Magnetars and the Dynamo Effect How do magnetars create/sustain such strong magnetic fields? If a dynamo effect did create a magnetar, then what creates the magnetic field? The dynamo effect requires an electrically conductive fluid, but magnetars are purely composed of neutrons. In Earth, the dynamo effect is supported with evidence, but how does it apply to magnetars?
Magnetars (and neutron stars in general) don't need a dynamo to create their magnetic fields. Their magnetic fields are "frozen in" at the time of their formation. To really see why this is, you have to understand a lot about electromagnetism, but I can boil it down to the basics. Keep in mind that neutron stars are highly mysterious objects and we don't have a huge amount of good, observational evidence behind our theories since they're so hard to find and observe.

Neutron stars (and magnetars) are superconductors (or at least most theory and objective evidence suggests that is the case). What this means is that there is literally no resistance to the motion of electric charges moving throughout the star. To point out, even if the entire star was all neutrons (which zibadawa timmy points out is not the case) you'd still have charges since neutrons themselves are composed of charged particles. In any case, since there's no resistance, there cannot exist any electric fields inside the star. Any field which arose would induce a force on the charged particles which would be able to immediately move to cancel said field out. All electric fields destroy themselves immediately in a superconductor.

If we venture into electromagnetic theory equations, you'll find the very useful equation:

$$\nabla \times \textbf{E} = -\frac{\partial \textbf{B}}{\partial t}$$

Without getting into the details of this equation, the general idea behind it is that electric fields result in time varying magnetic fields and vice versa. But we just said above that our neutron star was superconducting and thus has no electric fields. This means the left hand side of that equation is zero. The right side represents the change in magnetic field over time, but we know that has to be zero now so we're forced to conclude magnetic fields in neutron stars (and magnetars) cannot change. They're frozen in at the point of creation (when the star becomes superconducting).

We can venture one step further and say that the magnetic fields of neutron stars and magnetars is so strong simply because of magnetic flux conservation. That is, you have a huge star of a few solar masses which has a massive field in its own right. That star then collapses into a neutron star but in the process, the magnetic field flux through its surface has to stay conserved. Magnetic field flux is a function of both the field strength and the radius of the star. Since the radius is decreasing so immensely, the magnetic field strength has to increase in proportion to the radius decrease (squared) to compensate and keep the overall flux the same, at which point that magnetic field is locked into place due to the superconducting nature of the star.