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Knowledge of the magnetic ordering temperature is one of the fundamental physical properties characterizing material behavior. Magnetism is not only related to the magnitude of magnetic moments within specific magnetic ordering, but it also influences other physical properties. In the present work, we determine magnetic ordering temperatures for high-entropy alloys (HEAs), with examples of the Al- and Mo-based Cantor alloy derivatives. Nowadays, HEAs represent a promising class of materials in the sense of mechanical engineering. Regarding the paramagnetic state of the well-known and well-explored Cantor alloy, we deal with its Mo and Al derivatives, which offer higher possible ordering temperatures. We discuss the differences between $p$-type and $d$-type substitution as well as their influence on the magnetic behavior. We determine the ordering temperatures based on the ab initio calculated magnetic exchange interactions in terms of the mean-field approximation, random-phase approximation, and Monte Carlo simulations. Based on the thorough description of magnetic pair exchange interactions, a particular composition's influence on the achieved critical temperatures is described.

Within the RCo2 family of compounds, a structural distortion linked with the onset of magnetic ordering around the critical temperature can be observed. One of the less explored RCo2 compounds is TmCo2 probably due to its low Curie temperature. Exceptionally this compound, given its position at the end of the ferrimagnetic series, shows discrepancies in the ordering of the Co sub-lattice because of a weak Weiss molecular field. In this paper we focus on the structural distortion in TmCo2, which appears together with the magnetic ordering around the critical temperature of T C ∼ 3.6 K. Poly-crystals as well as single-crystals of TmCo2 were used in our experiments. For both kinds of samples we observed the same type of the rhombohedral distortion along the [111] direction from the cubic Fd 3 ¯ m to R 3 ¯ m space group. The relation between observed magnetic and structural properties in this compound is discussed.

Doping ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ by magnetic ions represents an interesting problem since it may break the time-reversal symmetry needed to maintain the topological insulator character. Mn dopants in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ represent one of the most studied examples here. However, there is a lot of open questions regarding their magnetic ordering. In the experimental literature different Curie temperatures or no ferromagnetic order at all are reported for comparable Mn concentrations. This suggests that magnetic ordering phenomena are complex and highly susceptible to different growth parameters, which are known to affect material defect concentrations. So far theory has focused on Mn dopants in one possible position, and neglected relaxation effects as well as native defects. We have used ab initio methods to calculate the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ electronic structure influenced by magnetic Mn dopants, and exchange interactions between them. We have considered two possible Mn positions, the substitutional and interstitial one, and also native defects. We have found a sizable relaxation of atoms around Mn, which affects significantly magnetic interactions. Surprisingly, very strong interactions correspond to a specific position of Mn atoms separated by a van der Waals gap. Based on the calculated data we performed spin dynamics simulations to examine systematically the resulting magnetic order for various defect contents. We have found under which conditions the experimentally measured Curie temperatures ${T}_{\mathrm{C}}$ can be reproduced, noticing that interstitial Mn atoms appear to be important here. Our theory predicts the change of ${T}_{\mathrm{C}}$ with a shift of Fermi level, which opens the way to tune the system magnetic properties by selective doping.