Internal field mapping in single‐domain and multidomain grains

Abstract

We have calculated the vector internal field Hi within a ferromagnetic cube with a one‐dimensional domain structure, consisting of lamellar domains separated by Bloch‐type walls. The internal field is not purely a demagnetizing field antiparallel to the spontaneous magnetization Ms. It has components perpendicular to Ms as well. These transverse fields are most conspicuous at grain surfaces, particularly along edges and at corners. They may act as centers for nucleation of non‐uniform magnetization structures in large single‐domain (SD) grains. An approximate picture of leakage of fringing fields is obtained by replacing the sheets of + and − magnetic poles that are the actual source of Hi by single + and − poles with a larger spacing. Thus Hi within an SD grain is approximately “bipolar,” a two‐domain (2D) grain has a “tetrapolar” field and so on. The full diagonalized “demagnetizing” tensor has been calculated for points inside a SD cube. Only at points along (100) axes through the cube center are the off‐diagonal elements zero. At the center point, Hi = −Ms/3, as for a sphere, and averaged over the cube, the demagnetizing factor is 1/3. Two‐domain grains with and without finite‐width walls have almost identical internal field patterns, except that finite‐width walls produce strong leakage fields along transverse faces which should be well imaged by the Bitter colloid technique. In a 2D cube with equal domains, the demagnetizing factor near the center of either domain is 0.12, close to the grain‐average N of 0.135 determined from the overall demagnetizing energy. When the domains are of unequal size, demagnetizing fields increase rapidly with wall displacement in the larger domain and decrease in the smaller domain, favoring a return to the demagnetized state. We demonstrate that, as expected, the field within either domain in a 2D cube is the superposition of Hi due to that domain alone plus the exterior field He of the other domain. The ability to calculate exterior as well as interior fields is vital in understanding magnetic particle interactions. Finally, we find that the rotation of the magnetization within rock bodies in response to self‐demagnetizing fields is well predicted by using the demagnetizing tensor for uniform magnetization, provided M ≤ 15 A/m. Deflection of the natural remanent magnetization due to specimen shape and the shape anisotropy contribution to magnetic anisotropy measurements could be determined by this method.