Competing Lattice Instability and Magnetism on the Surface of Kagome Metals

TL;DR

This study uncovers a complex interplay between magnetism and lattice instabilities on the surfaces of kagome metals, revealing surface charge orders suppressed by magnetism and demonstrating strong spin-lattice coupling.

Contribution

It provides the first detailed analysis of surface lattice instabilities and their suppression by magnetism in kagome metals, highlighting the competition between these phenomena.

Findings

Surface charge orders are observed on non-magnetic kagome surfaces.

Magnetism suppresses surface charge orders, stabilizing magnetic surfaces.

Surface instabilities are linked to spin-lattice coupling in kagome metals.

Abstract

Only a few magnetic kagome materials exhibit lattice instabilities among the large kagome material array. In this work, we find that kagome magnets $R$Mn$_6$Sn$_6$ ($R$ = rare-earth elements) and their non-magnetic counterparts $R$V$_6$Sn$_6$ exhibit intriguing interplay between magnetism and lattice dynamics on their surfaces. Notably, $R$V$_6$Sn$_6$ surfaces terminated by kagome layers demonstrate pronounced lattice instabilities, manifesting as $\sqrt{3} \times \sqrt{3}$ and $2 \times 2$ surface charge orders (SCOs). These instabilities are absent on corresponding magnetic materials $R$Mn$_6$Sn$_6$. Here, the SCO is suppressed by magnetism. Otherwise, surface distortions would significantly reduce the spin polarization, elevating the energy via Hund's rule. Thus, SCOs are energetically unfavorable on magnetic surfaces. The competition of magnetism and lattice instability is further substantiated by observing SCOs on V-substituted $R$Mn$_6$Sn$_6$ kagome surfaces, contrasting with their absence on Mn-substituted $R$V$_6$Sn$_6$ surfaces. Our findings reveal unexpected surface instability and profound spin-lattice coupling in these kagome magnets, highlighting the complex dynamics hidden within magnetic materials.