  In a previous paper, we showed that any Jacobi field along a harmonic map
from the 2-sphere to the complex projective plane is integrable (i.e., is
tangent to a smooth variation through harmonic maps). In this paper, in
contrast, we show that there are (non-full) harmonic maps from the 2-sphere to
the 3-sphere and 4-sphere which have non-integrable Jacobi fields. This is
particularly surprising in the case of the 3-sphere where the space of harmonic
maps of any degree is a smooth manifold, each map having image in a totally
geodesic 2-sphere.
