Rare earth metals (REM) occupy a special and important place in our lives. This became especially noticeable during the rapid development of industry in the industrial era of the twentieth century. The tendency of development of the rare-earth metals market certainly remains in the XXI century. According to experts estimates the industry demand for chemical compounds based on them will tend to grow during the nearest years until it reaches the market balance. At the same time, the practical use of high-purity rare-earth metals requires the most accurate understanding of the physical properties of metals, especially magnetic ones. Despite a certain decline in interest in the study of high-purity REM single crystals during the last decade, a number of scientific groups (Ames Lab, Lomonosov Moscow State University (MSU), Baikov Institute of Metallurgy and Materials Science Russian Academy of Science (RAS)) are still conducting high-purity studies on high-purity metal samples. The present article is a combination of a review work covering the analysis of the main works devoted to the study of heavy REMs from gadolinium to thulium, as well as original results obtained at MSU. The paper considers the electronic properties of metals in terms of calculating the density of states, analyzes the regularities of the magnetic phase diagrams of metals, gives the original dependences of the Neel temperature and tricritical temperatures for Gd, Tb, Dy, Er, Ho, Tm, and also introduces a phenomenological parameter that would serve as an indicator of the phase transformation in heavy REMs.

Nanoparticle (NP) assisted magnetic hyperthermia (NMH) is a clinically proven method for cancer treatment. High-Z magnetic NPs could also be a perspective object for combining hyperthermia with tumor radiosensitization. However, this application of NPs is little studied, and it is unclear as to what particle compositions one can rely on. Therefore, the present work focuses on the search of materials that combine alternating magnetic field induced heating and high atomic number related dose enhancement abilities. A theoretical evaluation of 24 promising NP compositions was performed: the values of dose enhancement factor (DEF) were determined for kilovoltage x-ray spectra (30–300 kVp), as well as specific absorption rate (SAR) values were calculated for various combinations of elemental compositions and particle size distributions. For the alternating magnetic fields with amplitude $75\text{–}200\mathrm{Oe}$ and frequency $100\mathrm{kHz}$ , the maximum obtained SAR values ranged from 0.35 to $6000\mathrm{W}{\mathrm{g}}^{-1}$ , while DEF values for studied compounds ranged from 1.07 to 1.59. The increase in the monodispersity of NPs led to a higher SAR, confirming well-known experimental data. The four types of SAR dependences on external magnetic field amplitude and anisotropy constant were found for various particle sizes. The most predictable SAR behavior corresponds to larger NPs (∼70–100 nm). Thus, based on these calculations, the most promising for the combination of NMH with radiotherapy, from a physical point of view, are $\mathrm{L}{\mathrm{a}}_{0.75}\mathrm{S}{\mathrm{r}}_{0.25}\mathrm{Mn}{\mathrm{O}}_3$ , $\mathrm{G}{\mathrm{d}}_5\mathrm{S}{\mathrm{i}}_4$ , $\mathrm{SmC}{\mathrm{o}}_5$ , and $\mathrm{F}{\mathrm{e}}_{50}\mathrm{R}{\mathrm{h}}_{50}$ . The greatest dose enhancement is expected for superficial radiotherapy (in the voltage range up to ∼60 kVp).

For a supercritical Coulomb source with a chargeZ > Zcr in 1+1 dimensions, we study the nonperturbative properties of the vacuum density ρVP(x) and the energy ɛVP. We show that for corresponding probl