The paper presents a review of theoretical and experimental studies of the electronic structure and electronic and magnetic properties of various systems of Heusler alloys in the states of a half-metallic ferromagnet, spin gapless semiconductor, and topological semimetal. These substances have unusual magnetic and electronic characteristics and are highly sensitive to external effects, due to the presence of energy gaps and exotic excitations in them. Peculiarities of the behavior and evolution of the electronic structure and properties in each of these states and upon the transition between them are considered. The possibility of purposeful control of the properties of such materials opens up prospects for their practical application.

The structural, magnetic, and electrical properties of half-metallic Heusler alloys Fe2MnAl, Fe2MnSi, and Co2MnAl have been investigated in the temperature range of 4–900 K. According to the X-ray...

The temperature dependences of the resistivity, Hall coefficient, and magnetic susceptibility of iron-vanadium-aluminum alloys have been investigated. It has been established that the alloy ${\mathrm{Fe}}_{1.9}{\mathrm{V}}_{1.1}\mathrm{Al}$ exhibits semiconductor behavior for the method used to obtain uniform alloys. It is shown that at temperatures below $30\mathrm{K}$ the semiconductor alloy possesses the characteristic low-temperature scale of the dependences observed, which could be responsible for the appearance of a narrow pseudogap in the electron density of states. A simple theoretical description of the effects of a pseudogap is proposed. A consistent fit of the theoretical to the experimental relations made it possible to determine the effective width of the pseudogap $(\sim 1\mathrm{MeV})$ and its relative depth $(\sim {10}^2)$ .