What happened to the magnetic domains and orientation of spins, and domain walls when we apply an external magnetic field to their surface? In a ferromagnetic material, there are many domains and domain walls present. What happened to the magnetic domains and orientation of spins and domain walls when we apply an external magnetic field to their surface?
 A: Even a single crystalline (or amorphous) - i.e. fully translation-symmetric ferromagnets - will form magnetic domains when not in a magnetic field. This minimizes its energy because the magnetic field can be kept away from the exterior.
When you apply a magnetic field, the spin momenta align with it and the domain walls completely disappear. Nothing changes with respect to the structure (atomic order) of the material. (In fact, slight shifts can occur, read about magnetostriction.)
Once you remove the field, depending on several factors, either the domain walls reappear or they don't (material stay magnetized).
What about powders or polycrystalline material?
If you have a powdered material, the domain walls go through the structural grain boundaries, again to minimize (domain wall) energy. Here as well, the structural grain boundaries cannot be changed. But magnetization in each grain will rotate to the magnetic field direction.
That means that the exact situation in your sketch is never going to happen.
But the powder is not really a single material in terms of magnetism. The grain boundaries are enough to almost or fully decouple the magnetization in each grain. That is why granular materials are a rather special case that is not useful to understand the concept of the magnetic domain wall
A: Depends on the temperature and the strength of the atomic bonds.
In the atom, the orientations of the magnetic dipoles of the subatomic particles are strongly interdependent. The deflection from their inner equilibrium succeeds - even if only partially - with external magnetic fields, the stronger the better, and under increasing temperatures.
Magnetic domains are areas with strong magnetic dependencies between the particles. Under a magnetic field, the magnetic dipoles in each domain align themselves somewhat with the external field, but the fundamental alignments of the domains remain the same.
If materials are pulverised and pressed under the influence of strong magnetic fields, domain formation can be suppressed. But beware, such magnets have large internal stresses - which the particles want to return to a magnetically more favourable position - and shatter when struck.
