Resolving where a density-wave gap opens in momentum space is pivotal for identifying the microscopic origin of instabilities in layered nickelates. Using polarization- and symmetry-resolved electronic Raman scattering, we map the momentum dependence of the spin-density-wave (SDW) gap in trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$. Highly momentum-selective spectral-weight depletion below the SDW transition is observed, indicative of gap formation. Gap openings are observed on the $\alpha$ Fermi pocket at the Brillouin zone (BZ) center and near the BZ boundary region of the $\beta$ pocket, while a conspicuous absence of gap signatures along the diagonal direction of the BZ on the $\beta$ pocket places strong constraints on the underlying scattering mechanism. Comparison with the bilayer compound ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ reveals qualitatively different momentum selectivity of the SDW order, despite similar transition temperatures and energy scales. These results are difficult to reconcile with a scattering wave vector strictly along the $\mathrm{\Gamma }-M$ line and are consistent with a momentum dependent wave vector shifted away from the BZ diagonal. Our work establishes symmetry-resolved Raman scattering as a powerful two-particle probe of momentum-selective SDW instabilities and provides insights into the nature of magnetism in layered nickelates.

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• Spin density waves
• Superconductivity
• Nickelates
• Raman spectroscopy