Magneton, Bohr, defined

Since the units of L are those of h, we have defined in equation (5.81) the Bohr magneton /tb as... 

If the external magnetic field B(r), and m(r) have only a nonvanishing Z-component, B(r) = (0,0, B(r)) and m(r) = (0,0, m(r)), the universal functional F[p, m] may then be considered as a functional of the spin densities ps(r) and p(r), F[ps(r), p(r)], because the spin density is proportional to the z-component of the magnetization m(r) = p-bPsW P-b is the electron Bohr magneton. It is of worth mentioning that it is possible to define two spin densities that are the diagonal elements of the density matrix introduced by von Barth and Hedin [3]. These correspond to the spin-up (alpha) electrons density pT(r), and the spin-down (beta) electrons density p (r). In terms of these quantities, the electron and spin densities can be written as... 

Three basic equations (3.34-3.36) are needed to describe the technique. In the equations, p is the magnetic moment of the electron, sometimes also written as pe, g is called the g factor or spectroscopic splitting factor, S is defined as the total spin associated with the electron (in bold type because it is considered as a vector), B is the imposed external magnetic field (also defined as a vector quantity), and p = (e/2m) x (/j/2jr) and is called the Bohr magneton. 

It is convenient for many purposes to have a quantity which summarizes magnetic properties and which is, ideally at least, independent of temperature. We define the magnetic moment , in units of the Bohr magneton ... 

One of the striking successes of the N< el model was its ability to account for the magnetization curves of the zinc-substituted ferro-spinels shown in Figure 23, where nB = Mq/N hb is the number of Bohr magnetons per molecule. From the intercept at x = 0, it is theoretically possible to obtain the spectroscopic splitting factor, as defined by equation 81. However, the discrepancies shown in Table IX between the original measurements by Guillaud et al. (243) and... 

If one defines the "effective Bohr magneton number" as the dimensionless, ueff, we obtain... 

Here, is called Bohr magneton and L is the dimensionless operator corresponding to the orbital angular momentum of an electron. They are defined as... 

We are dealing in our model with electrons in orbitals, which are defined to have both orbital motion and spin motion both contribute to the (para)magnetic moment. Quantum theory associates quantum numbers with both these motions. The spin and orbital motion of an electron in an orbital involve quantum numbers for both spin momentum (.S ), which is actually related to the number of unpaired electrons (n) as S = nil, and the orbital angular momentum (L). The magnetic moment (pi) (which is expressed in units of Bohr magnetons, pis) is a measure of the magnetism, and is defined by an expression (7.1) involving both quantum numbers. 

Bohr magneton (gg) - The atomic unit of magnetic moment, defined as ehl4jtm, where h is Planck s constant, m the electron... 

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