  Magnetars are highly-magnetised rotating neutron stars that are predominantly
observed as high-energy sources. Six of this class of neutron star are known to
also emit radio emission, and magnetars are, thus, a favoured model for the
origin for at least some of the Fast Radio Bursts (FRBs). If magnetars, or
neutron stars in general, are indeed responsible, sharp empirical constraints
on the mechanism producing radio emission are required. Here we report on the
detection of polarised quasi-periodic sub-structure in the emission of all
well-studied radio-detected magnetars. A correlation previously seen, relating
sub-structure in pulsed emission of radio emitting neutron stars to their
rotational period, is extended, and shown to now span more than six of orders
of magnitude in pulse period. This behaviour is not only seen in magnetars but
in members of all classes of radio-emitting rotating neutron stars, regardless
of their evolutionary history, their power source or their inferred magnetic
field strength. If magnetars are responsible for FRBs, it supports the idea of
being able to infer underlying periods from sub-burst timescales in FRBs.
