Soutenance de Geoffroy Haeseler

It is well known that spin ice materials like Ho2Ti2O7 present magnetisation plateaus when a field is applied along the [111] direction. The first of them is due to the freezing of apical spins which leaves an extensive entropy in the isolated kagomé planes lying perpendicular to the field. The Kagome spins are constrained into their K11 phase. Using the fragmentation process, the spins in the planes map, in part, onto a classical dimer model on honeycomb lattice. This system is studied in various conditions.

We first add an in plane magnetic field whose direction can vary. In the language of dimers, this field is represented by different chemical affinities depending on the orientation of the dimer. In this case the system presents a Kasteleyn transition with tuneable critical correlations. We then add a plaquette term, counting hexagon loops with three dimers, leading to a BKT transition into the ordered dimer-star phase when negative and a Kasteleyn transition to a columnar phase when positive. Finally, including both of these terms, we find a tri-critical point at which the BKT transition becomes first order.

We study a generalisation of this model, for fully packed dimers on diamond lattice under a field which can be tilted in all directions, leading to three dimensional Kasteleyn transitions. This model could be experimentally realised in pyrochlores that satisfy a 3-in 1-out, 3-out 1-in ice (like) ground state rule such as Ho2Ir2O7. This dimer model presents interesting triple points in which the critical temperature goes to zero and the ground state presents a residual entropy proportional to that of kagomé ice.

In a second part of the thesis, we add an off-diagonal quantum term to the 2D dimer model which allows resonant dimer flips around closed hexagon loops. This model is studied numerically in Monte Carlo simulations using the Suzuki-Trotter formalism. We confirm the existence of a first order transition from the classical star phase to a quantum resonating plaquette phase. Adding a field conjugated to the star order parameter we go in search of a quantum critical end point between the two phases. Detailed analysis of the plaquette phase reveal liquid like correlations that die as a power law with temperature indicating the existence of a continuous excitation spectrum above the ordered ground state, rather than the predicted energy gap. Finally, we study the quantum phase with fixed non-zero topological sector which frustrated the long-range order of the star phase, leaving correlations reminiscent of a quantum liquid. Dimer correlations are presented in the form of emergent polarized neutron scattering plots, formed by mapping back to the spins of kagomé ice and using the fragmentation process to extract the emergent transverse field of the dimers.