Spectrum of noncollinear metastable configurations of a finite-size discrete planar spin chain with a collinear ferromagnetic ground state

Abstract

A theoretical method is used to find, in an accurate and systematic way, all the possible equilibrium magnetic states of a finite-size one-dimensional chain of classical planar spins, interacting via ferromagnetic nearest-neighbor symmetric exchange and subjected to a uniaxial anisotropy which favors the orientation of the spins along an easy axis within the plane perpendicular to the chain. For a chain with $N$ spins, the energy is a function of $N$ absolute orientation angles $({\ensuremath{\theta}}_{i}$, $i=1,...,N)$ and, owing to the absence of energy competition, the ground state is collinear ferromagnetic and doubly degenerate (either ${\ensuremath{\theta}}_{i}=0$ $\ensuremath{\forall}i$, or ${\ensuremath{\theta}}_{i}=\ensuremath{\pi}$ $\ensuremath{\forall}i$). The ground state corresponds to a global minimum of the energy in the $N$-dimensional space, while metastable states correspond to local minima. As a function of $N$, we have numerically determined the minimal value ${\ensuremath{\gamma}}_{\mathrm{min}}$ to be assumed by the ratio $\ensuremath{\gamma}$ between the anisotropy and the exchange constant for the first noncollinear metastable state to appear. For $N\ensuremath{\le}13$, all the noncollinear equilibrium spin configurations of the system were calculated with great accuracy at two different values, $\ensuremath{\gamma}=0.18$ and 0.21. A stability analysis was subsequently performed, showing that metastable noncollinear states can appear in the model even in the absence of energy competition. The various kinds of metastable states can be classified, in order of increasing energy, on the basis of the increasing number of $\ensuremath{\pi}$ walls (including both domains and antidomains) which can be inserted into the discrete finite chain with open ends when $N$ and/or $\ensuremath{\gamma}$ are increased. The effects of open boundary conditions and finite size on the Peierls-Nabarro barrier (i.e., the difference between the energy of an unstable onsite-centered domain wall and the energy of a stable intersite-centered domain wall) were also investigated.