Spectroscopic g factor

The SOC induced orbital magnetic moments / oib as obtained by the SPR- and SOPR-KKR-CPA for the di.sordered alloy. sy.stem bcc-Fe Coi-a are given in Fig. 2. As for the pure elements one finds an enhancement of / oib by the OP-term by around 60 %. This enhancement brings the total theoretical orbital magnetic moment for the alloy in very satisfying agreement with experimental data derived from magneto mechanical as well as spectroscopic g-factor measurements [15]. 

Figure 2 Orbital magnetic moments in bcc-Fe Coi-a . The triangles pointing up-and downwards represent the theoretical moments of Fe and Co, respectively, while the concentration weighted sum is given by circles. Full and open symbols stand for results obtained with and without the OP-term included (SOPR- and SPR-KKR-CPA, resp.). Experimental data [15] for the average magnetic moment (bottom) stemming from magneto mechanical and spectroscopic g-factors are given by full squares and diamonds.

The same is true for the L—S-coupKng parameter A, which can be evaluated from ESR-measurements. For Cr +-doped a-AlsOa the spectroscopic g-factor 8 A ... 

For an electron the magnetic moment is proportional to the spin projection, /ig = —gePS, where /i is a conversion constant called the Bohr magneton and ge is the spectroscopic g-factor of the free electron and equals 2.0023192778 or about 2.00. In other words, the energies W) for an electron in a magnetic field along the z axis (Bo = Bok) with (i.e., for a and electrons) =1/2 and -1/2 are, respectively,... 

In Part F, we considered the results for the electron spin susceptibility Xg of metal-ammonia solutions which were obtained from electron resonance studies. In the present section, we shall hst other results of electron resonance measurements which also give valuable information as to the structure and d5mamics of these solutions. Among these results are (a) the spectroscopic g factor, (b) the relaxation times and describing respectively the time taken by the electron spins to attain a common spin temperature and the time taken for the spin temperature to become equal to the temperature of the solution, and (c) the failure or success to detect resonances in different solutions. The last named results give information about the extent of spin pairing among the electrons in the solutions. 

Three basic equations (3.10-3.12) 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... 

The calculation of magnetic parameters such as the hyperfine coupling constants and g-factors for oligonuclear clusters is of fundamental importance as a tool for the evaluation of spectroscopic data from EPR and ENDOR experiments. The hyperfine interaction is experimentally interpreted with the spin Hamiltonian (SH) H = S - A-1, where S is the fictitious, electron spin operator related to the ground state of the cluster, A is the hyperfine tensor, and I is the nuclear spin operator. Consequently, it is... 

If a free-atom state (Section 6.3.3) is subject to a magnetic field the (2J + l)-fold degeneracy is lifted so that, as shown in Figure 27, each level specified by the quantum number My is separated from its neighbour by the amount gjpH, where gj is the spectroscopic splitting factor. The value of g can be calculated from a knowledge of the term from which the state arose. 

Our spectroscopic study of the (ErxYi.x)2BaNiOs system (0.1wave functions, and g-factors of the Er3+ ion practically do not depend on x. It is physically reasonable to assume that the molecular-field constant X of the Er-Ni interaction also does not depend on x. In this case, Eqs. (2) and (3) are valid for an arbitrary x and the ordered magnetic moments of the Er and Ni magnetic subsystems can be extracted from the experimentally measured ground-state splittings. 

The spectroscopic splitting factor g that is determined from resonance experiments must be distinguished from the g factor determined by gyromagnetic experiments (347,526,632). In a gyromagnetic experiment (Einstein-DeHaas (164) or Barnett (40) methods), what is measured is the magnetomechanical ratio (see eq. 73)... 

If the orbital angular momentum is quenched by the crystalline fields, so that e is small, then it is possible to show (347) that for a resonance experiment the spectroscopic splitting factor g is given by... 

In the case of the transition element atoms or ions, the orbital angular momentum is usually quenched, and it has become customary to define the spectroscopic splitting factor g by equation 81 rather than by equation 13. Then equation 20 becomes... 

The factor g in Eqs. 8.14 and 8.15 is a dimensionless quantity called the electron, or Lande g factor (or spectroscopic sphtting factor) and, for the case of a. free electron, it equals precisely 2.0023193. However, it will be seen later that it can have other values when the electron is in condensed matter. 

Spin-orbit coupling, g-factors, nuclear quadrupole splitting, hyperfine interaction are some of the magnitude affected by the Ham effect and one can say that Ham s papers have opened up the wide field of the different spectroscopic techniques to investigate the JT effect. 

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