Magnetization reversal coherent rotation

The resistance to magnetization reversal indicates that an energy barrier separates the initial and the final magnetic states. This energy barrier is a consequence of magnetic anisotropy. This can be illustrated within the so-called Stoner-Wohlfarth (SW) model, in which reversal is assumed to occur by in-phase rotation of all moments (coherent rotation) [7], For HoPP, antiparallel to M, the energy may be expressed as ... 

In this section, we concentrate on the fundamental impact of particle size reduction on magnetization processes in individual particles. Although not directly related to coercivity, the classical effect of single domain particle formation is described. At small particle size, reversal by coherent rotation tends to be favoured with respect to nucleation/pinning-depinning finally thermal activation effects and macroscopic quantum tunnelling are discussed. 

In the two examples above on the right, observable magnetization (antiphase coherence) is transferred by the 90° 1H pulse from Hb to Ha (top) and from Ha to Hb (bottom). This is a key process in all advanced NMR experiments that depend on / couplings. The role of the two operators is reversed as the operator in the x-y plane (the observable net magnetization) rotates to the z axis and the operator on the z axis (the multiplier that represents microscopic z magnetization) rotates to the x-y plane. After the rotations, we reverse the order of the two operators because we always write the observable operator first in the product. 

Kirby et al. (1994) developed a simple model vdiich is particularly useful for describing magnetization reversal in amorphous magnetic materials and multilayers with strong perpendicular anisotropy. They assumed that magnetization reversal in the uniform thin film occurs locally by thermal activation over the anisobropy barrier. They divided the sample into identical small volumes (cells) V, assumed fliat reversal occurred by coherent rotation, and proposed that the energy of the yth volume could be written as... 

The same is true for the opposite side of the spectral window (—l/2r) as a 180° rotation gives the same result whether it is cw or ccw. If we put this 6-pulse sequence at the center of our PFGSE, it will reverse the sense of the coherence helix for the resonance l/2r away from the center, and it will maintain the sense of the coherence helix for the on-resonance water peak and for peaks 1/r away from the center. The resonance l/2r away will be unwound under the influence of the second gradient, whereas the on-resonance (water) peak will be wound twice as tightly, leading to zero net magnetization when summed over the whole sample (Fig. 8.21). 

A rapid decay of coherence between initially prepared states due to pure dephasing and reversible relaxation between rotational levels and/or magnetic sublevels. 

Figure 7.17 Pulse sequence diagram for T, IR experiment. The thick dashed line shows the T recovery rate of the longitudinal magnetisation with B,j. Spin states are reported at specific times (a) the magnetisation is reversed (b) partial T recovery of spins in alignment with the Bg magnetic field (c) spins that have partially or fully recovered are flipped onto the transverse plane for signal detection (d) partial loss of coherence among spins and (e) total loss of rotational coherence among spins.

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