Magnetic interactions, external

In addition, there could be a mechanical or electromagnetic interaction of a system with an external entity which may do work on an otherwise isolated system. Such a contact with a work source can be represented by the Hamiltonian U p, q, x) where x is the coordinate (for example, the position of a piston in a box containing a gas, or the magnetic moment if an external magnetic field is present, or the electric dipole moment in the presence of an external electric field) describing the interaction between the system and the external work source. Then the force, canonically conjugate to x, which the system exerts on the outside world is... 

While all contributions to the spin Hamiltonian so far involve the electron spin and cause first-order energy shifts or splittings in the FPR spectmm, there are also tenns that involve only nuclear spms. Aside from their importance for the calculation of FNDOR spectra, these tenns may influence the FPR spectnim significantly in situations where the high-field approximation breaks down and second-order effects become important. The first of these interactions is the coupling of the nuclear spin to the external magnetic field, called the... 

The external magnetic field could be due to a magnet or it could be due to the magnetomotive force induced by a current in a conductor (or another stationary coil). The relationship for torque developed when the fields of a stationary (stator) coil and a rotating (rotor) coil interact is given by... 

The energy 7i(S) of a given configuration of N spins is made up of two parts (1) a contribution that arises solely from the inter-spin molecular forces (= Hst s), and (2) a contribution that is due to the interaction between the spins and any external magnetic fields (= Since 5, is effectively the magnetic moment... 

On the basis of the observations, the enhancements of the p-values for the Q-Zni x MrLxS monolayer films can most likely be ascribed to the interaction between Mn ion as a magnetic ion and the external magnetic field. The enhancements are probably caused by magnetic orientation of the Q-Zni-xiMn S on the quartz substrates. 

The third prominent interaction in iron Mossbauer spectroscopy is the magnetic hyperfine interaction of the Fe nucleus with a local magnetic field. As explained in detail in Chap. 4, it can be probed by performing the Mossbauer experiment in the presence of an applied external magnetic field. 

Figure 5.9. Effect of spin-spin dipolar interaction and an external magnetic field on triplet levels.

Since spins and the external magnetic field are all vectors (i.e. they have both magnitude and direction), interactions between them must be described by a 3x3 matrix or tensor which characterizes the interaction. 

NMR spectroscopy is a powerful technique to study molecular structure, order, and dynamics. Because of the anisotropy of the interactions of nuclear spins with each other and with their environment via dipolar, chemical shift, and quadrupolar interactions, the NMR frequencies depend on the orientation of a given molecular unit relative to the external magnetic field. NMR spectroscopy is thus quite valuable to characterize partially oriented systems. Solid-state NMR... 

The physical interpretation of the anisotropic principal values is based on the classical magnetic dipole interaction between the electron and nuclear spin angular momenta, and depends on the electron-nuclear distance, rn. Assuming that both spins can be described as point dipoles, the interaction energy is given by Equation (8), where 6 is the angle between the external magnetic field and the direction of rn. 

With this spin Hamiltonian and the appropriate wave function it is relatively easy to determine (Appendix B) that the spin interactions give rise to four energy levels which are a function of the external magnetic field ... 

We have seen in Chapter 2 that the electronic Zeeman term, the interaction between unpaired electrons in molecules and an external magnetic field, is the basis of EPR, but we have also discussed in Chapter 4 the fact that if a system has more than one unpaired electron, their spins can mutually interact even in the absence of an external field, and we have alluded to the fact that this zero-field interaction affords EPR spectra that are quite different from those caused by the Zeeman term alone. Let us now broaden our view to include many more possible interactions, but at the same time let us be systematic and realize that this plethora of possibilities is eventually reducible to five basic types only, two of which are usually so weak that they can be ignored. 

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