Compositional Dependence of Curie Temperature and Magnetic Entropy Change in the Amorphous Tb–Co Ribbons

The Curie temperature (Tc) and magnetic entropy change (−ΔSm), and their relationship to the alloy composition of Tb–Co metallic glasses, were studied systematically in this paper. It was found that, in contrast to the situation in amorphous Gd–Co ribbons, the dependence of Tc on Tb content and the maximum −ΔSm vs. Tc -2/3 plots in Tb–Co binary amorphous alloys do not follow a linear relationship, both of which are supposed to be closely related to the non-linear compositional dependence of Tb–Co interaction due to the existence of orbital momentum in Tb.


Introduction
In recent years, with the increasing demands for reducing energy consumption and the mitigating global warming, new refrigeration technologies have been intensively investigated. Amongst these innovative refrigeration technologies, magnetic refrigeration (MR) technology has been extensively concerned since it is free contributing to the depletion of the ozone layer and due to its long-service life, superior to the that of traditional vapor compression refrigeration technology. Therefore, experts in the related research fields are paying more and more attention to the development of novel magnetocaloric materials in the last two decades because the efficiency of the magnetic refrigerator is determined by the magnetocaloric properties of its magnetic refrigerant [1][2][3][4][5].
Amorphous magnetocaloric alloys, as an important category of magnetic refrigerant, show potential applications from the perspective of magnetic refrigerators because they possess a rather broad "hillside" of magnetic entropy change (−∆S m ) and a low but adequate maximum −∆S m (−∆S m peak ), which results in an ultrahigh refrigeration capacity (RC) . This makes it possible to design and manufacture metallic glass composites with a flattened −∆S m peak within a tailorable temperature span because magnetic refrigerant with a flattened −∆S m peak within the cold end and the hot end of a refrigerator is expected to be optimal in an Ericsson cycle [6][7][8][9].
In the preliminary works, metallic glasses consisting of rare earth (RE) elements and transition metals (TM) elements, especially the Gd-TM-based amorphous alloys, have demonstrated excellent magnetocaloric properties [8][9][10][11][12][13][14][15][16][17][18][19]. However, RE-TM-based amorphous materials containing other rare earth (Tb, Dy, etc.) metals usually exhibit spinglass-like behaviors and high coercivity at low temperature [19][20][21][22][23][24][25][26][27]. The hard magnetic properties make the magnetocaloric behaviors irreversible and thus deteriorate the application perspective of these metallic glasses. Therefore, it is necessary to systematically observe the magnetic and the magnetocaloric properties of the Tb/Dy-TM binary metallic glasses, which may be helpful to understand the relationship between alloy composition and the magnetic properties, the origin of coercivity and their influences on the magnetocaloric effect of these metallic glasses. In this paper, the magnetic properties and magnetocaloric effect, including the Curie temperature (T c ), coercivity, spin freezing temperature (T f ) and the −∆S m of the binary Tb-Co amorphous alloys were measured. Based on these results, the dependence of Curie temperature on the composition of the alloys and the relationship between the maximum −∆S m and the Curie temperature of the glassy samples were established, and the mechanism involved was investigated.

Materials and Methods
Sample synthesis: Tb and Co pure metals with a purity higher than 99.9 at.% were mixed together according to the stoichiometric compositions of Tb x Co 100−x (x = 45, 50, 55, 60, 62.5) and were arc-melted, respectively, into the shape of ingots in the presence of a Ti getter under an Ar atmosphere. Ribbons of each alloy were manufactured by means of melt-spinning method under the protection of an argon atmosphere. The thickness of the ribbons is~40 µm in average.
Structural characterization: The disordered structure of the Tb x Co 100−x ribbons was confirmed by a Rigaku X-ray diffractometer (model D/max-rC) with Cu K α source.
Magnetic measurements: the T c and T f of the ribbons were obtained from the magnetization vs. temperature (M-T) curves measured under a magnetic field of 0.03 T (Tesla) after a cooling under a zero field (ZFC) and a cooling under a magnetic field (FC) of 0.03 T. Saturation magnetization (M s ) and the coercivity of the ribbons were obtained from the hysteresis loops measured under a field of 5 T. The plots of −∆S m vs. temperature ((−∆S m )-T curves) were constructed according to the Maxwell equation from the isothermal magnetization (M-H) curves measured at various temperatures under 5 T. The M-T curves, hysteresis loops and M-H curves were measured on a vibrating sample magnetometer module of a quantum design PPMS Evercool II system. Measurement precision is less than 5 × 10 −6 emu/T(Tesla). Figure 1 illustrates the X-ray diffraction (XRD) patterns of the as-spun Tb x Co 100-x (x = 45, 50, 55, 60, 62.5) ribbons. Only broad humps representing the first diffuse halo and the absence of visible crystalline peaks indicate the formation of a fully amorphous phase in each ribbon.

Results
Materials 2021, 14, 1002 2 of 8 and the magnetic properties, the origin of coercivity and their influences on the magnetocaloric effect of these metallic glasses.
In this paper, the magnetic properties and magnetocaloric effect, including the Curie temperature (Tc), coercivity, spin freezing temperature (Tf) and the −ΔSm of the binary Tb-Co amorphous alloys were measured. Based on these results, the dependence of Curie temperature on the composition of the alloys and the relationship between the maximum −ΔSm and the Curie temperature of the glassy samples were established, and the mechanism involved was investigated.

Materials and Methods
Sample synthesis: Tb and Co pure metals with a purity higher than 99.9 at.% were mixed together according to the stoichiometric compositions of TbxCo100−x (x = 45, 50, 55, 60, 62.5) and were arc-melted, respectively, into the shape of ingots in the presence of a Ti getter under an Ar atmosphere. Ribbons of each alloy were manufactured by means of melt-spinning method under the protection of an argon atmosphere. The thickness of the ribbons is ~40 μm in average.
Structural characterization: The disordered structure of the TbxCo100−x ribbons was confirmed by a Rigaku X-ray diffractometer (model D/max-rC) with Cu Kα source.
Magnetic measurements: the Tc and Tf of the ribbons were obtained from the magnetization vs. temperature (M-T) curves measured under a magnetic field of 0.03T(Tesla) after a cooling under a zero field (ZFC) and a cooling under a magnetic field (FC) of 0.03 T. Saturation magnetization (Ms) and the coercivity of the ribbons were obtained from the hysteresis loops measured under a field of 5 T. The plots of −ΔSm vs. temperature ((−ΔSm)-T curves) were constructed according to the Maxwell equation from the isothermal magnetization (M-H) curves measured at various temperatures under 5 T. The M-T curves, hysteresis loops and M-H curves were measured on a vibrating sample magnetometer module of a quantum design PPMS Evercool II system. Measurement precision is less than 5 × 10 −6 emu/T(Tesla). Figure 1 illustrates the X-ray diffraction (XRD) patterns of the as-spun TbxCo100-x (x = 45, 50, 55, 60, 62.5) ribbons. Only broad humps representing the first diffuse halo and the absence of visible crystalline peaks indicate the formation of a fully amorphous phase in each ribbon.      [28], as summarized in Table 1. The variation of the Curie temperature with the composition of the Tb x Co 100−x glassy samples, and the Dy x Co 100−x as well as Gd x Co 100−x binary metallic glasses for comparison purpose [11,23], are plotted, respectively, in Figure 2b. Along with the increase in RE content, the Curie temperature of the three kinds of RE-Co binary metallic glasses decreases monotonously. However, one can find that the compositional dependence of T c follows a linear relationship in Gd-Co binary alloys, which in contrast, is non-linear in Tb-Co and Dy-Co binary alloys.

Results
K for Tb50Co50, 105 K for Tb55Co45, 97 K for Tb60Co40 and 92 K for Tb62.5Co37.5 [28], as summarized in Table 1. The variation of the Curie temperature with the composition of the TbxCo100−x glassy samples, and the DyxCo100−x as well as GdxCo100−x binary metallic glasses for comparison purpose [11,23], are plotted, respectively, in Figure 2b. Along with the increase in RE content, the Curie temperature of the three kinds of RE-Co binary metallic glasses decreases monotonously. However, one can find that the compositional dependence of Tc follows a linear relationship in Gd-Co binary alloys, which in contrast, is nonlinear in Tb-Co and Dy-Co binary alloys.

TbxCo100−x Ribbons
Tc  [28] In order to reveal the mechanism for the dependence of Tc on composition in these RE-Co binary metallic glasses, it is necessary to study the interactions between atoms in these metallic glasses, including the Co-Co (direct) interaction, the RE-RE (indirect) interaction and RE-Co (indirect) interaction. If the variation of Curie temperature with the composition of the RE-Co binary glassy alloys is only induced by the RE-RE interaction, the relationship between the Curie temperature and the RE content in the RE-Co binary metallic glasses agrees well with the RKKY (Ruderman-Kittel-Kasuya-Yosida) indirect interaction model, that is, Tc will have a linear relationship with the G factor, which is a physical quantity simply related to the mole fraction of the RE element in the alloy system that contains merely one type of RE atoms [17,26]. For amorphous alloys containing only one RE element, the G factor is proportional to the molar fraction of the RE atoms. Therefore, from the viewpoint of 4f-4f indirect interaction, the compositional dependence of Tc in Tb-Co amorphous alloys should be linear. However, in addition to the 4f-4f indirect interaction between the RE-RE atoms, there are two other kinds of interactions in RE-TMbased amorphous alloys: 3d-3d direct interaction between the TM-TM atoms and the 3d-4f indirect interaction between the RE-TM atoms. The influence of the 3d-3d direct interaction on the Curie temperature in the RE-TM-based amorphous alloys is supposed to be similar to that of the 4f-4f indirect interaction. This is understandable because there is only   [28] In order to reveal the mechanism for the dependence of T c on composition in these RE-Co binary metallic glasses, it is necessary to study the interactions between atoms in these metallic glasses, including the Co-Co (direct) interaction, the RE-RE (indirect) interaction and RE-Co (indirect) interaction. If the variation of Curie temperature with the composition of the RE-Co binary glassy alloys is only induced by the RE-RE interaction, the relationship between the Curie temperature and the RE content in the RE-Co binary metallic glasses agrees well with the RKKY (Ruderman-Kittel-Kasuya-Yosida) indirect interaction model, that is, T c will have a linear relationship with the G factor, which is a physical quantity simply related to the mole fraction of the RE element in the alloy system that contains merely one type of RE atoms [17,26]. For amorphous alloys containing only one RE element, the G factor is proportional to the molar fraction of the RE atoms. Therefore, from the viewpoint of 4f-4f indirect interaction, the compositional dependence of Tc in Tb-Co amorphous alloys should be linear. However, in addition to the 4f-4f indirect interaction between the RE-RE atoms, there are two other kinds of interactions in RE-TM-based amorphous alloys: 3d-3d direct interaction between the TM-TM atoms and the 3d-4f indirect interaction between the RE-TM atoms. The influence of the 3d-3d direct interaction on the Curie temperature in the RE-TM-based amorphous alloys is supposed to be similar to that of the 4f-4f indirect interaction. This is understandable because there is only (100%) 3d-3d direct interaction in a pure TM metal, and no (0%) 3d-3d direct interaction in alloys free of TM elements. The contribution of the 3d-3d direct interaction is proportional to the molar fraction of the Co element in Tb-Co amorphous alloys and the compositional dependence of Tc in Tb-Co amorphous alloys is still linear from the viewpoint of 3d-3d direct interaction. However, the effect of 3d-4f indirect interaction on the Curie temperature in RE-TM-based amorphous alloys is more complicated [23]. On the other hand, the direct interaction between Co atoms is largely influenced by the surrounding environment of a Co atom, which means that the addition of the large-size RE atoms (e.g., Gd, Tb, Dy...) give rise to the expansion of the distance between Co atoms and thus weaken the interactions between Co atoms. In other words, if the variation of Curie temperature with the composition of the RE-Co binary glassy alloys is considered to be only induced by the Co-Co direct interaction, the Curie temperature of the RE-Co binary metallic glasses will decrease with the decreasing content of Co. The dependence of T c on the Co-Co interaction probably resembles the case of the RE-RE interaction, which indicates the linear relationship between T c and Co content when only Co-Co interaction is considered. The assumption can be ascertained in the binary Gd-Co metallic glasses [11]. Unlike other RE metals such as Tb and Dy, Gd has no orbital momentum due to its stable half-full 4f shell, and thus the interaction among Gd-Co atoms can generally be ignored. As such, the Curie temperature of the Gd-Co metallic glass system ultimately depends on the co-effect of the Co-Co direct interaction and Gd-Gd indirect interaction. Considering that the T c exhibits a linear relationship with the composition in the Gd-Co metallic glasses, as shown in Figure 2b, and the concentration of Gd element and T c are linearly related according to the RKKY model, the relationship between Co concentration and T c induced by the Co-Co interaction should also be linear. It is reported that the T c variation induced by the Gd-Gd indirect interaction is nearly equal to the variation of the T c induced by the direct interaction between Ni-Ni atoms, which makes the Curie temperature remains constant near 123 K in the Gd-Ni binary metallic glasses [12]. In contrast, the increase in Gd content in Gd-Co metallic glasses, that is, the decrease in Co concentration, makes the Curie temperature decrease linearly from 267 to 179 K because the direct interaction between Co atoms is much stronger than that of the Ni atoms.
The compositional dependence of the Curie temperature in the binary Tb-Co and Dy-Co amorphous alloy systems; however, is more complicated because of the existence of RE-Co interactions [23]. For the binary Tb-Co metallic glasses in the present work, the Tb-Co interaction is zero either in pure Tb or in pure Co, but exists in Tb-Co compounds, changing with the composition of the alloy and reaching a maximum value at a certain composition. As a result, the relationship between T c and Tb content in the Tb-Co metallic glass system will not be the linear relationship in Gd-Co alloys. The parabolic-like nonlinear curve exhibited in Tb-Co binary amorphous alloys is somewhat similar to the one in Dy-Co binary alloys, indicating the similar variation trend of T c induced by the RE-Co interaction in the binary Dy-Co and Tb-Co amorphous alloys.
In our preliminary work, the Gd-Co amorphous alloys are soft magnetic with almost zero hysteresis because the stable half full electron arrangement in the 4f shell of Gd atom does not produce orbital momentum and thus Gd has a relatively small magnetocrystalline anisotropy. In contrast, the unstable electronic arrangement of the 4f shell in the Tb or Dy atom gives rise to the existence of orbital momentum and produces a large magneto-crystalline anisotropy, which is expected to result in a relatively high coercivity at low temperature in Tb-Co and Dy-Co amorphous alloys. As shown in Figure 3a, the Tb 55 Co 45 amorphous ribbon is hard magnetic with a coercivity of~326 kA/m at 20 K, soft magnetic at 95 K and paramagnetic at 160 K. The high coercivity at 20 K is due to the random magnetic anisotropy (RAM) which exists in Tb-based amorphous system [20][21][22], which will lead to the preferential orientation between the magnetic moments, destroy the macroscopic effective anisotropy directions of the magnetic order and thereby produce the hysteresis. In order to reveal the magnetocaloric properties of Tb-Co binary metallic glass and explore the mechanism of the magnetic behaviors involved in a more intensive way, it is necessary to measure the isothermal magnetization curves at various temperatures ranging from a very low temperature of 20 K to a temperature of 160 K above the Tc. To prevent the effect of magnetization history on the M-H curve at low temperature, the glassy ribbon was heat treated to eliminate residual magnetism during the measurement process. As shown in Figure 3b, the initial magnetization obviously increases with the increasing temperature from 20 to 90 K within a low range of magnetic field before saturation magnetization, which indicates the spin glass behavior of the Tb55Co45 metallic glasses [19][20][21][22][23][24][25][26][27]. The spin glass behaviors of the amorphous TbxCo100−x (x = 45, 50, 55, 60, 62.5) samples are also illustrated in Figure 3c by their ZFC M-T curves. The spin freezing temperatures of these samples, as listed in Table 1, can be obtained from their ZFC M-T curves.
According to the isothermal M-H curves of the TbxCo100−x (x = 45, 50, 55, 60, 62.5) metallic glasses, the −ΔSm vs. temperature under various magnetic fields can be obtained. Unfortunately, the spin freezing behavior and the high coercivity at low temperature obviously deteriorate the magnetocaloric properties of these alloys at temperatures below their spin freezing temperature, even decrease the −ΔSm value to below zero at 20 K. Therefore, we only study the magnetocaloric behaviors of the reversible part above the Tf. The −ΔSm vs. temperature plots of the TbxCo100−x amorphous samples under the fields of 1.5 T and 5 T are demonstrated in Figure 4a. The −ΔSm peak of the TbxCo100−x metallic glasses increases with the increasing Tb content but decrease with the increasing Tc. The −ΔSm peak values of the TbxCo100−x glassy samples under 1, 1.5, 2, 3, 4 and 5 T are summarized in Table  1. The −ΔSm peak values of the Tb62.5Co37.5 amorphous alloy are much higher than those of the TbCo amorphous ribbons, which is most likely related to the higher magnetic moment of a Tb62.5Co37.5 amorphous alloy due to its high Tb concentration and the high magnetic moment of the Tb3+ ions (~9.72 μB) [28]. Considering the potential application perspective In order to reveal the magnetocaloric properties of Tb-Co binary metallic glass and explore the mechanism of the magnetic behaviors involved in a more intensive way, it is necessary to measure the isothermal magnetization curves at various temperatures ranging from a very low temperature of 20 K to a temperature of 160 K above the T c . To prevent the effect of magnetization history on the M-H curve at low temperature, the glassy ribbon was heat treated to eliminate residual magnetism during the measurement process. As shown in Figure 3b, the initial magnetization obviously increases with the increasing temperature from 20 to 90 K within a low range of magnetic field before saturation magnetization, which indicates the spin glass behavior of the Tb 55 Co 45 metallic glasses [19][20][21][22][23][24][25][26][27]. The spin glass behaviors of the amorphous Tb x Co 100−x (x = 45, 50, 55, 60, 62.5) samples are also illustrated in Figure 3c by their ZFC M-T curves. The spin freezing temperatures of these samples, as listed in Table 1, can be obtained from their ZFC M-T curves.
According to the isothermal M-H curves of the Tb x Co 100−x (x = 45, 50, 55, 60, 62.5) metallic glasses, the −∆S m vs. temperature under various magnetic fields can be obtained. Unfortunately, the spin freezing behavior and the high coercivity at low temperature obviously deteriorate the magnetocaloric properties of these alloys at temperatures below their spin freezing temperature, even decrease the −∆S m value to below zero at 20 K. Therefore, we only study the magnetocaloric behaviors of the reversible part above the  Table 1. The −∆S m peak values of the Tb 62.5 Co 37.5 amorphous alloy are much higher than those of the TbCo amorphous ribbons, which is most likely related to the higher magnetic moment of a Tb 62.5 Co 37.5 amorphous alloy due to its high Tb concentration and the high magnetic moment of the Tb3+ ions (~9.72 µB) [28]. Considering the potential application perspective the linear −∆S m peak ∝ T c −2/3 relationship in Gd-based amorphous alloys [10,11,17,29], we constructed the −∆S m peak -T c −2/3 plots of Tb x Co 100-x glassy ribbons obtained from the (−∆S m )-T plots under 5 T, as shown in Figure 4b. Unlike the linear relationship between the −∆S m peak -T c −2/3 plots in the binary Gd-Co glassy alloys, as also shown in Figure 4b for comparison purposes, the relationship between −∆S m peak and T c −2/3 in the Tb-Co binary amorphous samples is more like a para-curve than a linear relationship. The non-linear change of the −∆S m peak and T c −2/3 is also considered to be related to the non-linear relationship between the Tb concentration and Tb-Co interaction in the Tb-Co binary metallic glasses.
Materials 2021, 14, 1002 6 of 8 the linear −ΔSm peak ∝ Tc −2/3 relationship in Gd-based amorphous alloys [10,11,17,29], we constructed the −ΔSm peak -Tc −2/3 plots of TbxCo100-x glassy ribbons obtained from the (−ΔSm)-T plots under 5 T, as shown in Figure 4b. Unlike the linear relationship between the −ΔSm peak -Tc −2/3 plots in the binary Gd-Co glassy alloys, as also shown in Figure 4b for comparison purposes, the relationship between −ΔSm peak and Tc −2/3 in the Tb-Co binary amorphous samples is more like a para-curve than a linear relationship. The non-linear change of the −ΔSm peak and Tc −2/3 is also considered to be related to the non-linear relationship between the Tb concentration and Tb-Co interaction in the Tb-Co binary metallic glasses.

Conclusions
In summary, the compositional dependence of Tc and −ΔSm of the amorphous TbxCo100-x (x = 45, 50, 55, 60, 62.5) alloys, and the mechanism involved, were investigated in this paper. The magnetic properties and magnetocaloric effect of the binary Tb-Co amorphous alloys were measured systematically. Tc of the Tb-Co metallic glasses were obtained from their FC M-T curves and the dependence of Tc on the composition of the alloys was constructed. The spin-glass behaviors were observed in the isothermal M-H curves at low temperature and the ZFC M-T curves of the Tb-Co glassy alloys. To prevent the deterioration of the magnetocaloric properties by spin freezing behaviors, the (−ΔSm)-T curves of the TbxCo100-x glassy alloys were established above the spin freezing temperature. Based on these results, the −ΔSm peak vs. Tc −2/3 plots for the Tb-Co systems were obtained. It can be discovered that the compositional dependence of Tc and the −ΔSm peak vs. Tc −2/3 plots in Tb-Co binary metallic glasses does not follow a linear relationship compared with the Gd-Co binary metallic glasses, which is mostly due to the non-linear compositional dependence of Tb-Co interaction due to the existence of orbital momentum in Tb.
Author Contributions: Measurement and date analysis, L.C. and X.W.; data analysis and investigation, L.X.; investigation, writing-review and editing, D.D. All authors have read and agreed to the published version of the manuscript.