Interaction Domains

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The interaction of the magnetic domain structure with the physical microstructure of a material plays a key role in determining the overall magnetic properties.

In nanostructured, textured, hard magnetic materials so-called interaction domains occur. These are different in nature to the conventional magnetic domain structures we know from coarse grained materials e.g. sintered magnets. Interaction domains arise from the magnetic coupling between grains whose sizes are about equal to or smaller than the critical single-domain particle size, dc. For Nd2Fe14B, dc ~ 200-300 nm [Sagawa1984]. Interaction domains may encompass many such nanoscale grains (Fig. 1). Hot deformation has been employed to produce nanocrystalline Nd-Fe-B magnets containing interaction domains

 

Figure 1: Relation between microstructure and domain structure in hot-deformed Nd-Fe-B-based magnets. Well-pronounced interaction domains encompass several grains.

 

Though the phenomenon of interaction domains was recognized 55 years ago in elongated single-domain iron particles embedded in a nonmagnetic matrix [Craik1960], fundamental questions are still unanswered e.g. what is the nature of the boundaries between interaction domains? The boundaries cannot be conventional domain walls (Bloch walls or Néel walls) because they tend to be located at grain boundaries (structural discontinuities) rather than within a grain. Conventional domain walls are governed by the anisotropy constant K and the exchange constant A, whereas interaction domain boundaries may have other important influences.

For magnetic domain observations two methods are used. First Kerr microscopy which is suitable in order to study a large sample area and also to visualize all magnetization directions. Due to the resolution limit of about 200-300nm, Kerr microscopy cannot reveal very small features and in cases where high resolution is needed,  Magnetic Force Microscopy (MFM) is employed. In Figure 2 domain images of both techniques are compared.

 

 

 

Figure 2: (a) Kerr image and (b) MFM image of a hot-deformed Nd-Fe-B sample with same scale, (c) enlarged MFM image and (d) secondary electron image of a fracture surface with same scale.

 

The characteristic interaction domain width of the interaction domains was evaluated from Kerr images of the hot deformed Nd-Fe-B magnets using the linear intercept method. In the thermally demagnetized state, the average characteristic width of the interaction domains magnets produced here was about 1 µm, whereas the grain size was approx. 300 nm. The implication is that the interaction domains typically encompass about 2-3 grains in their width (Fig. 3). Although this is the typical width of the domains, the area covered by a single domain can be much larger (Fig. 3c).

 

 

Figure 3: (a) Kerr image of hot-deformed Nd-Fe-B sample with c-axis perpendicular to image plane, (b) binary image of domain structure from (a), (c) one yellow coloured domain in order to show the scale of interaction domains, (d) histogram of linear intercept domain size measured in 4 different directions.

 

With the Low-Temperature-MFM at IFW Dresden it was possible to visualize magnetization reversal processes while applying a magnetic field of up to 6T in-situ [Thielsch2012]. Since MFM is a surface sensitive technique one needs to check if a correlation between the information gained from the surface can be linked to processes within the bulk. Therefore the fractions of domains with the magnetization pointing in or out of the image plane were determined and assigned to a polarization (Fig. 4)

 

 

Figure 4: Procedure in order to determine polarization from domain fractions, (a) MFM image, (b) MFM image with domain boundaries, (c) only domain boundaries, (d) binary domain image to determine domain fractions.

 

In Fig. 5, the correlation of the initial magnetization curve measured with a Vibrating Sample Magnetometer (VSM) and the polarization values obtained from the procedure explained above is featured. The correlated values are in good agreement which leads to the assumption that observed domains from the surface reveal magnetization reversal processes within the bulk.

 

Figure 5: Correlation of initial magnetization curve from the thermally demagnetized state and polarization values obtained from MFM images.

 

Another type of material in which interaction domains occur is composites composed of hard and soft magnetic phases. Hot deformation was used to produce composites of Nd-Fe-B and Fe. Even though the size of the two different magnetic phases is far larger than the effective exchange length (thus precluding complete exchange coupling), the composites surprisingly show a uniform magnetization reversal along the easy axis [Thielsch2010]. The details of the magnetization reversal process were studied using Kerr microscopy (Fig. 6). The results showed that interaction domains tend to nucleate at phase boundaries. The growth of these domains was responsible for the magnetization reversal.

 

Figure 6: Domain evolution in Nd-Fe-B/Fe composite with c-axis of Nd-Fe-B in-plane, a magnetic field leads to domain rearrangement in soft magnetic phase and thus to a magnetic charge accumulation at the phase boundaries. This supports the subsequent nucleation of interaction domains at the phase boundaries and to the magnetization reversal [Thielsch2010].

 

A further example where interaction domains occur are nanostructured Nd-Fe-B thick films for MEMS applications [Woodcock2009]. Fig.  7 contains MFM images showing the magnetic domain structure of thick films deposited without heating the substrate (“cold”), with the substrate heated to 400°C and 500°C in both as-deposited and annealed states. In the as-deposited state when the substrate was cold or at 400°C, the resulting films were amorphous, resulting in the characteristic domain pattern (Fig. 7a and b). After annealing, the films crystallised and the domain pattern reflects the formation of small grains which are encompassed by interaction domains. For more details of magnetic properties and film preparation, please see [Woodcock2009].

 

Figure 7: MFM phase images of Nd-Fe-B-type thick films recorded using a hard magnetic tip. A greyscale key giving the phase range of each image is shown as is the deposition temperature: (a–c) in the as-deposited state (as-dep.); (d–f) following annealing (ann.) [Woodcock2009].

 

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