Glass Forming Ability, Magnetic Properties and Magnetocaloric Effect of the Tb₆₅Co₂₅Ni₁₀ Amorphous Tape

Abstract

In this paper, a ternary Tb₆₅Co₂₅Ni₁₀ amorphous tape was successfully prepared, and the glass forming ability (GFA), magnetic properties, and magnetocaloric characteristics of the amorphous tape were studied in detail. The values of the reduced glass transition temperature T_rg, parameter γ and critical section thickness Z_c indicate the good GFA of the Tb₆₅Co₂₅Ni₁₀ amorphous tape. The Tb₆₅Co₂₅Ni₁₀ amorphous tape exhibits spin-glass-like behavior, with a Curie temperature of 83 K and a spin-freezing temperature (T_f) of 73 K, and a large coercivity below T_f. The spin-glass-like behavior significantly deteriorates the magnetic entropy change (−∆S_m) of the Tb₆₅Co₂₅Ni₁₀ amorphous tape at low temperatures, resulting in the deviation of magnetic entropy change behavior from the predicted results. However, the Tb₆₅Co₂₅Ni₁₀ amorphous tape still shows an excellent magnetocaloric effect (the peak value of −∆S_m of 9.46 J kg⁻¹ K⁻¹ and the refrigeration capacity of 569.5 J kg⁻¹ under 5 T, both of which are higher than those of most other heavy rare earth-based amorphous alloys), indicating the great application potential in the field of magnetic refrigeration for the amorphous tape.

1. Introduction

With escalating climate change and energy consumption issues, developing energy-efficient green refrigeration technologies has become increasingly critical. Magnetic refrigeration, utilizing the magnetocaloric effect (MCE) of materials for heat exchange, offers some advantages such as environmental friendliness, high efficiency, low noise, and compact design compared to traditional gas compression refrigeration using fluorocarbons [1,2,3,4]. Consequently, MCE materials have garnered significant research interest.

The MCE performance is usually characterized by two key parameters: magnetic entropy change (−∆S_m) and refrigeration capacity (RC). Therefore, MCE materials primarily fall into two categories: first-order magnetic transition (FOMT) materials (such as Gd-Si-Ge, La-Fe-Si-based and Mn-based compounds) [5,6,7,8,9,10,11], and second-order magnetic transition (SOMT) materials (such as pure Gd metals, some Gd-based crystalline materials, and amorphous alloys) [3,12,13,14,15,16]. These FOMT crystalline compounds exhibit an ultra-high −∆S_m peak (−∆S_m^peak) but narrow full width at half maximum of the −∆S_m (∆T_FWHM), resulting in limited RC. Additionally, irreversible −∆S_m and material fracture caused by their abrupt structural mutation during cooling/heating cycles pose reliability concerns. The inevitable magnetic/thermal hysteresis also limits the practical application of such materials. While SOMT materials show a lower −∆S_m^peak than FOMT compounds, their broader operating temperature range (meaning larger ∆T_FWHM) enables superior RC, often exceeding that of FOMT materials by two to three times. Notably, amorphous alloys feature a disordered structure with many benefits, including reduced eddy current losses, minimal hysteresis, enhanced corrosion resistance, and tunable Curie temperature (T_c) [17,18,19,20]. These attributes make them ideal candidates for magnetic refrigeration if their −∆S_m^peak is high enough.

Rare earth (RE)-based and iron-based amorphous alloys are primary classes of amorphous MCE materials. Iron-based amorphous alloys typically exhibit a very low −∆S_m^peak, unsuitable for refrigeration applications [3,13,14]. RE-based amorphous alloys, particularly Gd-based systems, show superior MCE performance due to their large magnetic moments [12,20,21,22]. For instance, Gd-Co-Al amorphous alloys achieve an average −∆S_m^peak of 9.3 J kg⁻¹ K⁻¹ under 5 T, which is comparable to that of pure Gd [20]. The microalloying of different elements, including Mn, Fe, and Cu, brings about a −∆S_m^peak of 8.0~8.94 J kg⁻¹ K⁻¹ under 5 T at a temperature ranging from 100 K to 118 K in the Gd₅₅Co_17.5Al_24.5 metallic glass [21].

Recently, a high −∆S_m^peak has also been observed in Tb-based amorphous systems with larger magnetic moments. The Tb₆₅Ni₃₅ amorphous alloy delivers the −∆S_m^peak of 8.68 J kg⁻¹ K⁻¹ under 5 T at 64 K [23]. The Tb-Co binary systems show a continuously changing −∆S_m^peak with composition and the maximum −∆S_m^peak is up to 9.27 J kg⁻¹ K⁻¹ under 5 T in Tb_62.5Co_37.5 [24]. The high −∆S_m^peak of Tb-based amorphous alloys indicate their enormous potential in the field of magnetic refrigeration. However, a large gap still exists between practical refrigeration requirements and the magnetocaloric properties of Tb-based amorphous alloys. Therefore, maximizing the −∆S_m^peak of these Tb-based amorphous alloys is extremely important for their applications. Additionally, these Tb-based amorphous alloys usually exhibit spin-glass-like behavior, which is absent in Gd-based amorphous alloys. The exploration of the effects of this behavior on magnetic and magnetocaloric properties is still insufficient. In this study, a ternary Tb₆₅Co₂₅Ni₁₀ amorphous alloy with a high −∆S_m^peak and significant RC was fabricated with the form of tape, and the spin-glass-like behavior and associated MCE characteristics were elucidated.

2. Materials and Methods

The Tb₆₅Co₂₅Ni₁₀ alloy was prepared via arc melting the mixture of high-purity Tb, Co and Ni elements (≥99.95 wt.%) under Ar atmosphere, followed by quenching onto a rotating Cu wheel (~30 m/s) after induction melting to form amorphous tapes. The non-crystalline feature of the selected 3 mm width and 40 μm thickness tape was verified via a Rigaku D/max-2550 X-ray diffractometer (XRD, Rigaku, Tokyo, Japan) with Cu K_α radiation. The thermal properties and corresponding glass forming ability (GFA) of the tape were assessed using a Netzsch 404C differential scanning calorimeter (DSC, Netzsch, Selb, Germany). The microstructure of the Tb₆₅Co₂₅Ni₁₀ amorphous tape was observed using a JEOL JEM-2100 high-resolution transmission electron microscope (TEM, JEOL, Tokyo, Japan). The sample for TEM observation was prepared using a GATAN 691 precision ion-polishing system (PIPS, Ametek, Berwyn, PA, USA) under Ar atmosphere. Magnetic measurements, including magnetization–temperature (M–T) curves, hysteresis loops, and isothermal–magnetization (M–H) curves, were conducted using a vibrating sample magnetometer (VSM) in a Quantum Design 6000 physical performance measurement system (Quantum Design, San Diego, CA, USA). The measurement procedure of M–H curves was set to first heat the sample to the temperature above 150 K and then lower the sample to the measurement temperature to avoid the influence of thermal history.

3. Results and Discussion

3.1. Glass Forming Ability of Tb₆₅Co₂₅Ni₁₀ As-Spun Tape

To elucidate the structural characteristics of the Tb₆₅Co₂₅Ni₁₀ sample prepared in this work, the tape with a uniform thickness of 40 μm was subjected to XRD analysis. Due to the disordered arrangement of atoms in amorphous alloys, the diffraction pattern of amorphous alloys does not exhibit the sharp and strong diffraction peaks of crystalline alloys. Instead, several characteristic distances between atoms can cause scattering humps at multiple specific angles. As illustrated in Figure 1a, the XRD spectrum of the Tb₆₅Co₂₅Ni₁₀ tape exhibits a pronounced broad diffraction peak within the range of 2θ = 30°~40°, accompanied by a subtle hump between 2θ = 55°~60°, corresponding to the average distance between nearest neighboring atoms and the average distance between second nearest neighboring atoms, respectively. According to the Bragg formula, the average distance between nearest neighboring atoms in the Tb₆₅Co₂₅Ni₁₀ tape can be roughly calculated to be 3.23 Å, which is close to the experimental and simulation results of other amorphous alloys [25,26,27]. Additionally, the full width at half maximum (FWHM, inversely proportional to the particle size based on the Scherrer formula) value of the main peak of the Tb₆₅Co₂₅Ni₁₀ tape was determined to be about 7.60°, which is also close to that of other fully amorphous alloys [28,29]. The average distance between nearest neighboring atoms and the FWHM value of the main peak imply the strong short-range order in the Tb₆₅Co₂₅Ni₁₀ tape. More importantly, no sharp crystalline diffraction peaks are observed across the entire angular measurement range, further indicating that the Tb₆₅Co₂₅Ni₁₀ tape is an amorphous alloy.

Given that the short-range-ordered structure of amorphous alloys represents a metastable state, another crucial feature of such materials is the occurrence of glass transition behavior prior to their crystallization reactions. The DSC curve of the Tb₆₅Co₂₅Ni₁₀ tape, as depicted in Figure 1b, reveals a minor endothermic peak preceding a sharp exothermic crystallization peak. This endothermic peak corresponds to the glass transition phenomenon exhibited by the Tb₆₅Co₂₅Ni₁₀ tape during heating, thereby providing further corroboration of its amorphous nature. Consequently, the glass transition temperature (T_g) and crystallization temperature (T_x) of the Tb₆₅Co₂₅Ni₁₀ amorphous tape are determined to be 569 K and 585 K, respectively. From Figure 1c, the liquidus temperature (T_l) of the Tb₆₅Co₂₅Ni₁₀ amorphous tape is determined to be 982 K. Based on the values of T_g, T_x, and T_l, two common criteria can be employed to describe the GFA of the Tb₆₅Co₂₅Ni₁₀ amorphous tape; namely, the reduced glass transition temperature T_rg (=T_g/T_l) [30], and the parameter γ (=T_x/(T_g + T_l) [31]. As such, the values of T_rg and γ for the Tb₆₅Co₂₅Ni₁₀ amorphous tape are determined to be 0.579 and 0.377, respectively. Although these values of the Tb₆₅Co₂₅Ni₁₀ amorphous tape are not as high as those of Zr-based or Ti-based bulk metallic glasses, they are still significantly higher than the T_rg and γ values of most Fe-based and RE-based amorphous tapes. Additionally, the critical section thickness Z_c of the Tb₆₅Co₂₅Ni₁₀ amorphous tape, based on the parameter γ, can be calculated as 1.882 mm using the formula Z_c = 2.8 × 10⁻⁷exp(41.7γ) [31]. Taking into account the magnitudes of T_rg, γ and Z_c, the Tb₆₅Co₂₅Ni₁₀ amorphous tape demonstrates a remarkable glass forming ability, which facilitates the facile preparation of Tb₆₅Co₂₅Ni₁₀ alloy in the form of amorphous tapes. Additionally, in order to avoid the influence of possible nano-clusters or medium-range-ordered structures on the subsequent magnetic properties and magnetocaloric effect, we observed the microstructure of the Tb₆₅Co₂₅Ni₁₀ amorphous alloy through high-resolution TEM technology. As shown in Figure 1d, there are almost no nano-clusters or medium-range-ordered structures embedded on the disordered amorphous matrix. The diffraction halo and the disordered atomic configuration further confirm the completely amorphous structure of the Tb₆₅Co₂₅Ni₁₀ amorphous tape.

3.2. The Magnetic Properties of the Tb₆₅Co₂₅Ni₁₀ Amorphous Tape

To investigate the magnetization behavior of the Tb₆₅Co₂₅Ni₁₀ amorphous tape, we initially cooled the tape from room temperature to 10 K in the absence of an external magnetic field (zero-field cooling, ZFC), and measured its magnetization curve under a magnetic field of 0.03 T as the temperature increased from 10 K to 300 K. Subsequently, the tape was cooled again to 10 K under a magnetic field of 0.03 T (field cooling, FC), and its magnetization curve was then measured under the same magnetic field from 10 K to 300 K. Figure 2a presents the ZFC and FC M–T curves under 0.03 T of the Tb₆₅Co₂₅Ni₁₀ amorphous tape. It is evident from the figure that as the temperature decreases, the ZFC and FC M–T curves initially nearly coincide, with their magnetization increasing slowly until a rapid rise below 100 K. However, after reaching an inflection point, the magnetization of the ZFC M–T curve begins to gradually decline, while that of the FC M–T curve continues to increase and eventually stabilizes. This characteristic “λ”-shaped M–T curve has also been observed in other RE-based amorphous alloys, such as Tb-, Dy- and Nd-based amorphous alloys [22,23,24,32,33,34,35]. The magnetization behavior of amorphous alloys is reminiscent of traditional spin-glass systems, yet it differs fundamentally from the nature of spin-glasses and thus is referred to as “spin-glass-like behavior” [36]. The temperature at which the magnetization begins to decline in the ZFC M–T curve is defined as the spin-freezing temperature, denoted as T_f = 73 K for the Tb₆₅Co₂₅Ni₁₀ tape. Additionally, the temperature corresponding to the most rapid change in magnetization (i.e., the minimum value of the derivative of the M–T curve, as shown in Figure 2a) is identified as the Curie temperature, T_c = 83 K for the Tb₆₅Co₂₅Ni₁₀ tape.

Figure 2b displays the hysteresis loops of the Tb₆₅Co₂₅Ni₁₀ amorphous tape at 10 K, 80 K, 160 K, and 300 K under a magnetic field of 5 T. At 160 K and 300 K, the relationship between magnetization and magnetic field closely follows the Curie-Weiss law, exhibiting distinct paramagnetic behavior. At 80 K, which lies between T_f and T_c, the hysteresis loop shows negligible hysteresis with almost imperceptible coercivity (~5.6 kA/m), indicating that the Tb₆₅Co₂₅Ni₁₀ amorphous tape is an excellent soft magnetic alloy. Conversely, at 10 K, well below T_f, a pronounced hysteresis is observed in the hysteresis loop of the Tb₆₅Co₂₅Ni₁₀ amorphous tape, accompanied by a significantly high coercivity of 512.2 kA/m, which is the typical characteristic of hard magnetism. As with other RE-based amorphous alloys displaying spin-glass-like behavior, the random magnetic anisotropy induced by the coupling of anisotropic 3d-4f interactions between RE and TM atoms accounts for the magnetic hysteresis and large coercivity observed in these amorphous alloys at low temperatures [23,33,34,35,37].

Simultaneously, the spin-glass-like behavior and significant coercivity of RE-based amorphous alloys at low temperatures impede magnetization, leading to anomalous magnetization characteristics. Figure 3a presents the M–H curves of the Tb₆₅Co₂₅Ni₁₀ amorphous tape at various temperatures ranging from 10 K to 160 K, with an applied magnetic field of 5 T. It is evident that the magnetization of the Tb₆₅Co₂₅Ni₁₀ tape increases rapidly with the increase in magnetic field at temperatures below its T_c, exhibiting a very high initial permeability. As the temperature rises, the initial permeability decreases, and the magnetization also diminishes. Notably, at temperatures significantly above T_c, the relationship between magnetization and magnetic field even adheres to the linear relation described by the Curie-Weiss law. This variation pattern signifies the ferromagnetic-paramagnetic transition process in the Tb₆₅Co₂₅Ni₁₀ amorphous tape. Furthermore, it can be observed that at temperatures above T_f, the magnetization exhibits a negative correlation with temperature across the entire magnetic field range, meaning that the magnetization decreases with increasing temperature. However, at temperatures below T_f, the relationship between magnetization and temperature is positively correlated under a very small magnetic field, particularly pronounced for the magnetization curve at 10 K, where the magnetization below 1.5 T is significantly lower than that at 30 K. This anomalous magnetization behavior is primarily attributed to the hindering effect of large coercivity on magnetization, further underscoring the spin-glass-like behavior of the Tb₆₅Co₂₅Ni₁₀ amorphous tape.

For amorphous MCE materials, the ferromagnetic-paramagnetic transition is usually a second-order phase transition. However, whether the emergence of spin-glass-like behavior affects the type of phase transition warrants further investigation. Therefore, by analyzing the M–H curves of the Tb₆₅Co₂₅Ni₁₀ amorphous tape, we constructed the Arrott plots, which are graphs of H/M vs. M². Banerjee proposed that if the Arrott plot exhibits a “C” or “S” shape characterized by a negative slope, the alloy undergoes a first-order phase transition, whereas a positive slope indicates a second-order phase transition [38]. Figure 3b displays the Arrott plots of the Tb₆₅Co₂₅Ni₁₀ amorphous tape at various temperatures. It is evident that the slopes of the Arrott plots are positive and the curves at each temperature are nearly parallel above T_f, especially under the high field region of 1–5 T, indicative of typical SOMT behavior. However, the Arrott plots below T_f display a “C”-shaped feature under low field, particularly pronounced at 10 K, suggesting that the Tb₆₅Co₂₅Ni₁₀ amorphous tape does not undergo SOMT under low field at temperatures below T_f. Unlike first-order phase transition induced by structural mutation, however, the phenomenon in the Tb₆₅Co₂₅Ni₁₀ amorphous tape is more likely attributed to spin-glass-like behavior and nonuniform reversal, which leads to the deviation from mean-field Arrott behavior.

3.3. The Magnetocaloric Effect of the Tb₆₅Co₂₅Ni₁₀ Amorphous Tape

Previous studies have indicated that the presence of spin-glass-like behavior and large coercivity at low temperatures in RE-based amorphous alloys can significantly influence their magnetocaloric properties [23,24,32,33,34,35]. Generally, the magnetocaloric effect of magnetic materials is primarily characterized by −∆S_m and refrigeration capacity. To this end, we can determine −∆S_m at various temperatures and magnetic fields using Maxwell’s equation [39], which is expressed as follows:

$$\Delta S_m\left(T,H\right)=S_m\left(T,H\right)-S_m\left(T,0\right)={\int }_0^H{\left({\displaystyle \frac{\partial M}{\partial T}}\right)}_H\mathrm{d}H.$$

(1)

For amorphous alloys with SOMT or spin-glass-like behavior, the above equation can be well used in the reversible region. However, at temperatures below T_f where the system is in a nonequilibrium state, the direct application of the above equation should be performed in a special way due to the irreversible processes. Using the method in a reversible region as a reference, the entropy change, namely irreversible −∆S_m, was obtained by calculating the area between magnetic isotherms at adjacent temperatures and dividing it by the temperature difference [40,41]. The irreversible −∆S_m provides valuable information about the random magnetic anisotropy, and depends on the thermal history of the sample. Therefore, based on the M–H curves of the Tb₆₅Co₂₅Ni₁₀ amorphous tape, we obtained the temperature dependence of −∆S_m for the tape under different magnetic fields ranging from 1 to 5 T, i.e., the (−∆S_m)–T curves. As depicted in Figure 4, all (−∆S_m)–T curves exhibit a relatively broad temperature distribution, which is characteristic of SOMT materials. Under different magnetic fields, −∆S_m initially increases gradually with increasing temperature and reaches a maximum value near T_c, denoted as −∆S_m^peak. With further elevation of temperature, −∆S_m decreases slowly and eventually approaches zero. Notably, the −∆S_m of the Tb₆₅Co₂₅Ni₁₀ amorphous tape becomes negative below 40 K due to the influence of spin-glass-like behavior and large coercivity, which indicates that the random magnetic anisotropy dominates the magnetization behavior [41]. This phenomenon has also been observed in other Tb-, Nd- and Dy-based amorphous alloys [23,32,34,35]. Additionally, it is observed that as the magnetic field increases, the critical temperature for the sign change of −∆S_m in the Tb₆₅Co₂₅Ni₁₀ amorphous tape gradually decreases to around 30 K, which is attributable to the fact that a stronger magnetic field more effectively overcomes the impediments to magnetization imposed by the spin-glass-like behavior and large coercivity. The above speculation can also be used to explain the difference in the peak shape of the (−∆S_m)–T curve under various fields. As the magnetic field decreases, the peak shape of the (−∆S_m)–T curve becomes more and more gentle due to the gradual weakening of the driving force that overcomes the magnetization hindrance caused by the spin-glass-like behavior and large coercivity.

Despite the spin-glass-like behavior and large coercivity causing the irreversible −∆S_m at low temperatures, the gentle −∆S_m distribution still endows the Tb₆₅Co₂₅Ni₁₀ amorphous tape with a relatively wide ∆T_FWHM. As listed in

Table 1. The characterization parameters of the MCE in the Tb₆₅Co₂₅Ni₁₀ amorphous tapes.

MCE Parameters	Applied Field (T)
	1	1.5	2	2.5	3	3.5	4	4.5	5
∆TFWHM (K)	32.5	37.9	43.3	47.5	51.0	53.8	56.2	58.3	60.2
−ΔSmpeak (J kg−1 K−1)	2.58	3.69	4.69	5.60	6.45	7.27	8.04	8.77	9.46
RC1 (J kg−1) *	83.8	139.8	203.1	266.0	329.0	391.1	451.8	511.3	569.5
RC2 (J kg−1) **	65.9	108.8	156.2	204.2	252.6	300.3	347.5	394.1	440.3

* RC¹ denotes the refrigeration capacity calculated by the Wood-Potter method. ** RC² denotes the refrigeration capacity calculated by the Gschneidner method.

, the value of ∆T_FWHM for the Tb₆₅Co₂₅Ni₁₀ amorphous tape increases from 32.5 K under 1 T to 60.2 K under 5 T, which is larger than that of most FOMT materials, indicating that the Tb₆₅Co₂₅Ni₁₀ amorphous tape holds great promise for operations as a magnetic refrigerant over a considerable temperature range. Furthermore, the −∆S_m^peak values of the Tb₆₅Co₂₅Ni₁₀ amorphous tape remain notably high, 3.69 J kg⁻¹ K⁻¹ under 1.5 T and 9.46 J kg⁻¹ K⁻¹ under 5 T, as presented in Table 1. Under a magnetic field of 5 T, the −∆S_m^peak of the Tb₆₅Co₂₅Ni₁₀ amorphous tape is 9% higher than that of the Tb₆₅Ni₃₅ amorphous alloy [23], 26% higher than that of the Tb₅₅Co₂₀Al₂₅ amorphous alloy [42], and as much as 78% higher than that of the Tb₄₅Co₅₅ amorphous tape [24]. In fact, the −∆S_m^peak of the Tb₆₅Co₂₅Ni₁₀ amorphous tape is nearly the highest among the currently known Tb-based amorphous alloys. As shown in

Table 2. The characterization parameters of the MCE in some heavy RE-based amorphous alloys, pure Gd metal, and some FOMT materials (A—amorphous alloy; C—crystalline compound).

Compositions	Structure	Tc (K)	Applied Field (T)	∆TFWHM (K)	−ΔSmpeak (J kg−1 K−1)	RC1 (J kg−1)	RC2 (J kg−1)	Refs.
Tb45Co55	A	170	5	83	5.31	441		[24]
Tb50Co50	A	130	5	60	7.3	438
Tb55Co45	A	105	5	63	8.84	557
Tb60Co40	A	97	5	62	9.18	570
Tb62.5Co37.5	A	92	5	62	9.27	575
Tb65Ni35	A	64	5	63.7	8.68	553	435.7	[23]
Tb55Co20Al25	A	105	5	47	7.5	375		[42]
Dy36Ho20Co20Al24	A	23	5	44	9.49	417	326	[43]
Gd55Co20Al25	A	103	5	61.5	8.8	541		[44]
Gd25Tb25Co25Al25	A	73	5	65	8.88	577		[45]
Gd6Co2Si3	C	295	5	80	6.3	503	430	[46]
Gd	C	293	5	57	9.7	556	378
			2	39	5.5	214
Gd5Ge2Si2	C	276	5	16.4	18.6	305	265	[47]
Gd5Ge1.9Si2Fe0.1	C	276	5	51.4	7	360	240

, it can also be observed that the −∆S_m^peak of the Tb₆₅Co₂₅Ni₁₀ amorphous tape is comparable to that of some other heavy RE-based amorphous alloys, and is only slightly lower than that of pure Gd metal [43,44,45,46].

The relatively wide ∆T_FWHM and large −∆S_m^peak endow the Tb₆₅Co₂₅Ni₁₀ amorphous tape with a considerable refrigeration capacity. As another crucial parameter characterizing the magnetocaloric effect, the refrigeration capacity signifies the maximum cooling power that can be achieved over the broadest temperature interval by a magnetocaloric material. Two methods are usually adopted to calculate refrigeration capacity: the Wood-Potter method (RC = −ΔS_m^peak × ΔT_FWHM) [48] and the Gschneidner method (RC = ${\int }_{T_2}^{T_1}-\Delta S_m(T)\mathrm{d}T$, where T₁ and T₂ are the onset and end temperatures of ΔT_FWHM, respectively) [49]. Based on the aforementioned two methods, we can calculate the refrigeration capacity of the Tb₆₅Co₂₅Ni₁₀ amorphous tape under different magnetic fields. For convenience, the RC obtained by the Wood-Potter method is denoted as RC¹, and that obtained by the Gschneidner method is denoted as RC². As presented in Table 1, it is evident that the RC¹ of the Tb₆₅Co₂₅Ni₁₀ amorphous tape reaches 203.1 J kg⁻¹ under 2 T, which is nearly comparable to that of pure Gd metal [41]. Under a magnetic field of 5 T, the RC¹ and RC² of the Tb₆₅Co₂₅Ni₁₀ amorphous tape are 569.5 J kg⁻¹ and 440.3 J kg⁻¹, respectively, exceeding those of pure Gd metal and most other heavy RE-based amorphous alloys listed in Table 2 [23,24,42,43,44,45]. Furthermore, the RC¹ and RC² under 5 T of the Tb₆₅Co₂₅Ni₁₀ amorphous tape are even 86.7% and 66.2% higher than those of the traditional giant MCE material Gd₅Ge₂Si₂, respectively [47]. Therefore, considering its high −ΔS_m^peak, wide ΔT_FWHM, and considerable refrigeration capacity, the Tb₆₅Co₂₅Ni₁₀ amorphous tape exhibits excellent magnetocaloric properties and holds significant potential for application as a magnetic refrigerant in the field of magnetic refrigeration.

3.4. The Magnetic Entropy Change Behavior of the Tb₆₅Co₂₅Ni₁₀ Amorphous Tape

Oesterreicher et al. investigated the field dependence of the −ΔS_m^peak in amorphous alloys based on mean-field theory and proposed a linear relationship: −∆S_m^peak∝Hⁿ, where n = 2/3 [50]. Franco et al. suggested that the value of n at T_c for soft magnetic amorphous alloys should be close to 0.75 upon analyzing a large amount of experimental data, and this linear relationship for the field dependence of −ΔS_m is also applicable at other temperatures, with n approaching 1 and 2 at temperatures well below and above T_c, respectively [51]. Thus, the consistency between the n value and the theoretical results mentioned above is one of the main criteria for determining whether the spin-glass-like behavior affects the magnetic entropy change behavior of amorphous alloys. Furthermore, similar to the field dependence of −ΔS_m^peak, Law and Franco proposed that the field dependence of RC also follows a power-law relationship: RC∝H^N [52]. For a given alloy system, the exponent N should have a relatively consistent value.

Based on the data in Table 1, we plotted the field dependences of −ΔS_m^peak and RC for the Tb₆₅Co₂₅Ni₁₀ amorphous tape, as shown in Figure 5a. By fitting these curves, the values of n and N for the Tb₆₅Co₂₅Ni₁₀ amorphous tape can be approximately determined as n ≈ 0.80, N¹ ≈ 1.19, and N² ≈ 1.18 (where N¹ and N² correspond to RC¹ and RC², respectively). The N values for the Tb₆₅Co₂₅Ni₁₀ amorphous tape in the two curves are quite similar, both of which are close to those in other Tb-, Dy- and Gd-based amorphous alloys and align well with the predicted results by Franco [22,53]. The n value at T_c of the Tb₆₅Co₂₅Ni₁₀ amorphous tape is significantly higher than 2/3 predicted by mean-field theory. This discrepancy may arise because the short-range-ordered structure in amorphous alloys prepared via the rapid quenching method impede the magnetization of the alloy. Nevertheless, the n value at T_c remains slightly greater than 0.75, which is similar to the situation of other Tb- and Dy-based amorphous alloys exhibiting spin-glass-like behavior [23,24,32,35]. The above situation can be explained by the n value of the Tb₆₅Co₂₅Ni₁₀ amorphous tape at temperatures below T_f. Figure 5b illustrates the n–T curve of the Tb₆₅Co₂₅Ni₁₀ amorphous tape from 50 K to 150 K. The n value of the Tb₆₅Co₂₅Ni₁₀ amorphous tape reaches 1.09 at 50 K, which is inconsistent with the prediction by Franco. This phenomenon should be attributed to the inhibitory effect of spin-glass-like behavior on −ΔS_m. As the magnetic field decreases, this inhibitory effect becomes more pronounced, leading to a significant reduction in −ΔS_m under low magnetic fields, which increases the slope of the linear fitting between ln(−ΔS_m) and lnH. As shown in the inset of Figure 5b, the markedly deteriorated −ΔS_m under low fields of the Tb₆₅Co₂₅Ni₁₀ amorphous tape at 40 K makes the linear relationship between ln(−ΔS_m) and lnH to no longer be satisfied. Even below 40 K, the Tb₆₅Co₂₅Ni₁₀ amorphous tape exhibits irreversible −ΔS_m, further deviating from the linear relationship. When the Tb₆₅Co₂₅Ni₁₀ amorphous tape is in a paramagnetic state far above its T_c, the spin-glass-like state of the alloy is destroyed due to the elevated temperature, causing the n value to still tend towards 2. Therefore, the spin-glass-like behavior significantly affects the magnetic entropy change behavior of the Tb₆₅Co₂₅Ni₁₀ amorphous tape at low temperatures, and this influence gradually diminishes as the temperature increases.

On the other hand, Franco et al. proposed that there is a universal behavior in the (−∆S_m)–T curves of amorphous alloys under different magnetic fields, meaning that all curves almost coincide after appropriate scaling [51,54]. The −∆S_m values at different temperatures are normalized using the following formula:

$$\Delta S^{\text{′}}\left(T,H_{\max }\right)=\Delta S_m\left(T,H_{\max }\right)/\Delta S_m^{\mathrm{peak}}\left(T,H_{\max }\right).$$

(2)

The temperature axis is divided into two parts by the critical temperature T_c, and each part is rescaled in a different way:

$$\theta =\left\{\begin{array}{c}-\left(T-T_c\right)/\left(T_1-T_c\right),T\le T_c\\ \left(T-T_c\right)/\left(T_2-T_c\right),T>T_c\end{array}\right.,$$

(3)

where T₁ and T₂ are the onset and end temperatures corresponding to ΔT_FWHM of the (−∆S_m)–T curves under different magnetic fields, respectively. Figure 6 presents the normalized (−∆S_m)–T curves of the Tb₆₅Co₂₅Ni₁₀ amorphous tape under various magnetic fields. As can be seen from the figure, all normalized (−∆S_m)–T curves exhibit similar characteristics, and the normalized curves under 1.5 T to 5 T almost completely coincide, indicating the universal behavior of the (−∆S_m)–T curves for the Tb₆₅Co₂₅Ni₁₀ amorphous tape under different magnetic fields. However, the normalized (−∆S_m)–T curve under 1 T deviates slightly from those under other magnetic fields when θ < 0, which further demonstrates that the spin-glass-like behavior in the Tb₆₅Co₂₅Ni₁₀ amorphous tape severely affects the −∆S_m below T_c. As the temperature increases, the spin-glass-like behavior disappears, and the normalized (−∆S_m)–T curve under 1 T basically coincides with those under other magnetic fields when θ > 0.

4. Conclusions

In conclusion, the GFA, magnetic properties, MCE performances and −∆S_m behavior of a ternary Tb₆₅Co₂₅Ni₁₀ amorphous tape were studied in this work. The large values of T_rg (~0.579), γ (~0.377) and Z_c (~1.882 mm) demonstrate superior GFA of the Tb₆₅Co₂₅Ni₁₀ tape compared to most Fe-based and RE-based amorphous systems, which means that the Tb₆₅Co₂₅Ni₁₀ alloy is easier to prepare into continuous tapes under the same conditions. The ZFC and FC M-T curves reveal the distinct spin-glass-like behavior of the Tb₆₅Co₂₅Ni₁₀ amorphous tape, with a T_c of 83 K and a T_f of 73 K. The amorphous tape exhibits hard magnetic characteristics, with coercivity as high as 512.2 kA/m at temperatures significantly below T_f, soft magnetic behavior at temperatures between T_c and T_f, and paramagnetic behavior at temperatures far exceeding T_c. The positive correlation between magnetization and temperature under low temperatures and low fields further confirms the presence of spin-glass-like behavior. The Arrott plots indicate that the Tb₆₅Co₂₅Ni₁₀ amorphous tape exhibits non-SOMT characteristics at low temperatures, but gradually shifts toward SOMT behavior as the temperature increases. The spin-glass-like behavior induces the irreversible magnetocaloric effect below 40 K in the Tb₆₅Co₂₅Ni₁₀ amorphous tape. However, the tape retains a rather large −∆S_m^peak of 9.46 J kg⁻¹ K⁻¹ under 5 T, which exceeds the values reported for most heavy RE-based amorphous alloys, including Tb- and Gd-based systems. Notably, the refrigeration capacity of the Tb₆₅Co₂₅Ni₁₀ amorphous tape significantly surpasses that of traditional crystalline magnetocaloric materials and pure Gd metal. The n value at T_c of the Tb₆₅Co₂₅Ni₁₀ amorphous tape exceeds the predicted values from mean-field theory and Franco, aligning with the values observed in other amorphous alloys exhibiting the same spin-glass-like behavior. This discrepancy is attributed to the dual influence of local structure and spin-glass-like behavior in the alloy. Furthermore, the inhibitory effect of spin-glass-like behavior on −∆S_m in low field and low-temperature regions results in deviations from the −∆S_m∝Hⁿ linear relationship below 50 K and the universally normalized (−∆S_m)–T curve under 1 T.