**Simulating the Hysteretic Characteristics of Hard Magnetic Materials Based on Nd 2Fe14B and Ce 2Fe14B Intermetallics**

**Natalia B. Kolchugina 1,\*, Mark V. Zheleznyi 1,2, Aleksandr G. Savchenko 2, Vladimir P. Menushenkov 2, Gennadii S. Burkhanov 1, Yurii S. Koshkid'ko 1,3, Jacek Cwik ´ 3, Nikolai A. Dormidontov 1, Katerina Skotnicova 4, Miroslav Kursa 4 and Pavel A. Prokofev 1,5**


Received: 12 May 2020; Accepted: 14 June 2020; Published: 17 June 2020

**Abstract:** The Ce2Fe14B intermetallic, like Nd2Fe14B, has the tetragonal Nd2Fe14B-type structure (space group *P*42/*mnm*), in which Ce ions have a mixed-valence state characterized by the coexistence of trivalent 4*f* 1 and tetravalent 4*f* 0 electron states. Despite the fact that the saturation magnetization, magnetic anisotropy field, and Curie temperature of the Ce2Fe14B intermetallic are substantially lower than those of Nd2Fe14B and Pr2Fe14B, Ce2Fe14B retains the capacity of being able to be used in the manufacturing of rare-earth permanent magnets. Moreover, at low temperatures, the anisotropy field of C<sup>е</sup>2Fe14B is higher than that of Nd2Fe14B, and C<sup>е</sup>2Fe14B does not undergo the spin-reorientation transition. In this respect, studies of (Nd, Ce)-Fe-B alloys, which are intended for the improvement of the service characteristics-to-cost ratio, are very relevant. A model and algorithm for calculating the hysteresis loops of uniaxial hard magnetic materials with allowance for the K1 and K2 (K2 > 0 and K1 > 0 and K1 < 0) magnetic anisotropy constants were developed and allowed us to obtain data on their e ffect on the parameters of hysteresis loops for a wide temperature range (0–300 K). The simulation and analysis of hysteresis loops of the quasi-ternary intermetallics (Nd1−<sup>х</sup>C<sup>е</sup>х)2Fe14B (х= 0–1) was performed. Results of the simulation indicate that the alloying of the Nd2Fe14B intermetallic with Ce to *x* = 0.94 (1) does not completely eliminate the negative e ffect of spin-reorientation phase transition on the residual magnetization of the (Nd1−<sup>х</sup>Ceх)2Fe14B intermetallic and (2) slightly decreases the slope of magnetization reversal curve.

**Keywords:** R-Fe-B intermetallics; cerium; permanent magnets; simulation; magnetic anisotropy constant; hysteresis loop; coercive force; residual magnetization
