  Radiative damping is a strong dissipation source for the quantum emitters
hybridized with propagating photons, electrons, or phonons, which is not easily
avoidable for on-chip magnonic emitters as well that can radiate via the
surface acoustic waves of the substrate. Here we demonstrate in an array of
on-chip nano-magnets coupled in a long range via exchanging the surface
acoustic waves that a point defect in the array, which can be introduced by the
local magnon frequency shift by a local biased magnetic field or the absence of
a magnetic wire, strongly localizes the magnons, in contrast to the well
spreading Bloch-like collective magnon modes in such an array setting. The
radiation of the magnon defect states is exponentially suppressed by the
distance of the defect to the array edges. Moreover, this defect state is
strikingly inertial to the non-Hermitian topology that localizes all the
extended states at one boundary. Such configuration robust magnon defect states
towards radiation-free limit may be suitable for high-fidelity magnon quantum
information storage in the future on-chip magnonic devices.
