Effect of Er Substitution on Magnetic and Magnetocaloric Properties of Nd₆₀Ni₄₀ Metallic Glass

Abstract

In the present work, we selected an amorphous Nd₆₀Ni₄₀ alloy as a basic alloy and added Er with a higher effective magnetic moment and de Gennes factor to replace Nd for the purpose of improving the magnetocaloric performance of the Nd₆₀Ni₄₀ amorphous alloy. The formability, magnetization, and magnetocaloric behaviors of the Nd_60-xEr_xNi₄₀ (x = 5, 10, 15, 20) amorphous alloys were studied. It was found that Er substitution generally improved the glass formability, but simultaneously decreased the Curie temperature, coercivity, and magnetic entropy change peak of the basic alloy. The mechanism for these unexpected results was investigated, and it was supposed that the decreased Curie temperature and the deteriorated magnetocaloric properties may have resulted from the antiferromagnetic coupling between the Nd and Er atoms.

1. Introduction

Amorphous alloys (AAs), also known as metallic glasses (MG), are a special type of material system that is usually fabricated by rapidly cooling melted alloys to prevent the atoms from arranging into a periodic and ordered structure during solidification [1,2,3]. The unique atomic configuration of these amorphous materials, that is, long-range atomic disorder and short-range order, not only brings about mechanical advantages such as high strength and hardness, but also demonstrates excellent magnetic properties, including significant magnetocaloric effects (MCEs), outstanding magnetoelastic properties, and so on [4,5,6,7].

An MCE refers to an exothermic/endothermic phenomenon due to a change in the magnetic entropy in a magnet upon magnetization/demagnetization. The excellent MCEs in the amorphous alloys make them potential candidate materials for advanced applications in novel magnetic refrigeration solutions that are more efficient and environmentally friendly than the conventional vapor expansion/compression refrigeration technology [8,9,10,11,12,13,14,15,16]. As the key refrigerant materials, amorphous alloys show several advantages over intermetallic compounds: they present features of a second-order magnetic transition, accompanied by a broadened magnetic entropy change (−ΔS_m) peak, which is much more appropriate for working in an Ericsson cycle. In contrast, intermetallic compounds that exhibit strong magnetocaloric effects (such as Gd₅(Si,Ge)₄, La(Fe,Si)₁₃, MnFe(P,As), and so on) usually experience a first-order magnetic phase transition and show a sharp but narrow −ΔS_m, which results in a high maximum −ΔS_m (−ΔS_m^peak) but low refrigeration capacity (RC = −ΔS_m^peak × ΔT_FWHM, where ΔT_FWHM is the temperature interval at half of −ΔS_m^peak); their peak −ΔS_m temperatures, usually equal to their Curie temperatures (T_c), are tunable, because metallic glasses can be synthesized over a relatively wide range of compositions, and thus, the T_c of these amorphous alloys, depending on their composition, is tailorable. By comparison, the MCEs of intermetallic compounds undergoing a first-order magnetic phase transition are very sensitive to impurities; in other words, the Curie temperatures of these intermetallic compounds are difficult to adjust through micro-alloying or element substitution without dramatically deteriorating their magnetocaloric properties. Thus, the mechanical properties and corrosion resistance of amorphous alloys are better than those of intermetallic compounds [17,18,19].

Among these MGs, rare-earth (RE) transition metal (TM)-based MGs show great potential as high-performance magnetocaloric materials due to their high magnetic moments brought about by both the RE’s 4f electrons and the TM’s 3d electrons. For example, the −ΔS_m^peak of Gd-Co-based metallic glasses reaches 10.1 J/(kg × K) under 5 T [20], which is primarily attributed to the substantial magnetic moments of Gd due to its half-filled 4f electronic configuration. The Er₆₀Ni₃₀Co₁₀ amorphous alloy exhibits a −ΔS_m^peak of ~12.1 J/(kg × K) under 5 T [21], and the Er_67.5Co_32.5 binary metallic glass even shows a high −ΔS_m^peak of up to 17.47 J/(kg × K) under 5 T [22], both of which are closely related to the high effective magnetic moment of Er (9.58 μ_B). According to the multicomponent rule of metallic glasses, micro-alloying or element substitution may be advantageous for enhancing the glass-forming ability (GFA) of the mother alloys, which makes it easier for them to be fabricated into amorphous refrigerants, and, in addition, may further enhance the MCEs if the proper RE elements are added.

According to our preliminary results, Nd-Ni binary AAs show good GFA and good magnetocaloric performance at low temperatures [23]. In the present work, we considered introducing other earth elements with larger magnetic moments to replace the Nd element for the purpose of improving the GFA and MCE of the Nd-Ni binary MGs. A Nd₆₀Ni₄₀ binary MG, with good GFA and magnetocaloric properties, was selected as the basic alloy. Er, with a much higher effective magnetic moment than Nd (3.62 μ_B) and a higher de Gennes factor (G = 2.55 for Er and 1.84 for Nd) [24], was selected as the substitution element. The influences of Er-doping on the GFA, Curie temperature, −ΔS_m^peak, and RC of the Nd₆₀Ni₄₀ MG, and their mechanisms, were investigated.

2. Experimental Methods

Using a high-vacuum furnace under high-purity Ar protection, pure Nd, Er, and Ni metals (purity > 99.9 at%)—mixed simultaneously, pursuant to their respective parts in the composition of Nd_60-xEr_xNi₄₀ (x = 5, 10, 15, 20)—were arc-melted five times to prepare master alloy ingots. The broken pieces of the master alloy ingots were remelted and subsequently sprayed from a hole at the bottom of the quartz tube onto a high-speed rotating copper roller to prepare thin ribbons. Nd_60-xEr_xNi₄₀ ribbons with an average thickness of 40 ± 0.5 μm were chosen for the follow-up investigation. XRD analysis using Cu Kα radiation was performed on the Nd_60-xEr_xNi₄₀ ribbons to ascertain their amorphous structure. A scanning rate of 20 K/min was applied to obtain measurements of their differential scanning calorimetry (DSC) traces on a NETZSCH 404C calorimeter from Germany. The magnetization (M)-temperature (T) curves, the magnetization curves under isothermal conditions (M-H curve), and the hysteresis loops of the MG ribbons were determined by a vibrating sample magnetometer (VSM) module equipped on a Quantum Design 6000 Physical Property Measurement System (PPMS) from Quantum Design, a company based in the United States.

3. Results and Discussion

It was found that none of the Nd_60-xEr_xNi₄₀ (x = 5, 10, 15, 20) ribbons exhibited obvious sharp crystalline diffraction peaks according to their XRD patterns, as is displayed in Figure 1. Instead, all the samples exhibited smooth diffraction peaks between 30° and 40°, indicating the typical amorphous features of Nd_60-xEr_xNi₄₀ as-spun ribbons. The amorphous characteristics of the Nd_60-xEr_xNi₄₀ ribbons were also illustrated by an endothermic glass transition event and sharp exothermic crystallization reaction, as is clearly observed in their respective DSC plots, as shown in Figure 2: (a) x = 5, (b) x = 10, (c) x = 15, and (d) x = 20. The onset temperatures for the glass transition (T_g) and crystallization (T_x) of the MG ribbons, as determined by a tangent method, are summarized in

Table 1. T_g, T_x, T_l, T_rg, and γ of the Nd_60-xEr_xNi₄₀ MG ribbons.

Composition	Tg (K)	Tx (K)	Tl (K)	Trg (K)	γ
Nd55Er5Ni40	427	474	873	0.489	0.364
Nd50Er10Ni40	439	482	884	0.497	0.365
Nd45Er15Ni40	421	485	888	0.474	0.370
Nd40Er20Ni40	433	500	903	0.480	0.374

. The liquidus temperatures (T_l) for the Nd_60-xEr_xNi₄₀ MG ribbons obtained from the melting curves, as displayed in the inset of Figure 2a–d, are also enumerated in Table 1. Consequently, T_rg, defined by D. Turnbull [25], and parameter γ, defined by C. T. Liu and Z. P. Lu [26,27], can be calculated according to

$$T_{rg}={\displaystyle \frac{T_g}{T_l}}$$

(1)

$$\gamma ={\displaystyle \frac{T_x}{T_g+T_l}}$$

(2)

Figure 3 illustrates the variation in T_rg and γ in the Nd_60-xEr_xNi₄₀ MG ribbons according to their composition. According to the T_rg values of the samples, the GFA was enhanced by Er substitution from 5% to 10% and then decreased with any further addition of Er. However, the γ parameter increased monotonously with the addition of Er, indicating the increasing substitution of GFA by Er.

The M-T curves of the Nd_60-xEr_xNi₄₀ MG ribbons were obtained from 5 K to 100 K under an applied magnetic field of 0.03 T, after cooling from ambient temperature to 5 K without a magnetic field (zero field cooling, ZFC), and under a magnetic field of 0.03 T (field cooling, FC). As shown in Figure 4, all the MG ribbons show typical λ-shape characteristics in their field-cooled and zero-field-cooled M-T curves, indicating the significant spin-glass-like (SGL) behaviors of these MG ribbons. The Curie temperature and the spin-glass-like freezing temperature (T_f) of the Nd_60-xEr_xNi₄₀ (x = 5, 10, 15, 20) MG ribbons, acquired from their ZFC M-T curves, are listed in

Table 2. T_c, T_f, −ΔS_m^peak and RC of the Nd_60-xEr_xNi₄₀ MG ribbons.

Composition	Tc (K)	Tf (K)	−ΔSmpeak (J/(kg × K))					RC (5T) (J/kg)
			1T	2T	3T	4T	5T
Nd60Ni40	18.3	12.1	2.10	3.89	5.4	6.71	7.86	172
Nd55Er5Ni40	16.6	11.2	1.45	2.77	3.94	5.02	6.08	122
Nd50Er10Ni40	15.2	11.4	1.02	2.06	3.17	4.31	5.45	114
Nd45Er15Ni40	13.6	11.6	0.59	1.44	2.45	3.55	4.72	109
Nd40Er20Ni40	12.8	11.4	0.36	1.12	2.13	2.92	4.45	108

. The compositional dependence of T_c as well as T_f, as illustrated in Figure 5, indicates that the T_c of the ribbons decreased linearly with the ascending Er content, while the T_f of the Nd_60-xEr_xNi₄₀ ribbons decreased from x = 5 to x = 10 and then increased with any further addition of Er. The relationship between T_c and Er content was anomalous, because for Nd_60-xEr_xNi₄₀ MG ribbons with a constant Ni content, T_c maintains a positive proportion relative to the de Gennes factor (G) [28] of the ribbons, which can be calculated in a double RE ions system as follows:

$$G=c_1{G}_1+c_2{G}_2$$

(3)

Where c_n and G_n are the molar fraction and de Gennes factor of the respective RE ion. As is known, G equals 2.55 for Er and 1.84 for Nd, and thus the increasing substitution of Er for Nd should result in an increasing G in the MGs and give rise to an enhancement of T_c according to Er content, which is obviously the opposite of the experimental results. Considering that the coupling between light RE elements, such as Nd and Ni, is ferromagnetic, while the coupling between heavy RE elements, such as Er and Ni, is antiferromagnetic, the coupling between Nd and Er is most likely antiferromagnetic, according to the Ruderman–Kittel–Kasuya–Yosida (RKKY) indirect exchange model. In the RKKY model, the magnetic moments of localized 4f electrons in RE ions are coupled indirectly through the polarization of conduction electrons (primarily 5d and 6s states) [29,30,31]. The sign and strength of this exchange depend on the interatomic distances, the Fermi surface topology, and the de Gennes factor G. The de Gennes factor G may be calculated as follows:

$$G={\left(g_J-1\right)}^{2}J\left(J+1\right)$$

(4)

where g_J is the Landé g-factor, and J is the total angular momentum quantum number. For light rare-earth elements like Nd (g_J ≈ 0.727, (g_J − 1) < 0), the coupling with transition metals (e.g., Ni 3d states) is typically ferromagnetic, leading to a parallel alignment of moments. In contrast, heavy rare-earth elements like Er (g_J ≈ 1.2, (g_J − 1) > 0) exhibit antiferromagnetic coupling with TM moments, resulting in antiparallel alignment. When light and heavy rare-earth elements are mixed, the inter-RE exchange often introduces a competitive antiferromagnetic component arising from the opposing signs of (g_J − 1) and the resulting frustration in the RKKY-mediated interactions [32,33,34]. This competition disrupts the overall ferromagnetic ordering, effectively reducing the net exchange field and leading to a lower T_c. Furthermore, the antiferromagnetic Nd-Er coupling weakens the total magnetic moment per RE atom, manifesting as reduced magnetization in the M-H curves and diminished magnetic susceptibility. Consequently, the magnetocaloric effect deteriorates, with −ΔS_m^peak and RC decreasing due to a lower degree of magnetic entropy change associated with the frustrated spin ordering and enhanced spin-glass-like behavior.

To ascertain the above assumptions, the overall system energy of the amorphous Nd₅₅Er₅Ni₄₀ alloy was calculated based on a first-principles simulation and compared under two initial configurations: the Nd’s magnetic moments being parallel to Er’s, and the Nd’s magnetic moments being anti-parallel to the Er’s. The Nd₅₅Er₅Ni₄₀ amorphous structure was first constructed using the stochastic quenching (SQ) method [35,36,37]. This method commences with an initial structure of 100 atoms distributed in a random way in a cubic cell under a periodic boundary, and is rooted in the single random valley approximation of vibrational transitions (VT) theory. First-principles calculations were performed using the Vienna Ab initio Simulation Package (VASP) [38]. This approach relies on density functional theory (DFT), and the implementation of the projected augmented wave (PAW) pseudopotential [39]. As expected, the simulation results show that the overall energy of the system where the Nd’s magnetic moment is antiparallel to the Er’s magnetic moment is ~1 meV lower than that of the one where the Nd’s magnetic moment is parallel to the Er’s magnetic moment, indicating that the atomic magnetic moments between Nd and Er have a stronger propensity to form antiferromagnetic structures. By linearly fitting the T_c plots of the Nd_60-xEr_xNi₄₀ (x = 0, 5, 10, 15, 20) MG ribbons, the Curie temperature of the samples follows a T_c = 18.1 − 0.28x relationship. The negative slope (-0.28) of the T_c-x relationship may arise from the antiferromagnetic configuration of the atomic magnetic moments between Nd and Er. Supposing that the introduction of Er atoms brings about a negative G value, the total G values of the Nd_60-xEr_xNi₄₀ MGs will decrease with the addition of Er, which may lead to a decrease in Curie temperature in the MG samples with increasing Er content, and thus, a negative slope of the T_c-x relationship.

The magnetization behaviors of the Nd_60-xEr_xNi₄₀ MG ribbons are further affected by the SGL phenomena and the competition between ferromagnetic and antiferromagnetic interactions. The isothermal M-H curves of the Nd_60-xEr_xNi₄₀ ribbons at various temperatures are shown in Figure 6. The M-H curves of the Nd_60-xEr_xNi₄₀ ribbons clearly exhibit characteristics that are typical of SGL behaviors at temperatures lower than their T_f, and the magnetic susceptibility of the MG samples gradually decreases with increasing Er content. To illustrate the SGL behaviors in a more detailed way, the Arrott plots of the amorphous Nd_60-xEr_xNi₄₀ ribbons were constructed, as shown in Figure 7a for x = 5, (b) for x = 10, (c) for x = 15, and (d) for x = 20. All the samples show C-shaped Arrott plots with negative slopes below T_f, as shown in the insets of Figure 7a–d, which are the typical SGL characteristics in amorphous samples. On the other hand, the introduction of antiferromagnetic Er atoms may bring about a delay in the magnetic response, resulting in a gradual decrease in magnetic susceptibility with increasing Er content in the Er-doped Nd₆₀Ni₄₀ MGs.

The effect of SGL behaviors and the competition between ferromagnetic and antiferromagnetic interactions on the magnetization behaviors of the MG samples may also influence their magnetocaloric performance. Figure 8 shows the magnetic entropy change ((−ΔS_m)-T) curves of the Nd_60-xEr_xNi₄₀ MG ribbons under applied fields of 1 T, 2 T, 3 T, 4 T, and 5 T. The −ΔS_m^peak of the Nd_60-xEr_xNi₄₀ MG under various magnetic fields and its RC under 5 T are summarized in Table 2. −ΔS_m^peak under 5 T decreases gradually from 7.86 J/(kg × K) when x = 0, to 6.08 J/(kg × K) when x = 5, 5.45 J/(kg × K) when x = 10, 4.72 J/(kg × K) when x = 15, and 4.45 J/(kg × K) when x = 20. The RC of the Nd_60-xEr_xNi₄₀ MG ribbons under 5 T also decreases from 172 J/kg (x = 0), to 122 J/kg (x = 5), 114 J/kg (x = 10), 109 J/kg (x = 15), and finally 108 J/kg (x = 20). This suggests that the introduction of Er atoms gives rise to antiferromagnetic coupling in the alloy, subsequently reduces the total magnetic ordering degree, and finally, deteriorates the magnetocaloric properties of the Nd_60-xEr_xNi₄₀ MGs. As a result, the enhancement of the MCE of RE-TM-based amorphous alloys not only depends on using RE elements with high magnetic moments, but also on the magnetic coupling between RE elements.

4. Conclusions

In the present work, we replaced Nd atoms with Er atoms with a higher effective magnetic moment and de Gennes factor, with the hope of improving the GFA and magnetocaloric properties of a Nd₆₀Ni₄₀ amorphous alloy. Amorphous Nd_60-xEr_xNi₄₀ ribbons were successfully fabricated, and their amorphous structure was ascertained by XRD detection. Based on the thermal properties of the Nd_60-xEr_xNi₄₀ MG ribbons, as measured by DSC, the GFA of these alloys was studied. It was found that the γ parameter increased monotonously with the addition of Er, while T_rg v was enhanced by Er substitution from 5% to 10% and then decreased with any further addition of Er, indicating that the Er substitution generally increases the GFA of Nd₆₀Ni₄₀ MG. The Nd_60-xEr_xNi₄₀ MG ribbons show typical SGL behaviors in their M-T curves, and their T_c, as well as T_f, decrease gradually with the addition of Er, although the de Gennes factor of Er is higher than that of Nd. It is supposed that the antiferromagnetic structure of the atomic magnetic moment between Nd and Er brings about a negative G value in Er, resulting in a decrease in total G values in the Nd_60-xEr_xNi₄₀ MGs with the addition of Er, and finally leads to a decrease in Curie temperature with increasing Er content. On the other hand, Er substitution with a higher effective magnetic moment not only failed to improve the magnetocaloric performance of Nd₆₀Ni₄₀ MG, but actually reduced the −ΔS_m^peak and RC of the alloys. It was argued that the introduction of Er atoms gives rise to antiferromagnetic coupling in the alloy, subsequently reducing the total magnetic ordering degree, and finally deteriorating the magnetocaloric properties of the Nd_60-xEr_xNi₄₀ MGs. Therefore, the enhancement of the MCE of the RE-TM-based amorphous alloy depends not only on the high magnetic moments of the substituted RE elements but also on the magnetic coupling between the RE elements.