Ferromagnetic (FM) and incommensurate spin-density wave (ISDW) states are an unusual set of competing magnetic orders that are seldom observed in the same material without application of a polarizing magnetic field. We report, for the first time, the discovery of an ISDW state that is derived from a FM ground state through a Fermi surface (FS) instability in Fe$_3$Ga$_4$. This was achieved by combining neutron scattering experiments with first principles simulations. Neutron diffraction demonstrates that Fe$_3$Ga$_4$ is in an ISDW state at intermediate temperatures and that there is a conspicuous re-emergence of ferromagnetism above 360 K. First principles calculations show that the ISDW ordering wavevector is in excellent agreement with a prominent nesting condition in the spin-majority FS demonstrating the discovery of a novel instability for FM metals; ISDW formation due to Fermi surface nesting in a spin-polarized Fermi surface.
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