We use neutron scattering to determine spin excitations in single crystals of nonsuperconducting Li1-xFeAs throughout the Brillouin zone. Although angle resolved photoemission experiments and local density approximation calculations suggest poor Fermi surface nesting conditions for antiferromagnetic(AF) order, spin excitations in Li1-xFeAs occur at the AF wave vectors Q = (1, 0) at low energies, but move to wave vectors Q = (pm 0.5, pm0.5) near the zone boundary with a total magnetic bandwidth comparable to that of BaFe2As2. These results reveal that AF spin excitations still dominate the low-energy physics of these materials and suggest both itinerancy and strong electron-electron correlations are essential to understand the measured magnetic excitations.
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