  Hermitian theories play a major role in understanding the physics of most
phenomena. It has been found only in the past decade that non-Hermiticity
enables unprecedented effects such as exceptional points, spectral
singularities and bulk Fermi arcs. Recent studies further show that
non-Hermiticity can fundamentally change the topological band theory, leading
to the non-Hermitian band topology and non-Hermitian skin effect, as confirmed
in one-dimensional (1D) systems. However, in higher dimensions, these
non-Hermitian effects remain unexplored in experiments. Here, we demonstrate
the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional
(2D) acoustic metamaterials. Using a lattice of coupled whisper-gallery
acoustic resonators, we realize a spinful 2D higher-order topological insulator
(HOTI) where the spin-up and spin-down states are emulated by the
anti-clockwise and clockwise modes, respectively. We find that the
non-Hermiticity drives wave localizations toward opposite edge boundaries
depending on the spin polarizations. More interestingly, for finite systems
with both edge and corner boundaries, the higher-order non-Hermitian skin
effect leads to wave localizations toward two corner boundaries for the bulk,
edge and corner states in a spin-dependent manner. We further show that such a
non-Hermitian skin effect enables rich wave manipulation through the loss
configuration in each unit-cell. The reported spin-dependent, higher-order
non-Hermitian skin effect reveals the interplay between higher-order topology
and non-Hermiticity, which is further enriched by the spin degrees of freedom.
This unveils a new horizon in the study of non-Hermitian physics and the design
of non-Hermitian metamaterials.
