  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.
