Critical fluctuations in the spin-orbit Mott insulator Sr3Ir2O7

X-ray magnetic critical scattering measurements and specific heat measurements were performed on the perovskite iridate Sr3Ir2O7. We find that the magnetic interactions close to the Neel temperature T-N = 283.4(2) K are three-dimensional. This contrasts with previous studies which suggest two-dimensional behaviour like Sr2IrO4. Violation of the Harris criterion (d nu > 2) means that weak disorder becomes relevant. This leads a rounding of the antiferromagnetic phase transition at T-N, and modifies the critical exponents relative to the clean system. Specifically, we determine that the critical behaviour of Sr3Ir2O7 is representative of the diluted 3D Ising universality class.