Unconventional Crystal Electric Field Excitation Evolution in the Kagome Metal TbV₆Sn₆

The topological metal TbV₆Sn₆ features V-kagome and Tb-triangular layers that develop strong uniaxial ferromagnetic (FM) order below T_C = 4.4 K. Using inelastic neutron scattering, we have established the Tb crystal electric field (CEF) spectrum, finding the Ising-doublet ground state and evidence of a hidden magnetic ordering within the V-kagome sublattice. Here, we report the complex temperature- and field-dependent evolution of the primary CEF excitation from the ground state doublet to the first excited state. Below T_C, the ferromagnetic transition accompanies an unconventional softening of the excitation energy which is opposite to the hardening expected from the development of the internal molecular field. The energy of the transition continues to harden above T_C and reaches a maximum at T^*≈ 65 K before thermal volume expansion drives softening.  The evolution below T^* deviates from expected thermal behavior, suggesting additional magnetic interactions, such as Tb short-range FM ordering or magnetic order within the V sublattice, influence the CEF transition. The field dependence of the excitation energy shows a nonlinear response to field-induced magnetization in the paramagnetic regime.