Magnetic properties of two-dimensional dipolar squares: Boundary geometry dependence

By means of the molecular dynamics simulation of 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 the 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 multidomain structure whose domains consist of 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 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 the real space of the interacting spins.