Pyrochlore Sublattice Pairing States in a Magnetic Field

We investigate the J₁-J_3b classical Heisenberg model on the pyrochlore lattice in the presence of a magnetic field. We construct analytically exact ground states of the model. These are multi-Q configurations that generalize the previously found coplanar sublattice pairing states (SLP₁). Contrary to the SLP₁ states, the generalized states (SLP₃) are non-coplanar and have a large magnetic unit cell where the configuration varies between parallel triangular planes. We calculate the dynamical structure factor at low temperatures. Besides the usual Goldstone modes associated with the ordering Qs, we also find gapless modes with high intensity at momentum space points where the static structure factor is absent. Additionally, we construct an order parameter that captures the SLP₁ state by measuring the tendency to form staggered spin arrangements along parallel chains of alternating sublattices. A phase diagram is constructed using Monte Carlo simulations. For weak magnetic fields, we find that the ordering phase transition goes directly into a canted SLP₁ state, while for higher fields we find indications of an intermediate SLP₃ state before a cross-over into the SLP₁ state at lower temperatures. Quantitative details of the phase diagram are given.