Spin-triplet superconductors are of extensive current interest because they can host topological state and Majorana ferimons important for quantum computation. The uranium based heavyfermion superconductor UTe$_2$ has been argued as a spin-triplet superconductor similar to UGe$_2$, URhGe, and UCoGe, where the superconducting phase is near (or coexists with) a ferromagnetic (FM) instability and spin-triplet electron pairing is driven by FM spin fluctuations. Here we use neutron scattering to show that although UTe$_2$ exhibits no static magnetic order down to 0.3 K, its magnetism is dominated by incommensurate spin fluctuations near antiferromagnetic (AF) ordering wave vector and extends to at least 2.6 meV. We are able to understand the dominant incommensurate spin fluctuations of UTe$_2$ in terms of its electronic structure calculated using a combined density functional and dynamic mean field theory.
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