Citation: Zheleznyi, M.V.; Kolchugina, N.B.; Kurichenko, V.L.; Dormidontov, N.A.; Prokofev, P.A.; Milov, Y.V.; Andreenko, A.S.; Sipin, I.A.; Dormidontov, A.G.; Bakulina, A.S. Micromagnetic Simulation of Increased Coercivity of (Sm, Zr)(Co, Fe, Cu) z Permanent Magnets. Crystals 2023, 13, 177. https://doi.org/10.3390/ cryst13020177 Academic Editor: Arcady Zhukov Received: 8 December 2022 Revised: 12 January 2023 Accepted: 17 January 2023 Published: 19 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). crystals Article Micromagnetic Simulation of Increased Coercivity of (Sm, Zr)(Co, Fe, Cu) z Permanent Magnets Mark V. Zheleznyi 1,2,3 , Natalia B. Kolchugina 1,2, *, Vladislav L. Kurichenko 3 , Nikolay A. Dormidontov 1,2 , Pavel A. Prokofev 2 , Yuriy V. Milov 1 , Aleksandr S. Andreenko 1 , Ivan A. Sipin 1 , Andrey G. Dormidontov 1 and Anna S. Bakulina 2 1 LLC Magnitoelectromechanics, ul. Tvardovskogo 8, build. 1, Moscow 123458, Russia 2 Baikov Institute of Metallurgy and Materials Science, Russian Academy of Sciences, Leninskii pr. 49, Moscow 119334, Russia 3 National University of Science and Technology MISiS, Leninskii pr. 4, Moscow 119991, Russia * Correspondence: nkolchugina@imet.ac.ru Abstract: The finite element micromagnetic simulation is used to study the role of complex composi- tion of 2:17R-cell boundaries in the realization of magnetization reversal processes of (Sm, Zr)(Co, Cu, Fe) z alloys intended for high-energy permanent magnets. A modified sandwich model is considered for the combinations of 2:7R/1:5H phase and 5:19R/1:5H phase layers as the 2:17R-cell boundaries in the alloy structure. The results of the simulation represented in the form of coercive force vs. total width of cell boundary showed the possibility of reaching the increased coercivity at the expense of 180 ◦ -domain wall pinning at the additional barriers within cell boundaries. The phase and structural states of the as-cast Sm 1- x Zr x (Co 0.702 Cu 0.088 Fe 0.210 ) z alloy sample with x = 0.13 and z = 6.4 are studied, and the presence of the above phases in the vicinity of the 1:5H phase was demonstrated. Keywords: high-energy permanent magnets; (Sm, Zr)(Co; Cu; Fe) z alloys; as-cast state; coherent 1:5 phase; micromagnetic simulation; sandwich model; MuMax3 1. Introduction Despite the wide application of Nd-Fe-B permanent magnets, sintered Sm-Co-based permanent magnets continue to be of interest for research and practice. The magnetism in in- termetallic phases of rare-earth metals and transition metals, such as the high-performance magnet based on SmCo 5 and Sm 2 Co 17 , is a result of the synergy between the 4f RE electrons, which provide a high anisotropy due to spin-orbit coupling, and the 3d TM electrons, which have large magnetic moments and provide strong ferromagnetic exchange interactions, thus enabling long-range order [1]. The synergy between 3d and 4f electrons depends crucially on the local atomic environments, and thus, gives the variety of the magnetic prop- erties of Sm-Co system compounds. The coercivity of samarium-based magnets originates from the Sm sublattice anisotropy, whereas the transition metals, such as Co, sublattice yields a high Curie temperature and thus stabilizes through inter-sublattice exchange. The Sm(Co, Cu, Fe, Zr) z alloys, the microstructure of which is characterized by the presence of three constituents (rhombohedral 2:17R phase cells, coherent 1:5H phase bound- aries of the cells, and coherent Z-phase (1:3R) lamellae), are widely used as permanent magnets with the high time and temperature stability because of their capacity to retain the high intrinsic coercivity I H C due to the high magnetic anisotropy field of the 2:17R and 1:5H constituents and the high maximum energy product (BH) max , which is related to the high remanence remaining at elevated temperatures [2]. The above microstructure determines the coercivity of the magnets, and therefore the improvement or justification of the microstructure can result in an increase in the coercivity, which is the issue of numerous investigations. Crystals 2023, 13, 177. https://doi.org/10.3390/cryst13020177 https://www.mdpi.com/journal/crystals