Synthesis, Structure, and Physicochemical Characteristics of Zn1−xRexCr2Se4 Single Crystals

This study aimed to obtain and investigate ZnCr2Se4 single crystals doped with rhenium. The single crystals were obtained by applying chemical vapour transport. An X-ray study confirmed the cubic (Fd3¯m) structure of the tested crystals. Thermal, magnetic, electrical, and specific heat measurements accurately determined the physicochemical characteristics, which revealed that the obtained single crystals are p-type semiconductors with antiferromagnetic order below the Néel temperature TN = 21.7 K. The Debye temperature had a value of 295 K. The substitution of Re-paramagnetic ions, possessing a screened 5d-shell, in place of Zn-diamagnetic ions, caused an increase in the activation energy, Fermi energy, and Fermi temperature compared to the pure ZnCr2Se4. The boost of the dc magnetic field induced a shift of TN towards lower temperatures and a spin fluctuation peak visible at Hdc = 40 and 50 kOe. The obtained single crystals are thermally stable up to 1100 °C.


Introduction
In the modern world, the synthesis of single crystals is a vast field of activity, encompassing theoretical aspects and device fabrication. Single crystals create the foundations of modern technology. Many types of crystals are needed for lasers, optical components, light-emitting diodes, electron emitters for electron microscopes, and countless other applications.
Materials with a spinel structure based on chromium and selenium (ACr 2 Se 4 , where A=Cu, Cd, and Zn) and doped with various elements are attractive for their magnetic, electrical, and thermal properties. They can be insulators, semiconductors, conductors, superconductors, ferrimagnets, ferromagnets, antiferromagnets, and Pauli paramagnets. In addition, these compounds are stable at high temperatures, so they can be applied in machines and devices operating at high temperatures. Doped spinel compounds, in which thermal conductivity exists, are possible for commercial application because thermoelectricity is a phenomenon that allows energy to be converted inside a solid. Thermoelectric cooling is the only environmentally friendly cooling used in power generators, computers, infrared detectors, and electronics and optoelectronics [1]. Doped chromite selenides have catalytic properties and could replace expensive silver catalysts in many chemical reactions [2]. In laser technology, the same compounds are used as materials that enable the use of solar energy [3,4].

Chemical Vapour Transport (CVT)
The growth of ZnCr 2 Se 4 single crystals doped with rhenium was carried out using chemical vapour transport (CVT). The CVT method is of great practical and cognitive importance. Crystallisation may occur at a temperature below the melting point. Thanks to this fact, it is possible to obtain structurally pure, low-temperature polymorphs.
Chemical vapour transport (CVT) is based on heterogeneous reversible reactions that can occur in the investigated system.
The order of magnitude of the equilibrium constants K p (logK p ≈ 0) regulates the transport ability of the reactions. The change of free energy ∆G • (close to zero) guarantees the process's reversibility and ensures that significant amounts of products and substrates are in the equilibrium state. The value of ∆G • is calculated based on the formula below: where: R-gas constant, T-absolute temperature, K p -equilibrium constant, ∆G • , ∆H • , and ∆S • -changes in the reaction's free energy, enthalpy, and entropy. The set of transport reactions is chosen based on thermodynamic data. As a transport agent, volatile halides (e.g., NbCl 5 , AsCl 3 , CrCl 3 , and CdCl 2 ) or chlorine are usually used [32][33][34]. The details describing the basis of the chemical vapour transport are presented in [35]. The HSC Chemistry v6 computer program was used for preparing the model of single-crystal growth [36].

Physicochemical Characteristic
The physicochemical characteristics were achieved using various methods: (1) magnetic and electrical measurements; (2) X-ray study; (3) specific heat measurements; and (4) thermal analysis. Electrical conductivity, σ(T), of single crystals under study was measured along the [001] direction by the DC method using a Keithley 6517B Electrometer/High Resistance Meter (Keithley Instruments, LLC, Solon, OH, USA) and within the temperature range of 77-400 K. The crystal, whose surfaces at the edges of the octahedron were polished into a rectangular parallelepiped, was placed between copper electrodes and pressed mechanically. The Seebeck coefficient, S(T), was measured within the temperature range of 100-400 K with the help of a Seebeck Effect Measurement System (MMR Technologies, Inc., San Jose, CA, USA). The electrical and thermal contact between the single crystal and electrodes was achieved by a silver lacquer mixture (Degussa Leitsilber 200) [9,[20][21][22][23][24][25][26][27].
Dynamic magnetic susceptibility (ac) was measured at an internal oscillating magnetic field of Hac = 1 Oe with an internal frequency of f = 120 Hz. Magnetization isotherms were measured at 2, 4, 10, 20, 40, 60, and 300 K using a Quantum Design MPMS-XL-7AC SQUID magnetometer (Quantum Design, San Diego, CA, USA) in applied external fields up to 70 kOe. The details of research methods, conditions of measurements, and types of equipment used to prepare the physicochemical characteristic of Zn 1−x Re x Cr 2 Se 4 single crystals are described in Refs. [17,[27][28][29][30][31]37]. The effective magnetic moment µ eff was calculated using the equation presented in Refs. [38,39]. The effective number of Bohr magnetons p eff was calculated from the equation: where x is the content of rhenium ions in the sample, p = g J(J + 1) [40] for Cr 3+ (S = 3/2; L = 3; J = 3/2, g = 2/5, basic term 4 F 3/2 ; for g = 2, p eff = 3.873 [40]) and Re 2+ (S = 5/2; J = 5/2 for L = 5; g = 2/7, basic term 6 S 5/2 ; for L = 0 and g = 2, p eff = 5.916 [41]) ions with 3d 3 and 5d 5 electronic configuration, respectively. The equations for the magnetic superexchange integrals J 1 and J 2 are presented in Ref. [42]. Specific heat C(T) was measured in the 2-300 K temperature range and in the external magnetic field up to 4 T using Quantum Design PPMS (Physical Properties Measurement System) with heat-capacity and -resistivity options. Thermal measurements were conducted using a Labsys Evo (Setaram Inc., Cranbury, NJ, USA) apparatus. The measurements were carried out in the flowing high-purity Ar-atmosphere with a heating rate of 10 • C/min.
The scanning electron microscope JEM 6480 (JEOL USA, INC., Peabody, MA, USA) was applied with an energy-dispersive X-ray spectrometer (SEM/EDS) to determine the chemical composition.
The X-ray diffraction was conducted at 293(1) K. The data were collected using a Super Nova X-ray diffractometer (Agilnt, Oxfordshire, UK) with a microfocus X-ray tube, optimised multi-layer optics for Mo-Kα (λ = 0.71073 Å) radiation, and an Atlas CCD detector. Accurate cell parameters were determined and refined with CrysAlisPro software (version 1.171.37.35, Agilent Technologies, Wrocław, 2014). Also, the CrysAlisPro program was used to integrate the collected data. The spinel structure (Fd3m) was refined using the SHELXL-2013 program [43,44]. All atoms were refined with anisotropic displacement parameters.

Thermodynamic Model of Chemical Vapour Transport in the ZnSe-Re-Se-CrCl 3 System
The thermodynamic model is based on a set of hypothetical reactions that can occur in the ZnSe-Re-Se-CrCl 3 system (a set of reactions is presented in Supplementary Materials). Anhydrous CrCl 3 , used as a transport agent in temperatures above 773 K, dissociates on CrCl 2 and Cl 2 . The compound CrCl 2 reacts with Cl 2, and CrCl 4 forms. The partial pressure of Cl 2 and CrCl 2 are very low compared to that of CrCl 3 and CrCl 4 . The partial pressure coefficient Q (Q = p(CrCl 3 )/p(CrCl 4 ) is 20 at 830 K because, during the sublimation of CrCl 3 , the gas phase contains 5% CrCl 4 . In the reaction system, three transport agents co-exist. For this reason, the consideration of hypothetical reactions which could appear in the reaction system should consider reactions with CrCl 3 , CrCl 4, and Cl 2 [45,46].
Because the compound ReSe does not exist, pure Re was utilised to calculate the crystal growth model for the ZnCr 2 Se 4 single crystals doped with rhenium. The thermodynamic model of the chemical vapour transport in the ZnSe-Re-Se-CrCl 3 system is presented in Figures 1-3. The thermodynamic parameters (∆H • , ∆G • , ∆S • , and logK p ) were calculated using the HSC Chemistry 6 computer program [36].
The thermodynamic model of the chemical vapour transport in the ZnSe-Re-Se-CrCl 3 system proved that the synchronous transport of ZnSe, Re, and Se would occur via gaseous CrCl 3 and CrCl 4 in the temperature range: 1000-1300 K. In this temperature range, logKp and ∆G • values are close to zero (Figures 1 and 2), which indicates the proper conditions for chemical transport.
Materials 2023, 16, x FOR PEER REVIEW 6 of 21 Figure 3. The dependence of the thermodynamic parameters vs. temperature T for reactions with Cl2 as a transport agent (theoretical calculation using HSC Chemistry v6 computer program [36]).

Growth of ZnCr 2 Se 4 Single Crystals Doped with Rhenium
The process of growth of the ZnCr 2 Se 4 single crystals doped with rhenium was carried on in quartz-glass ampoules using a solid-state reaction in a high vacuum (10 −5 mbarr). The experiments were carried out in ampoules with an outer diameter of 20 mm and a length of about 200 mm. The stoichiometric amounts of ZnSe, Re, and Se, weighed according to the reaction: Were introduced to the quartz-glass ampoule, sealed, and put into the two-zone pipe furnace.
Based on the thermodynamic model data, reaction conditions were selected: the dissolution zone 1143-1203 K, crystallisation zone 1103-1173 K, and temperature gradient 30-40 K (Table 1), according to Refs. [24][25][26][27][28][29][30][31][32]. The stoichiometric amounts of ZnSe, Re, Se, and CrCl 3 placed in quartz ampoules were heated for 336 h and then cooled at about 50 degrees per hour. Based on the ideal gas equation of state where p-pressure, V-the volume of glass ampoule, n-the number of moles of transport agent, R-the universal gas constant, and T-temperature, it can be estimated that the average pressure in the quartz ampoule during the crystal growth. According to our calculations, the pressure inside the ampoule is about 0.3 MPa, which indicates that the substrates were transferred into the gas phase by diffusion [32,33]. The obtained ZnCr 2 Se 4 :Re single crystals are shown in Figure 4.
where p-pressure, V-the volume of glass ampoule, n-the number of moles of transport agent, R-the universal gas constant, and T-temperature, it can be estimated that the average pressure in the quartz ampoule during the crystal growth. According to our calculations, the pressure inside the ampoule is about 0.3 MPa, which indicates that the substrates were transferred into the gas phase by diffusion [32,33]. The obtained ZnCr2Se4:Re single crystals are shown in Figure 4. Td is the temperature of the dissolution zone, Tc is the temperature of the crystallisation zone, and ΔT is the temperature difference between the dissolution and crystallisation zones. * the theoretical (calculated) amount of ReSe.

Chemical Composition
Each tested single crystal was measured at 20 different locations. The measuring area was approximately 50 × 30 µm 2 ( Figure 4). The results are presented in Table 1.

Chemical Composition
Each tested single crystal was measured at 20 different locations. The measuring area was approximately 50 × 30 µm 2 ( Figure 4). The results are presented in Table 1.

Structural Study
The structural parameters were calculated based on the procedure depicted in Refs. [18,31]. The results showed that the Re ions share the tetrahedral positions with Zn-cations in every fifth crystal. The structural study confirmed that the obtained samples crystallise in the cubic system (SG Fd3m). The formula describing cation distribution in the obtained ZnCr 2 Se 4 single crystals doped with rhenium is Zn 1−x Re x Cr 2 Se 4 ( Figure 5). The presence of Re ions in ZnCr2Se4 is confirmed by an increase in lattice parameters of the unit cell (Table 2, Figure 6), by the difference of ionic and covalent radii (r = 0.60 Å, r = 0.96 Å, R = 1.33 Å, R = 1.41 Å, where r indices ionic radius, and R indices covalent radius [47,48]). The linear dependence of lattice parameters indicates that Vegard's rule is observed in Zn1−xRexCr2Se4.  The presence of Re ions in ZnCr 2 Se 4 is confirmed by an increase in lattice parameters of the unit cell (Table 2, Figure 6), by the difference of ionic and covalent radii (r i Zn = 0.60 , r i Re = 0.96 , R C Zn = 1.33 , R C Re = 1.41 , where r indices ionic radius, and R indices covalent radius [47,48]). The linear dependence of lattice parameters indicates that Vegard's rule is observed in Zn 1−x Re x Cr 2 Se 4 . The details about other structural parameters (CIF files, all measurement parameters, values of the parameter u, atomic coordinates, equivalent isotropic displacement parameters, interatomic distances, and bond angles) of the Zn1−xRexCr2Se4 single crystals are presented in the Supplementary Materials.

Electrical Studies
The activation energy E a was calculated according to the formula: where k is the Boltzmann constant and σ 0 is the reference conductivity. As illustrated in Figure 7, the electrical conductivity for measured crystals revealed two areas: the external area in the narrow temperature range of 77-130 K, in which the weak thermal activation of E a1~0 .08 eV is observed, and the internal area in the temperature range of 200-400 K with stronger thermal activation of E a2~0 .16 eV (Table 3). In the region of stronger activation, the value of electrical conductivity at 400 K is about 9 S/m, a typical value for a spinel matrix with an energy gap of 1.28 eV at room temperature [49]. The admixture of rhenium generally enhances the thermal activation of current carriers in the internal region compared to ZnCr 2 Se 4 , for which E a is about 1.35 eV [13] (Table 3). Similar behaviour was found for the ZnCr 2 Se 4 crystals doped with elements 3d [14], 5d [19,24], and 4f [29,31].

Electrical Studies
The activation energy Ea was calculated according to the formula: where k is the Boltzmann constant and σ0 is the reference conductivity.
As illustrated in Figure 7, the electrical conductivity for measured crystals revealed two areas: the external area in the narrow temperature range of 77-130 K, in which the weak thermal activation of Ea1 ∼0.08 eV is observed, and the internal area in the temperature range of 200-400 K with stronger thermal activation of Ea2 ∼0.16 eV (Table 3). In the region of stronger activation, the value of electrical conductivity at 400 K is about 9 S/m, a typical value for a spinel matrix with an energy gap of 1.28 eV at room temperature [49]. The admixture of rhenium generally enhances the thermal activation of current carriers in the internal region compared to ZnCr2Se4, for which Ea is about 1.35 eV [13] (Table 3). Similar behaviour was found for the ZnCr2Se4 crystals doped with elements 3d [14], 5d [19,24], and 4f [29,31].      Figure 8 demonstrates the dependence of thermoelectric power on temperature S(T). On the whole, the thermopower in conventional metals is composed of two various components: (1) a diffusion component (S diff ), which is proportional to temperature according to the Mott formula at higher temperatures [50], and a phonon drag component (S ph ), which is more complex. The S ph contribution comes from transferring phonon momentum to the electron gas. Both components drop at low temperatures, such as T 3 below θ D /10, when phonons freeze out (θ D is the Debye temperature), and at high temperatures, such as T −1 above approximately θ D /2, when the phonon's excess momentum is limited by anharmonic phonon-phonon scattering [51]. A Debye temperature of Zn 1−x Re x Cr 2 Se 4 , obtained from specific heat measurement, has a value of 295 K. Therefore, the peak of the phonon drag component of thermoelectric power should be in the temperature range of 30-140 K and is not visible in Figure 8. The diffusion share S diff is a direct application of the Boltzmann transport equation [50], described by the formula:

Chemical $$$$$ Formula
where e is the elementary charge, E F is the Fermi energy, and a is an empirical slope. Using Equation (5), the Fermi energy, E F , can be determined by the formula: Materials 2023, 16, x FOR PEER REVIEW 10 of 21 below θD/10, when phonons freeze out (θD is the Debye temperature), and at high temperatures, such as T −1 above approximately θD/2, when the phonon's excess momentum is limited by anharmonic phonon-phonon scattering [51]. A Debye temperature of Zn1−xRexCr2Se4, obtained from specific heat measurement, has a value of 295 K. Therefore, the peak of the phonon drag component of thermoelectric power should be in the temperature range of 30-140 K and is not visible in Figure 8. The diffusion share Sdiff is a direct application of the Boltzmann transport equation [50], described by the formula: where e is the elementary charge, EF is the Fermi energy, and a is an empirical slope. Using Equation (5), the Fermi energy, EF, can be determined by the formula: The experimental dependence of Sdiff on temperature is evident in Figure 8 by solid lines. Based on Equation (6), it is possible to estimate the Fermi energy EF and the Fermi temperature TF (defined as EF/k), knowing the experimental value of the slope of thermopower for every single crystal. The values of EF and TF are given in Table 3. Comparing metals, e.g., for pure copper, EF = 7 eV and TF = 8.19 × 10 4 K [52], and nonmetallic conductors, e.g., for Cu1−xGaxCr2Se4 single crystals, EF ∼0.3 eV and TF ∼3 × 10 3 K [53], it can be concluded that the Fermi energy EF has smaller values for the tested crystals. It bears out that the Fermi level is near the valence-band border, and the shallow acceptor level is just above the valence band. The source of the observed low p-type electrical conductivity, which is more thermally activated above room temperature, could be cationic vacancies in the spinel structure. Structural defects seem to always exist at thermal equilibrium in the crystal lattice, even in perfect samples. As evident from Figure 9, the power factor S 2 σ of the investigated spinel semiconductors has a small value of several tens of nW/(cmK 2 ), e.g., compared to the value of 0.1 µW/(cmK 2 ) for the non-metallic spinel conductor CuCr2Se4:Ga [1]. The value of S 2 σ substantially increases with increasing temperature, i.e., in the internal area already above 250 K for all investigated samples with rhenium. Similar behaviour of the power factor as a function of temperature, but, on a somewhat smaller scale, was observed in the The experimental dependence of S diff on temperature is evident in Figure 8 by solid lines. Based on Equation (6), it is possible to estimate the Fermi energy E F and the Fermi temperature T F (defined as E F /k), knowing the experimental value of the slope of thermopower for every single crystal. The values of E F and T F are given in Table 3. Comparing metals, e.g., for pure copper, E F = 7 eV and T F = 8.19 × 10 4 K [52], and non-metallic conductors, e.g., for Cu 1−x Ga x Cr 2 Se 4 single crystals, E F~0 .3 eV and T F~3 × 10 3 K [53], it can be concluded that the Fermi energy E F has smaller values for the tested crystals. It bears out that the Fermi level is near the valence-band border, and the shallow acceptor level is just above the valence band. The source of the observed low p-type electrical conductivity, which is more thermally activated above room temperature, could be cationic vacancies in the spinel structure. Structural defects seem to always exist at thermal equilibrium in the crystal lattice, even in perfect samples.
As evident from Figure 9, the power factor S 2 σ of the investigated spinel semiconductors has a small value of several tens of nW/(cmK 2 ), e.g., compared to the value of 0.1 µW/(cmK 2 ) for the non-metallic spinel conductor CuCr 2 Se 4 :Ga [1]. The value of S 2 σ substantially increases with increasing temperature, i.e., in the internal area already above 250 K for all investigated samples with rhenium. Similar behaviour of the power factor as a function of temperature, but, on a somewhat smaller scale, was observed in the somewhat conductive molybdate-tungstate ceramics doped with Ga 3+ and Co 2+ [54], as well as Nd 3+ and Mn 2+ [55]. The above studies indicate that, regardless of the chemical bond type, the appropriate admixture influences the power factor, increasing the thermal activation of electric current carriers.  [55]. The above studies indicate that, regardless of the chemical bond type, the appropriate admixture influences the power factor, increasing the thermal activation of electric current carriers.

Magnetic Properties
The measurement data in Figure 10a-e, recorded in the internal oscillating magnetic field Hac = 1 Oe with the internal frequency f = 120 Hz and with zero external static magnetic field, suggest that the dependence of both magnetic susceptibility components (real (χ′) and imaginary (χ″)) on temperature indicates the AFM behaviour below the Néel temperature TN = 21.7 K and at positive Curie-Weiss temperatures (θ) of about 80 K. These values are typical for short-range FM interactions, which are independent of the quantity of rhenium in the studied samples. On the other hand, the oscillations of the imaginary component of the ac magnetic susceptibility, χ″, visible around the value of zero ( Figure  10), suggest the lack of energy losses caused, among others, by spin reorientation or rotation of the domain walls.

Magnetic Properties
The measurement data in Figure 10a-e, recorded in the internal oscillating magnetic field H ac = 1 Oe with the internal frequency f = 120 Hz and with zero external static magnetic field, suggest that the dependence of both magnetic susceptibility components (real (χ ) and imaginary (χ )) on temperature indicates the AFM behaviour below the Néel temperature T N = 21.7 K and at positive Curie-Weiss temperatures (θ) of about 80 K. These values are typical for short-range FM interactions, which are independent of the quantity of rhenium in the studied samples. On the other hand, the oscillations of the imaginary component of the ac magnetic susceptibility, χ , visible around the value of zero (Figure 10 The determined values of θ, presented in Table 4, are much lower than the literature data shown in Refs. [5,6] and slightly lower than in [8], where θ is 115 K and 90 K, respectively. In contrast, the determined T N values for all tested crystals are the same and close to those of pure ZnCr 2 Se 4 [5,6,9]. Long-range AFM interactions are less sensitive to doping with paramagnetic ions, whose 4f and 5d orbitals are intensely screened. On the other hand, FM short-range interactions are more sensitive to the local spin ordering visible in the oscillatory character of the values of both the paramagnetic Curie-Weiss temperature and the J 1 and J 2 superexchange integrals for the first two coordination spheres ( Table 4). The values of the effective magnetic moment (µ eff ) are substantially similar to the values of the effective number of Bohr magnetons (p eff ) for the electron configuration of rhenium 5d 5 and the base term 6 S 5/2 . It may mean that the orbital magnetic contribution has been quenched and the contribution to the magnetic moment comes solely from the spin. The temperature dependences of ac magnetic susceptibility χ , recorded in the internal oscillating magnetic field H ac = 1 Oe with the internal frequency f = 120 Hz and taken at external static magnetic fields H dc = 0, 10, 20, 30, 40, and 50 kOe, are depicted in Figure 11a-e. This figure shows that T N is shifted toward lower temperatures and T m is shifted toward higher ones. A strong magnetic field diminishes the AFM order and enlarges the FM order. Table 4. Magnetic parameters of Zn 1−x Re x Cr 2 Se 4 single crystals recorded in the internal oscillating magnetic field H ac = 1 Oe with the internal frequency f = 120 Hz and with zero external static magnetic field.
x C (emu·K/mol) is a magnetization at 2K; J 1 and J 2 are the superexchange integrals for the first two coordination spheres; H c1 and H c2 are the critical fields measured at the static magnetic field up to 70 kOe; and E a is the energy activation at 300 K [12]. Experimental data for ZnCr 2 Se 4 were taken from refs. [5,6,9,13] for comparison.
Additionally, the Curie constant C and the effective moment µ eff are slightly higher than the chromium ion value per molecule. It is confirmed that the rhenium ions influence the magnetic moment. For H dc = 50 kOe, the J 1 superexchange integral for the first coordination sphere changes the sign from negative to positive, while the J 2 integral remains positive (not shown here), as in Zn 1−x Pb x Cr 2 Se 4 [18].
It corroborates that the short-range FM interaction expands through the whole temperature range. The (χ (T) curves above T N , in the paramagnetic region, illustrate character istic broad peaks at T m = 31-35 and 42-45 K in the fields H dc = 40 and 50 kOe, respectively. These broad peaks of ac magnetic susceptibility may be caused by the spin fluctuations that appear due to a static magnetic field strengthening short-range FM interactions. The thermal energy kT opposes this phenomenon. Similar peaks were observed in the ZnCr 2 Se 4 crystals doped with Al [56], Ce, Ga, In [57], and Pb [18]. erials 2023, 16, x FOR PEER REVIEW 14 of 21 Additionally, the Curie constant C and the effective moment µeff are slightly higher than the chromium ion value per molecule. It is confirmed that the rhenium ions influence the magnetic moment. For Hdc = 50 kOe, the J1 superexchange integral for the first coordination sphere changes the sign from negative to positive, while the J2 integral remains positive (not shown here), as in Zn1−xPbxCr2Se4 [18].
It corroborates that the short-range FM interaction expands through the whole temperature range. The (χ′(T) curves above TN, in the paramagnetic region, illustrate char-  Magnetic isotherms in Figure 12a-e indicate that the magnetic saturation value of the tested single crystals is close to 6 µ B /f.u., similar to pure ZnCr 2 Se 4 [4].
The first critical field H c1 , i.e., metamagnetic transition, is connected with the transition from the helical to the conical phase, and the second critical field H c2 is related to the change of the spiral spin order to the ferromagnetic phase. The critical fields H c1 (a value of approx. 12 kOe) and H c2 (a value of approx. 61 kOe) insignificantly depend on the rhenium quantity in the sample. Comparison with pure ZnCr 2 Se 4 revealed that H c1 has a somewhat higher value and H c2 has a slightly lower value (Table 4) [8]. The hysteresis loops have zero-field coercivity and zero remanences.

Specific Heat Measurements
The results of specific heat measurements are shown in Figure 13. Moreover, the dashed line indicates a Debye model fit for T > 35 K and sample composition Zn 0.95 Re 0.06 Cr 2 Se 4 with the following fit parameters: number of atoms n D~7 .59 and Debye temperature θ D~2 95 K [30]. The number of atoms fits the stoichiometry quite reasonably, and the pattern of the heat-capacity curves is similar for all the samples (which is expected, due to their composition). Therefore, the Debye temperature is also similar. The upper inset shows the magnetic peak at T N~2 1 K for various stoichiometries. The position of the peak does not shift monotonously with Re concentration. The difference in ordering temperature, as seen from the heat-capacity measurement, is below~1 K. Taking into account limitations of the pulse-measurement technique employed in the PPMS instrument, we can say that Re substitution does not change the ordering temperature in an observable and consistent way. The lower inset shows the position of the magnetic peak for the Zn 0.95 Re 0.06 Cr 2 Se 4 sample in magnetic fields up to 4 T. We see that the increasing field shifts the peak to lower temperatures, confirming the antiferromagnetic ordering. The dependence can be very well fitted with the quadratic formula T N = T(B = 0T) − α 2 (α = 0.63 and T(B = 0) = 20.34 K).
The results of specific heat measurements are shown in Figure 13. Moreover, the dashed line indicates a Debye model fit for T > 35 K and sample composition Zn0.95Re0.06Cr2Se4 with the following fit parameters: number of atoms nD ~7.59 and Debye temperature θD ~295 K [30]. The number of atoms fits the stoichiometry quite reasonably, and the pattern of the heat-capacity curves is similar for all the samples (which is expected, due to their composition). Therefore, the Debye temperature is also similar. The upper inset shows the magnetic peak at TN ~21 K for various stoichiometries. The position of the peak does not shift monotonously with Re concentration. The difference in ordering temperature, as seen from the heat-capacity measurement, is below ~1 K. Taking into account limitations of the pulse-measurement technique employed in the PPMS instrument, we can say that Re substitution does not change the ordering temperature in an observable and consistent way. The lower inset shows the position of the magnetic peak for the Zn0.95Re0.06Cr2Se4 sample in magnetic fields up to 4 T. We see that the increasing field shifts the peak to lower temperatures, confirming the antiferromagnetic ordering. The dependence can be very well fitted with the quadratic formula TN = T(B = 0T)-α 2 (α = 0.63 and T(B = 0) = 20.34 K). Figure 13. Specific heat, C, as a function of temperature T, measured for Zn1−xRexCr2Se4 single crystals at zero magnetic field (central figure). The dashed lines indicate that the Debye model fit experimental data for T > 40 K and the Zn0.94Re0.06Cr2Se4 sample (black-filled circles). The upper inset shows how the magnetic peak is affected by Re substitution. The lower inset shows how the magnetic field affects the magnetic transition temperature for the Zn0.93Re0.07Cr2Se4 sample. Experimental data is presented here with open circles, and the quadratic fit is given with the dashed line. Note that the temperature scales on the lower and upper insets are different. Hence, the peaks in the upper inset appear much broader than in the lower inset or the central figure.

Thermal Study
The thermal study results are presented in Figure 14 and Table 5. The shape of DSC curves revealed that the obtained Zn1−xRexCr2Se4 single crystals are stable up to above 500 °C. For the smaller amount of rhenium (x = 0.06; 0.07), the first endothermic peaks appear at 564 °C and 636 °C, respectively. For both compounds, the second endothermic peak is visible above 1100 °C ( Figure 12). With increasing rhenium, the endothermic peaks are shifted towards higher temperatures, and the second endothermic peak disappears. This phenomenon can be associated with rhenium ions in the crystal lattice of ZnCr2Se4.
Re 2+ ions have a bigger ionic radius (0.96 Å) than Zn 2+ ions (0.60 Å), which can influence the stability of the crystal lattice. Small changes in the sample mass are observed with the endothermic peaks. It may indicate melting and evaporation processes, which

Thermal Study
The thermal study results are presented in Figure 14 and Table 5. The shape of DSC curves revealed that the obtained Zn 1−x Re x Cr 2 Se 4 single crystals are stable up to above 500 • C. For the smaller amount of rhenium (x = 0.06; 0.07), the first endothermic peaks appear at 564 • C and 636 • C, respectively. For both compounds, the second endothermic peak is visible above 1100 • C ( Figure 12). With increasing rhenium, the endothermic peaks are shifted towards higher temperatures, and the second endothermic peak disappears. This phenomenon can be associated with rhenium ions in the crystal lattice of ZnCr 2 Se 4 .
Re 2+ ions have a bigger ionic radius (0.96 Å) than Zn 2+ ions (0.60 Å), which can influence the stability of the crystal lattice. Small changes in the sample mass are observed with the endothermic peaks. It may indicate melting and evaporation processes, which can occur in the system during heating. However, it is worth highlighting that the observed changes are insignificant and suggest the thermal resistance of obtained crystals. The mass loss is observed with increasing temperature on the DTG curve. The extensive mass loss is observed above 1100 • C.
can occur in the system during heating. However, it is worth highlighting that the observed changes are insignificant and suggest the thermal resistance of obtained crystals. The mass loss is observed with increasing temperature on the DTG curve. The extensive mass loss is observed above 1100 °C.

Conclusions
We have presented a new family of Zn 1−x Re x Cr 2 Se 4 single crystals. These single crystals have been obtained using the chemical vapour transport (CVT) technique. The conditions of the crystal growth process were refined using thermodynamic calculations. SEM and XRD studies indicated that the obtained single crystals are chemically pure and crystallised in the cubic system (SG: Fd3m), which aligns with the spinel structure. Thermal measurements confirmed the thermal stability of single crystals at temperatures up to 1100 • C. Increasing the external magnetic field shifts T N and the specific heat peak towards lower temperatures, while the values of T m -towards higher temperatures. A significant weakness of long-range AFM interactions is evidenced in the reduction of the superexchange integral J 1 for the first coordination sphere and spin fluctuations in the paramagnetic region. The dependence of magnetisation on the magnetic field showed two untypical phenomena below T N . These phenomena occurred at critical fields H c1 = 12 and H c2 = 57 kOe. It is correlated well with the change of the sign of the J 1 integral from negative to positive at H dc = 50 kOe, which is caused by the short-range FM interaction extending through the whole temperature range. Calculations of the Fermi energy (E F ) and the Fermi temperature (T F ) derived from the diffusive component of thermoelectric power revealed a slight increase in E F and T F with increasing rhenium content, indicating shallow acceptor levels above the valence band. A substantial increase in the thermoelectric power factor S 2 σ in the internal region above 250 K was observed for all samples containing rhenium.
Based on our investigations, we can conclude that obtained results provided compelling evidence that the materials found on the doped ZnCr 2 Se 4 compound could be appropriately implemented in a broad spectrum of new technological areas, e.g., as thermomagnetic and thermoelectric materials in electronic devices. Our results encourage future studies and should be explored on this type of material.