Nanocomposites and nanomaterials

The model of a giant magnetoresistance, built taking into account the bulk scattering of spins of conduction electrons
Politanskyi R.L.1, Vistak M.V.2, Rudyak Y.A.3
1 Department of RadioEngeeniring and CyberSecurity , Yuriy Fedkovych Chernivtsi National University, Kotsyubynsky, 2, Chernivtsi-58012, Ukraine. 
E-mail:polrusl@i.ua
2 Faculty of Pharmacy/Department of Biophysics, Danylo Halytsky Lviv National University, Pekarska 69, Lviv-79010, Ukraine.
3 Institute of Pathological Processes Simulation and Analysis, I. Horbachevsky Ternopil National Medical University, m. Voli, 1, Ternopil-46001, Ukraine.

The properties of the "ferromagnetic" - "non-magnetic metal" heterojunction in the geometry of the current perpendicular to the plane of the heterojunction are modeled. Unlike the existing Motta two-channel conductivity model, the developed model takes into account spin scattering in the volume of the structure, which leads to the interaction between the conduction channels formed by electrons in the spin-up and spin-down states. The basis of this model is the equations of conductivity of electrons with spin-up and spin-down states, obtained by Firth-Valletta theory [1], which uses the semiclassical Boltzmann approach to determine the transport properties of electrons in the conduction band where spin degeneracy occurs. The general solutions of the problem obtained in the framework of the Firth-Valletta model are supplemented by boundary conditions on the heterojunction boundary to determine the constants of the general problem. The physical meaning of these boundary conditions is the preservation of the total number of electrons on the inner surface of the heterostructure that are reflected and pass through it [1]. The coefficients of reflection and transmission of electrons are derived without taking into account spin scattering on the surface of the heterostructure. Based on this model, the effect of the giant magnetic resistance for the three-layer structure "cobalt" - "copper" - "cobalt" is calculated. The results of the calculations are compared with the values of the giant magnetoresistance obtained based on the classical model of two-channel conductivity without channel interaction, which has been studied by us before [2].
1.	Xiaoguang Zhang and William Butler, Theory of Giant Magnetoresistance and Tunneling Magnetoresistance, Handbook of Spintronics, pp. 5-59, 2016.
2.	R.L. Politanskyi, L.F. Politanskyi, I.I. Grygorchak, A.D. Veriga. Modeling of Spin Valves of Magnetoresistive Fast-Acting Memory// J. Nano- Electron. Phys.. - 2018. - Т.10, № 6. - 06027. - DOI: 10.21272/jnep.10(6).06027