Dynamical spin structure factor and heat capacity of the kagome lattice XXZ antiferromagnet - a case study of the hidden energy scale

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, 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 the hidden energy scale 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 DSSF of XXZ Hamiltonians on clusters of the kagome lattice using the finite-temperature Lanczos method (FTLM). For certain wavevectors, we observe a low-energy peak whose position varies linearly in α, the XXZ anisotropy parameter. We also compute the specific heats of the same clusters by the FTLM, which display a low-temperature peak with the same linear dependence on α, in agreement with prior exact diagonalization studies and experiments. This trend further supports that the essentially quantum signatures in the thermodynamic properties of these materials are well-captured by the Heisenberg XXZ model. Moreover, our results suggest INS as a viable probe of the hidden energy scale.