There is research protocol released by the University of Helsinki (2004) concerning this field of interest. I am looking for recent information or different results.
The magnetic permeability of ferromagnetic materials, such as alpha-ferrite (α-ferrite) and delta-ferrite (δ-ferrite), varies with factors like composition, temperature, and processing history. Alpha-ferrite, the stable form of iron at room temperature, is known for its high magnetic permeability. Delta-ferrite, stable at high temperatures, can be retained at room temperature in certain alloyed steels, but its exact magnetic properties can differ based on specific alloy compositions and thermal histories.
Martensitic stainless steels, which undergo a transformation from austenite to martensite upon cooling or deformation, exhibit different magnetic properties. The martensitic phase is ferromagnetic, but its magnetic permeability is generally lower than that of ferritic phases. This difference is significant in applications where magnetic properties are critical.
bssa.org.uk
Regarding recent studies comparing the magnetic permeability of α-ferrite and δ-ferrite, specific data is limited. However, discussions among materials scientists suggest that while both phases share a body-centered cubic (BCC) structure, their magnetic properties can differ due to factors like impurity content and grain structure. For instance, δ-ferrite may dissolve impurities such as sulfur, making it more prone to corrosion and potentially affecting its magnetic characteristics.