First Talk Abstract: Frustrated magnetism on the honeycomb lattice has recently received attention, partly due to the synthesis of Bi_3Mn_4O_12(NO_3) - a spin-3/2 bilayer honeycomb system that does not show long range order down to very low temperatures. Remarkably, this material becomes Neel ordered beyond a critical magnetic field. In this context, I will discuss two possible sources of frustration: next-nearest neighbour exchange and bilayer coupling. Both can explain  (i) the absence of long range order at zero field, and (ii) field-induced Neel ordering. I will point out connections to recent studies of the honeycomb lattice Hubbard model, and to experiments on bilayer antiferromagnets.

Second Talk Abstract:  We have studied the effect of pressure on the pyrochlore iridate Eu_2Ir_2O_7, which at ambient pressure has a thermally driven insulator to metal transition at T_{MI}\sim120 K. As a function of pressure the insulating gap closes, apparently continuously, near P \sim 6 GPa. However, rather than T_{MI} going to zero as expected, the insulating ground state crosses over to a metallic state with a negative temperature coefficient of resistivity, calling into question the true nature of both ground states. The high temperature state also crosses over near 6 GPa, from an incoherent to a conventional metal, suggesting a connection between the high and the low temperature states. I will discuss the relevance of our results to the recent theoretical predictions of topological insulating and semimetallic phases in pyrochlore iridates."