Multiple Solutions in Crystal Electric Field Simulation via gPy

Frustrated magnets with Rare-Earth (RE) elements have attracted intense interest in the condensed matter community due to exhibiting diverse magnetic and quantum behaviors. One of the mechanisms that causes magnetic diversity and complexity is the interaction between the 4f electron shell and the crystal electric field (CEF) generated by surrounding oxygen anions. Although the interactions on magnetic dipole moments can be complicated, there have been considerable success by treating the magnetic dipole moment as an effective spin - 1/2 system in the low energy limit. CEF analysis naturally lies at the center of determining the single ion anisotropy and evaluating the effectiveness of spin-1/2 approximation. It can tell g-tensor that represents the local magnetic anisotropy of a single spin. From here, one can define a Hamiltonian to describe the magnetic system and find the magnetic ground state. Currently, CEF Hamiltonian can be solved based on an effective point charge model, which replies on the good experience in properly assigning point charges around the RE to reach a reliable solution. Direct fitting of the CEF Hamiltonian at a low point-group symmetry position can be challenge due to more refinable parameters than that can be obtained from resolution limited experimental data. We have developed a Python3 based method, named as gPy, to efficiently survey large CEF parameter phase space and find the CEF parameter sets and corresponding g-tensor that best fit the CEF excitations and magnetic susceptibility data in powder samples. It is based on two gradient free optimization methods Particle Swarm Optimization (PSO)and Covariance matrix adaptation evolution strategy (CMA-ES)and bypasses the initial step of generating starting values from point-charge model which has proven to be inaccurate at times. In this talk, I will present the results we tested on two reported well-known magnetic lattices, pyrochlore Yb₂Ti₂O₇ [1] and tripod- Er₃Mg₂Sb₃O₁₄ [2]. We found multiple solutions that could fit the data equivalently well and propose to use the local magnetic susceptibility with polarized neutrons to tell the right g-tensor.

[1] J.Gaudet et al. PRB 92 (13),134420 (2015)

[2] Z.Dun et al.PRR 3 023012 (2021)