  In this paper, using both quantum magnetohydrodynamic (MHD) and
magnetohydrostatic (MHS) models of a relativistically degenerate magnetic
compact star, the fundamental role of Landau orbital ferromagnetism (LOFER) on
the magneto-gravitational stability of such star is revealed. It is shown that
the previously suggested magnetic equation of state for LOFER with some
generalization of form $B=\beta \rho^{2s/3}$ only within the range $0\leq s\leq
1$ and $0\leq \beta< \sqrt{2\pi}$ leads to magneto-gravitational stability with
distinct critical value $\beta_{cr}=\sqrt{2\pi}$ governing the
magnetohydrostatic stability of the compact star. Furthermore, the value of the
parameters $s$ and $\beta$ is shown to fundamentally control both the quantum
and Chandrasekhar gravitational collapse mechanisms and the previously
discovered mass-limit on white dwarfs. Current findings can help to understand
the origin of magnetism and its inevitable role on the stability of the
relativistically degenerate super-dense magnetized matter encountered in many
white-dwarfs and neutron stars.
