earth, M=metal) form a very rich family in which a large diversity of new physics can be explored  [@Gardner10]. Specifically, the rare-earth ions lie on the vertices of corner sharing tetrahedra, forming the highly frustrated pyrochlore lattice. Depending on the rare-earth element, the anisotropy of the spins as well as the exchange and dipolar interactions can be varied so that different model Hamiltonians can be studied within this structure. One of the most spectacular realizations is the spin-ice phase (R=Dy,Ho, M=Ti) [@Harris97; @Ramirez99] in which the local spin arrangement obeys the ice-rule (two spins point into and two spins point out of every tetrahedron in the structure) and which possesses a macroscopically degenerate ground state. This state is induced by the strong uniaxial anisotropy along the local $<$111$>$ axes of the tetrahedra, combined with a resultant ferromagnetic interaction. With these ingredients and in the presence of strong transverse fluctuations, a new magnetic state is expected to be stabilized, the quantum spin ice (QSI) in which exotic excitations are predicted [@Onoda10; @Savary12; @Shannon12].

[Yb$_2$Ti$_2$O$_7$]{}  has been proposed as a good candidate for stabilizing the QSI state [@Ross11a; @Applegate12]. Indeed, the exchange in [Yb$_2$Ti$_2$O$_7$]{}  is highly anisotropic, with a strong ferromagnetic component 