Orbital character of the spin-reorientation transition in TbMn$_6$Sn$_6$

TL;DR

This study investigates the orbital character of the spin-reorientation transition in TbMn$_6$Sn$_6$, revealing how orbital fluctuations and anisotropy influence topological magnetic states and transitions.

Contribution

It provides new insights into the orbital nature of Tb ions and their role in the spin-reorientation transition in TbMn$_6$Sn$_6$ using inelastic neutron scattering.

Findings

Tb ions exhibit two orbital states with different anisotropies.

Orbital fluctuations are slow and act as a spatially-random orbital alloy.

A critical concentration of isotropic Tb ions triggers the SR transition.

Abstract

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 TbMn$_{6}$Sn$_{6}$, the uniaxial magnetic anisotropy of the Tb$^{3+}$ 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.