  The theory of quantum order-by-disorder (QOBD) explains the formation of
modulated magnetic states at the boundary between ferromagnetism and
paramagnetism in zero field. PrPtAl has been argued to provide an archetype for
this. Here, we report the phase diagram in magnetic field, applied along both
the easy $a$-axis and hard $b$-axis. For field aligned to the $b$-axis, we find
that the magnetic transition temperatures are suppressed and at low temperature
there is a single modulated fan state, separating an easy $a$-axis
ferromagnetic state from a field polarised state. This fan state is well
explained with the QOBD theory in the presence of anisotropy and field.
Experimental evidence supporting the QOBD explanation is provided by the large
increase in the $T^2$ coefficient of the resistivity and direct detection of
enhanced magnetic fluctuations with inelastic neutron scattering, across the
field range spanned by the fan state. This shows that the QOBD mechanism can
explain field induced modulated states that persist to very low temperature.
