Magnetic-polarization model

To develop the magnetic-polarization model, note that an isolated magnetizable particle of radius a acquires a magnetic dipole m in the presence of a magnetic field H ... 

It is worth mentioning that for the communication of useful information the operating point of the sensors must always be specified in terms of sensor temperature, electrical or magnetic polarization, and number of fundamental blocks of the sensor model (figure 2). 

The bond polarization model gives the chemical shift of an atom a as the sum over the Na bonds of this bond. The bond contributions are formed of a component for the unpolarized bond (which also includes the inner shell contributions to the magnetic shielding) and a polarization term. The bond contributions are represented by a tensor with its principal axes along the basis vectors of the bond coordinate system. The transformation from the bond coordinate system into a common cartesian system is given by the transformation matrix Z). ... 

The current theories of chemically induced magnetic polarization can therefore be summarized into the two basically different mechanisms the photoexcited triplet mechanism (PTM) responsible for the initial electron polarization and the observed Overhauser effect in nuclear polarization, and the radical-pair mechanism which, to date, accounts for almost the remaining bulk of the known polarization systems. We proceed to describe the simple physical models of these two mechanisms by beginning with the more sophisticated radical-pair theory. 

As model systems for scientific study, MR fluids are superior to ER fluids, because complications due to charging and conductivity in ER fluids have no counterpart in MR fluids, since magnetic monopoles, the analog of electric charges, are unknown in nature. Thus, a magnetic analog of the simple polarization model described in Section 8.2.1 for ER fluids should be even more appropriate for MR fluids. 

In evaluating the spectral peak energy, we practically use non-spin-polarized model for a non-magnetic material at the ground state, namely, the exchange potential for non-spin-polarized system,... 

As already mentioned, the phenomenon of magnetic circular dichroism in photoemission originates from spin-orbit and exchange interactions in combination with the dipole selection rules. In the atomic model picture, the splitting of the 3p level (into sublevels with orbital momentum m) is caused by the electrostatic interaction of the core level with the magnetically polarized valence electrons [57]. The observed intensity differences and the respective asymmetry values in photoemission from the Fe 3p levels are small (typically 3%) compared to the large MCDAD and MLDAD asymmetries (up to about 12%) observed in valence band photoemission [27]. 

A more complex magnetic behaviour is expected for RI compounds in which the second component is a 3d transition metal such as Mn, Fe, or Co. The magnetic behaviour of the transition metal component is now based on the magnetic polarization of the electronic d-bands. Consequently, in this section we summarize the theory of itinerant or band magnetism and its application to transport properties. We begin with the Stoner-Wohlfarth model and include a summary of recent works. 

Nuclear magnetic resonance of A1 in the paramagnetic state of R-Al intermetallic compounds. Values of the s-f exchange interaction parameter /sf are based on the uniform polarization model [Jaccarino et al. (I960)]. 

We have extended the Bohr-Weisskopf theory, based largely on the nuclear single particle model with the inclusion of core polarization in the evaluation of the effect of finite size of the nuclear magnetization. This model was found quite successful in ac-... 

Using this model in analogy with previous studies we can calculate a magnetic moment (fi) of the system with fixed Stoner exchange parameter Id and occupation of the d states. The total energy could then be calculated as the balance between the kinetic energy and the spin-polarization energy ... 

Figure 2. The structural energy difference (a) and the magnetic moment (b) as a function of the occupation of the canonical d-band n corresponding to the Fe-Co alloy. The same lines as in Fig. 1 are used for the different structures. In (b) the concentration dependence of the Stoner exchange integral Id used for the spin-polarized canonical d-band model calculations is shown as a thin dashed line with the solid circles. The value of Id for pure Fe and Co, calculated from LSDA and scaled to canonical units, are also shown in (b) as solid squares.

The frustration effects are implicit in many physical systems, as different as spin glass magnets, adsorbed monomolecular films and liquid crystals [32, 54, 55], In the case of polar mesogens the dipolar frustrations may be modelled by a spin system on a triangular lattice (Fig, 5), The corresponding Hamiltonian consists of a two particle dipolar potential that has competing parallel dipole and antiparallel dipole interactions [321, The system is analyzed in terms of dimers and trimers of dipoles. When the dipolar forces between two of them cancel, the third dipole experiences no overall interaction. It is free to permeate out of the layer, thus frustrating smectic order. 

---