Orientation of spontaneous magnetisation in cooling ferromagnet I'm trying to understand the direction of magnetic moments in a ferromagnetic material after cooling down below it's Curie temperature.
A permanent magnet of ferromagnetic material will loose it's order and become paramagnetic above the it's Curie temparature.
As far as I understand, all information about the direction of it's previous magnetisation is lost here - is that correct?
I understand that spontaneous magnetisation happens when cooling down. 
What's unclear to me is what influences the direction of the spontaneous magnetisation:


*

*It could be random, depending on some initial cluster of parallel magnetic moments that gets dominant

*it could be determined by the external magnetic field - for example of the earth, if there is no stronger one.

*or does it somehow relate to the previous magnetisation? Maybe based on contminations with material of higher 
curie temperature?

 A: If there is a magnetic field present, it will dictate the direction of the magnetization, as you anticipated and as @user3683367 said. This is then not referred to as spontaneous symmetry breaking but the external magnetic field breaks the symmetry explicitly.
In the absence of an external magnetic field, the alignment is indeed random. You intuition that one of the clusters or domains will become dominant is actually quite right. This can be observed very nicely in Monte Carlo-simulations. As the temperature approaches the critical temperature from above, the domain sizes grow larger and larger but there is no long-range-order (LRO). Upon crossing $T_c$, one domain will eventually take up the whole (simulation) volume, establishing a definite LRO. While the temperature is still above zero, there will be fluctuations on top of that (opposite domains inside the big one) but they are rather short-ranged and short-lived.
The information on alignment of the magnetic moments before the temperature is raised above $T_c$ should be lost entirely, at least in theory. This would require that the magnet is heated homogeneously such that LRO is destroyed throughout the bulk.
Contaminations a.k.a. impurities will in general complicate the story from a theoretical point of view. Keep in mind that the Curie temperature or critical temperature of a material is only meaningful as a many-body property, i.e. it tells you something about the interactions of the electrons in iron with each other. The critical temperature for iron will not really tell you what will happen if you dope another material with a different critical temperature with iron.
A: As far as I understand it is determined by an external field. 
The ferromagnetic system has two ground states for its magnetization both with equal energy (degenerate ground states). If you distort the system with an external magnetic field you make one of those states the preferred one so that your system magnetizes in this direction. 
