Magnetic susceptibility of a neutron star crust

The magnetic susceptibility of the degenerate free electrons in the crust of a neutron star is computed for a range of densities, temperatures, and field strengths. It is shown that when the temperature is low enough (typically less than 10 7 K for densities of about 10 7 g cm -3 and 10 12 G fields), the susceptibility undergoes large de Haas-van Alphen oscillations. The crust is then unstable to the formation of layers of domains of alternating magnetisation. Associated with these domains are magnetic field fluctuations of a few per cent amplitude and anisotropic magnetostrictive stresses which may be large enough to crumble the crust. It is argued that these domains are unlikely to directly influence the surface properties of the neutron star but may possibly be coupled indirectly to observable effects.