Spin density and non-collinear magnetization in frustrated pyrochlore Tb₂ Ti₂ O₇ from polarized neutron scattering

We used a local susceptibility approach in extensive polarized neutron diffraction studies of the spin liquid Tb₂ Ti₂ O₇. For a magnetic field applied along the [1 1 0] and [1 1 1] directions, we found that, at high temperature, all Tb moments are collinear and parallel to the field. With decreasing temperature, the Tb moments reorient from the field direction to their local anisotropy axes. For the [1 1 0] field direction, the field induced magnetic structure at 10 K is spin ice-like, but with two types of Tb moments of very different magnitudes. For a field along [1 1 1], the magnetic structure resembles the so-called "one in-three out" found in spin ices, with the difference that all Tb moments have an additional component along the [1 1 1] direction due to the magnetic field. The temperature evolution of the local susceptibilities clearly demonstrates a progressive change from Heisenberg to Ising behavior of the Tb moments when lowering the temperature, which appears to be a crystal field effect.