Macroscopic magnetization

The effect of an MW pulse on the macroscopic magnetization can be described most easily using a coordinate system (x, y, z) which rotates with the frequency about tlie z-axis defined by the applied field B. 

A.P. Malozemoff, "Macroscopic Magnetic Properties of High Temperature Superconductors", in Physical Properties of High Temperature Superconductors /, ed. by D. M. Ginsberg, World Scientific, Singapore, Ch. 3, and references therein (1989). 

Nowadays, self-diffusion coefficients are almost exclusively measured by NMR methods, through the use of methods such as the 90-8-180-8-echo technique (Stejs-kal and Tanner sequence) [10-12]. The pulse-echo sequence, illustrated in Figure 4.4-2, can be divided into two periods of time r. After a 90° radio-frequency (RF) pulse the macroscopic magnetization is rotated from the z-axis into the x-y-plane. A gradient pulse of duration 8 and magnitude g is appHed, so that the spins dephase. 

Here, h(M0) denotes the inverse function to M0(h), where M0 is the macroscopic magnetization of the spins in the absence of carriers at a field h and temperature T. It is usually possible to parameterize M0(h) by the Brillouin function Bs according to... 

It is clear from eq. (17) that A describes how the Ginzburg-Landau functional F[8Mq] varies with q. Here, 8Mq are the Fourier components of the difference between local and macroscopic magnetization M(T, H). In the long-wave limit, in which eq. (17) is valid. 

To visualize the spin behavior in FT-NMR, it is easy to use the classical description, where the nuclei are regarded as an ensemble of small magnets spinning at their Larmor frequency along the direction (z-axis) of the applied magnetic field, B0. The macroscopic magnetization points to the z-axis. 

Figure 2. The revolution of macroscopic magnetization in a rotating frame of reference (a), application of additional magnetic field (BL) along x -axis as a 90° pulse which tips the macroscopic magnetization into the x y -plane (b), as they precess in the x y -plane, the macroscopic magnetization diminishes because nuclear magnets actually precess at slightly different frequencies which causes dephasing.

Figure 4. Schematic explanation of T] and T2 relaxation phenomena. The equilibrium macroscopic magnetization vector, MCi is tipped away from the direction of the magnetic field (z-axis) by application of a radio frequency field. After the rf field is removed, it continues to rotate in x y -plane about the z -axis. Two relaxation processes occur recovery of the magnetization Mz (component along the z-axis) to equilibrium value M and decay of Mxy (magnetization in the x y -plane) to zero due to the loss of phase coherence.

Fig. 1.19. The spiral-type movement of the macroscopic magnetization vector subject to the simultaneous action of an external static magnetic field and of an r.f. field rotating at the resonance frequency.

Fig. 1.20. The spiral movement of the macroscopic magnetization of Fig. 1.19 becomes a rotation about the x (or y ) axis of the rotating frame if the sphere rotates about z with the proper frequency.

Fig. 9.11. The time constant for the process of reaching the equilibrium value of the macroscopic magnetization at a certain weak field Me J]eak is the same starting from a higher field (A) or from zero field (B).

In the statistical description delivered by Eq. (4.125), the observed (macroscopic) magnetic moment per particle is given by the average... 

FIGURE 3.4 Assemblage of precessing nuclei with net macroscopic magnetization Mn in the direction of the stationary magnetic field B0. 

An assemblage of equivalent protons precessing in random phase around the z axis (i.e., in the direction of the stationary magnetic field B0) has a net macroscopic magnetization M0 along the z axis, but none in the xy plane (Figure 3.4). 

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