  We investigate synthesis of a hyperfine spin lattice in an atomic
Bose-Einstein condensate, with two hyperfine spin components, inside a
one-dimensional high-finesse optical cavity, using off-resonant superradiant
Raman scattering. Spatio-temporal evolution of the relative population of the
hyperfine spin modes is examined numerically by solving the coupled
cavity-condensate mean field equations in the dispersive regime. We find,
analytically and numerically, that beyond a certain threshold of the transverse
laser pump, Raman superradiance and self-organization of the hyperfine spin
components simultaneously occur and as a result a magnetic lattice is formed.
The effects of an extra laser pump parallel to the cavity axis and the
time-dependence of the pump strength on the synthesis of a sharper lattice are
also addressed.
