  It was recently shown that the optical excitation of rare-earth ions produces
a local change of the host matrix shape, attributed to a change of the
rare-earth ion's electronic orbital geometry. In this work we investigate the
consequences of this piezo-orbital backaction and show from a macroscopic model
how it yields a disregarded ion-ion interaction mediated by mechanical strain.
This interaction scales as $1/r^3$, similarly to the other archetypal ion-ion
interactions, namely electric and magnetic dipole-dipole interactions. We
quantitatively assess and compare the magnitude of these three interactions
from the angle of the instantaneous spectral diffusion mechanism, and reexamine
the scientific literature in a range of rare-earth doped systems in the light
of this generally underestimated contribution.
