  Nonlinear-optical microscopy and spectroscopy provide detailed spatial and
spectroscopic contrast, specifically sensitive to structural symmetry and
order. Ferroics, in particular, have been widely studied using second harmonic
generation imaging, which provides detailed information on domain structures
but typically lacks spectroscopic detail. In contrast, infrared-visible
sum-frequency generation (SFG) spectroscopy reveals details of the atomic
structure and bonding via vibrational resonances, but conventionally lacks
spatial information. In this work, we combine the benefits of nonlinear optical
imaging and SFG spectroscopy by employing SFG spectro-microscopy using an
infrared free-electron laser. Specifically, we demonstrate the feasibility of
SFG spectro-microscopy for spectroscopy using in-plane anisotropic
wurtzite-type aluminum nitride as a model system. We find the experimental
spectra to agree well with our theoretical calculations and we show the
potential of our microscope to provide spatially resolved spectroscopic
information in inhomogeneous systems such as ferroics and their domains in the
near future.
