Dipolar ground state of planar spins on triangular lattices

TL;DR

This paper investigates the ground state configurations of classical dipolar spins on finite and large triangular lattices, revealing size and shape dependencies, the stability of vortex states, and limitations of finite range approximations.

Contribution

It demonstrates that ground state properties depend on lattice size and aspect ratio, challenging the assumption of ferromagnetic ground states in such systems.

Findings

Domain walls are energetically favored below a critical aspect ratio.

Vortex states are favored in the thermodynamic limit but may not appear in large finite lattices.

Finite range dipole sum approximations may incorrectly predict ground states.

Abstract

An infinite triangular lattice of classical dipolar spins is usually considered to have a ferromagnetic ground state. We examine the validity of this statement for finite lattices and in the limit of large lattices. We find that the ground state of rectangular arrays is strongly dependent on size and aspect ratio. Three results emerge that are significant for understanding the ground state properties: i) formation of domain walls is energetically favored for aspect ratios below a critical valu e; ii) the vortex state is always energetically favored in the thermodynamic limit of an infinite number of spins, but nevertheless such a configuration may not be observed even in very large lattices if the aspect ratio is large; iii) finite range approximations to actual dipole sums may not provide the correct ground sta te configuration because the ferromagnetic state is linearly unstable and the domain wall energy is negative for any finite range cutoff.