  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.
