  Two-dimensional kagome metals consisting of corner-sharing triangles offer a
unique platform for studying strong electron correlations and band topology due
to its geometrically frustrated lattice structure. The similar energy scales
between spin, lattice, and electronic degrees of freedom in these systems give
rise to competing quantum phases such as charge density wave (CDW), magnetic
order, and superconductivity. For example, kagome metal FeGe first exhibits
A-type collinear antiferromagnetic (AFM) order at T_N ~ 400 K, then establishes
a CDW phase coupled with AFM ordered moment below T_CDW ~ 100 K, and finally
forms a $c$-axis double cone AFM structure around T_Canting ~ 60 K. Here we use
neutron scattering to demonstrate the presence of gapless incommensurate spin
excitations associated with the double cone AFM structure at temperatures well
above T_Canting and T_CDW that merge into gapped commensurate spin waves from
the A-type AFM order. While commensurate spin waves follow the Bose population
factor and can be well described by a local moment Heisenberg Hamiltonian, the
incommensurate spin excitations first appear below T_N where AFM order is
commensurate, start to deviate from the Bose population factor around T_CDW,
and peaks at T_Canting, consistent with a critical scattering of a second order
magnetic phase transition, as a function of decreasing temperature. By
comparing these results with density functional theory calculations, we
conclude that the incommensurate magnetic structure arises from the nested
Fermi surfaces of itinerant electrons and the formation of a spin density wave
order. The temperature dependence of the incommensurate spin excitations
suggests a coupling between spin density wave and CDW order, likely due to flat
electronic bands near the Fermi level around T_N and associated electron
correlation effects.
