Two-dimensional incommensurate and three-dimensional commensurate magnetic order and fluctuations in La2-xBaxCuO4

We present neutron-scattering measurements on single crystals of lightly doped La2-xBaxCuO4, with 0 <= x <= 0.035. These reveal the evolution of the magnetism in this prototypical doped Mott insulator from a three-dimensional (3D) commensurate (C) antiferromagnetic ground state, which orders at a relatively high T-N, to a two-dimensional (2D) incommensurate (IC) ground state with finite-ranged static correlations, which appear below a relatively low effective T-N. At low temperatures, the 2D IC magnetism coexists with the 3D C magnetism for doping concentrations as low as similar to 0.0125. We find no signal of a 3D C magnetic ground state by x similar to 0.025, consistent with the upper limit of x similar to 0.02 observed in the sister family of doped Mott insulators, La2-xSrxCuO4. The 2D IC ground states observed for 0.0125 <= x <= 0.035 are diagonal, and are rotated by 45 degrees within the orthorhombic basal plane compared with those previously reported for samples with superconducting ground states: La2-xBaxCuO4, with 0.05 <= x <= 0.095. We construct a phase diagram based solely on magnetic order-parameter measurements, which displays much of the complexity of standard high-temperature superconductivity phase diagrams discussed in the literature. Analysis of high-energy resolution inelastic neutron scattering at moderately low temperatures shows a progressive depletion of the very low-energy dynamic magnetic susceptibility as x increases from 0.0125 to 0.035. This low-energy, dynamic susceptibility falls off with increasing temperature on a scale much higher than the effective 2D IC T-N appropriate to these materials. Appreciable dynamic 2D IC magnetic fluctuations inhabit much of the "pseudogap" regime of the phase diagram.