--X-Y---X-Y---X-Y---X-Y-- (periodical)

In the following 2 cases, will the magnetic moment depend on whether the magnetic field is applied to the right or to the left? (The atoms are close enough to each other so that they orbitals may overlap.)

Case 1:

No exchange interaction.

Case 2:

Ferromagnetic exchange interaction exists between atoms X.

Atoms X have a spin-orbit coupling.

Thanks!