Hidden Topological Transitions in Emergent Magnetic Monopole Lattices

TL;DR

This paper presents a theoretical model revealing various topological transitions in magnetic monopole lattices, including hidden ones, enhancing understanding of experimental phenomena and the emergent electromagnetism in such systems.

Contribution

The study introduces a model that stabilizes different hedgehog lattices and uncovers multiple topological transitions, including hidden ones, using exact solutions in the thermodynamic limit.

Findings

Identification of topological transitions with monopole density changes.

Discovery of hidden transitions with minimal thermodynamic anomalies.

Observation of pair annihilation of vortices in 3D monopole systems.

Abstract

Topological defects, called magnetic hedgehogs, realize emergent magnetic monopoles, which are not allowed in the ordinary electromagnetism described by Maxwell's equations. Such monopoles were experimentally discovered in magnets in two different forms: tetrahedral $4Q$ and cubic $3Q$ hedgehog lattices. The spin textures are modulated by the chemical composition, an applied magnetic field, and temperature, leading to quantum transport and optical phenomena through movement and pair annihilation of magnetic monopoles, but the theoretical understanding remains elusive, especially in the regions where different types of hedgehog lattices are competing. Here we propose a theoretical model that can stabilize both tetrahedral and cubic hedgehog lattices, and perform a thorough investigation of the phase diagram while changing the interaction parameters, magnetic field, and temperature, by using a recently developed method that delivers exact solutions in the thermodynamic limit. We find that the model exhibits various types of topological transitions with changes of the density of monopoles and antimonopoles, some of which are accompanied by anomalies in the thermodynamic quantities, while the others are hidden with less or no anomaly. We also find another hidden topological transition with pair annihilation of two-dimensional vortices in the three-dimensional system. These results not only provide useful information for understanding the existing experimental data, but also challenge the identification of hidden topological transitions and the exploration of emergent electromagnetism in magnetic monopole lattices.