Correlation between Magnetocaloric Properties and Magnetic Exchange Interaction in Gd54Fe36B10−xSix Amorphous Alloys

Gd54Fe36B10−xSix (x = 0, 2, 5, 8, 10) amorphous ribbons were fabricated by melt-spinning technique. Based on the molecular field theory, the magnetic exchange interaction was analyzed by constructing the two-sublattice model and deriving the exchange constants JGdGd, JGdFe and JFeFe. It was revealed that appropriate substitution content of Si for B can improve the thermal stability, maximum magnetic entropy change and widened table-like magnetocaloric effect of the alloys, while excessive Si will lead to the split of the crystallization exothermal peak, inflection-like magnetic transition and deterioration of magnetocaloric properties. These phenomena are probably correlated to the stronger atomic interaction of Fe-Si than that of Fe-B, which induced the compositional fluctuation or localized heterogeneity and then caused the different way of electron transfer and nonlinear variation in magnetic exchange constants, magnetic transition behavior and magnetocaloric performance. This work analyzes the effect of exchange interaction on magnetocaloric properties of Gd-TM amorphous alloys in detail.


Introduction
Magnetic refrigeration (MR) using solid magnetic material as a refrigerant has the advantages of environmental friendliness, low energy consumption and high efficiency. MR has been regarded as a potential alternative to replace traditional gas compression refrigeration [1]. The basic principle of MR is the intrinsic magnetocaloric effect (MCE) of magnetic materials: when a magnetic material is adiabatically magnetized, its total entropy S (S = S M + S E + S L , where S M , S E and S L denote magnetic entropy, electron entropy and lattice entropy, respectively) retains unchanged; the spin will align parallel to the direction of the applied magnetic field, inducing a decrease in S M as well as an increase in S E and S L , and therefore the enhanced lattice vibration leads to an increase in temperature [2]. The process is reversible during demagnetization. Usually, the isothermal magnetic entropy change ∆S M or adiabatic temperature change ∆T ad is utilized to estimate the magnitude of the magnetocaloric effect [3].
Magnetocaloric materials can be classified into first-order magnetic transition (FOMT) and second-order magnetic transition (SOMT) materials, according to the order of ferromagnetic (FM)-paramagnetic (PM) phase transition. FOMT material has a discontinuous magnetic transition process with temperature, which is usually related to the giant magnetocaloric effect (GMCE) [3]; however, narrow operating temperature span, high thermal and magnetic hysteresis, and inferior mechanical stability restrict its practical application. The mainly studied FOMT materials for near-room-temperature MR are Gd 5 (Si, Ge) 4 alloys [4], respectively) under Ti-gettered argon atmosphere. Each ingot was overturned and remelted four times to ensure homogeneity. Then the as-spun ribbons were fabricated by single roller melt-spinning method with a copper wheel linear surface velocity of 50 m/s under a high-purity argon atmosphere. The structure of the as-spun ribbons was determined using an X-ray diffractometer (XRD, Bruker D8 Advance) in the 2θ range of 20 • -80 • with Cu K α radiation (λ = 0.154178 nm). Thermal analyses of the samples were carried out using a differential scanning calorimeter (DSC, Netzsch STA499 F3) under the protection of an argon gas flow at a heating rate of 0.33 K/s. A physical property measurement system (PPMS, Quantum Design PPMS Evercool-II) was adopted to measure the temperature dependence of magnetization (M-T) curves under the external magnetic field of 10 Oe and 6 kOe. A superconducting quantum interference device (SQUID, Quantum Design MPMS 3) was utilized to detect the isothermal magnetization (M-H) curves under an applied field change of 0-20 kOe at various selected temperatures in the vicinity of the magnetic transition temperature (T tr ). All the magnetic properties were collected with the direction of the applied field parallel to the surface of the ribbons. To evaluate the magnetocaloric properties, the magnetic entropy change |∆S M | was calculated from the M-H curves using the Maxwell equation as follows [27]: which indicates that the magnetic entropy change ∆S M (T,H) of a specific material is proportional to the derivative of magnetization with respect to temperature under a fixed field and to the magnetic field change. Typically, Equation (1) was numerically approximated as follows [6]: where M i (T n+1 , H i ) and M i (T n , H i ) are experimental values of magnetization at temperatures T n+1 and T n under the applied field H i , respectively. Figure 1a shows the XRD patterns of the Gd 54 Fe 36 B 10−x Si x (x = 0, 2, 5, 8, 10) as-spun ribbons. Only one broad diffraction peak at around 2θ = 33 • without obvious peaks corresponding to the crystalline phase was obtained in each sample, which indicates the typical amorphous structure of the as-spun ribbons. The amorphous feature can be confirmed by the crystallization-related exothermic peaks in their DSC curves, as exhibited in Figure 1b, and the onset crystallization temperature (T x ) of Gd 54 Fe 36 B 10−x Si x amorphous alloys is 749, 762, 766, 743 and 686 K for x = 0, 2, 5, 8 and 10 respectively. With increasing content of Si, the T x increases firstly and then decreases, implying that appropriate co-addition of Si and B effectively enhanced the thermal stability of amorphous Gd 54 Fe 36 B 10−x Si x , while immoderate Si content (x ≥ 8) induced the split of the exothermal peak and even two-step crystallization. There is no obvious glass transition in the DSC curves since the competing transformation to crystalline is predominant under the heating rate of 0.33 K/s [28]. For all the samples, the T x is high enough to ensure the amorphous structure near room temperature.  Figure 2a shows the M-T curves of the Gd54Fe36B10-xSix amorphous ribbons measured under the applied field of 10 Oe. It can be seen that the magnetization reduced with rising temperature, presenting a ferrimagnetic-paramagnetic transition. The magnetic transition temperature Ttr was determined by the inflection-point method, taking the temperature corresponding to the minimum derivative of M-T curve (namely the dM/dT vs. T plot, displayed in the inset of Figure 2a). For the samples with x = 0, 2, 5, 8 and 10, the Ttr is 282, 296, 316, 342 and 364 K, respectively. As illustrated in Figure 2b, the Ttr increased nearly linearly with increasing Si content for the Gd54Fe36B10-xSix amorphous alloys, with the fitting expression of Ttr = 8.1x + 279.7, which is possibly due to the increase in magnetic exchange coupling [19,29,30]. Although only the concentration of non-magnetic B or Si elements changed, it may affect the magnetic moment and exchange interaction in the materials [25]. Similar results have been reported in amorphous alloys Gd65Fe10Co10Al10X5 (X = B, Si) and (Gd0.6Co0.2Fe0.2)95BxSi5−x (x = 0, 2, 5) [26,31].  Figure 2a shows the M-T curves of the Gd 54 Fe 36 B 10−x Si x amorphous ribbons measured under the applied field of 10 Oe. It can be seen that the magnetization reduced with rising temperature, presenting a ferrimagnetic-paramagnetic transition. The magnetic transition temperature T tr was determined by the inflection-point method, taking the temperature corresponding to the minimum derivative of M-T curve (namely the dM/dT vs. T plot, displayed in the inset of Figure 2a). For the samples with x = 0, 2, 5, 8 and 10, the T tr is 282, 296, 316, 342 and 364 K, respectively. As illustrated in Figure 2b, the T tr increased nearly linearly with increasing Si content for the Gd 54 Fe 36 B 10−x Si x amorphous alloys, with the fitting expression of T tr = 8.1x + 279.7, which is possibly due to the increase in magnetic exchange coupling [19,29,30]. Although only the concentration of non-magnetic B or Si elements changed, it may affect the magnetic moment and exchange interaction in the materials [25]. Similar results have been reported in amorphous alloys Gd 65 Fe 10 Co 10 Al 10 X 5 (X = B, Si) and (Gd 0.6 Co 0.2 Fe 0.2 ) 95 B x Si 5−x (x = 0, 2, 5) [26,31].

Magnetocaloric Properties
As indicated by Equation (1), the magnetic entropy change is approximately proportional to the dM/dT, and thereby the M-H isotherms of Gd 54 Fe 36 B 10−x Si x (x = 0, 2, 5, 8, 10) amorphous alloys at different temperatures near their individual T tr were measured under a magnetic field changing from 0 to 20 kOe, as exhibited in Figure 3. The sweeping rate of the field was slow enough to ensure that the data were recorded in an isothermal process. The obvious magnetic transition process near the T tr could be observed in all the samples except Gd 54 Fe 36 Si 10 , which had not achieved a paramagnetic state at 385 K.

Magnetocaloric Properties
As indicated by Equation (1), the magnetic entropy change is approximately proportional to the dM/dT, and thereby the M-H isotherms of Gd54Fe36B10-xSix (x = 0, 2, 5, 8, 10) amorphous alloys at different temperatures near their individual Ttr were measured under a magnetic field changing from 0 to 20 kOe, as exhibited in Figure 3. The sweeping rate of the field was slow enough to ensure that the data were recorded in an isothermal process. The obvious magnetic transition process near the Ttr could be observed in all the samples except Gd54Fe36Si10, which had not achieved a paramagnetic state at 385 K.  Table 1, the RCP values of the presently studied materials are higher in spite of their lower |∆S M pk |, which results from the broadened entropy curve and larger ∆T FWHM . This is the typical characteristic of MCE obtained in Gd-based amorphous alloys with the second-order magnetic transition (SOMT) [18,19,29,30,33,34]. The Arrott plots (M 2 vs. H/M) of Gd 54 Fe 36 B 10−x Si x ribbons were derived from the M-H isotherms, as shown in Figure 5. According to Banerjee criteria [35], the slopes of the Arrott plots are positive in the whole temperature range for all the samples, indicating that their magnetic transition is SOMT.  the broadened entropy curve and larger ΔTFWHM. This is the typical characteristic of MCE obtained in Gd-based amorphous alloys with the second-order magnetic transition (SOMT) [18,19,29,30,33,34]. The Arrott plots (M 2 vs. H/M) of Gd54Fe36B10-xSix ribbons were derived from the M-H isotherms, as shown in Figure 5. According to Banerjee criteria [35], the slopes of the Arrott plots are positive in the whole temperature range for all the samples, indicating that their magnetic transition is SOMT.  However, the RCP is now recognized to overestimate the actual refrigerating capacity of the materials with a minor magnetic entropy change in an unreasonably broad temperature range [32]. In this regard, the temperature average entropy change (TEC) was introduced as a reliable figure of merit to assess the magnetocaloric efficiency; it is calculated by the following equation [36]: where ∆T lift is the desired lift temperature of the device and T mid is the central temperature that maximizes the TEC(∆T lift ) value for a given ∆T lift . In this research, the ∆T lift was chosen between 10 K and 100 K with an interval of 10 K, and Figure 6a illustrates the variation in TEC values with respect to ∆T lift in the magnetic field change of 20 kOe for the Gd 54 Fe 36 B 10−x Si x amorphous alloys. The correlation between TEC and the content of Si indicates that the partial replacement of B by Si improves the magnetocaloric performances in this series of materials, as reflected by the changing tendency of |∆S M |. Additionally, the TEC values gradually decrease with increasing ∆T lift for each sample, and similar behavior has been reported previously [6,37,38]. It should be noted that the TEC changes very gently with the different ∆T lift values, which is ascribed to the table-like |∆S M |(T) curves (the |∆S M | retains almost constant in a wide temperature range). As revealed in Figure 6b, the TEC(30 K) and |∆S M pk | of amorphous Gd 54 [38] and higher than those of Fe 63.5 Cr 10 Si 13.5 B 9 Nb 3 Cu 1 amorphous alloy (TEC(10 K, 15 kOe) = 0.83 J kg −1 K −1 ) [36,[38][39][40]. Although the magnetocaloric performance estimated by TEC is not very good, the table-like MCE with a wide temperature range was observed in all the samples, enabling them to be more suitable for the Ericsson thermodynamic cycle [32]. However, the RCP is now recognized to overestimate the actual refrigerating capacity of the materials with a minor magnetic entropy change in an unreasonably broad temperature range [32]. In this regard, the temperature average entropy change (TEC) was introduced as a reliable figure of merit to assess the magnetocaloric efficiency; it is calculated by the following equation [36]: where ΔTlift is the desired lift temperature of the device and Tmid is the central temperature that maximizes the TEC(ΔTlift) value for a given ΔTlift. In this research, the ΔTlift was chosen

Magnetic Exchange Interaction
In Figure 2, it can be found that the ferrimagnetic-paramagnetic magnetic transition process becomes broad and gentle with increasing Si content, which is possibly attributed to the variation in Fe magnetic moment and magnetic exchange constant (JGdGd, JGdFe, JFeFe) induced by the replacement of B with Si [25,42]. Additionally, the Ttr obtained in the low magnetic field of 10 Oe is higher than the Tpk achieved under the high magnetic field of 20 kOe, while the Ttr is similar to the Tpk for the other series of alloys, as displayed in Table 1. Especially for the present Si-containing Gd54Fe36B10-xSix amorphous samples, the discrepancy between Ttr and Tpk becomes larger with increasing content of Si, and this may be caused by the varied antiferromagnetic coupling between Fe and Gd sublattices associated with the composition and magnetic field [24,25].
To investigate the origin of these phenomena in detail, an MFT analysis was carried out with the two-sublattice model [43]. First of all, the M-T curves of Gd54Fe36B10-xSix amorphous ribbons were measured under the magnetic field of 6 kOe, which ensures the saturation state of the samples, as exhibited in Figure 7 (open circle). The inflection-like behavior with the characteristic of an inversely bent curve in a relatively wide temperature   [5,9]

Magnetic Exchange Interaction
In Figure 2, it can be found that the ferrimagnetic-paramagnetic magnetic transition process becomes broad and gentle with increasing Si content, which is possibly attributed to the variation in Fe magnetic moment and magnetic exchange constant (J GdGd , J GdFe , J FeFe ) induced by the replacement of B with Si [25,42]. Additionally, the T tr obtained in the low magnetic field of 10 Oe is higher than the T pk achieved under the high magnetic field of 20 kOe, while the T tr is similar to the T pk for the other series of alloys, as displayed in Table 1. Especially for the present Si-containing Gd 54 Fe 36 B 10−x Si x amorphous samples, the discrepancy between T tr and T pk becomes larger with increasing content of Si, and this may be caused by the varied antiferromagnetic coupling between Fe and Gd sublattices associated with the composition and magnetic field [24,25].
To investigate the origin of these phenomena in detail, an MFT analysis was carried out with the two-sublattice model [43]. First of all, the M-T curves of Gd 54 Fe 36 B 10−x Si x amorphous ribbons were measured under the magnetic field of 6 kOe, which ensures the saturation state of the samples, as exhibited in Figure 7 (open circle). The inflection-like behavior with the characteristic of an inversely bent curve in a relatively wide temperature range can be observed for x = 8 and 10, similar to the transition type revealed in Gd-rich region Gd-Fe amorphous ribbons [25]. In the next step, each sublattice magnetization M Gd and M Fe and the total magnetization M were calculated by assigning some values to three exchange integration constants, J GdGd , J GdFe and J FeFe , at a certain temperature T, then the M-T curves in the field of 6 kOe was fitted through adopting the nonlinear least square method [44]. The ferrimagnetic model was constructed with the following parameters: The Landé factors of Gd and Fe are g Gd = g Fe = 2. The coordination number Z ij (i, j = Gd, Fe) is expressed as Z GdGd = Z FeGd = 7.2 (= 12X Gd X Gd +X Fe ) and Z GdFe = Z FeFe = 4.8 (= 12X Fe X Gd +X Fe ), where X Fe and X Gd are atomic content of Fe and Gd respectively. The spin quantum number S Gd is 7/2 for the Gd sublattice, while the S Fe was derived from Fe magnetic moment µ Fe (µ Fe = g Fe S Fe ), and µ Fe was evaluated from the magnetization µ a at 10 K under 6 kOe by µ a =|X Gd µ Gd − X Fe µ Fe |/100 (where µ Gd = g Gd S Gd = 7 µ B ) [45]. As a result, the J GdGd , J GdFe and J FeFe were derived, and the fitting profiles of M Gd , M Fe and M are depicted in Figure 7 (solid line). It can be seen that all the calculated results are in good accordance with the experimental data.
The content dependence of µ Fe , J GdGd , −J GdFe , J FeFe , the −J GdFe /J FeFe ratio and |∆S M pk | for Gd 54 Fe 36 B 10−x Si x amorphous alloys is displayed in Figure 8. The µ Fe increases from 1.60 µ B (for x = 0) to 2.68 µ B (for x = 2) first and then decreases to 1.4 µ B (for x = 10). Similar results can be found in amorphous alloys Fe 56 Gd 24 Si 12 B 8 (µ Fe ≈ 1.40 µ B ) and Fe 56 Gd 24 B 20 (µ Fe = 1.22 µ B ) [45,46]. On one side, compared with the B element, Si possesses more covalent electrons (mainly 3p electrons), which possibly intensifies the transfer of electrons to the 3d orbital of Fe, leading to the lower value of µ Fe [25,46,47]. On the other side, the substitution of Si for B could change the local environment and affect the magnetic moment of Fe atoms [48]. In this study, for the moderate Si content, B may absorb electrons from Fe atoms and promote µ Fe [49]; for the alloys with high content of Si or B (x = 0 and 10), the p-d hybridization dominates the reduction in µ Fe [50].
With the replacement of B by Si in amorphous Gd 54 Fe 36 B 10−x Si x alloys, the J GdGd increases slightly, reflecting the decrease in the average distance between Gd atoms [24], which is probably attributed to the stronger atomic interaction between Fe and Si (in comparison with the Fe-B pairs), and more metalloid atoms tend to surround Fe atoms [51]. Furthermore, after the addition of Si, fewer B atoms appear at the nearest neighbor locations around Fe atoms, and as described above, B absorbs electrons from Fe for the lower B content [52].
In Figure 8, the variation tendency of −JGdFe/JFeFe and |ΔSM | with Si content is similar, except for the Gd54Fe36B5Si5; the atomic-scale structure and accurate µFe of this series of alloys need to be clarified further. Nevertheless, it can be revealed that the appropriate substitution of Si for B promotes the value of |ΔSM pk | and table-like MCE of amorphous Gd54Fe36B10-xSix alloys; this can be attributed to the enhancement of the −JGdFe/JFeFe and modified magnetic transition behavior. An excessive amount of Si results in a decline in the −JGdFe/JFeFe, an inflection-like transition and the deterioration of magnetocaloric properties. It can be seen that the introduction of Si has stronger impacts on −J GdFe and J FeFe than on J GdGd . Additionally, both −J GdFe and J FeFe decrease firstly and then increase with increasing Si content; the variation rule is opposite to that of µ Fe , as displayed in Figure 8. The overlap between 5d electron wave-functions of Gd and 3d electron wave-functions of Fe is considered to be the origin of the antiferromagnetic exchange coupling −J GdFe [53]; therefore, the lost 3d electron of Fe absorbed by the surrounding B (with moderate content of Si, i.e., x = 2, 5 and 8) is in accordance with the weakened 3d-5d interaction [25]. The effect of B addition on J FeFe in the amorphous Gd 54 Fe 36 B 10 alloys is neglectable [25], which can be interpreted by its statistically random distribution in the structure [24]. However, Si has a stronger atomic interaction with Fe and then preferentially neighbors Fe, resulting in the deviation from the statistical distribution, which is reflected by the great increase in exchange constant J FeFe in the Gd 54 Fe 36 Si 10 [24]. For the Gd 54 Fe 36 B 10−x Si x samples, partial replacement of B by Si may reduce the distance between Fe atoms, and the exchange interaction decreases according to the Bethe-Slater curve [54].    The sign of J GdGd and J FeFe is positive but J GdFe is negative.
It has been reported that the inflection-like magnetic transition of a Gd-TM amorphous alloy can be adjusted to normal ferromagnetic-paramagnetic transition by increasing the ratio of −J GdTM /J TMTM when the J GdGd remains constant [55]. As shown in Figure 8, the value of −J GdFe /J FeFe increases first and then decreases with Si content rising from 0 to 10, which can explain the inflection-like M-T curves observed for Gd 54 Fe 36 B 10−x Si x amorphous alloys with x = 8 and 10. Moreover, adding more Si probably makes the atomic structure deviate from the statistical distribution, which leads to compositional fluctuation or localized heterogeneity [24]; then the larger discrepancy between T tr and T pk was obtained [56].
In Figure 8, the variation tendency of −J GdFe /J FeFe and |∆S M pk | with Si content is similar, except for the Gd 54 Fe 36 B 5 Si 5 ; the atomic-scale structure and accurate µ Fe of this series of alloys need to be clarified further. Nevertheless, it can be revealed that the appropriate substitution of Si for B promotes the value of |∆S M pk | and table-like MCE of amorphous Gd 54 Fe 36 B 10−x Si x alloys; this can be attributed to the enhancement of the −J GdFe /J FeFe and modified magnetic transition behavior. An excessive amount of Si results in a decline in the −J GdFe /J FeFe , an inflection-like transition and the deterioration of magnetocaloric properties.

Conclusions
In summary, the effect of Si substitution for B on thermal stability, magnetic transition behavior and magnetocaloric properties of melt-spun Gd 54 Fe 36 B 10−x Si x (x = 0, 2, 5, 8, 10) amorphous alloys was researched. With appropriate content of Si, the alloys showed enhanced thermal stability and broadened table-like MCE; with excessive Si, the alloys exhibited poorer thermal stability, inflection-like transition behavior and weakened MCE. Among present alloys, Gd 54 Fe 36 B 8 Si 2 possesses the largest values of |∆S M pk | (1.43 J kg −1 K −1 ), RCP (374 J kg −1 ) and TEC(30 K) (1.42 J kg −1 K −1 ) under an applied field of 20 kOe, as well as a table-like MCE, which makes it more suitable for the MR with the Ericsson cycle.
The variation in magnetic exchange constants J GdGd , J GdFe and J FeFe was obtained by fitting the temperature dependence of magnetization according to the molecular field theory and two-sublattice model. Substitution of B with Si induces the different ways of electron transfer and different atomic interaction (Fe-Si pairs are stronger than Fe-B), resulting in the nonlinear correlation between µ Fe , J GdGd , −J GdFe , J FeFe and −J GdFe /J FeFe and Si content. Therefore, the shape of the magnetic transition curve and the magnetocaloric properties changed nonlinearly.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.