# Quantum topological transitions and spinons in metallic ferro- and antiferromagnets

## TL;DR

This paper develops an effective Hamiltonian for magnetic phases in the Hubbard model using spinon excitations, analyzing topological quantum transitions and their relation to metal-insulator phenomena in magnetic materials.

## Contribution

It introduces a topological perspective to quantum magnetic transitions and compares different spinon representations in the Hubbard model.

## Key findings

- Identification of a Lifshitz transition as the quantum transition to half-metallic ferromagnetism.
- Topological interpretation of itinerant-localized and Mott transitions in antiferromagnetic states.
- Discussion of metal-insulator transitions in Heusler alloys within a topological framework.

## Abstract

An effective Hamiltonian describing fluctuation effects in the magnetic phases of the Hubbard model in terms of spinon excitations is derived. A comparison of spin-rotational Kotliar-Ruckenstein slave boson and Ribeiro-Wen dopon representations is performed. The quantum transition into the half-metallic ferromagnetic state with vanishing of spin-down Fermi surface is treated as the topological Lifshitz transition in the quasimomentum space. The itinerant-localized magnetism transitions and Mott transition in antiferromagnetic state are considered in the topological context. Related metal-insulator transitions in Heusler alloys are discussed.