Numerical study of the temperature-dependent magnetization and susceptibility of Tm3+in LiTmF4

Studying magnetic properties of LiTmF4, a recognized insulating Van Vleck paramagnet, can hold promise for advancements in quantum computing, MRI, spintronics, material design, and potentially, single-photon technologies. This study may be pivotal due to challenges in simulating noncollinear magnetism using density functional theory (DFT), requiring more sophisticated spin configurations and time-consuming spin relaxations or embedded dynamical mean field theory. Instead, we utilize two distinct efficient and reliable schemes- ab initio DFT and a semiempirical superposition model, both integrated with crystal field (CF) theory (including Zeeman effect) and underpinned by statistical mechanics-to analyze noncollinear paramagnetic properties. At the core of this investigation is the S4 site symmetry of the Tm3+ ion, which admits several sets of six (seven) independent CF parameters (CFPs) under the reduced (complete) approach generated by suitable rotations of the coordinate system. By applying the Noether theorem, we show that these numerically distinct sets are physically equivalent. This is evidenced by computing the several conserved CFP quantities predicted by the Noether theorem, which exhibit notable coherence across different data sets. Using one of these equivalent sets of 7 CF parameters, as computed in [Phys. Rev. B 102, 045120 (2020)] under the complete approach, this study explores the theoretical analysis of multiplet splitting induced by the CF and the external magnetic field within the Tm3+ ion lattice in LiTmF4. We investigate the magnetic moment per ion and the temperature dependencies of magnetic susceptibility, utilizing a Hamiltonian, including the free ion, CF terms, and Zeeman interaction. The agreement of our findings with existing experimental data accentuates the efficacy of the proposed approach in reproducing magnetic properties in LiTmF4, providing a significant analytical tool for the analysis of EPR spectra in terms of the defined Zeeman g tensor. This research may stand as a pivotal guide in the accurate determination of magnetic properties, potentially influencing significant advancements in technology and materials science.