  Lieb lattice is one of the simplest bipartite lattices where compact
localized states (CLS) are observed. This type of localisation is induced by
the peculiar topology of the unit cell, where the modes are localized only on
one sublattice due to the destructive interference of partial waves. The CLS
exist in the absence of defects and are associated with the flat bands in the
dispersion relation. The Lieb lattices were successfully implemented as optical
lattices or photonic crystals. This work demonstrates the possibility of
magnonic Lieb lattice realization where the flat bands and CLS can be observed
in the planar structure of sub-micron in-plane sizes. Using forward volume
configuration, we investigated numerically (using the finite element method)
the Ga-dopped YIG layer with cylindrical inclusions (without Ga content)
arranged in a Lieb lattice of the period 250 nm. We tailored the structure to
observe, for the few lowest magnonic bands, the oscillatory and evanescent spin
waves in inclusions and matrix, respectively. Such a design reproduces the Lieb
lattice of nodes (inclusions) coupled to each other by the matrix with the CLS
in flat bands.

Mesoscale and Nanoscale Physics;Optics