Initial magnetization

In effect of loads acting in the scope of elastic deformations (proportional) in polycristalline bodies, changes in distances between atomic surfaces of the net are observed, which change the initial magnetic permeability. 

Fig. 4. The effect of temperature for Mng 6 Zng 3 Fe Fe on (a) initial magnetic permeabiUty, )J., measured on a polycrystalline toroid appHed as a core for a coil driven by a low (B <0.1 mT) ampHtude, low (10 kHz) frequency sinusoidal signal and (b) magnetocrystalline anisotropy constant, measured on a monocrystalline sphere showing the anisotropy/compensation temperature Tq and the Curie temperature, T. To convert joules to calories, divide by...

It should be noted that the decomposition shown in Eq. 3.7.2 is not necessarily a subdivision of separate sets of spins, as all spins in general are subject to both relaxation and diffusion. Rather, it is a classification of different components of the overall decay according to their time constant. In particular cases, the spectrum of amplitudes an represents the populations of a set of pore types, each encoded with a modulation determined by its internal gradient. However, in the case of stronger encoding, the initial magnetization distribution within a single pore type may contain multiple modes (j)n. In this case the interpretation could become more complex [49]. 

In practice, CP is achieved using the pulse sequence shown in Fig. 10.23. This shows the case for protons as the high abundance nuclei and carbons as the low abundance nuclei. First a standard 90° pulse is applied to the protons to create the initial magnetization. Then a pair... 

Fig. 10.23. Cross-polarization pulse sequence. The high abundance nuclei, such as protons, are first irradiated with a standard 90° pulse to create the initial magnetization. A special pair of spin-locking pulses is applied during a period called the contact time in order to transfer the magnetization from the protons to the low abundance nuclei, such as carbons. Protons are then decoupled from carbons during the acquisition of the carbon signal. In the case of protons and carbons, cross-polarization can enhance the observed carbon signal by as much as four-fold.

Figure 8. Nearest-neighbor concurrence C at zero temperature as a function of the initial magnetic field a for the step function case with final field b.

Magnetization of a material. Initially, magnetization increases by growth of favorably oriented domains. At high fields, the direction of magnetization rotates out of the easy direction. 

In order to apply quantitatively the Landau-Zener formula Eq. (2), we first saturated the crystal of Fes clusters in a field of Hz = -1.4 T, yielding an initial magnetization Min = -Ms. Then, we swept the applied field at a constant rate over one of the resonance transitions and measured the fraction of molecules which reversed their spin. This procedure yields the tunneling rate P 1010 and thus the tunnel splitting A 1010 , Eq. (2), with n = 0, 1, 2,. 

Here Min is the initial magnetization at time / = 0 (after a rapid field change), and Meq (Hz) is the equilibrium magnetization at H,. The rate function rsqrt(7/z) is proportional to the normalized distribution P(HZ) of molecules which are in resonance at Hz... 

Figure 13. Initial magnetization curves and hysteresis loops for self-assembled Fe58Pti2 assemblies annealed at (A) 550°C, (B) 600°C, and (C) 800°C, respectively [57].

Fig. 25. Trajectory of an initial magnetization vector during the composite pulse R = 90° 180° 90, which forms the basis of the MLEV-16 sequence. The spin is assumed to be irradiated on resonance. (Adapted from Schleucher et al., 1996, courtesy of John Wiley Sons Ltd.)...

Here T2 is the effective transverse relaxation time, and the Larmor frequency wl is taken to be time dependent in order to account for effects of slow molecular motion as well as for the effects of time-dependent magnetic field gradients. The initial magnetization before the 90° excitation pulse at f = 0 is taken to be Mz which can be different from the thermodynamic equilibrium value Mo as a result of incomplete relaxation or the use of a filter for longitudinal magnetization. 

If the repetition time is made shorter, more scans can be measured in a given time, but the initial magnetization will be smaller than the thermodynamic equilibrium value Mo- This effect is called partial saturation. Depending on the excitation flip angle a the... 

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