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Abstract: 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. © 2021, Pleiades Publishing, Ltd. ; This work was carried out as part of the state assignment of the Ministry of Education and Science of the Russian Federation (topic "Spin," no. AAAA-A18-118020290104-2, and "Quantum," no. AAAA-A18-118020190095-4) and was supported by the Russian Foundation for Basic Research (project no. 20-12-50004) and the Government of the Russian Federation (resolution no. 211, contract no. 02.A03.21.0006).

The Hall Effect and magnetization of Heusler alloys Co2YSi (Y = Ti, V, Cr, Mn, Fe, Co, Ni) were measured at T = 4.2 K and 300 K in magnetic fields of up to 100 kOe as well as the temperature dependence of the electroresistivity from 4.2 to 300 K. The normal and anomalous Hall coefficients, saturation magnetization, residual resistivity, type and concentration of current carriers and their mobility were obtained. It was demonstrated that there is a clear correlation between the electronic and magnetic parameters obtained, depending on the number of valence electrons z, at the transition from Co2TiSi (z=26) to Co2NiSi (z=32). The observed peculiarities of electronic and magnetic parameters may be due to the appearance of the states of the half-metallic ferromagnet and/or spin gapless semiconductor. © Published under licence by IOP Publishing Ltd. ; This work was carried out as part of the state task of the Russian Ministry of Education and Science (themes "Spin",No. AAAA-A18-118020290104-2) with partial support from the Russian Foundation for Basic Research (projects Nos. 18-32-00686 and 18-02-00739) and the Government of the Russian Federation (Act No. 211, contract No. 02.A03.21.0006).

The Hall resistivity and magnetoresistivity of topological insulator Bi2Se3 thin films with a thickness from 30 nm to 75 nm in the temperature range from 4.2 to 80 K and magnetic fields of up to 10 T were measured. A size effect in the kinetic properties of bismuth selenide films was studied, i.e. a dependence of the Hall coefficient and magnetoconductivity of film dimensions. It was suggested that a similar size effect should be observed in other kinetic electronic properties, both of topological insulators and topological semimetals. © Published under licence by IOP Publishing Ltd. ; The results of paper were obtained within the state assignment of Ministry of Science and Higher Education of the Russian Federation (theme "Spin" No. АААА-А18-118020290104-2) and partly supported by the Russian Foundation for Basic Research (grant No. 20-32-90069) and by the Government of Russia (contract No. 02.A03.21.0006).

The electrical resistivity of thin films of a topological insulator of Bi2Se3 with a thickness of 10 nm to 75 nm, single crystal of Bi2Se3 with thickness of 0.65 mm in the temperature range from 4.2 to 300 K was measured. A size effect in the electrical conductivity of Bi2Se3 films was observed, i.e. linear dependence of the conductivity of the sample on its inverse thickness. It was suggested that similar effects should be observed in other TIs and systems with non-uniform distribution of direct current over the cross section of the sample. © Published under licence by IOP Publishing Ltd. ; Russian Foundation for Basic Research, RFBR: 17-52-52008 ; Government Council on Grants, Russian Federation: 02. ; Ministry of Science and Higher Education of the Russian Federation: АААА-А18-118020290104-2 ; This work was partly supported by the state assignment of Ministry of High Education and Science of Russia (theme "Spin" No. АААА-А18-118020290104-2), by the RFBR (project No. 17-52-52008) and by the Government of the Russian Federation (state contract No. 02.A03.21.0006).

The electro- and magneto-transport as well as magnetic properties of Co2MeSi (Me = Ti, V, Cr, Mn, Fe, Co, Ni) Heusler alloys were studied. The electroresistivity was measured from 4.2 to 300 K, the galvanomagnetic properties (magnetoresistivity and Hall effect) were measured at T = 4.2 K in magnetic fields of up to 100 kOe, and the magnetization at T = 4.2 and 300 K in fields of up to 70 kOe. The normal and anomalous Hall coefficients, saturation magnetization, residual resistivity, current carrier concentration, coefficients at linear contributions into the electroresistivity and magnetoresistivity were obtained. It was shown that on the one hand, there is quite clear correlation between the electronic and magnetic characteristics of Heusler alloys studied, and the spin polarization coefficients of current carriers, taken from well know literature data, on the other hand. The obtained results can be used for creation of new materials for spintronics. © 2021 Author(s). ; The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation (theme "Spin" No. AAAA-A18-118020290104-2), was supported in part by the Russian Foundation for Basic Research (Projects Nos. 18-02-00739 and 20-32-90065) and by the Government of the Russian Federation (decision No. 211, contract No. 02.A03.21.0006).

The electrical resistivity of thin films of a topological insulator of Bi2Se3 with a thickness of 10 nm to 75 nm, single crystal of Bi2Se3 with thickness of 0.65 mm and single crystals of topological Weyl semimetals MoxW1-xTe2 (x = 0; 0.5; 1) in the temperature range from 4.2 to 300 K was measured. A size effect in the electrical conductivity of Bi2Se3 films was observed, i.e. linear dependence of the conductivity of the film on its reciprocal thickness. It is suggested the existence of two different conduction channels in the Mo0.5W0.5Te2 compound. © Published under licence by IOP Publishing Ltd. ; Russian Foundation for Basic Research, RFBR: 17-52-52008 ; Government Council on Grants, Russian Federation ; АААА-А18-118020290104-2 ; This work was partly supported by the state assignment of Ministry of High Education and Science of Russia (theme "Spin" No. АААА-А18-118020290104-2), by the RFBR (project No. 17-52-52008) and by the Government of the Russian Federation (state contract No. 02.A03.21.0006).

The Co2 YSi (Y = Ti, V, Cr, Mn, Fe, Co, Ni) Heusler alloys can manifest the properties of half-metallic ferromagnets. These compounds are promising materials for spintronics since almost 100 % spin polarization of charge carriers can be realized at room temperature. We measured the electroresistivity, magnetic and galvanomagnetic properties of the Co2 YSi (Y = Ti, V, Cr, Mn, Fe, Co, Ni) Heusler alloys from 4.2 K to 300 K and in magnetic fields up to 100 kOe. The type, concentration and mobility of charge carriers were estimated. The Y-component variation in the Co2 YSi Heusler alloys is found to affect strongly the number of current carriers and alter the electronic band structure near the Fermi level E F and, consequently, the electronic transport and magnetic properties of the Co2 YSi (Y = Ti, V, Cr, Mn, Fe, Co, Ni) Heusler alloys. © Published under licence by IOP Publishing Ltd. ; Russian Foundation for Basic Research, RFBR: 18-32-00686, 18-02-00739 ; Government Council on Grants, Russian Federation: 02. ; Ural Branch, Russian Academy of Sciences, UB RAS: 18-10-2-37 ; АААА-А18-118020290129-5 ; This work was partly supported by the state assignment of Minobrnauki of Russia (themes "Spin" No. АААА-А18-118020290104-2 and "Magnet" No. АААА-А18-118020290129-5), RFBR grants (Nos. 18-32-00686 and 18-02-00739), the Scientific Program of UB RAS (project No. 18-10-2-37) and the Government of the Russian Federation (state contract No. 02.A03.21.0006).

Parameters of the energy gap and, consequently, electronic, magnetic and galvanomagnetic properties in different X2YZ Heusler alloys can vary quite strongly. In particular, half-metallic ferromagnets (HMFs) and spin gapless semiconductors (SGSs) with almost 100% spin polarization of charge carriers are promising materials for spintronics. The changes in the electrical, magnetic and galvanomagnetic properties of the Co2YSi (Y = Ti, V, Cr, Mn, Fe) and Co2MnZ Heusler alloys (Z = Al, Si, Ga, Ge) in possible HMF- and/or SGS-states were followed and their interconnection was established. Significant changes in the values of the magnetization and residual resistivity were found. At the same time, the correlations between the changes in these electronic and magnetic characteristics depending on the number of valence electrons and spin polarization are observed. © 2021 Author(s). ; The work was performed within the framework of the state assignment of the Ministry of Science and Higher Education of Russia (the themes "Spin," No. AAAA-A18-118020290104-2-2 and "Quantum" No. AAAA-A18-118020190095-4) with partial support from the RFBR (projects No. 18-02-00739 and 20-32-90065) and the Government of the Russian Federation (Decree No. 211, Contract No. 02.A03.21.0006).

Thin films of a topological insulator (TI) Bi 2 Se 3 of various thicknesses from 20 nm to 75 nm were obtained. The resistivity measurements were carried out according to the conventional 4-contact DC technique. This allows to "separate" the bulk and surface conductivities at different temperatures and magnetic fields. It was suggested that similar effects should be observed in other TIs and systems with inhomogeneous distribution of dc-current on sample cross section. © 2018 The Authors, published by EDP Sciences. ; This work was partly supported by the state assignment of FASO of Russia (theme "Spin" No. ȺȺȺȺ Ⱥ 4 ), by the RFBR (project No. 17-52-52008), by the Government of the Russian Federation (state contract No. 02.A03.21.0006), and by grant of Russian Ministry of Education and Science No 14.Z50.31.0025.

The field dependence of magnetization at T = 4.2 K and in magnetic fields of up to 70 kOe, temperature dependences of magnetization (2 K 11 kOe) magnetization is described in the Stoner models with the Rhodes-Wohlfarth parameter pRW = 1.3 for Mn1.99Co0.96Al1.05 and pRW = 2.3 for Mn1.79Co1.25Al0.96. When the composition deviates from the stoichiometric Mn2CoAl, the spontaneous moment decreases slightly, the effective moment, on the contrary, increases. In this case, a negative sign of the temperature-independent component of the paramagnetic susceptibility is observed. The density of states n(EF) at Fermi level and the Debye temperature ΘD of studied alloys have the usual values for 3d-metal alloys. © 2021 Author(s). ; The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation (theme "Spin" No. AAAA-A18-118020290104-2), was supported in part by the Russian Foundation for Basic Research (projects Nos. 18-02-00739 and 20-32-90065) and by the Government of the Russian Federation (decision No. 211, contract No. 02.A03.21.0006). The authors would like to thank D. A. Shishkin and P. B. Terentyev for measuring the magnetic properties of alloys at high temperatures.

WTe2 and MoTe2 single crystals were grown, some of them were quenched, and the following properties were studied: electroresistivity in the temperature range from 1.8 to 300 K, magnetoresistivity at temperatures from 1.8 to 300 K in magnetic fields of up to 9 T. On the one hand, quenching leads to dramatic changes in the behaviour and value of the electroresistivity of MoTe2; the type of the electroresistivity changes from "semiconductor"to "metallic", and the electroresistivity values of MoTe2 before and after quenching differ by 8 orders of magnitude (!) at low temperatures. On the other hand, quenching is shown not to lead to significant changes in the behaviour and value of the electroresistivity of WTe2. A relatively small increase in the electroresistivity of quenched WTe2 at low temperatures can be associated with the scattering of current carriers by structural defects. The magnetoresistivity of MoTe2 increases from 7 to 16% in a field of 9 T at a temperature of 12 K as a result of quenching. The magnetoresistivity of WTe2 is shown to reach ∼1700% in a field of 9 T at 2 K. The behaviour of the magnetoresistivity of non-quenched samples is typical for compensated conductors with a closed Fermi surface. © 2021 Author(s). ; The research was carried out within the state assignment of Ministry of Education and Science of the Russian Federation (theme "Spin", No. AAAA-A18-118020290104-2), supported in part by RFBR (Project No. 20-32-90069) and the Government of the Russian Federation (Decree No. 211, Contract No. 02.A03.21.0006).

The electro- and magnetoresistivity of MoTe2 single crystals before and after quenching were measured at temperatures from 1.8 to 300 K and in magnetic fields of up to 9 T. It was demonstrated that quenching can lead to strong changes in values of the electro-and magneresistivity studied as well as in their temperature and field dependences. The peculiarities of these electronic transport characteristics changes were studied in detail. © Published under licence by IOP Publishing Ltd. ; The research was carried out within the state assignment of the Ministry of Education and Science of the Russian Federation (theme "Spin", No. АААА-А18-118020290104-2), supported in part by RFBR (Project No. 17-52-52008) and the Government of Russian Federation (Decree No. 211, Contract No. 02.A03.21.0006).

A single crystal of a topological Weyl semimetal WTe2 was grown and its electrical resistivity and galvanomagnetic properties (magnetoresistivity and the Hall effect) were investigated in detail in the temperature range from 1.8 K to 300 K and in magnetic fields of up to 9 T. © Published under licence by IOP Publishing Ltd. ; The research was carried out within the state assignment of Ministry of Education and Science of the Russian Federation (theme "Spin", No. АААА-А18-118020290104-2), supported in part by RFBR (Project No. 20-32-90069) and the Government of Russian Federation (Decree No. 211, Contract No. 02.A03.21.0006).

Half-metallic ferromagnets and spin gapless semiconductors are promising materials for spintronic devices since a high degree of the spin polarization of charge carriers can be realized in such materials. Spin gapless semiconductors make it possible to combine the properties of half-metallic ferromagnets with semiconductor characteristics and to perform fine tuning of the energy gap value. The Mn2 MeAl (Me = Ti, V, Cr, Mn, Fe, Co, Ni) Heusler alloys can possess such features. We studied the electrical, magnetic and galvanomagnetic properties of the Mn2 MeAl (Me = Ti, V, Cr, Mn, Fe, Co, Ni) Heusler alloys from 4.2 K to 900 K and in magnetic fields up to 100 kOe. The features in the electronic and magnetic properties of Mn2MeAl Heusler alloys were observed, which can be a manifestation of the electronic energy spectrum peculiarities with occurrence of the half-metallic ferromagnet and/or spin gapless semiconductor states. © Published under licence by IOP Publishing Ltd. ; Russian Foundation for Basic Research, RFBR: 18-02-00739 ; Government Council on Grants, Russian Federation: 02, 211 ; Ministry of Science and Higher Education of the Russian Federation: AAAA-A18-1118020190095-4 ; Ural Branch, Russian Academy of Sciences, UB RAS: 18-10-2-37 ; The work was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation (themes "Spin", No. AAAA-A18-118020290104-2-2 "Magnet", No. АААА-А18-118020290129-5 and "Quant", No. AAAA-A18-1118020190095-4), supported in part by RFBR (projects No. 18-02-00739), the Complex Program of the UB RAS (Project No. 18-10-2-37) and the Government of the Russian Federation (Decree No. 211, Contract No. 02.A03.21.0006).

WTe2 and MoTe2 single crystals were grown, and their electrical resistivity in the temperature range from 80 K to 300 K, optical properties at room temperature in the spectral range of 0.17-5.0 eV were studied as well as theoretical calculations of the electronic structure were performed. It is shown that the temperature dependence of the electrical resistivity of orthorhombic WTe2 has a metallic type with resistivity value of (0.5-1) mOhmcm, while hexagonal MoTe2 has a semiconductor one and resistivity value (0.5-1) Ohmcm, which is three orders of magnitude larger than the resistivity of WTe2. Optical properties indicated that there is no contribution from free carriers in the entire spectral range studied. The calculated densities of the electronic states of MoTe2 and WTe2 showed the presence of a bunch of the molybdenum and tungsten electronic states in a wide energy interval with strong admixing of tellurium states. In the WTe2 compound, the larger number of the electronic states is located near the Fermi energy, characterizing a more metallic state in this compound as compared to MoTe2. © Published under licence by IOP Publishing Ltd. ; Government Council on Grants, Russian Federation: 02, 211 ; Russian Foundation for Basic Research, RFBR: 17-52-52008 ; Ministry of Education and Science of the Russian Federation, Minobrnauka: АААА-А18-118020190098-5 ; The research was carried out within the state assignment of Ministry of Education and Science of the Russian Federation (theme "Spin" No. АААА-А18-118020290104-2 and theme "Electron" No. АААА-А18-118020190098-5), supported in part by RFBR (Project No. 17-52-52008) and the Government of Russian Federation (Decree No. 211, Contract No. 02.A03.21.0006).