Spontaneous magnetization of solid quark-cluster stars

Abstract: Pulsar-like compact stars usually have strong magnetic fields, with strengths from ~10⁸ to ~10¹² G on the surface. How such strong magnetic fields can be generated and maintained is still an unsolved problem, which is, in principle, related to the interior structure of compact stars, i.e., the equation of state of cold matter at supra-nuclear density. In this paper we are trying to solve the problem in the regime of solid quark-cluster stars. Inside quark-cluster stars, the extremely low ratio of number density of electrons to that of baryons n_e/n_b and the screening effect from quark-clusters could reduce the long-range Coulomb interaction between electrons to short-range interaction. In this case, Stoner's model could apply, and we find that the condition for ferromagnetism is consistent with that for the validity of Stoner's model. Under the screened Coulomb repulsion, the electrons inside the stars could be spontaneously magnetized and become ferromagnetic, and hence would contribute non-zero net magnetic momentum to the whole star. We conclude that, for most cases in solid quark-cluster stars, the amount of net magnetic momentum, which is proportional to the amount of unbalanced spins ξ=(n₊-n_-)/n_e and depends on the number density of electrons n_e=n₊-n_-, could be significant with non-zero ξ. The net magnetic moments of electron system in solid quark-cluster stars could be large enough to induce the observed magnetic fields for pulsars with B10¹¹ to ~B10¹³ G.