  Until the late 1980s, phases of matter were understood in terms of Landau's
symmetry breaking theory. Following the discovery of the quantum Hall effect
the introduction of a second class of phases, those with topological order, was
necessary. Phase transitions within the first class of phases involve a change
in symmetry, whereas those between topological phases require a change in
topological order. However, in rare cases transitions may occur between the two
classes in which the vanishing of the topological order is accompanied by the
emergence of a broken symmetry. Here, we report the existence of such a
transition in a two-dimensional electron gas hosted by a GaAs/AlGaAs crystal.
When tuned by hydrostatic pressure, the $\nu=5/2$ fractional quantum Hall
state, believed to be a prototype non-Abelian topological phase, gives way to a
quantum Hall nematic phase. Remarkably, this nematic phase develops
spontaneously, in the absence of any externally applied symmetry breaking
fields.
