Ho2Ti2O7 and Dy2Ti2O7 spin ices exhibit elementary excitations akin to magnetic monopoles. Here we focus on Tb2Ti2O7 spin liquid, where correlated magnetic moments keep fluctuating down to very low temperatures. Using a monopole picture, we have re-analyzed the field-induced magnetic structure previously determined by neutron diffraction in Tb2Ti2O7. We show that under a high field applied along a [110] direction, Tb2Ti2O7 orders as a three dimensional arrangement of monopole and antimonopole double layers. In contrast, Ho2Ti2O7 spin ice in the same conditions behaves as a monopole-free state. By symmetry analysis we derived the distortions compatible with the observed magnetic structure of Tb2Ti2O7 which can be related to the appearance of the doublelayered monopolar order.

We studied the field-induced magnetic structures of the Tb2Ti2O7 pyrochlore by single-crystal neutron diffraction with a magnetic field applied along a [110] axis, focusing on the influence of a small misalignment. Both induced magnetic structures with k = 0 and k = (0, 0, 1) propagation vectors are found to be sensitive to the misalignment, which controls the magnitude and orientation of the Tb moments involved in the β chains, with local [111] anisotropy axis perpendicular to the field. For k = 0, spin-ice-like structures are observed for a misalignment of a few degrees, whereas other structures, where the Tb-β moments flip by "melting" on the field axis, occur when the field is perfectly aligned. The field evolution of the k = 0 structure is well reproduced by a molecular field model with anisotropic exchange. We give a complete symmetry analysis of the k = 0 and k = (0, 0, 1) magnetic structures, both being described by the basis functions of single irreducible representations.