Magnetisation rotation

Permanent magnets, made of hard ferrites, are used in applications where a constant magnetic field without electric current is needed. A permanent 

Ba hexaferrite particles usually grow as plates with their c-axis perpendicular to the plate surface. This growth habit leads to a shape anisotropy perpendicular to the magnetocrystalline anisotropy and therefore to a 

Adapted from Cullity (1972) and Lotgering, Vromans Huybert (1980). 

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An original technique was developed by Konishi et al. (1969) and extended later on by Narita et al. (1980). This method is known as the small-angle magnetisation rotation (SAMR) method a static bias field H and a tensile stress (o) are applied in the direction of the film a small-amplitude ac driven field H = W max sin(wf) is applied perpendicular to H. It is this ac magnetic field that induces a magnetisation rotation, which can be detected as an induced voltage in a sensor coil wound around the film axis. This response is measured as a function of the applied stress, i.e. of the strain-induced anisotropy. An experimental SAMR set-up is illustrated in fig. 5. The sensitivity of this method was 2 x 10-7 (Narita et al. 1980) and even much higher, namely 10-9 (Hernando et al. 1983). 

Fig. 4.30. Two extreme configurations of domain wall (a) magnetisation reversal in one interatomic distance (b) magnetisation rotation shared by as many spins as possible.

Rotating frame model A means of visualising the processes taking place in an NMR experiment by observing these processes as if you were riding on a disc describing the movement of the bulk magnetisation vector. 

For the rotation of the magnetisation out of the easy axis into the field direction, the magnetostriction is related to the magnetisation as (Chikazumi 1964) ... 

The normalised magnetostriction as a function of normalised magnetisation for films with perpendicular and parallel anisotropy is plotted in fig. 27(a, b) for (Tbo.27Dyo.73)o.42Feo.58 (Schatz et al. 1994). The films with in-plane anisotropy appear to show high magnetostriction and magnetisation at low fields (the coercivity is less than 0.01 T), due to the easy rotation of the spins in the isotropic plane. The motion of 180°... 

The individual vectors p, before irradiation, are out of phase with one another and this can be represented by the vector M0 aligned in the Oz direction (Fig. 9.4). As the resonance condition is reached, all the vectors pack together and rotate in phase with B[. Hence, M0 changes direction and finally reaches an angle a with the Oz axis, which is controlled by the time and power of irradiation (Fig. 9.7). Thus M0 acquires an Mxv component in the horizontal plane that is maximum when a — 7t/2, while maintaining a component Mz in the direction of the Oz axis (except if a = tt/2). The frequency of rotation of the magnetisation vector is equal to that of the precession movement. Under these conditions, some nuclei will proceed to the second orientation allowed (in the case where I = 1/2). The system will slowly return to its original state after the irradiation is stopped. A coil is used to detect the component in the Oy direction (Fig. 9.8). 

Figure 9.7—Change of the magnetisation vector Af0 with irradiation and relaxation of the system after resonance. Schematic representation showing only the individual vectors resulting from the non-equilibrium of populations ( numerical). An independent observer rotating at the same frequency as the precession would see the magnetisation vector tilted by an angle of a. Relaxation to the original position is also shown.

There is a simple and well-known model for the description of DNMR phenomenon, provided no scalar coupling is involved.11 In Section 3.2.1, the macroscopic magnetisation vector of the vector model gives the detected signal (the FID). This vector rotates in the xy plane perpendicular to the direction of the external magnetic field during the detection its frequency is determined by the shielding effect of the chemical environment of the nuclei. 

During the detection, the examined nucleus is in the two conformers with Ki and Kz probabilities. At the start of the detection, the conformation of a given spin set (A(1) in this example) can be determined by knowing these probabilities and by using a pseudo-random number (see Section 3.1). The magnetisation vector starts to rotate with ft/1 frequency ... 

The partial recovery of the quantum phase coherence of nuclear dipoles originates from the non-commutative property of the Zeeman energy with the quantum operator which represents the residual interaction after rotating the spins. This rotation has no effect on the magnetisation dynamics when the residual interaction, hHR, is equal to zero. No... 

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