Magnetic displacement vector moment

Take a moment to look back at Figure 2.10. It shows how the magnitude of the z-component net magnetization vector M, when displaced from its Boltzmann equilibrium value, always recovers exponentially back to this equilibrium value at a rate determined by Th the spin-lattice (longitudinal) relaxation time. In this case, we will label this value Mq, the equilibrium magnitude of M in the magnetic field. Since the magnitude of M at any time (M,) is solely dependent on the difference between the populations of the up and down spin states, we can recast Eq. (2.9) in the form... 

In addition to one-dimensional modulations considered above, both two-and three-dimensional modulations are possible. Furthermore, atomic parameters affected by modulations may be one or several of the following positional (as shown in Figure 1.52 and Figure 1.53), occupancy, thermal displacement, and orientation of magnetic moments. The latter, i.e. commensurately or incommensurately modulated orientations of magnetic moments are quite common in various magnetically ordered structures (e.g. pure lanthanide metals such as Er and Ho), and both the value of the modulation vector and the amplitude of the modulation function often vary with temperature. 

It is well known that for any polarizable medium an electric field E induces a polarization P =D-EoE, where D is the displacement electric vector. Now, in a nematic the molecular dipolar moments are oriented ap>proximately parallel with respiect to the long axis of the molecules. Thus, the induced polarization gives rise to a director orientation. In contrast the influence of the magnetic field in a nematic is much weaker and in general, the induced magnetization can be neglected. A very well known result based on conventional thermodynamic arguments establishes that the work associated to an electric field E =-V, is... 

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