Angular momentum, magnetic

5 ORBITAL ANGULAR MOMENTUM CONTRIBUTION 8.5.1 Magnetic angular momentum 

The spin Hamiltonian that accounts for the orbital angular momentum contribution is 

A non-zero contribution of the orbital angular momentum—a magnetic angular momentum—requires that the matrix elements of the atomic term functions 19/,) = L, ML, S, Ms) are non-zero 

To predict this property, group theory is applicable (Table 8.32). The angular momentum operator La (a = x, y, z) has the same transformation properties as the rotation operator Ra in the point group characterising the symmetry of the molecule. It transforms as the irreducible representation ra of this group. The above requirement is equivalent to the condition that the direct product of the irreducible representations rt of the wave function (which is a reducible representation Tr) contains the irreducible representation of the angular momentum (or rotation) operator ra, viz. 

The involvement of the orbital angular momentum has the following consequences  

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Magnetic angular momentum, isotropic [octahedral Ti(ni) complex, S = 1/2]... 

In dn complexes with triply degenerate ground states, the first-order contribution of the orbital angular momentum brings with it the magnetic angular momentum (Table 10). 

In turn, the monochromatic multipole photons are described by the scalar wavenumber k (energy), parity (type of radiation either electric or magnetic), angular momentum j 1,2,..., and projection m = —j,..., / [2,26,27]. This means that even in the simplest case of monochromatic dipole (j = 1) photons of either type, there are three independent creation or annihilation operators labeled by the index m = 0, 1. Thus, the representation of multipole photons has much physical properties in comparison with the plane waves of photons. For example, the third spin state is allowed in this case and therefore the quantum multipole radiation is specified by three different polarizations, two transversal and one longitudinal (with respect to the radial direction from the source) [27,28], In contrast to the plane waves of photons, the projection of spin is not a quantum number in the case of multipole photons. Therefore, the polarization is not a global characteristic of the multipole radiation but changes with distance from the source [22],... 

Magnetic angular momentum with lowered symmetry... 

The zero-field Hamiltonian in a dinuclear system that accounts for first-order (magnetic) angular momentum may be written in the form of... 

J total magnetic angular momentum Neel temperature... 

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