Possibility of ferromagnetic neutron matter

We study ferromagnetism at high density of neutrons in the QCD hadron phase, by using the simplest chiral effective model incorporating magnetic fields and the chiral anomaly. Under the assumption of spatial homogeneity, we calculate the energy density as a function of neutron density, with a magnetization and a neutral pion condensation in the style of Dautry and Neyman. We find that at a high density the energy of the ferromagnetic order is lower than that of the ordinary neutron matter, and the reduction effect is enhanced by the anomaly. Compared to the inhomogeneous phase with the alternating layer structure, our ferromagnetic phase turns out to be unfavored. However, once an axial vector meson condensation is taken into account in our simplest model, the ferromagnetic energy density is lowered significantly, which still leaves some room for a possible realization of a QCD ferromagnetic phase and ferromagnetic magnetars.

Figure 1

The fermi surface and polarization of spins. The spin-magnetic coupling modifies the depth of the dispersion relation according to the fermion spins. Left: all the spins are polarized. Right: there remains some density of the opposite component of the spin.

Figure 2

A plot of the energy per neutron, as a function of the neutron density ${\rho }_n$. Straight line: ordinary neutron matter without the pion condensation. Thick curved line: our result with both pion condensation $q$ and magnetization $B$ with the QCD anomaly term. Thin curved line: the result of Dautry and Neyman [15] with only the pion condensation $q$. Dashed line: the energy with both $q$ and $B$ but without the QCD anomaly term.

Figure 3

A plot of the magnetic field spontaneously generated, as a function of the neutron density ${\rho }_n$. The neutron density is normalized by ${\rho }_0$ (the standard nuclear density). The evaluation is with the fully polarized neutrons.

Figure 4

An energy plot taken from [13], comparing the ALS phase and the Fermi gas (ordinary neutron matter). The horizontal axis is the neutron density $\rho$ in the unit of the standard nuclear density ${\rho }_0$, while the vertical axis is the energy gain per neutron. The upper curve is for the Fermi gas and the lower curve is for the ALS. Solid lines are for neutrons, and dashed lines are for symmetric nuclear matter. The arrows indicate the energy reduction by the ALS.

Figure 5

A plot of the energy per neutron, as a function of the neutron density ${\rho }_n$. Beyond the previous figure for the pion condensation, here we added two thick dashed lines, showing the axial vector condensation. The upper thick dashed line is for $g_{aNN}=9$ and the lower is for $g_{aNN}\sim 18$.