**1. Introduction**

In the last few decades, searching for new materials for high-performance permanent magnets is an overriding task for modern physicists and technologists as these magnets are key driving components for electric motors, wind turbines, mobile phones, magnetic memory, and several other products [1–3].

Curie temperature Tc, magnetic anisotropy constant K, and saturation magnetization Ms of such materials are fundamental characteristics used to classify the existing permanent magnets. At Curie temperature, a material loses its ferromagnetic properties; hence, the higher the Tc, the better are the magnets to be used under extreme conditions. High values of saturation magnetization and magnetic anisotropy constants contribute to the creation of high-coercivity magnets that are very important for different practical applications [4–8].

Scientists pay the greatest attention to intermetallic compounds based on rare earth metals (R) and iron, in the fundamental magnetic properties, including exchange interaction parameters of R-Fe compounds, which can be studied most effectively by magnetization measurements in high magnetic fields. Ferrimagnetically ordered compounds are the most interesting because the ferrimagnetic structure is affected by applied external magnetic field, and a sequence of spin–reorientation phase transitions can be observed until the compound reaches magnetic saturation. In order to achieve the full magnetic saturation and

**Citation:** Kostyuchenko, N.V.; Tereshina, I.S.; Bykov, A.I.; Galanova, S.V.; Kozabaranov, R.V.; Korshunov, A.S.; Strelkov, I.S.; Makarov, I.V.; Filippov, A.V.; Kudasov, Y.B.; et al. Field-Induced Transition in (Nd,Dy)2Fe14B in Ultrahigh Magnetic Fields. *Crystals* **2022**, *12*, 1615. https://doi.org/10.3390/ cryst12111615

Academic Editor: Xiaoguan Zhang

Received: 26 October 2022 Accepted: 8 November 2022 Published: 11 November 2022

**Copyright:** © 2022 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/).

to maintain the compound in the forced-ferromagnetic state, the ultrahigh magnetic fields are required [9–12]. In addition, interest of magnetic phase transitions study in (R,R')2Fe14B compounds is increasing due to the recent discovery of skyrmions in Nd2Fe14B [13].

Obtaining high and ultrahigh fields, as well as obtaining reliable experimental data on the magnetization of samples, is a technically difficult task, which is the subject of great efforts of scientists from different countries as a rule. Generation of magnetic fields involves having an electric current flow through a coil, and the field intensity *B* is proportional to the current *I*. The heat dissipation *I* <sup>2</sup>*R* is proportional to the square of the magnetic field, where *R* is the coil's resistance. The mechanical pressure is also proportional to *B*2, with a proportionality coefficient of approximately 4 atm/T2. Heating and mechanical forces are the two essential problems for the generation of high fields. The stored energy in magnetic field depends on the volume of the magnet, so the size of the field volume is also an important characteristic of the magnet. Another key parameter is whether a magnet is DC or pulsed and, in the latter case, additional important parameters are the duration, temporal profile of the pulse, and the pulse repetition rate. There are several different approaches to overcome the heat–dissipation and mechanical-stability challenges, which is demonstrated in Figure 1 [14]. In all cases, choice of materials is crucially important, so such development is a task at the intersection of physics, engineering, and materials sciences.

**Figure 1.** Overview of methods for obtaining high and ultrahigh magnetic fields [14].

It should be noted that the highest-field magnet is not necessarily the best choice for a particular experiment. The figure-of-merit (FOM), depending on the experiment, could be the stored energy *B*2*V* (where *V* is the field volume), or the effective *B*2*L* (where *L* is the length of the field), or something else such as the tunability to a desired field value, or the broad operating range of the field values while keeping spatial homogeneity.

There are several laboratories around the world that conduct generation and research of high magnetic fields: the French Laboratoire National des Champs Magnetiques Intenses (LNCMI) with two locations; the German Dresden High Magnetic Field Laboratory (Hochfeld-Magnetlabor Dresden, HLD); and the High Field Magnet Laboratory (HMFL) in the Netherlands. These laboratories operate within the European Magnetic Field Laboratory (EMFL). The US National High Magnetic Field Laboratory (NHMFL) also has three locations. There are two laboratories in China: the High Magnetic Field Laboratory of the Chinese Academy of Sciences (CHMFL) and the Wuhan National High Magnetic Field Center (WHMFC), and four laboratories in Japan: the Tsukuba Magnet Laboratory (TML), the High Field Laboratory for Superconducting Materials, the International Megagauss Science Laboratory (IMGSL), and the Center for Advanced High Magnetic Field Science.

In our work, magnetization measurements were carried out at the Russian Federal Nuclear Center in Sarov in pulsed magnetic fields up to 170 T. This laboratory was one of the first in the world to obtain megagauss magnetic fields [15]. As the object of our study, we used the composition (Nd0.5Dy0.5)2Fe14B, which, due to the Dy atoms, is a ferrimagnet. Previously, this composition was studied by us in magnetic fields up to 58 T at the Dresden High Magnetic Field Laboratory. The experiment showed that the fields used were not enough to observe the forced-ferromagnetic state but allowed us to discuss the transition to the non-collinear phase and make a prediction about the place of the transition in a forced-ferromagnetic state. In addition, at the Megagauss Laboratory of Institute for Solid State Physics of University of Tokyo, the transition from a collinear ferrimagnet and a non-collinear spin-flop-like phase was observed in the Dy2Fe14B compound in magnetic fields up to 120 T [16]. It was also shown that such studies make it possible to compare the obtained experimental data with existing modern theoretical models and obtain the most important information about the main fundamental parameters for the (Nd,Dy)2Fe14B compound.
