Some neutron stars have magnetic fields strong enough to suck a pen out of your pocket at a distance of 50,000 miles.
As far as I know, neutrons are not very good at generating magnetic fields, so is the field created by the nondegenerate crust, the surrounding nebula or where ?
Well, until someone more knowledgeable comes along, let me offer that a) the neutron star’s crust is not necessarily made of neutrons and hence may generate magnetic fields and b) the precursor star’s magnetic field is now the property of the neutron star, but much more concentrated.
There are loads of links, I think, on this topic. Here’s one.
Neutron stars conserve the angular momentum of the star from which they formed, so because of their small diameters they tend to spin rapidly. They also conserve the charge of the star from which they formed. Perhaps it is this charge, which would concentrate at the surface by its mutual repulsion, and therefore is circulating, which generates the magnetic field.
But it’s just a guess. Good question - never thought of it - I think you’re right, neutrons are not good magnets.
http://astrosun.tn.cornell.edu/courses/astro201/neutron_star.htm
“The neutron star acts like an enormous magnet, with the magnetic poles tipped at an angle to the axis of rotation. Like the Earth, the pulsar is surrounded by a magnetosphere, a region in which electrons and other particles are accelerated by the magnetic field. However, the magnetic field of the neutron star is much stronger than the Earth’s and the electrons move at velocities close to the speed of light, emitting synchrotron radiation in a narrow beam along the direction of the magnetic poles.”
http://www.astro.umd.edu/~miller/nstar.html
Introduction to neutron stars
“The difference comes at the subatomic level. In a magnetic field, a charged particle such as an electron or proton will spiral around the field at a preferred frequency, the cyclotron frequency, that is proportional to the strength of the field. This principle is used in magnetic resonance imaging, where the preferred frequency (of nuclei) is in the radio wavelengths. When magnetic fields of neutron star strength are introduced, the electron cyclotron frequency is in the X-rays, and when the field is 4.414 times 10^13 Gauss the electron cyclotron frequency equals the electron rest mass energy. This field turns out to be a critical field in quantum electrodynamics, such that (essentially) above that field there are a number of bizarre processes (e.g., single photon pair production, photon splitting) that can be very important, whereas below the critical field those processes are negligible. We don’t have a prayer of accessing this regime of ultrastrong fields in the laboratory, and we only have our quantum mechanical predictions to guide us. So, if we can establish that such fields exist in astronomy, then by studying those objects we can test our quantum mechanical theories in a new physical regime.”
I am not absolutely certain, but I think that neutrons DO have a magnetic moment, contrary to what was implied above.
Ah, the inner core is swimming with degenerate electrons, and probably doing some sort of convection deal as well. A good link is sometimes hard to find; thanks.
Yup. Pesky little quarks! 
Also, some models estimate that as much as 10% of a neutron star’s mass is protons, with an equal number of electrons to match. Since the interior of a neutron star is a superfluid and has charges embedded in it, it’s also a superconductor, which can create tremendous magnetic fields.
There’s one sentence in the page astro mentioned that really bothers me:
How can the cyclotron frequency equal the rest mass energy? The units in those two quantities are completely different, whether in conventional or relativistic units. Does anyone know what they mean by this?
Hbar equals one, so energy and frequency are in the same units. It’s quantum mechanical units, not relativistic.