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The series of triangular compounds ACrO$_2$ is a model series for studying the Heisenberg model on S=3/2 (Cr$^{3+}$: half-filled t$_{2g}$ orbitals) triangular antiferromagnets and the impact of interlayer couplings on the dynamics. For this, we report µSR measurements on α-HCrO$_2$ and KCrO$_2$ [1] which complete former studies on the series of triangular compounds ACrO$_2$, A = Li , Na [2, 3]. Coupled to $^1$H and $^{39}$K nuclear magnetic resonance (NMR), we establish the static character at low-T, as expected for a near neighbour Heisenberg model, yet displaying a broad and remarkable regime with slow fluctuations extending from $T_N$ down to 0.2 $T_N$. This regime is marked by a maximum in the μSR relaxation rate occuring at 0.7 $T_N$, associated with an NMR wipe-out .
The scaling of the NMR and μSR data with respect to J or T$_N$ supports a scenario where a crossover from 2D to 3D correlations sets in around 0.7 T$_N$ preceded by a typical 2D regime of the TLHAF which appears to be a hallmark of the TLHAF with ABC stacking. We discuss the role of interlayer frustration which may bear implications to recent spin-liquid candidates with the triangular geometry and exclude a scenario à la Berezinskii-Kostelitz-Touless of vortex-antivortex topological excitations in that regime. In turn, this underlines the crucial need of further neighbour interactions, anisotropy typical of rare earth or even disorder to stabilize a quantum spin liquid state in triangular antiferromagnets such as YbMgGaO$_4$.
[1] K. Somesh et al. Phys. Rev. B 104, 104422 (2021).
[2] A. Olariu et al. Phys. Rev. Lett. 97, 167203 (2006).
[3] A. Olariu et al. Phys. Rev. B 79, 224401 (2009).
