Dynamical spin structure factor and the hidden energy scale in the kagome lattice XXZ antiferromagnet

Geometrically frustrated (GF) magnetic systems are the most-studied material platforms in which coveted quantum spin-liquid (QSL) phases could be realized. Key to understanding the behavior of GF magnets in the low-temperature regime where QSLs might exist is the so-called “hidden energy scale”, which is significantly exceeded by the characteristic strength of spin-spin interactions in the corresponding materials. This hidden energy scale T^*, which is observed in thermodynamic properties such as spin-glass freezing trends and a low-temperature peak in the specific heat, has recently been explained microscopically in terms of the Heisenberg XXZ Hamiltonian. In the present work, we connect T^* also to the dynamical spin structure factor (DSSF) of GF magnets, which is effectively a simulation of inelastic neutron scattering (INS) experiments. In particular, we compute the transverse DSSF of the XXZ Hamiltonian on the kagome lattice by the finite-temperature Lanczos method. At certain wavevectors and sufficiently low temperatures, we find a distinct feature at an energy of order T^*, which we relate to zero-energy spin-flips in the corresponding Ising model. These results further support that the essentially quantum signatures in the thermodynamic properties of GF magnets are well-described by the XXZ model. Moreover, our work suggests that polarized INS can be an effective probe of the hidden energy scale.