Magnetization process in Er2Ti2O7 at very low temperature

We present a model which accounts for the high-field magnetization at very low temperature in the frustrated pyrochlore compound Er2Ti2O7. In Er2Ti2O7, the Er(3+) ion has a planar crystal field anisotropy and the material undergoes a transition to antiferromagnetism at TN = 1.2 K. Our model is a mean-field self-consistent calculation involving the four rare earth sites of a tetrahedron, the building unit of the pyrochlore lattice. It includes the full crystal field Hamiltonian, the infinite range dipolar interaction and anisotropic nearest neighbour exchange described by a 4-component tensor. We discuss the equivalence of our treatment of the exchange tensor, taken to be diagonal in a frame linked to a rare earth-rare earth bond, with the pseudo-spin Hamiltonian recently developed for Kramers doublets in a pyrochlore lattice.