  The subtle interplay between competing degrees of freedom, anisotropy, and
spin correlations in frustrated Kitaev quantum materials offer an ideal
platform to host myriads of non-trivial quantum states with exotic fractional
excitations. The signature of spin-freezing behavior of these spin-orbit driven
frustrated magnets is characterized by a bifurcation of zero-field-cooled and
field-cooled magnetic susceptibility at low temperatures much below the
characteristic interaction energy scale. The magnetic-specific heat exhibits a
T^2 dependence below the freezing temperature. The field-independent behavior
of magnetic-specific heat below the freezing temperature implies the presence
of exotic low-energy excitations. The aging and memory effect experiments in
the Kitaev magnets suggest the non-hierarchical free energy distribution, which
differs from the hierarchical organization of conventional spin-freezing.
Furthermore, NMR spin-lattice relaxation rate follows a power law behavior
below the spin-freezing temperature suggesting the persistence of
unconventional spin excitation spectra. Herein, we demonstrate that the
observed low-temperature spin-freezing phenomena in a few representative Kitaev
quantum materials can be effectively explained by the Halperin and Saslow (HS)
hydrodynamic modes relevant for non-trivial spin glass materials. The linearly
dispersive HS modes are hypothesized to account for instigating non-abelian
defect propagation, thereby inducing a spin jam state in the low-temperature
regime in frustrated Kitaev magnets. Our investigation reveals that HS modes
capture the essence of unconventional spin-freezing ascribed to topological
origin in two-dimensional (2D) Kitaev magnets decorated on a honeycomb lattice
and its 3D analog hyperhoneycomb that offers a viable ground to extend this
framework to a large class of frustrated quantum materials.
