Nuclear and magnetic spin structure of the antiferromagnetic triangular lattice compound LiCrTe$_2$ investigated by $\mu^+$SR as well as neutron and X-ray diffraction

Two$-$dimensional (2D) triangular lattices antiferromagnets (2D$-$TLA) often manifest intriguing physical and technological properties, due to the strong interplay between lattice geometry and electronic properties. The recently synthesized 2$-$dimensional transition metal dichalcogenide LiCrTe$_2$, being a 2D$-$TLA, enriched the range of materials which can present such properties. In this work, muon spin rotation ($\mu^+$SR) and neutron powder diffraction (NPD) have been utilized to reveal the true magnetic nature and ground state of LiCrTe$_2$. From high$-$resolution NPD the magnetic spin order at base$-$temperature is not, as previously suggested, helical, but rather collinear antiferromagnetic (AFM) with ferromagnetic (FM) spin coupling within the $ab-$plane and AFM coupling along the $c-$axis. The ordered magnetic Cr moment is established as $\mu_{\rm Cr}=$ 2.36 $\mu_{\rm B}$. From detailed $\mu^+$SR measurements we observe an AFM ordering temperature $T_{\rm N}\approx$ 125 K. This value is remarkably higher than the one previously reported by magnetic bulk measurements. From $\mu^+$SR we are able to extract the magnetic order parameter, whose critical exponent allows us to categorize LiCrTe$_2$ in the 3D Heisenberg AFM universality class. Finally, by combining our magnetic studies with high$-$resolution synchrotron X$-$ray diffraction (XRD), we find a clear coupling between the nuclear and magnetic spin lattices. This suggests the possibility for a strong magnon$-$phonon coupling, similar to what has been previously observed in the closely related compound LiCrO$_2$.