Heisenberg Hamiltonian
Hamiltonian
The Spin-Hamiltonian is defined as
Zeeman
Anisotropy
The anisotropy term is implemented in terms of three components:
uniaxial anisotropy
cubic anisotropy
biaxial anisotropy
Where for any site \(j\) the vectors \(\hat{K}_j^{(1)}\), \(\hat{K}_j^{(2)}\) and \(\hat{K}_j^{(3)} = \hat{K}_j^{(1)} \times \hat{K}_j^{(2)}\) are pairwise orthonormal.
The uniaxial anisotropy is equivalent to the biaxial anisotropy up to an offset to the total energy when setting
Exchange
symmetric exchange interaction
Dzyaloshinskii–Moriya interaction (antisymmetric exchange)
where it is important to note that <ij>
denotes the unique pairs of interacting spins i
and j
.
Dipole-Dipole Interaction
Quadruplet Interaction
Gaussian (test-) Hamiltonian
The Hamiltonian is defined as