The dense electron gas interior neutron star is high degenerate and relativistic. The observation of neutron star about its thermal and magnetic effects depends on transport properties of the electron gas which is thought as the magnetic carrier. Its Landau levels in magnetic field are quantized and highly degenerate. The energy difference of an electron gas between in and not in magnetic field determines the magnetization of the gas, and the corresponding susceptipilities can be obtained through the thermodynamic calculation. When the magnetic field is weak, the susceptipility is 10-3 having similar order as in white dwarf. While in strong field the magnetization has the de Haas-van Alphen fluctuant effect like in microtherm metals. The differential susceptipilities can equal or exceed critical for high order harmonic frequency. Correspondingly, there is probably the phase-instability occuring in dense electron gas and the stable state is consisted of two different magnetization phases similar as the first-order phase transition of water. But if, there is a surface energy at the boundary then there is metastable state of homogeneous magnetization. The phase transition of interior neutron star can be observed through its electromagnetic radiation.This electromagnetic radiation may provide the extra energy in starquake model which was proposed to explain the giant flash of a magnetar.