Classical crystal formation of dipoles in two dimensions

TL;DR

This paper investigates how the crystal structure of classical dipolar particles in a two-dimensional layer changes with dipole orientation, revealing a transition from hexagonal to striped arrangements and analyzing phonon spectra.

Contribution

It introduces a classical approach to determine the optimal crystal structure of dipoles in 2D and explores the effects of dipole orientation on structure and phonon properties.

Findings

Crystal structure transitions from hexagonal to striped with orientation change

Phonon spectrum develops local minima as structure deforms

Speed of sound varies with dipole orientation

Abstract

We consider a two-dimensional layer of dipolar particles in the regime of strong dipole moments. Here we can describe the system using classical methods and determine the crystal structure that minimizes the total energy. The dipoles are assumed to be aligned by an external field and we consider different orientations of the dipolar moments with respect to the two-dimensional plane of motion. We observe that when the orientation angle changes away from perpendicular and towards the plane, the crystal structure will change from a hexagonal form to one that has the dipoles sitting in equidistant rows, i.e. a striped configuration. In addition to calculating the crystal unit cell, we also consider the phonon spectrum and the speed of sound. As the orientation changes away from perpendicular the phonon spectrum develops local minima that are a result of the deformation to the crystal structure.