Discussions on Magnetic Domains
In this section we intend to review discussions which may arise from our book either in private communications or in the form of published material. The subjects may be new observations or insights, but also errors or misrepresentations as they are brought to our attention.
1. The Usefulness of Neutron Depolarization Techniques
Cf. Sect. 2.8 and 6.2.4.
Thanks to P.J. van der Zaag and M.Th. Rekveldt
2. 12. 1998
Neutron depolarization was mentioned in Sect. 2.8 among the integral methods for domain analysis. Only a few introductory references were given because the technique was considered quite demanding and not unambiguous in its conclusions. There is one aspect of this technique, however, which was overlooked by us. Evaluating the trace of the depolarization tensor, the average domain size of a sample can be obtained directly [1, 2], without any model assumptions which make most other conclusions from neutron depolarization studies somewhat uncertain.
The conditions that have to be fulfilled for this possibility are:
- The volume of the domain walls must be negligible compared to the domain volume.
- The domains must be small enough so that the precession angle of the neutron spins stays small compared to unity.
- The thickness of the domain walls must be small compared to the precession length of the neutrons.
All three conditions are safely fulfilled in the investigation of regular magnetic microstructures.
The possibility to determine the average domain size even in bulk material can be quite important, as demonstrated in a series of papers by van der Zaag et al. on bulk ferrites [3, 4]. They explored the domain size as a function of grain size and found a sharp transition from uniformly magnetized grains below 4 µm thickness to multidomain states in larger grains. This finding correlated in a convincing fashion with permeability and loss measurements on the same materials, which should have been taken into account in the discussion of bulk soft magnetic ferrites in Sect. 6.2.4. Surface domain observations on bulk ferrites were found to be compatible with this insight .
We are not sure, however, that the interpretation of the single domain feature as a consequence of exchange-decoupling between the grains introduced in  is correct, although it was supported by some theoretical arguments in . A similar transition between multi-domain grains and uniformly magnetized grains can also be observed in other materials in which an exchange coupling over the grain boundaries is undoubtedly present (see for example Fig. 5.45). We suppose that the results of the neutron depolarization experiments could also indicate the transition from strongly disturbed domains extending over the grains to domain patterns that are closed partially inside the grains.
A decrease in coercivity with decreasing grain size even in an exchange-coupled, continuous material is not implausible in view of the transition to nanocrystalline behaviour reproduced in the sketch on p. 546. In ferrites the individual grains have much smaller anisotropy levels compared to the silicon iron grains in conventional nanocrystalline materials. Therefore the domain wall width parameter is much larger than in iron, and the threshold for nanocrystalline behaviour may be shifted from the 10-100-nanometre range into the micrometre range. It is true that grain boundaries in sintered ferrites are preferred to be electrically insulating. But this does not mean that they must be non-magnetic, which would in fact be a most unusual feature in a high-permeability soft magnetic material. Systematic studies of the grain size dependence of soft magnetic properties and of the corresponding domain structures should be able to decide these differences in the interpretation.
1. M.T. Rekveldt, F.J. van Schaik: Static and dynamic neutron depolarization studies of ferromagnetic domain structures. J. Appl. Phys. 50, 2122-2127 (1979)
2. M.T. Rekveldt: Neutron depolarization in submicron ferromagnetic materials. Texture and Microstructures 11, 127-142 (1989)
3. P.J. van der Zaag, J.J.M. Ruigrok, A. Noordermeer, M.H.W.M. van Delden, et al.: The initial permeability of polycrystalline MnZn ferrites: The influence of domain and microstructure. J. Appl. Phys. 74, 4085-4095 (1993)
4. P.J. van der Zaag, P.J. van der Valk, M.T. Rekveldt: A domain size effect in the magnetic hysteresis of NiZn-ferrite. Appl. Phys. Lett. 69, 2927-2929 (1996)
5. R. Schäfer, B.E. Argyle, S. Takayama, D. Dingley: Grain influences on domains and read-back pulse distortions of ferrite MIG heads. IEEE Trans. Magn. 29, 3876-3878 (1993)
6. A. Aharoni, J.P. Jakubovics: Theoretical single-domain size of NiZn ferrite. J. de Phys. IV 8.Pr2, 389-392 (1998)