd2), energy(sd3)
(-4.5, -4.5, -6.75)
>>> # You can request other units
>>> print(f"{energy(sd1, units='Joule'):.4e}")
-7.2098e-22

Methods:

E_0(spin_directions[, units, _normalize])	Computes classical energy of the spin Hamiltonian.
gradient(spin_directions[, units, _normalize])	Computes first derivatives of energy (\(E^{(0)}\)) with respect to the components of the spin directional vectors.
optimize([initial_guess, energy_tolerance, ...])	Optimize classical energy by varying the directions of spins in the unit cell.
optimize_generator([initial_guess, ...])	Optimize classical energy by varying the directions of spins in the unit cell.
torque(spin_directions[, units, _normalize])	Computes torque on each spin.