  The magnetic properties of $\alpha$-NaFeO$_2$ are studied by neutron
diffraction and magnetization measurements. An ordered phase with spins aligned
along the b$_hex$ axis exists at low temperatures (T < 4 K). At intermediate
temperatures (4 K < T < 11 K), the system passes through an incommensurate
ordered phase before transforming into a short range ordered state at higher
temperatures that persists up to at least 50 K. Although the short range
ordering does not persist to room temperature according to neutron diffraction,
the magnetic susceptibility does not follow Curie-Weiss behavior, even up to
320 K. This rich magnetic behavior can be understood qualitatively as a
competition between different magnetic exchange interactions that are similar
in magnitude. The delicate balance between these interactions makes
$\alpha$-NaFeO$_2$ a candidate for more detailed theoretical work to understand
magnetic behavior in frustrated magnetic systems.
