Time dependence of the magnetization

The time dependence of the magnetization vector, M(t), is thus related to the cross-product of M and B. Keep in mind also that the magnetic field can be time-dependent. We have replaced B0 by B to indicate that the magnetic field can consist... 

First of all, one can introduce relaxation phenomenologically by amending the equation describing the time-dependence of the magnetization vector [Eq. (1.2)] by a decaying term ... 

By multiplying eq. (1.18) with the gyromagnetic ratio y one obtains the time dependence of the magnetic moment ft, remembering that fi = yp ... 

Looking at eq. (1.21), it is seen that the time dependence of the magnetization vector M results from two contributions. One is the partial time derivate of M in the rotating coordinate system ... 

Experiment shows that the time dependence of the magnetization is often logarithmic rather than exponential [16, 99, 136, 159, 166, 167]. As pointed out long ago [99], a logarithmic time dependence is obtained by... 

For both NMR and EPR, the phenomenological Bloch equations [47] can be used to track the time-dependence of the magnetization of the sample M in the total field H ... 

Brocklehurst et al. employed squalane as S and fluorene as M. They measured the time profile of fluorene fluorescence during and after pulse radiolysis and found that the fluorescence intensity was increased by a 0.3 T magnetic field as shown in Fig. 6-3(a). They also measured the time dependence of the magnetic field enhancement of the fluorescence intensity as shown in Fig. 6-3(b). This figure shows that the MFE is very small or zero during the pulse, but that it rapidly reaches an apparent plateau (40 % increase) after about 100 ns. This is due to the fact that the MFE grows in several tens ns, which is the order of the S-T conversion due to the HFCM as shown in Chapter 3. 

Fig. 6-3. Magnetic field effects observed in the radiation reaction of a squalane (S) solution of fluorene (M) for pulse radiolysis with a 4-MeV electron accelerator. The reaction temperature is not described in the present papers, but may be room temperature, (a) Time profile of fluorine fluorescence during and after pulse radiolysis of a squalane solution (1) at the minimum field less than 0.05 mT, where the residual field of an electromagnet is cancelled by passing a small reverse current through the magnet s coils (2) at 0.3 T. (b) The time dependence of the magnetic field enhancement of the fluorescence intensity (A) 15-ns pulse ( ) 50-ns pulse, (c) The MFE on the increase in fluorescence intensity at 200 ns after the pulse. (Reproduced from Ref. [18b] by permission from The American Chemical Society)...

Figure 1-15 Time dependence of the magnetization M following a 90° pulse.

The time dependence of the magnetization for the proton systems in a hydrated protein may be described heuristically by two coupled equations containing three relaxation rates R- , the longitudinal relaxation rate for the water in the absence of the protein proton interaction R]p, the longitudinal relaxation rate for protein protons in the absence of a relaxation path provided by water protons and Rt, a rate of magnetization transfer between the two spin systems. The equations then become... 

In principle, the time dependence of the magnetic interactions responsible for the relaxation processes can be exploited to investigate dynamic processes as the chemical exchange of ligands in coordination complexes. 

The most common experimental approach to study the magnetization reversal is to measure the time dependence of the magnetization (or Kerr rotation angle) near the coercivity field. We summarize here the results of such measurements for Tb/Fe and Dy/Fe and discuss a newly developed model proposed by Kirby et al. (1994). 

As is evident from eqns (23), the time-dependencies of the magnetizations of I and S spins are rather conplicated because they are mutually correlated even if the conjugated differential equations (23) can be generally solved. 

The first contribution to the induced electric dipole moment in O Eq. 11.74 from the time dependence of the magnetic field, w G, gives rise to two different observable properties. In the dispersive region, this property determines the optical rotatory power, or just optical rotation (OR) for short, and in the absorptive region it determines the rotational strength observed in electronic circular dichroism (ECD). 

Influence of the switching times Provided that the time dependence of the magnetic flux density... 

The time dependence of the magnetization is then calculated by solving the equation of motion for the density matrix a to the second order in The results are... 

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