On determining the energy dispersion of spin excitations with scanning tunneling spectroscopy

TL;DR

This paper explores how scanning tunneling spectroscopy can be used to determine the energy dispersion of certain spin excitations in finite systems, highlighting conditions for success and limitations.

Contribution

It provides a theoretical framework for extracting dispersion relations from STM-IETS spectra in finite spin systems and compares predictions with experimental data.

Findings

STM-IETS can reveal magnon and triplon dispersions

It cannot determine spinon dispersion in Heisenberg chains

Success depends on formation of standing waves

Abstract

Conventional methods to measure the dispersion relations of collective spin excitations involve probing bulk samples with particles such as neutrons, photons or electrons, which carry a well-defined momentum. Open-ended finite-size spin chains, on the contrary, do not have a well-defined momentum due to the lack of translation symmetry, and their spin excitations are measured with an eminently local probe, using inelastic electron tunneling spectroscopy (IETS) with a scanning tunneling microscope (STM). Here we discuss under what conditions STM-IETS spectra can be Fourier-transformed to yield dispersion relations in these systems. We relate the success of this approach to the degree to which spin excitations form standing waves. We show that STM-IETS can reveal the energy dispersion of magnons in ferromagnets and triplons in valence bond crystals, but not that of spinons, the spin excitations in Heisenberg spin-1/2 chains. We compare our theoretical predictions with state-of-the-art measurements on nanographene chains that realize the relevant spin Hamiltonians.