[Paper Review] Antiferromagnetic magnons and local anisotropy: dynamical mean-field study

A. Niyazi, D. Geffroy+1 more|arXiv (Cornell University)|May 26, 2021

Physics of Superconductivity and Magnetism65 references12 citations

TL;DR

This study employs dynamical mean-field theory (DMFT) with exact two-particle correlation functions to investigate antiferromagnetic magnons in multi-orbital Hubbard models on square and bcc cubic lattices. It demonstrates that even small symmetry-breaking terms—such as external magnetic fields or single-ion anisotropy—significantly alter magnon dispersions, with results consistent with spin-wave theory and symmetry principles, validating DMFT's ability to capture collective magnetic excitations in correlated electron systems.

ABSTRACT

We present a dynamical mean-field study of antiferromagnetic magnons in one-, two- and three-orbital Hubbard model of square and bcc cubic lattice at intermediate coupling strength. Weinvestigate the effect of anisotropy introduced by an external magnetic field or single-ion anisotropy.For the latter we tune continuously between the easy-axis and easy-plane models. We also analyzea model with spin-orbit coupling in cubic site-symmetry setting. The ordered states as well as themagnetic excitations are sensitive to even a small breaking ofSU(2)symmetry of the model andfollow the expectations of spin-wave theory as well as general symmetry considerations.

Motivation & Objective

• To investigate the impact of local anisotropy on antiferromagnetic magnon dispersions in multi-orbital correlated systems.
• To assess the sensitivity of ordered magnetic states and their excitations to small SU(2) symmetry breaking.
• To validate the use of DMFT with two-particle correlation functions for studying collective modes in realistic multi-orbital models.
• To explore the continuous tuning between easy-axis and easy-plane anisotropy in 2D and 3D lattices.
• To examine the effects of spin-orbit coupling in cubic site-symmetry settings on magnetic excitation spectra.

Proposed method

• Uses dynamical mean-field theory (DMFT) to map the lattice Hubbard model onto an impurity problem with self-consistent hybridization functions.
• Calculates dynamical spin susceptibility χαα(q, ω) via analytic continuation of Matsubara-frequency correlation functions using the maximum entropy method.
• Solves the Bethe-Salpeter equation (BSE) for two-particle correlation functions (2PCFs) with local 2P-irreducible vertices and lattice bubbles.
• Employs the Legendre basis representation for fermionic indices to efficiently handle high-dimensional 2PCFs in multi-orbital systems.
• Tunes single-ion anisotropy continuously from easy-axis to easy-plane limits and applies external Zeeman fields to probe symmetry-breaking effects.
• Uses CT-QMC for exact 1PCF calculations and ALPS libraries for numerical implementation.

Experimental results

Research questions

• RQ1 How do small symmetry-breaking terms like external magnetic fields or single-ion anisotropy affect magnon dispersions in multi-orbital antiferromagnets?
• RQ2 To what extent do DMFT calculations of 2PCFs reproduce the predictions of spin-wave theory for magnon spectra?
• RQ3 How does the transition between easy-axis and easy-plane anisotropy influence the gap structure and dispersion of magnons?
• RQ4 What is the role of spin-orbit coupling in modifying the magnetic excitation spectrum in cubic lattices with multi-orbital character?
• RQ5 How robust are the ordered magnetic phases and their collective modes under continuous tuning of anisotropy parameters?

Key findings

• Even small breaking of SU(2) spin symmetry leads to measurable changes in magnon dispersions, consistent with spin-wave theory predictions.
• The magnon spectrum exhibits a gap in the easy-plane limit and a soft mode in the easy-axis limit, reflecting the expected symmetry-broken behavior.
• The dynamical spin susceptibility calculated via DMFT respects Goldstone's theorem, confirming the presence of gapless modes in the broken symmetry phase.
• The 2PCF approach successfully captures the anisotropy-induced splitting of magnon branches and the evolution of the dispersion across the easy-axis to easy-plane crossover.
• Spin-orbit coupling induces additional splitting and modifies the magnon dispersion, particularly in the three-orbital model with cubic site symmetry.
• The method demonstrates numerical feasibility and accuracy for computing 2PCFs in realistic multi-orbital models with three or more orbitals and multiple atoms per unit cell.