Effects of the Crystalline Electric Field in the $KErTe_{2}$ Quantum Spin Liquid Candidate

In this paper, we performed thermodynamic and electron spin resonance (ESR) measurements to study low-energy magnetic excitations, which were significantly affected by crystalline electric field (CEF) excitations due to relatively small gaps between the CEF ground state and the excited states. Based on the CEF and mean-field (MF) theories, we analyzed systematically and consistently the ESR experiments and thermodynamic measurements including susceptibility, magnetization, and heat capacity. The CEF parameters were successfully extracted by fitting high-temperature (> 20 K) susceptibilities in the ab-plane and along the c-axis, allowing to determine the Lande factors ($g_{ab,calc}$ = 5.98(7) and $g_{c,calc}$ = 2.73(3)). These values were consistent with the values of Lande factors determined by ESR experiments ($g_{ab,exp}$ = 5.69 and $g_{c,exp}$ = 2.75). By applying the CEF and MF theories to the susceptibility and magnetization results, we estimated the anisotropic spin-exchange energies and found that the CEF excitations in \ce{KErTe2} played a decisive role in the magnetism above 3 K, while the low-temperature magnetism below 10 K was gradually correlated with the anisotropic spin-exchange interactions. The CEF excitations were demonstrated in the low-temperature heat capacity, where both the positions of two broad peaks and their magnetic field dependence well corroborated our calculations. The present study provides a basis to explore the enriched magnetic and electronic properties of the QSL family.