Effect of Ni Substitution on the Structural, Magnetic, and Electronic Structure Properties of Gd0.4Tb0.6(Co1−xNix)2 Compounds

The comprehensive research of magnetic and electronic structure properties of the new class of Gd0.4Tb0.6(Co1−xNix)2 compounds, crystallizing in the cubic Laves phase (C15), is reported. The magnetic study was completed with electrical resistivity and electronic structure investigations. The analysis of Arrott plots supplemented by a study of temperature dependency of Landau coefficients revealed that all compounds undergo a magnetic phase transition of the second type. Based on magnetic isotherms, magnetic entropy change (ΔSM) was determined for many values of the magnetic field change (μ0H), which varied from 0.1 to 7 T. For each compound, the ΔSM had a maximum around the Curie temperature. Both values of the |ΔSMmax| and relative cooling power RCP parameters increased with increasing nickel content. It is shown that structural disorder upon Co/Ni substitution influences some magnetic parameters. The magnetic moment values of Co atoms determined from different methods are quantitatively consistent. From the M(T) dependency, the exchange integrals JRR, JRT, and JTT between rare-earths (R) and transition metal (T) moments were evaluated within the mean-field theory (MFT) approach. The experimental study of the electronic structure performed with the use of the X-ray photoelectron spectroscopy (XPS) was completed by calculations using the full-potential linearized augmented plane waves (FP-LAPW) method based on the density functional theory (DFT). The calculations explained experimentally observed changes in the XPS valence band spectra upon the Ni/Co substitution.


Introduction
Among magnetic materials, RCo 2 compounds (R = rare earth) having the Laves phase structure of C15 type have attracted particular interest [1,2]. Attention to these materials is mainly due to their attractive properties, which strongly depends on the type of rare-earth element in the composition [3]. Furthermore, their simple cubic crystal structure facilitates the interpretation of the obtained results. The RCo 2 compounds with nonmagnetic R-ions, such as Y or Lu, show enhanced Pauli paramagnetism and underwent a metamagnetic transition [1,3]. Under the influence of an external magnetic field exceeding a certain critical H c value, a transition from a paramagnetic to a ferromagnetic state occurs accompanied by the increase in initially negligible magnetic moments on the Co site, even by 0.5 µ B [4,5]. In RCo 2 compounds with magnetic R-ions, cobalt atoms have induced magnetic moment, which occurs due to the 4f -3d interaction between localized moments of rare earth and the metamagnetic moments of cobalt [1]. Substitution of other kinds of atoms in RCo 2 results in a new family of compounds called pseudobinaries, such as the R(Co 1−x T x ) 2 , the R 1−y R y Co 2 , or even four-component R 1−y R y (Co 1−x T x ) 2 compounds (R -rare earth, T-3d element). They are particularly interesting because of additional interactions between

Crystal Structure
The crystal structure of all analyzed compounds was refined using the Rietveld method, and the analysis was carried out using noncommercial Maud software ver. 1.6.4 (Pandata, Berlin, Germany) [8,9]. The study showed that the samples with x = 0.00, 0.05, 0.10, 0.15, and 0.50 crystallized in the MgCu 2 type of structure (Fd-3m space group) and were free from undesirable magnetic impurities. In contrast, the sample with x = 0.80 contained additionally about 3.5% of the Gd 40 Tb 60 phase. The sample with x = 1.00 crystallized in the superstructure of MgCu 2 with double cell parameter a and contained two additional undesirable magnetic phases (Tb 2 O 3 , 9.8%) and TbNi (7.2%). With increasing Ni content, the value of the a, which for the Gd 0.4 Tb 0.6 Co 2 compound was equal to 7.256 Å ± 0.001 Å, first decreases rapidly for x less than 0.15 and then for higher concentrations decreases following Vegard's law (Figure 1, left axis). The cell parameter generally lowers because nickel atoms have smaller ionic radii than cobalt atoms. The deviation from Vegard's law, visible for small Ni concentration (<0.15) can be attributed to magneto-volume effects, as the measurements (at 294 K) have been carried out not far away from T C . A similar situation was observed in Gd(Co 1−x Ni x ) 2 compounds [10,11].

Magnetic Properties
The temperature dependence of the magnetization M(T) measured in zero-field cooling (ZFC) and field cooling (FC) mode at the external magnetic field of 0.1 T is shown in Figure 2. The thermomagnetic curves exhibit irreversible behavior in the low-temperature range. The difference between the MFC and MZFC at 2 K changes with Ni concentration and is most significant for x = 0.5 ( Figure 3).

Magnetic Properties
The temperature dependence of the magnetization M(T) measured in zero-field cooling (ZFC) and field cooling (FC) mode at the external magnetic field of 0.1 T is shown in Figure 2.

Magnetic Properties
The temperature dependence of the magnetization M(T) measured in zero-field cooling (ZFC) and field cooling (FC) mode at the external magnetic field of 0.1 T is shown in Figure 2. The thermomagnetic curves exhibit irreversible behavior in the low-temperature range. The difference between the MFC and MZFC at 2 K changes with Ni concentration and is most significant for x = 0.5 ( Figure 3). The thermomagnetic curves exhibit irreversible behavior in the low-temperature range. The difference between the M FC and M ZFC at 2 K changes with Ni concentration and is most significant for x = 0.5 ( Figure 3).
Several reasons may be responsible for the observed M FC -M ZFC (x) differences. Some of these include structural and magnetic disorders; others point to spin-orbit coupling changes that influence magnetic anisotropy, the domain wall pinning effect, or the impact of the crystal field [12][13][14][15][16][17]. According to our results discussed later, we are rather convinced that the indicated difference is due to structural and magnetic disorders.  Several reasons may be responsible for the observed MFC-MZFC(x) differences. Some of these include structural and magnetic disorders; others point to spin-orbit coupling changes that influence magnetic anisotropy, the domain wall pinning effect, or the impact of the crystal field [12][13][14][15][16][17]. According to our results discussed later, we are rather convinced that the indicated difference is due to structural and magnetic disorders.
The real parts of the magnetic susceptibility AC ( ' (T) in Figure 4) showed characteristic peaks at magnetic transition temperatures TC. The values of TC determined from  ' 1 and from minima of dM/dT in both ZFC and FC modes are in perfect agreement, showing a significant decrease with increasing Ni content ( Figure 1, right axis). This effect can be related to the dilution of the Co subsystem when replacing Co atoms with weaker magnetically Ni atoms. Similar behavior was observed in many Laves phase compounds doped by nickel [18,19]. The noticeable consistency of a(x) and TC(x) plots confirm that TC and magnetic properties have a strong lattice volume dependence in these compounds [10,20]. The hysteresis loops measured at 2 K, 25 K, 50 K, 100 K, and 300 K show minimal hysteresis losses for all investigated samples ( Figure 5). Moreover, no saturation has been observed even at μ0H = 7 T. Using M(H) data at 2 K, the saturation magnetization (MS) was The real parts of the magnetic susceptibility AC (χ (T) in Figure 4) showed characteristic peaks at magnetic transition temperatures T C . The values of T C determined from χ 1 and from minima of dM/dT in both ZFC and FC modes are in perfect agreement, showing a significant decrease with increasing Ni content ( Figure 1, right axis). This effect can be related to the dilution of the Co subsystem when replacing Co atoms with weaker magnetically Ni atoms. Similar behavior was observed in many Laves phase compounds doped by nickel [18,19]. The noticeable consistency of a(x) and T C (x) plots confirm that T C and magnetic properties have a strong lattice volume dependence in these compounds [10,20]. Several reasons may be responsible for the observed MFC-MZFC(x) differences. Some of these include structural and magnetic disorders; others point to spin-orbit coupling changes that influence magnetic anisotropy, the domain wall pinning effect, or the impact of the crystal field [12][13][14][15][16][17]. According to our results discussed later, we are rather convinced that the indicated difference is due to structural and magnetic disorders.
The real parts of the magnetic susceptibility AC ( ' (T) in Figure 4) showed characteristic peaks at magnetic transition temperatures TC. The values of TC determined from  ' 1 and from minima of dM/dT in both ZFC and FC modes are in perfect agreement, showing a significant decrease with increasing Ni content ( Figure 1, right axis). This effect can be related to the dilution of the Co subsystem when replacing Co atoms with weaker magnetically Ni atoms. Similar behavior was observed in many Laves phase compounds doped by nickel [18,19]. The noticeable consistency of a(x) and TC(x) plots confirm that TC and magnetic properties have a strong lattice volume dependence in these compounds [10,20]. The hysteresis loops measured at 2 K, 25 K, 50 K, 100 K, and 300 K show minimal hysteresis losses for all investigated samples ( Figure 5). Moreover, no saturation has been observed even at μ0H = 7 T. Using M(H) data at 2 K, the saturation magnetization (MS) was The hysteresis loops measured at 2 K, 25 K, 50 K, 100 K, and 300 K show minimal hysteresis losses for all investigated samples ( Figure 5). Moreover, no saturation has been observed even at µ 0 H = 7 T. Using M(H) data at 2 K, the saturation magnetization (M S ) was determined from extrapolation to zero of 1/H in the M vs. 1/H dependence. The value of M S grew monotonically with the nickel content, except for the sample with x = 1.0 (Table 1). Using the obtained values for M S , we estimated the magnetic moment of the 3d sublattice (2 µ 3d ) versus x, applying the formula M S = 0.4 µ Gd + 0.6 µ Tb + 2 µ 3d with µ 3d = (1 − x) µ Co + x µ Ni , µ Gd = 7 µ B , and µ Tb = 9 µ B . For x = 0 (M S = 5.86 µ B ), the procedure gave µ Co = −1.17 µ B , which is in accordance with earlier results in these kinds of compounds [6,11]. The negative sign indicates the antiparallel alignment of the R and Co moments. With the growing content of Ni, which is nearly nonmagnetic [11,21], the 3d sublattice moment 2 µ 3d decreases (Table 1). Because µ 3d and µ R are oriented antiparallel, it yields the observed increase in M S (x).
which is in accordance with earlier results in these kinds of compounds [6,11]. The negative sign indicates the antiparallel alignment of the R and Co moments. With the growing content of Ni, which is nearly nonmagnetic [11,21], the 3d sublattice moment 2 μ3d decreases (Table 1). Because μ3d and μR are oriented antiparallel, it yields the observed increase in MS(x).  All the hysteresis loops show a symmetric course after changing the external magnetic field direction; however, for the sample with x = 0.05, a slight deformation was observed in the M(H) chart, suggesting a coexistence of hard and soft magnetic phases (inset of Figure 5). Materials showing such behavior are known as exchange spring magnets [22,23]. In the case of our sample, it may be related to the presence of a foreign magnetic phase in tiny amounts below the XRD detectability.  Table 1. Curie temperature (T C ), saturation magnetization (M S ), and 3d sublattice contribution to the magnetic moment (2 µ 3d ) in the Gd 04 Tb 0.6 (Co 1−x Ni x ) 2 system. In the table, the exp. and the calc. denote the experimental and ab initio results. The results denoted as fit were estimated using the formula M S (x) = 2.104 x +5.942 obtained by fitting the linear function to ab initio results for M S (R square = 0.998). All the hysteresis loops show a symmetric course after changing the external magnetic field direction; however, for the sample with x = 0.05, a slight deformation was observed in the M(H) chart, suggesting a coexistence of hard and soft magnetic phases (inset of Figure 5). Materials showing such behavior are known as exchange spring magnets [22,23]. In the case of our sample, it may be related to the presence of a foreign magnetic phase in tiny amounts below the XRD detectability. Figure 6a,b shows the residual magnetization M R and coercive fields H c as a function of T in the Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 system. As can be seen, with the increase in the nickel content, the H c measured at 2 K grows up to the maximum value of 0.083 T for x = 0.5, then decreases to 0.005 T for x = 0.8 (inset in Figure 6b). A similar trend, with a maximum at the same Ni concentration, was observed for M R (x) (inset in Figure 6a). A slight rise of the H c value for x = 1.0 might be related to additional magnetic phases in the sample. The H c (x) dependence perfectly reflects the ρ 0 (x) dependence (which will be discussed later) and is consistent with the M FC -M ZFC one ( Figure 2). Thus, all these dependencies appear to have a common origin: the structural disorder and magnetocrystalline anisotropy influence that occur with doping. the same Ni concentration, was observed for MR(x) (inset in Figure 6a). A slight rise of the Hc value for x = 1.0 might be related to additional magnetic phases in the sample. The Hc(x) dependence perfectly reflects the ρ0(x) dependence (which will be discussed later) and is consistent with the MFC-MZFC one ( Figure 2). Thus, all these dependencies appear to have a common origin: the structural disorder and magnetocrystalline anisotropy influence that occur with doping. The magnetic properties of materials containing R (4f) and T (3d) elements are determined by exchange interactions between spins of constituent atoms. The strength of these interactions is described by the exchange integrals JRR, JTT, and JRT (= JTR). To estimate the 3d-3d and 3d-4f exchange interactions in Gd0.4Tb0.6(Co1-xNix)2 compounds, we considered its magnetic structure as consisting of two magnetic sublattices formed by R(Gd/Tb) and T(Co/Ni) moments. We performed the estimation by applying the approach described in detail in [6,24,25]. In the evaluation, we used the M(T) dependence under the magnetic field of 5 T, which was high enough to avoid the influence of domain effects and achieve a relatively high saturation (black curves in Figure 7). Table 2 shows the results of exchange coupling integrals calculated under the assumption that the average coordination numbers of RR (ZRR), RT (ZRT), TR (ZTR), and TT (TTT) are equal: 4, 12, 6, and 6, respectively [26]. The magnetic properties of materials containing R (4f ) and T (3d) elements are determined by exchange interactions between spins of constituent atoms. The strength of these interactions is described by the exchange integrals J RR , J TT , and J RT (= J TR ). To estimate the 3d-3d and 3d-4f exchange interactions in Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 compounds, we considered its magnetic structure as consisting of two magnetic sublattices formed by R(Gd/Tb) and T(Co/Ni) moments. We performed the estimation by applying the approach described in detail in [6,24,25]. In the evaluation, we used the M(T) dependence under the magnetic field of 5 T, which was high enough to avoid the influence of domain effects and achieve a relatively high saturation (black curves in Figure 7). Table 2 shows the results of exchange coupling integrals calculated under the assumption that the average coordination numbers of RR (Z RR ), RT (Z RT ), TR (Z TR ), and TT (T TT ) are equal: 4, 12, 6, and 6, respectively [26]. Table 2. The exchange integrals J RR , J RT , J TT, and magnetic moments of the 3d sublattice calculated in the framework of MFT theory (2 µ 3d-MFT ).  The results showed that the R-R interactions remain constant for the samples with 0≤ x ≤ 0.5 ( Table 2). The lower values of exchange interactions obtained for x = 0.8 and x = 1.0 may be related to the presence of foreign magnetic phases in these samples and the superstructure of the last one. As Ni concentration increases, R-T and T-T interactions weaken, but the latter is almost one order of magnitude higher than the others. The negative sign of J RT means the antiparallel coupling between R and T moments. Taking µ Gd = 7 µ B and µ Tb = 9 µ B , we determined the average magnetic moment per 3d sublattice (2 µ 3d-MFT ), as a function of x ( Table 2). The obtained values are slightly higher than those derived from M S ( Table 1), but the same decreasing trend is preserved. One has to note that M s was determined from the magnetization curve up to 7 T, while for MFT analysis, we used magnetization curves measured at 5 T. Based on the obtained results, we claim that the weakening of R-T and T-T interactions is responsible for decreasing T C and the magnetic moment of the 3d sublattice in the investigated system.  The results showed that the R-R interactions remain constant for the samples with 0 x  0.5 ( Table 2). The lower values of exchange interactions obtained for x = 0.8 and x = 1.0 may be related to the presence of foreign magnetic phases in these samples and the superstructure of the last one. As Ni concentration increases, R-T and T-T interactions weaken, but the latter is almost one order of magnitude higher than the others. The negative sign of JRT means the antiparallel coupling between R and T moments. Taking μGd= 7 The Arrott plots (not shown here) indicate that the investigated compounds undergo a phase transition of the second-order (SOPT). To confirm the observation, we determined the type of phase transition using the Landau expression for the magnetic free energy (F) [14]: The temperature dependence of Landau coefficients a(T), b(T), and c(T) are usually used to identify the type of phase transition. They are accessible through the following relation between M and H [15]: Essentially, the order of the magnetic transition is governed by the sign of b(T). The FOPT takes place if b(T C ) < 0, while the SOPT occurs when b(T C ) ≥ 0 in the vicinity of T C [15]. The coefficients were determined by fitting Equation (2) to magnetic isotherms µ 0 H(M) (not shown here).
As shown in Figure 8, the a(T) exhibits a minimum nearby T C . The b(T) parameter is positive, proving that we are dealing with SOPT and confirming the result obtained from Arrott's plots.
relation between M and H [15]: Essentially, the order of the magnetic transition is governed by the sign of b(T). The FOPT takes place if b(TC) < 0, while the SOPT occurs when b(TC) ≥ 0 in the vicinity of TC [15]. The coefficients were determined by fitting Equation (2) to magnetic isotherms μ0H(M) (not shown here).
As shown in Figure 8, the a(T) exhibits a minimum nearby TC. The b(T) parameter is positive, proving that we are dealing with SOPT and confirming the result obtained from Arrott's plots.

Magnetocaloric Properties
In materials showing SOPT, the magnetic entropy change is lower than in those with FOPT. However, the former usually has a broader working temperature range. This property of SOPT is significant for potential applications, e.g., in magnetic refrigerators [16].
To calculate the magnetic entropy change ∆S M based on the measured magnetic isotherms, we used Maxwell's relation: where H 0 and H 1 are the initial and final magnetic fields in the above formula, respectively. As can be seen in Figure 9, the maxima of the entropy changes −∆S M occur near T C , which is typical for compounds exhibiting SOPT. It is noteworthy that the value of |∆S M | max increases with growing nickel content (Figure 9h, Table 3). In addition, we found that the ∆S M curves are only symmetrical to T C in a limited temperature range (T C ± 50 K). For the compound with x = 0.0, this effect may be related to a partial reorientation of the Tb spin toward the easy axis direction [6,27]. For x = 0, this may also be influenced by the magnetic disorder. The height and the width of curves increase with the growth of the magnetic field for all compounds. As a result, the value of δT FWHM (called the operating temperature and defined as the full width at half-maximum of the −∆S M peak) also increases with µ 0 H.    The most significant rise of the δT FWHM values occurs for the compound with x = 0.15 (Figure 10a). To assess the cooling efficiency, we calculated the relative cooling power parameter RCP using the formula: The most significant rise of the δTFWHM values occurs for the compound with x = 0.15 (Figure 10a). To assess the cooling efficiency, we calculated the relative cooling power parameter RCP using the formula:

= | |
The cooling efficiency was also evaluated by using the value of refrigerant capacity (RC), defined as an amount of the heat that can be transferred from the cold end (at Tcold) to the hot end (at Thot): The RCP parameters vs. μ0H show the most rapid increase for Ni-rich samples, in which the presence of foreign phases was detected (Figure 10b). The ΔSM max , RC, RCP, and δTFWHM parameters for all investigated samples are collected in Table 3.

Electrical Resistivity
The electrical resistivity as a function of temperature for the investigated compounds is presented in Figure 11. We analyzed experimental data using Matthiessen's rule, which combines individual contributions to the resistivity according to [28]:  The cooling efficiency was also evaluated by using the value of refrigerant capacity (RC), defined as an amount of the heat that can be transferred from the cold end (at T cold ) to the hot end (at T hot ): The RCP parameters vs. µ 0 H show the most rapid increase for Ni-rich samples, in which the presence of foreign phases was detected (Figure 10b). The |∆S M | max , RC, RCP, and δT FWHM parameters for all investigated samples are collected in Table 3.

Electrical Resistivity
The electrical resistivity as a function of temperature for the investigated compounds is presented in Figure 11. We analyzed experimental data using Matthiessen's rule, which combines individual contributions to the resistivity according to [28]: In the formula, ρ 0 indicates residual resistivity, which is temperature independent but strongly depends on the crystal structure [28]. ρ ph (T), ρ s-d (T) and ρ e-e (T) are the contributions from electron-phonon scattering, s-d scattering and electron-electron scattering, respectively [29,30].
Considering the temperature dependence of the individual contributions, Equation (6) for low temperatures takes the form: and δTFWHM parameters for all investigated samples are collected in Table 3.

Electrical Resistivity
The electrical resistivity as a function of temperature for the investigated compounds is presented in Figure 11. We analyzed experimental data using Matthiessen's rule, which combines individual contributions to the resistivity according to [28]:  All the studied compounds show an evident change in the slope of the ρ(T) curves at the Curie temperatures T CR , which were determined from the dρ/dT (not presented here). The values of T CR are in reasonable agreement with those obtained from magnetic studies. The experimental data of ρ(T) fitted very well with Formula (7) below T CR , as shown in Figure 11b for the sample with x = 0.10. The resulting parameters α, β, ω, residual resistivity ρ 0, and T CR are collected in Table 4. One can notice that the amplitudes of individual contributions to the resistivity (α, β, ω) show an increasing tendency with the growth of nickel content. The rise of the value of the β parameter, which reflects s-d scattering, is due to the substitution of Ni for Co and increasing the number of 3d electrons in the band, which may influence the scattering centers of the d states. An increasing number of 3d electrons can also lead to enhanced electron-electron scattering, which was reflected in the growth of the ω parameter. The behavior of residual resistivity as a function of nickel concentration ρ 0 (x) satisfies the Nordheim rule [31]. Namely, the highest value of the ρ 0 is reached for x = 0.50 (Figure 3 right axis). Similar behavior is often observed in alloys during doping. The substitution of one type of atom by others generally leads to a disorder of the compound's crystal structure, which manifests as an increase in residual resistivity. It is worth noting that magnetic parameters, such as H c (x) and (M FC -M ZFC ) (x), also showed a similar behavior as ρ 0 (x), which indicates that structural disorder may be responsible for the observed trends. Table 4. The Curie temperatures T CR from resistivity measurements, residual resistivity ρ 0 , and fitting parameters from the Equation (7). An evident change in the shape of the 3d valence band is observed when nickel content increases (Figure 13). In the energy range from 0 eV to −3 eV, the band intensity increases with growing Ni content. Slightly less increment is visible at the Fermi level (inset (b) in Figure 13). Simultaneously, a shift in the maximum intensity of the 3d states toward higher binding energies is observed (inset (a) in Figure 13). From the multiplet splitting of the Co3s (Figure 14), we obtained information about the magnetic moments μCo. The multiplet splitting of the 3s spectra of 3d metals occurs due to the exchange interaction between unfilled 3d and 3s (ionized) shells [33]. As a result, two final states are observed, and the equation gives the intensity relation of these two peaks [34]: An evident change in the shape of the 3d valence band is observed when nickel content increases ( Figure 13). In the energy range from 0 eV to −3 eV, the band intensity increases with growing Ni content. Slightly less increment is visible at the Fermi level (inset (b) in Figure 13). Simultaneously, a shift in the maximum intensity of the 3d states toward higher binding energies is observed (inset (a) in Figure 13). An evident change in the shape of the 3d valence band is observed when nickel content increases (Figure 13). In the energy range from 0 eV to −3 eV, the band intensity increases with growing Ni content. Slightly less increment is visible at the Fermi level (inset (b) in Figure 13). Simultaneously, a shift in the maximum intensity of the 3d states toward higher binding energies is observed (inset (a) in Figure 13). From the multiplet splitting of the Co3s (Figure 14), we obtained information about the magnetic moments μCo. The multiplet splitting of the 3s spectra of 3d metals occurs due to the exchange interaction between unfilled 3d and 3s (ionized) shells [33]. As a result, two final states are observed, and the equation gives the intensity relation of these two peaks [34]: From the multiplet splitting of the Co3s (Figure 14), we obtained information about the magnetic moments µ Co . The multiplet splitting of the 3s spectra of 3d metals occurs due to the exchange interaction between unfilled 3d and 3s (ionized) shells [33]. As a result, two final states are observed, and the equation gives the intensity relation of these two peaks [34]: Here, S is the spin of the unpaired 3d electrons, I1 and I2 are intensities of the main and the satellite 3s line, respectively. The magnetic moment of the Co can be estimated using Formula [35]: The μNi was similarly estimated only for x = 1, since the Ni 3s satellite lines are hardly resolved in XPS spectra for lower Ni concentration.
The I1/I2 ratio (Equation (8)) was evaluated by fitting the Co3s and Ni3s lines applying iterative Shirley background and using the combination of Gaussian-Lorentz curves. This procedure enabled us to reproduce the main shape line and obtain the intensity of the individual contributions [36] (Figure 14). Using the above-described approach, we got the following values of the μCo: 0.95 μB, 0.80 μB, 1.02 μB, 0.97 μB and 0.98 μB for x = 0.0, 0.05, 0.10, 0.15 and 0.50, respectively. The values of μCo deviate slightly from those obtained from the Here, S is the spin of the unpaired 3d electrons, I 1 and I 2 are intensities of the main and the satellite 3s line, respectively. The magnetic moment of the Co can be estimated using Formula [35]: The µ Ni was similarly estimated only for x = 1, since the Ni 3s satellite lines are hardly resolved in XPS spectra for lower Ni concentration.
The I 1 /I 2 ratio (Equation (8)) was evaluated by fitting the Co3s and Ni3s lines applying iterative Shirley background and using the combination of Gaussian-Lorentz curves. This procedure enabled us to reproduce the main shape line and obtain the intensity of the individual contributions [36] (Figure 14). Using the above-described approach, we got the following values of the µ Co : 0.95 µ B , 0.80 µ B , 1.02 µ B , 0.97 µ B and 0.98 µ B for x = 0.0, 0.05, 0.10, 0.15 and 0.50, respectively. The values of µ Co deviate slightly from those obtained from the saturation magnetization and the MFT calculations. However, we must remember that the XPS experiment was performed in different conditions than the previous ones (room temperature, no magnetic field). Furthermore, since the intensity of the Co3s line became weaker with increasing nickel content, the resulting moments were subjected to greater error. The magnetic moment of Ni estimated from the fit presented in Figure 14f was equal to 0.05 µ B . It is worth noting that the result confirms the rightness of our earlier assumption about the small magnetic moment on nickel.

Ab Initio Results
Quantitative magnetic results of ab initio calculations (M S and µ 3d ) are shown in Table 1. The magnetization M S for compositions Gd 0.375 Tb 0.625 (Co 1−x Ni x ) 2 was estimated using the relation: M S = 0.375·µ Gd + 0.625·µ Tb + 2·((1 − x)·µ Co + x·µ Ni ), where the z-projected average R4f magnetic moment was evaluated using the formula µ 4 f R = g J ·(L + S) [35]. The values of µ Co and µ Ni were taken from ab initio calculations. Since within the superstructures, Gd 3 Tb 5 Co 16-n Ni n (n = 0, 2, 4, 6, 8, 16) applied in calculations, each component atom occupies several Wyckoff positions with specified multiplicity, and the µ Co , µ Ni were obtained by averaging local (Co and Ni) atomic moments over Wyckoff positions. Due to the lack of ab initio results for the orbital angular momentum of R, we assumed L = 3, S = 3, and L = 0, S = 7/2, corresponding to Tb and Gd in an ionic state with valency 3 + [35].
The calculated T and R local magnetic moments align oppositely in agreement with experimental observations. Furthermore, the dependence of calculated magnetization M S on Ni content quantitatively follows the determined experiment. Detailed analysis displayed that with increasing Ni content in the range x = 0.0-0.5, the magnitudes of both µ Co and µ Ni decrease in the range of 1.28-1.21µ B and 0.25-0.21µ B , respectively. Only in the Ni-rich Gd 0.375 Tb 0.625 Ni 2 compound the average µ Ni has dropped to 0.13 µ B . For the considered Ni concentrations, the magnetization M S increases following the simple magnetic dilution in the Co-Ni sublattice, where the higher magnetic moment of Co is replaced by the lower one of Ni. The linear fit to calculated M S yields the relation M S (x) = 2.104 x + 5.942(R 2 = 0.998). The values of M S estimated with the formula are compared with the experimental ones in Table 1. Some discrepancy between experimental data and theoretical estimates occurs for x = 0.1 and x = 0.15, where calculations underestimate M S but at most by a few percent. It can be related to the atomic disorder, as evidenced by the residual resistivity measurements (see Figure 3). The more significant deviations occur between the calculated average µ 3d and derived from the MFT approach (Table 1). Although both results show diminishing 3d lattice magnetization, the ab initio calculations give the µ 3d moment systematically overestimated.
To get insight into the microscopic origin of the changes of XPS spectra with increasing Ni content in the Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 series, we performed a detailed analysis of the electronic densities of states (DOS) obtained from ab initio calculations. Figure 15 confirms an almost strict correspondence between the shape of the XPS spectrum and the calculated DOS in Gd 0.4 Tb 0.6 (Co 0.5 Ni 0.5 ) 2 . Noticeable inconsistencies between the DOS and the XPS spectrum exist near the Fermi level and in the range of the R4f band. We presented the explanation of the discrepancies in [6].
In the observed XPS spectra related to the 3d band (Figure 13a), the intensity increases and the maximum shifts simultaneously to higher BE energy with rising Ni content. To understand the reasons for such behavior in the first stage, we analyze the DOS of endpoint compounds presented in Figure 16.
The valence band structure of the endpoint compounds comprises the 4f states of R atoms, lying deeply (around −8 eV) below Fermi energy (ε F ) and the 3d states of Co (Ni), forming the band at the energy range −4-2 eV split into bonding and antibonding subbands. The minority spin 3d bands (down arrow) in both compounds are almost entirely occupied. Upon the Co/Ni substitution, the band only narrows slightly and shifts minutely toward the Fermi level. In the observed XPS spectra related to the 3d band (Figure 13a), the intensity increases and the maximum shifts simultaneously to higher BE energy with rising Ni content. To understand the reasons for such behavior in the first stage, we analyze the DOS of endpoint compounds presented in Figure 16. The valence band structure of the endpoint compounds comprises the 4f states of R atoms, lying deeply (around −8 eV) below Fermi energy ( ) and the 3d states of Co (Ni), forming the band at the energy range −4-2 eV split into bonding and antibonding subbands. The minority spin 3d bands (down arrow) in both compounds are almost entirely occupied. Upon the Co/Ni substitution, the band only narrows slightly and shifts minutely toward the Fermi level.
Additional 3d electrons contributed by Ni atoms populate only the majority spin 3d bands. The partially populated antibonding majority spin states in the Gd0.375Tb0.625Co2 get fully occupied in the Gd0.375Tb0.625Ni2. In effect, the majority spin 3d band in the second compound shifts toward higher binding energies and becomes slightly narrower. It is worth noting that the bands of 3d states with opposite spin directions in Gd0.375Tb0.625(Co0.5Ni0.5)2 are almost symmetrical, which explains the vanishingly small magnitude of ̅ appearing in the compound.  In the observed XPS spectra related to the 3d band (Figure 13a), the intensity increases and the maximum shifts simultaneously to higher BE energy with rising Ni content. To understand the reasons for such behavior in the first stage, we analyze the DOS of end point compounds presented in Figure 16. The valence band structure of the endpoint compounds comprises the 4f states of R atoms, lying deeply (around −8 eV) below Fermi energy ( ) and the 3d states of Co (Ni) forming the band at the energy range −4-2 eV split into bonding and antibonding sub bands. The minority spin 3d bands (down arrow) in both compounds are almost entirely occupied. Upon the Co/Ni substitution, the band only narrows slightly and shifts mi nutely toward the Fermi level.
Additional 3d electrons contributed by Ni atoms populate only the majority spin 3d bands. The partially populated antibonding majority spin states in the Gd0.375Tb0.625Co2 ge fully occupied in the Gd0.375Tb0.625Ni2. In effect, the majority spin 3d band in the second compound shifts toward higher binding energies and becomes slightly narrower. It is worth noting that the bands of 3d states with opposite spin directions in Gd0.375Tb0.625(Co0.5Ni0.5)2 are almost symmetrical, which explains the vanishingly smal magnitude of ̅ appearing in the compound. Additional 3d electrons contributed by Ni atoms populate only the majority spin 3d bands. The partially populated antibonding majority spin states in the Gd 0.375 Tb 0.625 Co 2 get fully occupied in the Gd 0.375 Tb 0.625 Ni 2 . In effect, the majority spin 3d band in the second compound shifts toward higher binding energies and becomes slightly narrower. It is worth noting that the bands of 3d states with opposite spin directions in Gd 0.375 Tb 0.625 (Co 0.5 Ni 0.5 ) 2 are almost symmetrical, which explains the vanishingly small magnitude of µ Ni appearing in the compound.
The variation of the calculated band structure upon Co/Ni substitution in the Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 series is displayed in Figure 17a. As concern the minority spin 3d band, besides a slight shift toward the Fermi level, the changes are negligible. The apparent changes occur in the majority spin bands DOS, in which the dominant peak shifts toward higher binding energy by almost 0.5 eV. The magnitude of the shift is close to that displayed by experimental spectra (Figure 13a). Figure 17b shows the variation of separated contributions of constituent Co and Ni atoms to the 3d band upon increasing Ni concentration. As expected, the amplitude of co-contribution decreases while that of Ni increases with the growing Ni content. However, detailed inspection indicates that upon Co/Ni substitution, the Co3d states shift minutely toward the Fermi level when the dominant peak of the Ni contribution shifts noticeably in the opposite direction. The last effect could explain the observed shift of maximum intensity of the XPS spectra, related to the 3d band, with rising concentration of Ni in Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 series. band, besides a slight shift toward the Fermi level, the changes are negligible. The apparent changes occur in the majority spin bands DOS, in which the dominant peak shifts toward higher binding energy by almost 0.5 eV. The magnitude of the shift is close to that displayed by experimental spectra (Figure 13a). Figure 17b shows the variation of separated contributions of constituent Co and Ni atoms to the 3d band upon increasing Ni concentration. As expected, the amplitude of co-contribution decreases while that of Ni increases with the growing Ni content. However, detailed inspection indicates that upon Co/Ni substitution, the Co3d states shift minutely toward the Fermi level when the dominant peak of the Ni contribution shifts noticeably in the opposite direction. The last effect could explain the observed shift of maximum intensity of the XPS spectra, related to the 3d band, with rising concentration of Ni in Gd0.4Tb0.6(Co1−xNix)2 series.

Methods and Materials
The Gd0.4Tb0.6(Co1−xNix)2 samples x = 0.00, 0.05, 0.10, 0.15, 0.50, 0.80, 1.00 were prepared by arc melting method from high purity elements (99.99% purity) under argon atmosphere. An excess of 1% wt. of gadolinium and terbium was added to overcome weight losses during the melting. The samples have been re-melted several times to obtain the homogeneity of prepared compounds. Afterward, the as-cast samples were wrapped in tantalum foil, placed in a quartz tube, and annealed at 800 C for two weeks. The crystal structure was determined by the X-ray diffraction technique using the XRD diffractometer Empyrean (PANalytical, Malvern, UK). The measurements were performed at room temperature with Cu Kα source and 2θ changing from 15 to 140 degrees. All magnetic measurements were carried out using the SQUID magnetometer MPMS XL-7 (Quantum Design, San Diego, CA, USA) in the temperature range from 2 K to 350 K-400 K under a magnetic field up to 7 T. The electronic structure of the investigated compounds was studied using the XPS method. The XPS spectra were obtained with monochromatized Al Kα radiation (hω = 1486.6 eV) at room temperature using PHI 5700/660 physical electronics spectrometer. All spectra were measured immediately after breaking the sample in a 10 −9 Torr vacuum. The breaking in the high vacuum resulted in clean surfaces free of oxygen

Methods and Materials
The Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 samples x = 0.00, 0.05, 0.10, 0.15, 0.50, 0.80, 1.00 were prepared by arc melting method from high purity elements (99.99% purity) under argon atmosphere. An excess of 1% wt. of gadolinium and terbium was added to overcome weight losses during the melting. The samples have been re-melted several times to obtain the homogeneity of prepared compounds. Afterward, the as-cast samples were wrapped in tantalum foil, placed in a quartz tube, and annealed at 800 • C for two weeks. The crystal structure was determined by the X-ray diffraction technique using the XRD diffractometer Empyrean (PANalytical, Malvern, UK). The measurements were performed at room temperature with Cu K α source and 2θ changing from 15 to 140 degrees. All magnetic measurements were carried out using the SQUID magnetometer MPMS XL-7 (Quantum Design, San Diego, CA, USA) in the temperature range from 2 K to 350 K-400 K under a magnetic field up to 7 T. The electronic structure of the investigated compounds was studied using the XPS method. The XPS spectra were obtained with monochromatized Al K α radiation (hω = 1486.6 eV) at room temperature using PHI 5700/660 physical electronics spectrometer. All spectra were measured immediately after breaking the sample in a 10 −9 Torr vacuum. The breaking in the high vacuum resulted in clean surfaces free of oxygen and carbon contamination. Electrical resistivity was carried out by the PPMS system. The samples were cut into rectangular shapes with dimensions of 1 × 1 × 3 mm. The measurements were performed in the temperature range of 2 K-350 K.
The ab initio electronic structure calculations for selected concentrations of Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 were performed using the FP-LAPW method [37] implemented in the WIEN2k computer programs [38]. In the present investigations, we applied the same approach and computational setup used in calculations for the reference Gd 0.4 Tb 0.6 Co 2 compound [6].
We followed the supercell approach to simulate the fractional concentration of Co-Ni elements in Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 alloys. We adopted the superstructure Gd 3 Tb 5 Co 16 applied in [6] in the present calculations as a base supercell. The concentrations x Ni = 0.125, 0.25, 0.375, and 0.50 were simulated using superstructures Gd 3 Tb 5 Co 16-n Ni n where, respectively, 2, 4, 6, 8 Co atoms were replaced by Ni ones at selected sites. We are aware that for each considered concentration, there is an enormous number of Co-Ni configurations. However, we assumed that a single reasonably selected configuration (not of cluster shape) can reproduce essential features of the electronic structure of Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 alloys.

Conclusions
The new class of the Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 intermetallic compounds with the Laves phase structure of C15 type was synthesized. Structural, electronic, and magnetic properties were studied using experimental and theoretical methods.
The experimental and theoretical studies (ab initio and MFT) have shown that the magnetic moments of the R and 3d subnets align oppositely. With increasing nickel content, the values of 2 µ 3d decreased. Values of Curie temperatures determined by different methods were consistent and diminished with growing nickel content too. Arrott plots and Landau's coefficients indicated a second-order phase transition in all studied compounds.
The values of the maximum entropy change |∆S M | max , obtained under the magnetic field change of 5 T, increased with growing Ni content from 4.13 [J/kgK] to 11.99 [J/kgK] for samples with x = 0.0 and 1.0, respectively. RCP parameters also grew significantly with Ni concentration.
Presented results revealed that the replacement of Co with Ni enhanced the magnetocaloric effect in the Gd 0.4 Tb 0.6 (Co 1−x Ni x ) 2 , making these materials more attractive in terms of potential applications in magnetic refrigeration. An additional advantage is that they have minimal losses observed in hysteresis loops.
Our studies have also shown that the substitution of Ni in place of Co significantly affects the resistive properties of investigated compounds. Due to a disorder of the compound's crystal structure, an increase in the residual resistivity increases up to x = 0.50, which follows Nordheim's rule. A similar variation of H c (x) and (M FC -M ZFC )(x) indicates that structural disorder may be responsible for magnetic properties.
Both XPS measurements and ab initio calculations revealed that Co3d and Ni3d states dominate the shape of the valence band near the Fermi level. With growing Ni contents, the observed intensity of the XPS spectra corresponding to 3d bands increases, and its maximum shifts to the higher binding energy. Ni doping, however, did not affect the positions and shapes of the Gd4f and Tb4f lines. Ab initio calculations confirmed the XPS picture.