Magnetisation mechanisms

Fig. 4.34. Schematic magnetisation curve showing the important parameters initial permeability, Hi (the slope of the curve at low fields), the critical field. He and the main magnetisation mechanism in each magnetisation range.

In addition to domain wall bowing and displacement, there are two other magnetisation mechanisms spin rotation and spin waves. In the former, Fig. 4.44, magnetic moments within domains are simply rotated out of their easy direction by the external field. This mechanism occurs for virtually any magnitude of field the rotational permeability is a linear function of the field it is reversible and is typically small. It is discussed in Section 4.5.1. 

Many of the specific applications of ferrites depend on their behaviour at high frequencies. When subjected to an ac field, ferrite permeability shows several dispersions as the field frequency increases, the various magnetisation mechanisms become unable to follow the field. The dispersion frequency for each mechanism is different, since they have different time constants. Fig. 4.59. The low-frequency dispersions are associated with domain wall dynamics and the high-frequency dispersion, with spin resonance the latter, usually in the GHz range, is discussed in Section 4.6.2. 

The two main magnetisation mechanisms are wall bowing and wall displacement (see Section 4.3.2) in fact, any field results in a bowing of pinned walls, and if this field has a higher value than the corresponding critical field, walls are unpinned and displaced. Otherwise, bowed walls remain pinned to material defects. Measurements at low fields therefore show only one wall dispersion. Fig. 4.60 at high fields, several, complex dispersions are observed, such as those in Fig. 4.59. Wall displacement... 

At very high frequencies, domain walls are unable to follow the field and the only remaining magnetisation mechanism is spin rotation within domains. This mechanism eventually also shows a dispersion, which always takes the form of a resonance. Spins are subjected to the anisotropy field, representing spin-lattice coupling as an external field is applied (out of the spins easy direction), spins experience a torque. However, the response of spins is not instantaneous spins precess around the field direction for a certain time (the relaxation time, r) before adopting the new orientation. Fig. 4.62. The frequency of this precession is given by the Larmor frequency ... 

The magnetisation mechanism with the highest coercive force is domain rotation (or coherent rotation), in which all the spins within the sample are collectively reoriented in the field direction. In uniaxial materials. 

Metastable amorphous materials can be produced by the rapid quenching of melts in the form of metallic alloys with glassy structures [149]. These materials have attracted the attention of metallurgists, physicists, and, recently, chemists because of their exceptional properties (easy magnetisation, superior corrosion resistance, high mechanical toughness, interesting electronic properties) [150]. The use of these materials in catalysis was reported some years ago [151]. 

Figure 1.28 NMR spectra obtained after saturation transfer of the P nucieus trans to amide in the [Rh(dipamp)(enamide)] diastereoisomer 103a. Direct exchange of magnetisation is observed between the atoms trans to amide in the diastereomers 103a and 103b. The arrows pointing upwards indicate the most affected resonance. The proposed mechanism of intramolecular equilibration of 103a and 103b is shown.

H NMR transverse magnetisation relaxation experiments have been used to characterise the interactions between NR, isoprene rubber, BR, EPDM and polyethylacrylate rubbers with hydrophilic silica and silicas modified with coupling agents [124-129]. These studies showed that the physical interactions and the structures of the physical networks in rubbers filled with carbon black and rubbers filled with silicas are very similar. In both cases the principal mechanism behind the formation of the bound rubber is physical adsorption of rubber molecules onto the filler surface. 

The above has adopted a classical picture for describing the interaction between an rf field and the magnetisation. However, just as for the interaction with the main static applied magnetic field there is an analogous quantum mechanical description. The interaction between the rf magnetic field and the nuclear spins is simply another Zeeman interaction. The difference for this field is that it is time-dependent. In practice, the sample is irradiated with a linearly polarised rf-field of strength 2Bj, frequency corf and phase a. 

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