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We report x-ray diffraction, magnetic susceptibility, heat capacity, $^{1}$H nuclear magnetic resonance (NMR), and muon spin relaxation ($mu$SR) measurements, as well as density-functional band-structure calculations for the frustrated $S=3/2$ triangular lattice Heisenberg antiferromagnet (TLHAF) $alpha$-HCrO$_{2}$ (trigonal, space group: $Rbar{3}m$). This compound undergoes a clear magnetic transition at $T_{rm N} simeq 22.5$~K, as seen from the drop in the muon paramagnetic fraction and concurrent anomalies in the magnetic susceptibility and specific heat. Local probes (NMR and $mu$SR) reveal a broad regime with slow fluctuations down to $0.7,T_{rm N}$, this temperature corresponding to the maximum in the $mu$SR relaxation rate and in the NMR wipe-out. From the comparison with NaCrO$_{2}$ and $alpha$-KCrO$_{2}$, the fluctuating regime and slow dynamics below $T_{rm N}$ appear to be hallmarks of the TLHAF with $ABC$ stacking that leads to a frustration of interlayer couplings between the triangular planes. This interlayer frustration is a powerful lever to generate spin states with persistent dynamics and may bear implications to spin-liquid candidates with the triangular geometry.
In this paper we study the switching properties of the dynamics of magnetic moments, that interact with an elastic medium. To do so we construct a Hamiltonian framework, that can take into account the dynamics in phase space of the variables that des
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