Magnons and Excitation Continuum in XXZ triangular antiferromagnetic model: Application to $Ba_3CoSb_2O_9$

TL;DR

This paper studies the excitation spectrum of the XXZ triangular antiferromagnetic model using series expansions and mean field approaches, revealing rotonic minima and excitation continua that relate to experimental observations in Ba3CoSb2O9.

Contribution

It demonstrates the presence of excitation continua and rotonic minima in the XXZ model, connecting theoretical predictions with experimental spectra in a specific material.

Findings

Rotonic minima in the magnon spectrum across anisotropy range.

Extended excitation continuum above spin wave excitations.

Enhanced continuum with second neighbor exchange interaction.

Abstract

We investigate the excitation spectrum of the triangular-lattice antiferromagnetic $XXZ$ model using series expansions and mean field Schwinger bosons approaches. The single-magnon spectrum computed with series expansions exhibits rotonic minima at the middle points of the edges of the Brillouin zone, for all values of the anisotropy parameter in the range $0\leq J^z/J\leq1$. Based on the good agreement with series expansions for the single-magnon spectrum, we compute the full dynamical magnetic structure factor within the mean field Schwinger boson approach to investigate the relevance of the $XXZ$ model for the description of the unusual spectrum found recently in $Ba_3CoSb_2O_9$. In particular, we obtain an extended continuum above the spin wave excitations, which is further enhanced and brought closer to those observed in $Ba_3CoSb_2O_9$ with the addition of a second neighbor exchange interaction approximately 15% of the nearest-neighbor value. Our results support the idea that excitation continuum with substantial spectral-weight are generically present in two-dimensional frustrated spin systems and fractionalization in terms of {\it bosonic} spinons presents an efficient way to describe them.