Spin orbit coupling induces the (usually) most important contribution to the magnetocrystallline anisotropy. This contributes a large deal to the stability of magnetization in form of the barrier to be overcome upon rotating the magnetization.

The main point is therefore that in an atomic lattice the spin orbit interaction depends on the orientation of magnetization. Btw, the magnitude of the orbital magnetic polarization shares this anisotropy, i.e. it is different, in particular, along the hard and easy axes, respectively.

This is interesting to know, because experiments such as "XMCD" are able to detect this difference, since they can extract spin and orbital moments separately.

Spin-orbit coupling adds a complex term to the Hamiltonian of the system that lifts the spin degeneracy of the states. In essence, this term turns spin into a dynamical variable, thus altering the nature of the time-reversed states; in such case, in applying the time-reversal operator, the spins must also be reversed. Without spin-orbit coupling and/or an applied magnetic field, spin index is just a passive index for bookkeeping.

I have realized that the total magnetic moment of the system is a result of spin contribution plus the orbital contribution (if it contributes). BUT, if I look to the recording media i only need a quantity of the magnetic moment of the material or molecule which can be used for fabrication of device. I mean the percentage of orbital contribution to the total magnetic moment is nothing to do with the efficiency of the recording media.

Spin orbit coupling induces the (usually) most important contribution to the magnetocrystallline anisotropy. This contributes a large deal to the stability of magnetization in form of the barrier to be overcome upon rotating the magnetization.

The main point is therefore that in an atomic lattice the spin orbit interaction depends on the orientation of magnetization. Btw, the magnitude of the orbital magnetic polarization shares this anisotropy, i.e. it is different, in particular, along the hard and easy axes, respectively.

This is interesting to know, because experiments such as "XMCD" are able to detect this difference, since they can extract spin and orbital moments separately.

To appreciate the underlying physics, consider the spin Hamiltonian in Eq. (4.6.7) of the book by Chaikin & Lubensky (Cambridge University Press, 2000, p. 177). Here the coefficient D, multiplying the term proportional to the square of the projection of the spin operator along the preferred direction of the lattice, arises from spin-orbit coupling. Because of the square, for D > 0 and sufficiently low temperatures (before the entropic contribution to free energy becomes dominant) the free energy is minimized for non-vanishing sublattice magnetizations m_A and m_B. For the vanishing staggered magnetization m_s (that is for m_A = m_B), the free-energy density f(m,m_s) reduces to the Bragg-Williams free energy, which has two minima, at -m0 and +m0, below the critical temperature Tc (see Fig. 4.1.1 on p. 147, and for the relevant Tc see Eq. (4.1.7) on p. 148). Magnetic recording requires Tc to be sufficiently lower than room temperature. With 1 eV being approximately equal to 10,000 K, spin-orbit coupling need not be very strong for a spin-orbit coupled material to be of practical use.