  We studied a two-band magnon insulating model whose geometry is that of a
modified Lieb lattice in which one of the sites was removed. Anisotropic
ferromagnetic exchange interactions exist between the three nearest neighbors,
and the anisotropy opens a gap in the magnon energy band structure. A
non-vanishing Berry curvature is induced by a Dzyaloshinskii-Moriya interaction
(DMI). The topology of the bands is trivial (in the sense of a null Chern
number), but the finite Berry curvature induces Hall-like transport effects
whose coefficients were calculated. Their dependence on temperature was studied
and shows a resemblance with other magnon insulating systems found in the
literature. The dependence on exchange couplings, DMI parameter, and external
magnetic field was also investigated.
