Spin waves, order-by-disorder phenomena, and pseudo-Goldstone modes in MPX₃ magnets

Layered honeycomb transition-metal trichalcogenides (MPX₃) materials were recently studied in a number of experimental works and were shown to host a variety of zigzag and Neel magnetic orders. From a theoretical perspective, classical Luttinger-Tisza analysis of Heisenberg models for these materials leads to a large manifold of classically degenerate ground states. In our work we show how accounting for symmetry-allowed anisotropies and quantum fluctuations significantly lifts this degeneracy and gives rise to magnetic ordering via the order-by-disorder mechanism. We then calculate the spin wave spectrum in a number of relevant magnetic phases and analyze the corresponding soft modes. Remarkably, besides true Goldstone modes, we observe the appearance of pseudo-Goldstone modes, which appear due to the aforementioned accidental degeneracy at the classical level but acquire a small gap due to quantum effects.