I am having difficulty with the seemingly contradictory explanations of ferromagnetic material as a magnetic field "amplifier" and a field "concentrator".
The amplifier analogy is usually referred to when the material is in a solenoid for an electromagnet application, while the concentrator analogy is common when discussing the distorting effects of a ferromagnetic material in an otherwise simple field (e.g. due to a bar magnet) in air.
Based on the fact that a magnetic field will polarize the dipoles in a ferromagnetic material -- which should add to the overall field -- it seems to me that the "concentrator" analogy is not really accurate. Rather, the material creates its own local field that overpowers the pre-existing field.
Following from this, it seems that if you place two soft ferromagnetic materials in a pre-existing magnetic field (e.g. due to Earth), then they should each be polarized to create their own local fields. If the relative magnetic permeability (due to material type), magnetic moment (due to volume), and proximity is high enough, then it seems that there would be a 'mutual magnetization' between the ferromagnetic materials.
If calculating the 'mutual magnetization' iteratively (e.g. calculate induced magnetic moment in first material due to pre-existing field; then calculate induced magnetic moment in second material due to pre-existing field and magnetic moment of first material; etc..), it also seems that this mutual magnetization would continue until each material was saturated. However, this can't be true because a single ferromagnetic material (which is also two ferromagnetic materials right next to each other) doesn't necessarily saturate in an ambient field.
So, all this to ask: Can two soft ferromagnetic materials in an ambient field induce magnetization in each other? And if so, why don't they saturate?
Edit: Thinking more, it seems that a 'snowballing' of mutual magnetization may not occur in practice because materials have finite magnetization (M), and therefore a non-infinitesimal volume through which their magnetic dipoles must be spread. So even though there may be some mutual magnetization between two ferromagnetic materials in a pre-existing magnetic field, it does not lead to saturation because the internal dipoles are too weak to induce alignment/magnetization in the other material -- just as a single aligned domain in a magnetic material does not induce alignment in the entire material. Is this accurate?