Effective magnetic Hamiltonian at finite temperatures for rare-earth chalcogenides
Zheng Zhang, Jianshu Li, Weiwei Liu, Zhitao Zhang, Jianting Ji, Feng Jin, Rui Chen, Junfeng Wang, Xiaoqun Wang, Jie Ma, Qingming Zhang
Abstract
Alkali-metal rare-earth chalcogenide $AREC{h}_{2}$ (A = alkali or monovalent metal, RE = rare earth, Ch = O, S, Se, Te) is a large family of quantum spin liquid candidates we discovered recently. Unlike ${\mathrm{YbMgGaO}}_{4}$, most members in the family, except for the oxide ones, have a relatively small crystalline electric field (CEF) energy gap from the ground state to the first excited state. This makes the conventional Curie-Weiss analysis at finite temperatures inapplicable and the CEF excitations may play an essential role in understanding the low-energy spin physics. Here we consider an effective magnetic Hamiltonian incorporating the CEF excitations and spin-spin interactions, to accurately describe thermodynamics in such a system. By taking ${\mathrm{NaYbSe}}_{2}$ as an example, we were able to analyze magnetic susceptibility, magnetization under pulsed high fields, and heat capacity systematically and comprehensively. The analysis allows us to produce accurate anisotropic exchange coupling energies and unambiguously determine a crossover temperature ($\ensuremath{\sim}25$ K in the case of ${\mathrm{NaYbSe}}_{2}$), below which the CEF effects fade away and pure spin-spin interactions stand out. We further validated the effective picture by successfully explaining the anomalous temperature dependence of electron spin resonance spectral width. The effective scenario in principle can be generalized to other rare-earth spin systems with small CEF excitations.