Non-collinear Magnetic Configurations at Finite Temperature in Thin Films

The finite-temperature magnetism of a monolayer on a bcc (110) surface was examined using a model Hamiltonian containing ferromagnetic or antiferromagnetic exchange interactions, Dzyaloshinsky-Moriya interactions and easy-axis on-site anisotropy. We examined the competition between the collinear ground state parallel to the easy axis and the spin spiral state in the plane perpendicular to this axis preferred by the Dzyaloshinsky-Moriya interaction. Using approximative methods to calculate the magnon spectrum at finite temperatures, it was found that even if the ground state is collinear, increasing the Dzyaloshinsky-Moriya interaction strongly decreases the critical temperature where this collinear order disappears. Using atomistic spin dynamics simulations it was found that at this critical temperature the system transforms into the non-collinear state. Including external magnetic field helps stabilising the ferromagnetic state. An effect due to the finite size of the magnetic monolayer was included in the model by considering a different value for the anisotropy at the edges of the monolayer. This effect was shown to stabilize the spin spiral state by fixing the phase at the ends of the stripe.

Langevin spin dynamics based on ab initio calculations: numerical schemes and applications

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.

Relativistic and thermal effects on the magnon spectrum of a ferromagnetic monolayer

A spin model including magnetic anisotropy terms and Dzyaloshinsky-Moriya interactions is studied for the case of a ferromagnetic monolayer with C2v symmetry like Fe/W(110). Using the quasiclassical stochastic Landau-Lifshitz-Gilbert equations, the magnon spectrum of the system is derived using linear response theory. The Dzyaloshinsky-Moriya interaction leads to asymmetry in the spectrum, while the anisotropy terms induce a gap. It is shown that in the presence of lattice defects, both the Dzyaloshinsky-Moriya interactions and the two-site anisotropy lead to a softening of the magnon energies. Two methods are developed to investigate the magnon spectrum at finite temperatures. The theoretical results are compared to atomistic spin dynamics simulations and a good agreement is found between them.