We have studied incommensurate spin ordering in single crystal underdoped La_{2-x}Ba_{x}CuO_{4} with x~0.08, 0.05 and 0.025 using neutron scattering techniques. Static incommensurate magnetic order is observed in the La_{2-x}Ba_{x}CuO_{4} (x=0.05 and
0.025) compounds with ordering wavevectors which are rotated by 45 degree about the commensurate (0.5,0.5,0) position, with respect to that in the superconducting x=0.08 material. These spin modulations are one dimensional in the x=0.05 and 0.025 samples, with ordering wavevectors lying along the orthorhombic b* direction. Such a rotation in the orientation of the static spin ordering as a function of increasing Ba doping, from diagonal to collinear, is roughly coincident with the transition from an insulating to a superconducting ground state and is similar to that observed in the related La_{2-x}Sr_{x}CuO_{4} system. This phenomenon is therefore a generic property of underdoped La-214 cuprates.
We have studied structural phase transitions in high quality underdoped La$_{2-x}$Ba$_x$CuO$_4$ single crystals using high resolution x-ray scattering techniques. Critical properties associated with the continuous High Temperature Tetragonal (HTT, $I
4/mmm$) to Middle Temperature Orthorhombic (MTO, $Cmca$) phase transition were investigated in single crystal samples with x=0.125, 0.095, and 0.08 and we find that all behavior is consistent with three dimensional XY criticality, as expected from theory. Power law behavior in the orthorhombic strain, 2(a-b)/(a+b), is observed over a remarkably wide temperature range, spanning most of the MTO regime in the phase diagram. Low temperature measurements investigating the Low Temperature Tetragonal (LTT, $P4_{2}/ncm$) phase, below the strongly discontinuous MTO$to$LTT phase transition, in x=0.125 and x=0.095 samples show that the LTT phase is characterized by relatively broad Bragg scattering, compared with that observed at related wavevectors in the HTT phase. This shows that the LTT phase is either an admixture of tetragonal and orthorhombic phases, or that it is orthorhombic with very small orthorhombic strain, consistent with the ``less orthorhombic low temperature structure previously reported in mixed La$_{2-x}$Sr$_{x-y}$Ba$_y$CuO$_4$ single crystals. We compare the complex temperature-composition phase diagram for the location of structural and superconducting phase transitions in underdoped La$_{2-x}$Ba$_x$CuO$_4$ and find good agreement with results obtained on polycrystalline samples.
