Double-layered monopolar order in the Tb2Ti2O7 spin liquid

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 reanalyzed 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 double-layered monopolar order.