Ferrimagnetism and Minority Magnons in the Hubbard Model on the Lieb Lattice

Abstract

This thesis investigates minority magnon excitations, firstly proposed by T. Skovhus and T. Olsen (Phys. Rev. B 110.16 (2024)), in the half-filled Hubbard model on the two-dimensional Lieb lattice. Starting from the mean-field ground state with finite Hubbard interaction, we find the splitting Hubbard bands with ferrimagnetic features and identify gapless Goldstone and gapped Higgs magnon modes with the dynamical transverse magnetic susceptibility within the Random Phase Approximation (RPA) framework. We show that the Lieb lattice’s inequivalent sublattices induce the distinct majority and minority magnon branches, the latter appearing at negative frequencies. In the strong-coupling regime, where RPA is not applicable, we employ multi-orbital Dynamical Mean-Field Theory (DMFT) to include local vertex corrections, plotting the finite-temperature magnetic phase diagram and studying interaction-driven and thermal-driven effects on the ferrimagnetic order. Our results clarify the essential conditions for the appearance of minority magnons and show the fundamental understanding for studies of more complex and topological magnonic systems.

Popular Abstract

Imagine a world where electronics run at incredible speeds without overheating, using waves of magnetic excitation instead of electric currents. This is the promise of spintronics, an emerging field of technology that uses the spin of electrons, along with their charge, to store, process, and transmit information. It starts with understanding magnons, the ripples that travel through aligned electron spins when one flips, much like a stone creating waves in a pond.

Normally, magnons form when spins flip from a majority (spin-preference) band to a minority band. But researchers at DTU have recently identified minority magnons, created by flips in the opposite direction. The minority magnon could unlock novel spintronic devices capable of faster information transfer and storage. But these new excitations were only first seen in weakly interacting systems, where electrons barely influence each other.

Real materials, however, often feature strong electron interactions, making their behavior far more complex. To illustrate the difference between weak and strong correlations, imagine a playground with kids running around. If each child is playing alone and ignoring others, it’s easy to track one and study their behavior. But in reality, most kids find it more fun to play together, forming groups and interacting in ways that make individual tracking difficult. Understanding minority magnons in such strongly correlated systems show great promise because they offer complex spin band structure that could help us to uncover the properties of minority magnons.

However, studying magnons in these complex systems isn’t easy. The strong interactions between electrons make the usual computation methods ineffective. So we need advanced computational models. By simulating magnons in the ferrimagnetic Lieb lattice system, we hope to understand how minority magnons form and propagate, which may help people to understand the properties of magnons and handle the utility of them.

This research on minority magnons is driven by a mix of curiosity and practical potential. On one hand, uncovering the mysteries of how magnons behave in strongly interacting materials could deepen our understanding of quantum mechanics, bringing us closer to understand the world of condensed matter physics. On the other, understanding these theories could lead to more efficient technologies, like data storage and computing systems that use magnons instead of electrons.

• author: Ying, Tengfei
• supervisor: Erik van Loon
• organization: Department of Physics; Mathematical Physics
• course: FYSM64 20251
• year: 2025
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• language: English
• id: 9194323
• date added to LUP: 2025-06-09 08:35:00
• date last changed: 2025-06-09 08:35:00