We consider a magnetic system of spins in the classical
many-spin approach, i.e., taking account of its intrinsic
properties such as the lattice structure and system size.
The magnetic properties of such system are described by the anisotropic
Heisenberg model for classical
spins (with ). The
Hamiltonian includes the (nearest-neighbor) exchange interactions,
single-site bulk () and
surface anisotropy ():
1 Atomistic model
where J is the exchange parameter.
The anisotropy energy will be
different if we are working with bulk spins or surface spins. For bulk
spins, i.e., those spins with full coordination, the
anisotropy energy is taken
uniaxial with easy axis along
and anisotropy constant
atomic volume), that is
where is the volume
of the atomic atom i, is the number of bulk spins in the thin film.
For surface spins the anisotropy is taken according to the
model, expressed as:
where is the number of surface
spins, the number of
nearest neighbors of site ,
and a unit vector
connecting this site to its nearest neighbors labeled by .
The magnetic systems modeled in this chapter are thin films. The
magnetic parameters of the system under study are presented in table 4.1.