Magnetic Properties of 2-Dimensional Dipolar Squares: Boundary Geometry Dependence
By means of the molecular dynamics simulation on gradual cooling processes, we investigate magnetic properties of classical spin systems only with the magnetic dipole-dipole interaction, which we call dipolar systems. Focusing on their finite-size effect, particularly their boundary geometry dependence, we study two finite dipolar squares cut out from a square lattice with $Φ=0$ and $π/4$, where $Φ$ is an angle between the direction of the lattice axis and that of the square boundary. Distinctly different results are obtained in the two dipolar squares. In the $Φ=0$ square, the ``from-edge-to-interior freezing'' of spins is observed. Its ground state has a multi-domain structure whose domains consist of the two among infinitely (continuously) degenerated Luttinger-Tisza (LT) ground-state orders on a bulk square lattice, i.e., the two antiferromagnetically aligned ferromagnetic chains (af-FMC) orders directed in parallel to the two lattice axes. In the $Φ=π/4$ square, on the other hand, the freezing starts from the interior of the square, and its ground state is nearly in a single domain with one of the two af-FMC orders. These geometry effects are argued to originate from the anisotropic nature of the dipole-dipole interaction which depends on the relative direction of sites in a real space of the interacting spins.