Phase diagram of the two-dimensional dipolar Heisenberg model with the Dzyaloshinskii-Moriya interaction and the Ising anisotropy

TL;DR

This paper investigates the complex phase diagram of a two-dimensional dipolar Heisenberg model with Dzyaloshinskii-Moriya interaction and Ising anisotropy, revealing various skyrmion and helical phases under different conditions.

Contribution

It provides the first detailed phase diagrams for this model, highlighting the effects of dipolar interactions on skyrmion and helical phase stability and structure.

Findings

Identified three types of skyrmion-lattice phases.

Demonstrated how dipolar interactions expand ordered phase regions.

Showed that dipolar interactions increase skyrmion density and shorten helical pitch.

Abstract

We study phase transitions in the two-dimensional Heisenberg model with the Dzyaloshinskii-Moriya interaction, the Ising anisotropy ($\eta$), and the dipolar interaction under zero and finite magnetic fields ($H$). For three typical strengths (zero, weak, and strong) of the dipolar interaction, we present the $H$-$\eta$ phase diagrams by estimating order parameters for skyrmion-lattice and helical phases and in-plane magnetization by using a Monte Carlo method with an $O(N)$ algorithm. We find in the phase diagrams three types of skyrmion-lattice phases, i.e., two square lattices and a triangular lattice, helical phases with diagonal and vertical (or horizontal) stripes, canted ferromagnetic phase and polarized ferromagnetic phase. The effect of the dipolar interaction varies the types of the skyrmion and helical phases in a complex manner. The dipolar interaction also expands the regions of the ordered phases accompanying shifts of the phase boundaries to the positive $H$ and $\eta$ directions, and causes increase of the density of skyrmions and shortening of the pitch length (stripe width) of helical structures. We discuss the details of the features of the phase transitions.