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4. P.W. Palmberg, R.E. De Wames, L.A. Vredevoe, T. Wolker, J. Appl. Phys. 40, 1158 (1969). A) Interaction of an incoming electron with the spin system of magnetic sublattices (a) and (b) was given by $$H_{int} = 2\mathop \sum \limits_{i} I( {{\varvec{r}} - {\varvec{R}}_{i}^{( a )} } ){\varvec{S}}_{e} \cdot {\varvec{S}}_{i}^{( a )} + 2\mathop \sum \limits_{l} I( {{\varvec{r}} - {\varvec{R}}_{l}^{( b )} } ){\varvec{S}}_{e} \cdot {\varvec{S}}_{l}^{( b )}$$, where Se is the spin angular momentum of the incoming electron with the position vector r, and Si(a),and Sl(b) are the spin angular moment operator of the atom at Ri(a), Rl(b). B) The set of self-consistent coupled equations; $$\sigma_{\gamma } = B_{S} \left[ {\left( {3/2\tau } \right)\left( {\varepsilon_{\gamma } \sigma_{\gamma } + \delta_{\gamma + 1} \sigma_{\gamma - 1} + \delta_{\gamma + 1} \sigma_{\gamma + 1} } \right)} \right],$$ where, $$\sigma_{\gamma }^{\left( a \right)} = - \sigma_{\gamma }^{\left( b \right)} = \sigma_{\gamma }$$, $$\tau = T/T_{N} = {{\left( {3/2} \right) kT} \mathord{\left/ {\vphantom {{\left( {3/2} \right) kT} {ZJS}}} \right. \kern-0pt} {ZJS}}$$, $$ \varepsilon_{\gamma } = ( {Z^{( p )} /Z} )( {J_{\gamma }^{( p )} /J} )$$, $$\delta_{\gamma } = ( {Z^{{( {pn} )}} /Z} )( J_{\gamma }^{( n )} /J )$$. Z is the total number of nearest neighbors, Z (p) is the number of nearest neighbors on the same plane, Z (n) the number of nearest neighbors on the adjacent plane.
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