  A method is proposed to study the finite-temperature behaviour of small
magnetic clusters based on solving the stochastic Landau-Lifshitz-Gilbert
equations, where the effective magnetic field is calculated directly during the
solution of the dynamical equations from first principles instead of relying on
an effective spin Hamiltonian. Different numerical solvers are discussed in the
case of a one-dimensional Heisenberg chain with nearest-neighbour interactions.
We performed detailed investigations for a monatomic chain of ten Co atoms on
top of Au(001) surface. We found a spiral-like ground state of the spins due to
Dzyaloshinsky-Moriya interactions, while the finite-temperature magnetic
behaviour of the system was well described by a nearest-neighbour Heisenberg
model including easy-axis anisotropy.
