# Asymmetric isolated skyrmions in polar magnets with easy-plane anisotropy

## TL;DR

This paper introduces a new class of asymmetric isolated skyrmions in polar magnets with easy-plane anisotropy, revealing their unique energy patterns, interactions, and stability properties, with implications for experimental observation.

## Contribution

The study presents the theoretical discovery of asymmetric skyrmions in tilted ferromagnetic phases of polar magnets, detailing their structure, interactions, and stability, which is a novel contribution.

## Key findings

- Asymmetric skyrmions have positive and negative energy asymptotics.
- Skyrmion interactions are anisotropic and orientation-dependent.
- Stable asymmetric skyrmions can transform into axisymmetric ones when the host phase's tilt decreases.

## Abstract

We introduce a new class of isolated magnetic skyrmions emerging within tilted ferromagnetic phases of polar magnets with easy-plane anisotropy. The asymmetric magnetic structure of these skyrmions is associated with an intricate pattern of the energy density, which exhibits positive and negative asymptotics with respect to the surrounding state with a ferromagnetic moment tilted away from the polar axis. Correspondingly, the skyrmion-skyrmion interaction has an anisotropic character and can be either attractive or repulsive depending on the relative orientation of the skyrmion pair. We investigate the stability of these novel asymmetric skyrmions against the elliptical cone state and follow their transformation into axisymmetric skyrmions, when the tilted ferromagnetic moment of the host phase is reduced. Our theory gives clear directions for experimental studies of isolated asymmetric skyrmions and their clusters embedded in tilted ferromagnetic phases.