Mutual Influence of Short-Range Atomic and Magnetic Orderings in Substitutional Binary Alloys within the Scope of the Semi-Elliptic Model

T. D. Shatnii$^{1}$, E. G. Len$^{2,1}$, V. V. Lizunov$^{1}$, T. S. Len$^{3}$, M. V. Ushakov$^{1}$

$^{1}$G. V. Kurdyumov Institute for Metal Physics, NAS of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine

$^{2}$Kyiv Academic University, N.A.S. and M.E.S. of Ukraine, 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine

$^{3}$National Aviation University, 1 Lyubomyr Huzar Ave., UA-03058 Kyiv, Ukraine

Received: 23.06.2021. Download: PDF

The interconsistently atomic and magnetic short-range orderings in binary substitutional alloys with strong electron-electron correlations are investigated at $T$ = 0 K by the coherent potential method based on cluster expansion for the Green's function of a disordered system in the framework of the one-band Hubbard model. The magnetic (MPD) and atomic (APD) phase diagrams in $U–n$ variables (potential of the Coulomb repulsion–electron concentration) in the semi-elliptic model for the initial density of electronic states are constructed in the case of equal concentrations of the b.c.c.-alloy components. As determined, at values of $U$, exceeding one for an upper bound of the paramagnetic phase appearance, in central part of MPD (near $n$ = 1) the static fluctuations of the charge and spin densities lead to a difference in the values of electron concentrations and magnetic moments on atoms of different types, which contributes to suppression of the atomic order (promotes the atomic separation). In the paramagnetic region with moving away $n$ = 1, the atomic ordering is suppressed due to an increasing of a difference between the values of the electron concentrations on atoms of various types only and phase separation is observed according to the Hume-Rothery rules. The magnetic subsystem of the alloy, as in the case of one-component systems and completely atomically disordered alloys, retains a tendency to realization of antiferromagnetic order in the central part of the MPD (near $n$ = 1). However, the boundaries of the magnetic phases are shifted due to influence of atomic ordering, breaking the electron-hole symmetry of the MPD, which is characteristic of one-component systems.

**Key words:**
atomically and magnetically disordered alloys, strong electron-electron correlations, electronic structure, parameters of atomic and magnetic short-range orders, atomic and magnetic phase diagrams.

**URL:**
https://mfint.imp.kiev.ua/en/abstract/v43/i09/1269.html

**DOI:**
https://doi.org/10.15407/mfint.43.09.1269

**PACS:**
05.30.Rt, 71.10.Fd, 71.20.Be, 71.23.-k, 71.27.+a, 71.28.+d, 75.10.Lp, 71.30.+h

**Citation:**
T. D. Shatnii, E. G. Len, V. V. Lizunov, T. S. Len, and M. V. Ushakov, Mutual Influence of Short-Range Atomic and Magnetic Orderings in Substitutional Binary Alloys within the Scope of the Semi-Elliptic Model, *Metallofiz. Noveishie Tekhnol.*, **43**, No. 9: 1269—1288 (2021) (in Ukrainian)

- S. M. Stishov, Uspekhi Fizicheskikh Nauk, 174: 853 (2004) (in Russian). Crossref
- V. F. Gantmakher and V. T. Dolgopolov, Uspekhi Fizicheskikh Nauk, 178: 3 (2008) (in Russian). Crossref
- V. V. Lizunov, E. G. Len, I. M. Melnyk, M. V. Ushakov, T. S. Len, and V. A. Tatarenko, Metallofiz. Noveishie Tekhnol., 36: 575 (2014) (in Russian). Crossref
- V. V. Lizunov, E. G. Len, M. V. Ushakov, T. S. Len, and V. A. Tatarenko, Metallofiz. Noveishie Tekhnol., 37: 1405 (2015) (in Russian). Crossref
- S. P. Repetsky and T. D. Shatnii, Theoretical and Mathematical Physics, 131: 832 (2002). Crossref
- S. P. Repetsky, V. A. Tatarenko, I. M. Melnyk, and E. G. Len, Usp. Fiz. Met., 9, No. 3: 259 (2008) (in Ukrainian). Crossref
- E. G. Len, T. D. Shatnii, V. V. Lizunov, T. S. Len, and M. V. Ushakov, Metallofiz. Noveishie Tekhnol., 43, No. 8: 1005 (2021). Crossref
- A. A. Smirnov, Obobshchennaya Teoriya Uporyadochivayushchikhsya Splavov [Generalized Theory of Ordered Alloys] (Kyiv: Naukova Dumka: 1986).
- I. V. Vernyhora, S. M. Bokoch, and V. A. Tatarenko, Usp. Fiz. Met., 11, No. 3: 313 (2010). Crossref
- D. I. Pushkarov, Pisma v JETP, 27, Iss. 6: 359 (1978)
- D. E. Laughlin and T. B. Massalski, Progress in Materials Science, 120, Article Number 100715 (2021). Crossref
- A. N. Andriotis, E. N. Economou, L. Qiming, and C. M. Soukoulis, Phys. Rev. B, 47, No. 15: 9208 (1993). Crossref
- Yu. A. Izyumov, Uspekhi Fizicheskikh Nauk, 165: 403 (1995) (in Russian). Crossref
- H. Jones F.R.S., The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Series 7, 44, No. 355: 907 (1953). Crossref
- U. Mizutani and H. Sato, Crystals, 7: 9 (2017). Crossref