  We have performed resonant magnetic x-ray scattering (RMXS) measurements on
single crystal samples of the bilayer iridate Sr3Ir2O7. We observe the
development of antiferromagnetic order below T* ~ 260 K, which persists down to
T = 4 K under both field-cooled (fc) and zero-field-cooled (zfc) conditions.
The temperature dependence of the fc and zfc magnetic Bragg peaks suggests the
presence of competition between canted and collinear antiferromagnetic ground
states. Under zfc conditions, we observe a suppression of magnetic peak
intensity at T_D ~ 50 K which can be attributed to a spin reorientation
transition. Under fc conditions, we find that the canted antiferromagnetic
state is stabilized over a much wider range of temperatures, with significantly
enhanced magnetic correlation lengths within the Ir-O layers. The field
dependence of the magnetic Bragg peaks provides no evidence of field-induced
phase transitions for H < 4 T.
