Orbitals magnetic moments

Figure 1 Orbital magnetic moments for bcc-Fe, fcc-Co and fcc-Ni. The columns denoted by E, K, L and K represent from left to right the experimental data [15] and the theoretical data obtained by the SPR-KKR-, the LMTO-SOC-OP [16] as well as the SOPR-KKR-methods.

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.

In summary, the OP-term introduced by Brooks and coworkers has been transferred to a corresponding potential term in the Dirac equation. As it is demonstrated this approach allows to account for the enhancement of the spin-orbit induced orbital magnetic moments and related phenomena for ordered alloys as well as disordered. systems by a corresponding extension of the SPR-KKR-CPA method. 

If the perturbation function shows cubic symmetry, and in certain other special cases, the first-order perturbation energy is not effective in destroying the orbital magnetic moment, for the eigenfunction px = = i py leads to the same first-order perturbation terms as pi or pv or any other combinations of them. In such cases the higher order perturbation energies are to be compared with the multiplet separation in the above criterion. 

The spin magnetic moment Ms of an electron interacts with its orbital magnetic moment to produce an additional term in the Hamiltonian operator and, therefore, in the energy. In this section, we derive the mathematical expression for this spin-orbit interaction and apply it to the hydrogen atom. 

Hamiltonian with the energy from appropriate terms in the true Hamiltonian. The latter terms include the interaction between the external field and the magnetic moment produced by the orbiting electron, the interaction between the external field and the magnetic moment due to electron spin, and the interaction between the orbital magnetic moment and the spin magnetic moment. These interactions may be expressed as a perturbation to the total Hamiltonian for the system where... 

An indirect mode of anisotropic hyperfine interaction arises as a result of strong spin-orbit interaction (174)- Nuclear and electron spin magnetic moments are coupled to each other because both are coupled to the orbital magnetic moment. The Hamiltonian is... 

In transition metal complexes there may be a substantial orbital magnetic moment (reflected by deviations of the g-values from ge) which leads to an isotropic as well as an anisotropic contribution to the hf interaction125,132. These contributions arise from a second order term of the form % Vtu 9 Lsl l/ o), where fm denotes the MO of... 

The calculations discussed above considered spin magnetic moments but not the orbital magnetic moments. However, it is known that orbital correlation has a strong effect in low-dimensional systems, which leads to orbital polarized ground states.67-69 Based on this fact, Guirado-Lopez et al.69 and... 

The eigenvalue equation corresponding to the Hamiltonian of Eq. [57] can be solved self-consistently by an iterative procedure for each orientation of the spin magnetization (identified as the z direction). The self-consistent density matrix is then employed to calculate the local spin and orbital magnetic moments. For instance, the local orbital moments at different atoms i are determined from... 

We now can get further information on the electronic configuration by studying the magnetism of the compounds. Any electron revolving around a nucleus in a closed orbital is equivalent to a circular electric current, and thus produces a magnetic moment. Usually these orbital magnetic moments are directed in such a way that they just cancel each other, in which case the orbital moments are of no further interest for our present purpose. 

Interactions among the orbital magnetic moments of the electrons. 

In a naive and incorrect way we can say that the electron with S = lk senses the orbital magnetic moment. Actually, a charged particle cannot sense the orbital magnetic moment due to its own movement. However, the electron moves in the electric potential of the charged nucleus. If we change the system of reference,... 

Since the s orbitals do not have orbital magnetic moment, g — ge — 2.0023. A is an eneigy, which in SI units is expressed in joule. Sometimes it is convenient to have it expressed in frequency units, i.e. in hertz or in radians per second, and then we have to divide A by h or by h (ft = h/2n). In magnetic resonance there often is a factor 2jt which complicates life. The frequency which we refer to is the angular frequency or the Larmor precession frequency. Such frequency co is... 

Mechanisms analogous to those illustrated in Fig. 3.1 apply also to electron relaxation (see below). However, electrons have other more efficient relaxation mechanisms which overcome the former ones. They are based on the presence of spin orbit coupling. Molecular motions modulate the orbital magnetic moment and then affect the electron spin. Several possible mechanisms for electron relaxation... 

The magnetic case is treated similarly except that terms in the derivatives of the field are not considered to be important and have not been calculated, the constant H analogue of equation (6) being used. The spin-orbit magnetic moment... 

Commonly, the frequency v is about 9000 Mc/s which means that fields in the region 3000 G are required for resonance. The -factor is generally very close to the free-spin value for organic radicals deviations occur if there is an appreciable electronic orbital magnetic moment, and this will mean that resonance will occur either at higher or lower fields than that required for the free electron. This variation in the -value is discussed in Section V, D. 

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