SPR-KKR

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.

SPR-KKR can. straightforwardly be combined with the CPA alloy theory to deal with disordered alloys. 

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. 

The use of a spherically symmetric potential is also not a necessary requirement for the SPR-KKR formalism. Representing the angular dependency of the potential terms V(r) and B(r) in terms of spherical harmonics leads to a coupled system of radial differential equations analogous to Equations (5.25) and (5.26). This implies that the details of the potential enter the calculation of the single-site wave functions... 

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]. 

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