Orbital character of the spin-reorientation transition in TbMn₆Sn₆

Ferromagnetic (FM) order in a two-dimensional kagome layer is predicted to generate a topological Chern insulator without an applied magnetic field. The Chern gap is largest when spin moments point perpendicular to the kagome layer, enabling the capability to switch topological transport properties, such as the quantum anomalous Hall effect, by controlling the spin orientation. In TbMn₆Sn₆, the uniaxial magnetic anisotropy of the Tb³⁺ ion is effective at generating the Chern state within the FM Mn kagome layers while a spin-reorientation (SR) transition to easy-plane order above T_SR = 310 K provides a mechanism for switching. Here, we use inelastic neutron scattering to provide key insights into the fundamental nature of the SR transition. The observation of two Tb excitations, which are split by the magnetic anisotropy energy, indicates an effective two-state orbital character for the Tb ion, with a uniaxial ground state and an isotropic excited state. The simultaneous observation of both modes below T_SR confirms that orbital fluctuations are slow on magnetic and electronic time scales < ps and act as a spatially-random orbital alloy. A thermally-driven critical concentration of isotropic Tb ions triggers the SR transition.