Quasi-two-dimensional ferromagnetism and anisotropic interlayer couplings in the magnetic topological insulator MnBi2Te4

${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ (MBT) is a promising van der Waals layered antiferromagnetic (AFM) topological insulator that combines a topologically nontrivial inverted Bi-Te band gap with ferromagnetic (FM) layers of Mn ions. The inelastic neutron scattering on single crystals reported here describes rather complex magnetism in MBT. The magnetic anisotropy that controls the bulk and surface magnetic field response of MBT is found to have contributions from both single-ion and interlayer two-ion terms. A description of the quasi-two-dimensional intralayer FM spin waves requires long-range, competing FM and AFM interactions and anomalous damping. While this might suggest carrier-mediated magnetic coupling, $\mathit{ab}\mathit{initio}$ calculations in insulating MBT also find long-range interactions, and classical spin dynamics simulations suggest that magnetic vacancies are at least partially responsible for observations of anomalous damping near the zone boundary.