We construct exact ground states of the J1-J3b classical Heisenberg model on the pyrochlore lattice in the presence of a magnetic field. They are noncoplanar multi-Q spin configurations with a large magnetic unit cell that generalize the previously found coplanar sublattice pairing states. Using linear spin-wave theory, we show that entropy favors these multi-Q states at low temperatures in high magnetic fields. This is confirmed by Monte Carlo simulations, and a phase diagram is constructed. We also calculate the zero-temperature dynamical structure factor. Besides the usual Goldstone modes associated with the ordering Qs, we find high intensity gapless modes at momenta where there are no Bragg peaks.
