Nanoscale physics

Nanosize regions of homogeneous magnetic ordering in binary alloys with strong electron correlations
Len E. G.1,2, Lizunov V. V.1, Ushakov M. V.1, Len T. S.3
1 G.V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine
E-mail: len@imp.kiev.ua
2 Kyiv Academic University, NAS and MES of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine
3 National Aviation University, 1 Kosmonavt Komarov Ave., 03058 Kyiv, Ukraine.

In the phenomenological theories of magnetism, the sizes and shapes of homogeneous magnetic ordering regions are determined from the minimum condition of free energy of the crystal, which includes magnetostatic, magnetoelastic, magnetocrystalline anisotropy, and exchange energies. In the magnetic alloys, interatomic interaction, including its ionic, electronic and elastic components, as well as the effects of atomic ordering, should be considered additionally. In this case, the mentioned energy characteristics of the atomic and magnetic subsystems are expressed through the phenomenological parameters of the theory, which do not allow adequately and fully to take into account the quantum nature of homogeneous atomic and/or magnetic ordering regions formation at the nanoscale level. The cause of this lies in neglecting the contribution of the electronic structure of matter into the effects of atomic and magnetic ordering/disordering. The abovementioned phenomenological parameters are found from a very limited set of experimental data and only indirectly take into account the contribution of the electronic structure, which is not enough for the reproduction of complicated tendencies to magnetic ordering, especially in systems with strong electron-electron correlations.
In the present work, a theoretical model is proposed for describing the tendencies for the formation of local areas of homogeneous magnetic ordering in binary substitutional alloys with strong electron correlations, in which the type and size of such regions are determined predominantly by changes in the electronic structure. Such systems include, for example, transition metals alloys. Numerical calculations in generalized single-band Hubbard model [1] of magnetic homogeneity regions are carried out for 0 K, when we cannot take into account entropy contributions to alloy free energy, electron-phonon interaction, and dynamical excitations of charge and spin subsystems. It is shown that the change in the electron concentration and the magnitude of the Coulomb repulsion potential of electrons at one site in the atomically full-disordered b.c.c. alloys considered in the work can change the type and sizes (in a wide range) of homogeneous magnetization. However, the real way of changing these quantities by varying the types and concentrations of chemical elements can lead to specific limitations of the allowable types of magnetic structures and the size range of their homogeneity regions, even without taking into account the concentration restrictions on the chemical single-phase state of system.
1.	Len E. G. et al. // Metallofiz. Noveishie Tekhnol. -2015.-37, N 10.-P. 1405-1424.