The Magnetic Equation of State and Transport Properties in Reduced Dimensions

Abstract

Basing our considerations on magnetic equation of state applied to the description of magnetic systems of confined geometry we developed the model of calculations of the electrical resistivity for metallic multilayers. It was shown that in the transport of charge in ferromagnetic material d-electrons play an important role. The key parameters in the presented model are: the width of the electron energy band and the shift of the energy level for two spin orientations as well as the Fermi energy and size of the sample (the thickness of magnetic and nonmagnetic layers and the total number of layers). The presented results of calculations for temperature dependence of magnetoresistance are in qualitative agreement with the available experimental data. The model calculations introduced in this paper can be applied to current-in-plane geometry as well as to current-perpendicular-to-plane geometry. The calculations are valid within the limitations of the resistor network model.

A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure

“…Furthermore, Zhang's results agree with some experimental results, which are carefully performed with high accuracy (see in [31], for instance). After its publication [3], Zhang's conjectured solution has received supports from several groups, for instance, March and his co-workers [32][33][34][35][36], Ławrynowicz and some mathematicians [6,7,37,38], Kaupuzs and his colleagues [30,39,40], and others [41][42][43][44][45][46][47][48][49][50][51][52][53]. In [8], Zhang-Suzuki-March rigorously proved four Theorems, which verifies the correctness of the Zhang's conjectured solution [3].…”