Effective Spin-1/2 Hamiltonians Determined for Er2Ti2O7 & Yb2Ti2O7 Through Inelastic Neutron Scattering

Abstract

We used time-of-flight inelastic neutron scattering to measure the excitation spectra from field-polarized states of exotic frustrated magnets. A knowledge of these spin-wave excitations in various directions in reciprocal space allows a robust determination of exchange parameters in suitable model Hamiltonians.  We have taken this approach with two pyrochlores, Er2Ti2O7 and Yb2Ti2O7, whose magnetic properties have until this point been somewhat puzzling.  The model we use is an effective spin-1/2 exchange Hamiltonian that incorporates the full anisotropy allowed by symmetry at the rare earth site.  Er2Ti2O7, an XY anti-ferromagnet on the pyrochlore lattice, is found to reach its unexpected ordered ground state via quantum-order-by-disorder.  Meanwhile, Yb2Ti2O7's effective Hamiltonian reveals the possibility of a Coulombic quantum spin liquid through what we have revealed to be "quantum spin ice" interactions.   I will focus on the experimental side of these collaborative studies.