We suggest an explanation based on the Blume-Capel model of why some layered compounds of the iron-intercalated transition metal dichalcogenides TaS2(Se2) exhibit spin-glass behavior, while another group of this family demonstrates low-temperature paramagnetism. In these materials, the doped Fe atoms either substitute the Ta atoms with losing their magnetic moments or sit between the TaS2(Se2) layers keeping their spin states. The Blume-Capel model allows us to introduce a chemical potential to control a balance of the intercalated elements of both types. The Ghatak-Sherrington theory of spin-glass behavior of this model predicts an existence of a tricritical point that means that there is a concentration threshold of Fe ions retaining their magnetic moments, above which spin-glass ordering occurs. Below the threshold, Fe ions behave as independent paramagnetic centers. We build temperature dependencies of magnetic susceptibility and field dependencies of magnetization to highlight specific features of the model related with a variable content of Fe ions in the high-spin state. A specific crystal structure of the layered transition metal dichalcogenides gives an opportunity to increase the concentration of ions with nonzero magnetic moments by co-intercalating non-Kramers 3d ions into the van der Waals gaps. This process may trigger spin-glass ordering in the initially paramagnetic Fe-doped TaS2(Se2) polytype complexes.

The Fe0.25TaSe2 polycrystalline samples have been synthesized using two routes of solid-state reactions and various heat treatments and cooling conditions. The obtained samples have been studied by x-ray diffraction, magnetization and electrical resistivity measurements. It has been revealed that various methods of preparation and heat treatment do not have a strong effect on the lattice parameters of the main phase in the samples, but they significantly affect the magnetic critical temperature and magnetic hysteresis of the samples. Depending on the sample preparation procedure magnetic ordering temperature of Fe0.25TaSe2 is observed to vary in the range 33-60 K. The coercive field values from 31.7 kOe to 65.3 kOe at T = 2 K are indicative of a very high magnetocrystalline anisotropy in this material. The observed distinctions in the magnetic characteristics of the Fe0.25TaSe2 samples obtained by various methods and after different heat treatments can be ascribed to the difference in the distribution of Fe atoms over the crystal lattice.

Using the solid-phase method, a series of layered compounds Fe0.25TaS2-ySey has been synthesized and studied using X-ray diffraction, magnetization, electrical resistivity and magnetoresistance measurements to reveal the evolution of the crystal structure and properties with the replacement of sulfur by selenium. The crystal structure of Fe0.25TaS2-ySey consists of chains along the c axis, in which tantalum and iron atoms alternate in trigonalprismatic and trigonal-antiprismatic coordination, respectively. The replacement of sulfur by selenium is accompanied by an anisotropic expansion of the crystal and a relative elongation of the structure in the direction perpendicular to the plane of the layers. All the Fe0.25TaS2-ySey compounds exhibit ferromagnetic behavior with a huge coercive field (Plc - 40-60 kOe at low temperatures) which decreases exponentially with increasing temperature. It is assumed that an almost twofold decrease in the value of TC (from 120 K to - 60 K) when sulfur is replaced by selenium occurs mainly due to a decrease in the polarization of the 5d electrons of tantalum, through which an indirect exchange interaction between the 3d electrons of Fe occurs. The change of the lowtemperature (2 K) coercive field with the Se for S substitution is found to correlate with the concentration dependence of the Curie temperature, which is indicative of the Ising spin state of Fe ions in these compounds.

Magnetic susceptibility data obtained above the magnetic critical temperatures of the intercalated transition metal dichalcogenides CrxNbSe2 and FexTiS2 are indicative of the presence of short-range magnetic correlations (clusters) in a wide temperature range in the nominally paramagnetic state. Bearing in mind that the Cr and Fe atoms located between Se-Nb-Se and S-Ti-S tri-layers, respectively, are diluted with vacancies, these compounds can be considered as appropriate systems for the appearance of the so-called Griffiths phase. To identify the Griffiths behavior among the intercalated materials, the consistency of the magnetization behavior of these compounds, with that expected for the Griffiths phase, was tested using the scaling law proposed by Chan et al. [Phys. Rev. Lett. 97, 137201 (2006)]. As a result, the compounds CrxNbSe2 with x = 0.33 and x = 0.45 and Fe0.25TiS2 are found to exhibit the Griffiths phase above magnetic ordering temperatures while other compounds demonstrate non-Griffiths behavior.

The results of investigation of the CrxNbSe2 chalcogenides (x = 0.33, 0.5) by the nuclear magnetic resonance (NMR) method on Cr-53 and Nb-93 nuclei in the magnetically ordered state at zero external magnetic field have been presented. Ab initio calculations have been performed to theoretically estimate NMR parameters and interpret the experimental data. It has been shown that the intercalation of Cr atoms into NbSe2 results in spin and charge redistributions. The lower magnetic moment of chromium nuclei, 2.2 mu(B), compared to the theoretical value mu = 3 mu(B) for Cr3+ is attributed to the high degree of hybridization of the a(1g) and e(g) orbitals of 3d Cr electrons with 4d(z2) and 5s niobium orbitals. Such a hybridization also results in the presence of a high local magnetic field in the niobium nuclei location in CrxNbSe2.

The results of investigation of the ${\mathrm{Cr}}_{x}\mathrm{Nb}{\mathrm{Se}}_{2}$ chalcogenides $(x=0.33,0.5)$ by the nuclear magnetic resonance (NMR) method on $^{53}\mathrm{Cr}$ and $^{93}\mathrm{Nb}$ nuclei in the magnetically ordered state at zero external magnetic field have been presented. Ab initio calculations have been performed to theoretically estimate NMR parameters and interpret the experimental data. It has been shown that the intercalation of Cr atoms into $\mathrm{Nb}{\mathrm{Se}}_{2}$ results in spin and charge redistributions. The lower magnetic moment of chromium nuclei, $2.2\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$, compared to the theoretical value $\ensuremath{\mu}=3\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$ for ${\mathrm{Cr}}^{3+}$ is attributed to the high degree of hybridization of the ${a}_{1g}$ and ${e}_{g}$ orbitals of $3d$ Cr electrons with $4{d}_{{z}^{2}}$ and $5s$ niobium orbitals. Such a hybridization also results in the presence of a high local magnetic field in the niobium nuclei location in ${\mathrm{Cr}}_{x}\mathrm{Nb}{\mathrm{Se}}_{2}$.