Topological magnon in exchange frustration driven incommensurate spin spiral of a kagome lattice YMn$_6$Sn$_6$

TL;DR

This paper reveals the emergence of topological magnons in the incommensurate spin spiral phase of YMn$_6$Sn$_6$, driven by frustrated magnetic interactions and spin-orbit coupling, with results aligning well with experimental observations.

Contribution

It introduces a detailed theoretical model explaining the incommensurate spin spirals and topological magnons in YMn$_6$Sn$_6$, highlighting the role of exchange frustration and spin-orbit coupling.

Findings

Identification of incommensurate spin spirals with specific pitch and wave vector.

Discovery of topological magnon modes with non-zero Berry curvature.

Agreement of theoretical Dirac magnon energy with experimental data.

Abstract

YMn$_6$Sn$_6$ consists of two types of Mn-based kagome planes stacked along $c$-axis having a complex magnetic interactions. We report a spin reconstruction in YMn$_6$Sn$_6$ from ferromagnet (FM) into a combination of two incommensurate spin spirals (SSs) originating from two different type of Mn kagome planes driven by frustrated magnetic exchanges along the $c$-axis with inclusion of Hubbard U. The pitch angle and wave vector of the incommensurate SSs are $\sim$89.3$^{\circ}$ and $\sim$ (0 0 0.248) respectively which are in excellent agreement with experiment. We employed an effective model Hamiltonian constructed out of exchange interactions to capture experimentally observed non-equivalent nature of the two incommensurate SSs which also explain FM-SS crossover due to antiferromagntic spin exchange with correlation. We further report the existence of topological magnon with spin-orbit coupling in incommensurate SS phase of YMn$_6$Sn$_6$ by calculating the topological invariants and Berry curvature profile. The location of Dirac magnon in energy landscape at 73 meV matches with another experimental report. We demonstrate the accuracy of our results by highlighting experimental features in YMn$_6$Sn$_6$.