Toroidic phase transitions in a direct-kagome artificial spin ice

TL;DR

This paper reports the creation of an artificial nanomagnet system that exhibits ferrotoroidic phase transitions, providing a controllable model to study magnetic states and phase transitions that are difficult to observe in natural materials.

Contribution

The authors design a direct-kagome artificial spin ice system that demonstrates ferrotoroidic phases and phase transitions, advancing the understanding of ferrotoroidicity in engineered materials.

Findings

Observation of a phase transition between ferrotoroidicity and paratoroidicity.

Demonstration of robust toroidal moments in artificial spin ice.

Identification of a crossover to a non-toroidal paramagnetic phase.

Abstract

Ferrotoroidicity, the fourth form of primary ferroic order, breaks both space and time inversion symmetry. So far, direct observation of ferrotoroidicity in natural materials remains elusive, which impedes the exploration of ferrotoroidic phase transitions. Here, we overcome the limitations of natural materials using an artificial nanomagnet system that can be characterized at the constituent level and at different effective temperatures. We design a nanomagnet array as to realize a direct-kagome spin ice. This artificial spin ice exhibits robust toroidal moments and a quasi-degenerate ground state with two distinct low-temperature toroidal phases: ferrotoroidicity and paratoroidicity. Using magnetic force microscopy and Monte Carlo simulation, we demonstrate a phase transition between ferrotoroidicity and paratoroidicity, along with a crossover to a non-toroidal paramagnetic phase. Our quasi-degenerate artificial spin ice in a direct-kagome structure provides a model system for the investigation of magnetic states and phase transitions that are inaccessible in natural materials.