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We present neutron scattering measurements on single crystals of lightlydoped $La_{2-x}Ba_{x}CuO_{4}$, with $0 \leq x \leq? 0.035$. These reveal theevolution of the magnetism in this prototypical doped Mott insulator from athree dimensional (3D) commensurate (C) antiferromagnetic ground state, whichorders at a relatively high TN, to a two dimensional (2D) incommensurate (IC)ground state with finite ranged static correlations, which appear below arelatively low effective TN. At low temperatures, the 2D IC magnetism co-existswith the 3D C magnetism for doping concentrations as low as ? 0.0125. We findno signal of a 3D C magnetic ground state by x $\sim$? 0.025, consistent withthe upper limit of x $\sim$? 0.02 observed in the sister family of doped Mottinsulators, $La_{2-x}Sr_{x}CuO_{4}$. The 2D IC ground states observed for$0.0125 \leq x \leq 0.035$ are diagonal, and are rotated by 45 degrees withinthe orthorhombic basal plane compared with those previously reported forsamples with superconducting ground states: $La_{2-x}Ba_{x}CuO_{4}$, with $0.05\leq? x \leq? 0.095. We construct a phase diagram based solely on magneticorder parameter measurements, which displays much of the complexity of standardhigh temperature superconductivity phase diagrams discussed in the literature.Analysis of high energy-resolution inelastic neutron scattering at moderatelylow temperatures shows a progressive depletion of the very low energy dynamicmagnetic susceptibility as x increases from 0.0125 to 0.035. This low energy,dynamic susceptibility falls off? with increasing temperature on a scale muchhigher than the effective 2D IC TN appropriate to these materials. Appreciabledynamic 2D IC magnetic fluctuations inhabit much of the "pseudogap" regime ofthe phase diagram.

Two Dimensional Incommensurate and Three Dimensional Commensurate Magnetic Order and Fluctuations in $La_{2-x}Ba_{x}CuO_{4}$