  The bulk-boundary correspondence is a defining feature of topological states
of matter. However, for quantum magnets such as spin liquids or topological
magnon insulators a direct observation of topological surface states has proven
challenging because of the charge-neutral character of the excitations. Here we
propose spin-polarized scanning tunneling microscopy as a spin-sensitive local
probe to provide direct information about charge neutral topological edge
states. We show how their signatures, imprinted in the local structure factor,
can be extracted by specifically employing the strengths of existing
technologies. As our main example, we determine the dynamical spin correlations
of the Kitaev honeycomb model with open boundaries. We show that by contrasting
conductance measurements of bulk and edge locations, one can extract direct
signatures of the existence of fractionalized excitations and non-trivial
topology. The broad applicability of this approach is corroborated by a second
example of a kagome topological magnon insulator.
