Revisiting the Structural and Magnetic Properties of SmCo₅/Sm₂Co₁₇ Interface from First-Principles Investigations

Abstract

The formation and evolution of SmCo₅/Sm₂Co₁₇ (1:5_H/2:17_R/H) cellular structures play an essential role in understanding the coercivity of Sm-Co magnets. Herein, the pristine and different elemental-doped 1:5/2:17_R and 1:5/2:17_H interfaces are investigated to evaluate the elemental site preferences, interface configurations, and magnetic properties in Sm₂Co₁₇-type magnets with general alloy elements M (M = Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Al, Si, and Ga). Comparing the calculated results of 1:5/2:17_H with those of the 1:5/2:17_R interface, we found that Cu and Mn always segregate at the 1:5 phase, and Ga elements first appear at the 1:5 phase in 1:5/2:17_H and then change to the 2:17 phase in 1:5/2:17_R. While Ti, V, Fe, Zn, Al, and Si elements always tend to segregate at the 2:17 phase, Ni first segregates at the 2:17 phase in 1:5/2:17_H and then occupies the 1:5 phase of 1:5/2:17_R. The 1:5/2:17_H interface along the c-axis expands about 1.98~3.28%, while the 1:5/2:17_R interface slightly shrinks about 0.04~0.87% after element doping. This suggests that different interface stress behaviors exist for high-temperature and room-temperature phase Sm₂Co₁₇-type magnets. Furthermore, Mn, Fe, and Ga doping improved the saturation magnetization strength. Our results provide new insights into understanding the effect of elemental doping at the interfaces of 1:5_H/2:17_R cellular structures.

1. Introduction

SmCo-based permanent magnets with a 2:17-type structure have garnered considerable attention in high-temperature magnetic applications such as aerospace, rail transportation, electronic vehicles, and microwave devices [1,2,3], as SmCo magnets have impressive characteristics, such as being a high energy product and having high intrinsic coercivity, a high Curie temperature, and superior thermal stability [4]. Various studies [4,5] have confirmed that the magnetic performance of Sm₂Co₁₇-type magnets originates from their distinctive cellular microstructures. The fully cellular microstructure comprises a Fe-rich cell interior phase (2:17_R phase, Th₂Zn₁₇ structure, R-3m), Cu-rich cell boundaries (1:5_H phase, CaCu₅ structure, P6/mmm), and a Zr-rich lamellar phase (1:3_R phase, Be₃Nb structure, R-3m), and these microstructures in the cell boundary phases contain defects, such as vacancies, extra impurity atoms, and so on [6,7].

Previous research has proposed the attractive and repulsive models to explain the coercivity mechanism of 2:17-type magnets [6], which is deemed as a pinning-controlled effect dominated by the large domain wall energy density difference between 1:5_H and 2:17_R phases. Moreover, the formation of 1:5_H/2:17_R cellular structures is a complicated process that involves both phase transformation, chemical redistribution, and a different interface microstructure [8,9]. For example, experimental work has reported that phase transformation exists for SmCo-magnets with the pathway 1:7_H + 2:17_H → 1:5_H + 2:17_R^′ + 1:3_R →1:5_H + 2:17_R + 1:3_R during the heat treatment process, and this process is controlled by a diffusion-controlled displacive mechanism. Recently, Sepehri-Amin et al. found that the SmCo₅/Sm₂Co₁₇ interface is sharp and defect-free for a slowly cooled sample which possesses a relatively high coercivity, while it is rough and zigzag-shaped for a quenched sample with low coercivity. Further study indicates that there are different dopants of Cu/Fe distribution found at the SmCo₅/Sm₂Co₁₇ interface in slowly cooled or quenched samples [10]. In addition, experimental work shows that 2:17-type Sm-Co magnets have some nanoscale interfacial defects including a retained phase at the grain edges and an intermediate rhombohedral phase at the interfaces between the cell walls and the cell interiors, which build up inhomogeneous pinning sites and finally deteriorate the coercivity [11]. Most recently, the effect of interfacial stress [12] and the nanoscale transition zone [13] have been investigated to optimize the magnetic performance of 2:17-type SmCo permanent magnets. Liu et al. observed a 1.3 nm thick nanoscale transition zone sandwiched between 2:17_R and 1:5_H phases. Based on TEM observation, they suggest the atomic ratios TM/Sm of the transition zones across the interface between 1:5_H and 2:17_R phases are within 5.0–8.5. In other words, there is a variable Sm and Fe/Cu concentration gradient in the transition zone, where partial 1a sites of Sm atoms at the 1:5_H phase interface are gradually substituted by Fe/Co dumbbell pairs. This transition zone plays a crucial role in determining the coercivity of Sm₂Co₁₇-type magnets.

Many theoretical studies investigated the effects the site preference of transition metal elements (Fe, Cu, Ti, Zr) on the magneto-crystalline anisotropy, electronic structure, and magnetic moment for bulk SmCo₅- and Sm₂Co₁₇-based alloys, respectively [14,15,16,17]. Unfortunately, the effects of the third-component impurities, which are hard to avoid during the preparation process, are lacking in Sm₂Co₁₇-type magnets to understand the atom-scaled structural stability and magnetism of cellular microstructures.

In this work, we adopt first-principles calculations to analyze the underlying site preference and atomistic configurations on the interface zone of 2:17-type SmCo magnets. We establish SmCo₅/Sm₂Co₁₇-H (1:5/2:17_H) and SmCo₅/Sm₂Co₁₇-R (1:5/2:17_R) vertical stacking interfaces with widths of around 1.79 or 1.85 nm, respectively, to simulate the transition zone of 2:17-type SmCo magnets. The site preference behaviors of 11 types of elements M (M = Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Al, Si, and Ga) in the 1:5/2:17_R and 1:5/2:17_H interfaces are investigated to access their impacts on the interfacial stabilities, elemental preferences, and magnetic properties.

2. Calculation Details

The projector augmented-wave method [18,19] based on density functional theory (DFT) is used as implemented in the Vienna ab initio package (VASP 6.3.0) [20,21] to study structural and magnetic properties. The Perdew–Burke–Ernzerhof (PBE) [22] type generalized gradient approximation (GGA) [23] and exchange–correlation functional is applied to treat the interaction of electrons. Van der Waals (vdW) correction is incorporated using the DFT-D3 method [24]. An on-site Coulomb interaction with U_Sm = 4.7 eV from the literature [25] and U_Co = 3.8 eV via testing calculations (see Tables S1 and S2 in Supplementary Materials) is chosen for this study. After energy convergence testing for surface thickness in Figure S1 in Supplementary Materials, the five layers $\sqrt{3}\times \sqrt{3}\times 1$ SmCo₅ slab, nine layers 1 × 1 × 1 Sm₂Co₁₇-R, and Sm₂Co₁₇-H slab are chosen to construct SmCo₅/Sm₂Co₁₇-R (1:5/2:17_R) and SmCo₅/Sm₂Co₁₇-H (1:5/2:17_H) interfaces (Figure 1) with a lattice mismatch of 3.5% and 5.5% along the x-axis, respectively. During the relaxation process, the five atomic layers of Sm₂Co₁₇ and three atomic layers of SmCo₅ away from the interface zone are constrained along the x and y direction to reserve the bulk’s lattices. A vacuum space of about 18 Å is applied along the z direction. More calculations details are shown in Section I of the Supplementary Materials.

3. Results

3.1. Interfacial Configurations of SmCo₅/Sm₂Co₁₇ Structure

To specify the precise configurations, four distinct interface terminations were evaluated, including Co-Co, Co-SmCo, SmCo-SmCo, and SmCo-Co, for both the SmCo₅/Sm₂Co₁₇-R and SmCo₅/Sm₂Co₁₇-H interfaces, depicted in Figures S2 and S3 in the Supplementary Materials. Taking the SmCo-Co (or Co-SmCo) termination interface as example, it refers to SmCo (Co) termination in SmCo₅ slab contacts the Co (SmCo) termination in the Sm₂Co₁₇-R (Sm₂Co₁₇-H) slabs to form an interface. The other configurations are similar. The most favorable configurations are SmCo-Co- (or Co-SmCo)-terminated interfaces by comparing the binding energies of all kinds of alternatives for SmCo₅/Sm₂Co₁₇-R (or SmCo₅/Sm₂Co₁₇-H) interfaces. Unless otherwise specified, all subsequent pristine- or doped- interfaces refer to the SmCo-Co- (or Co-SmCo)-terminated interface. More details regarding the binding energies of 1:5/2:17_H/R interfaces can be found in Section II of the Supplementary Materials.

The lattice constants for the bulk 1:5_H phase are a = 5.18 Å and c = 3.91 Å, whereas for the bulk 2:17_R phase, they are a = 8.69 Å and c = 12.38 Å (Tables S1 and S2). The lattice mismatch is 3.5% and 5.5% in the a direction of 1:5/2:17_R and 1:5/2:17_H (Figure 1), respectively, which is close to the previously reported value of approximately 3.6% [12]. In addition, our research reveals that the energy difference between SmCo-SmCo and SmCo-Co configurations of the 1:5/2:17_R interface is tiny, with 8 meV/atom, as shown in Table S3. This suggests that both SmCo-SmCo and SmCo-Co configurations are promising arrangements for the 1:5/2:17 interfacial stacking. Previous experimental work also exhibits the SmCo-SmCo stacking configuration for the 1:5_H/2:17_R interface in atomic-resolved HAADF-STEM images [12].

Based on the optimal contacts of 1:5/2:17_H/R interfaces, we systematically investigate five distinct vertical stacking configurations: namely hollow-Co, hollow-Sm, top-Co, and top-Sm stackings (Figure S4 of Supplementary Materials). Take the “hollow-Sm stacking” configuration as an example, which refers to the interface Sm atoms of SmCo₅ slab located at the hollow sites of interface Co hexagons of the Sm₂Co₁₇ slab (Figure 1a,c). The others stacking configuration are similar. It is observed that the hollow-Sm configuration has a lower energy than the hollow-Co, top-Co, and top-Sm configurations by 0.67, 0.04, and 1.08 eV, respectively. For the 1:5/2:17_H interface, the hollow-Sm stacking also exhibits the lowest energy among different stacking configurations for the 1:5/2:17_H interface (Figure S5 of Supplementary Materials). If the Sm₂Co₁₇ layer of 1:5/2:17 interface is fixed, then by shifting the SmCo₅ layer from top-Sm to hollow-Sm configurations, we can clearly find that the glide direction is equivalent to the partial dislocation with a Burgers vector of a/3 [$1\stackrel{-}{1}00$] or a/3 [$\stackrel{-}{1}100$]. Our interfacial stacking configurations further give evidence to support the findings of previous results [26,27], indicating that the basal stacking faults maybe glide along the a/3 [$1\stackrel{-}{1}00$] partial dislocations direction while transforming from the 2:17_H to 2:17_R structure. Therefore, the hollow-Sm stacking is recognized as the best stacking arrangement for both the 1:5/2:17_R and 1:5/2:17_H interfaces.

The dopants at the interface include transition metals (Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Al, and Ga) and the nonmetal element Si (Figure 1e). In addition, the entire interfacial zone (L₀) is categorized into the atomic layers (H₀) and the interfacial spacing (d₀) to discern the influence of elemental doping on individual interfacial interactions (Figure 2). The pristine interface spacing d₀ of 1:5/2:17_R and 1:5/2:17_H are 1.758 Å and 1.666 Å, as shown in Figure 1. The interface spacing of 1:5/2:17_R is about 0.092 Å larger than that of 1:5/2:17_H interface, which implies that there is an extra interfacial tensile interaction while transforming from the pure Sm₂Co₁₇-H phase to the Sm₂Co₁₇-R phase, which always occur in heat treatment process. On one hand, we do not observe obvious correlations between elemental doping and interfacial spacing d₀ for both interfaces (Figure 2). The alloy elements Fe, Cu, Zn, Si, and Ga increase the interfacial spacing, while Ti, V, Cr, Mn, Ni, and Al decrease the interfacial distance for the room-temperature 1:5/2:17_R interface. On the other hand, it is interesting that elemental doping exhibits a completely opposite impact on the interfacial zone for the 1:5/2:17_H and 1:5/2:17_R interfaces (Figure 2c,d). The interfacial zone along the c-axis in the 1:5/2:17_H interface expands by approximately 1.98% to 3.28% for all the doping structures. Apart from V and Zn, the other dopants result in a reduction in the interfacial spacing of the 1:5/2:17_H interface systems. In contrast, the impact of element doping for the 1:5/2:17_R interface is relatively moderate. It causes a minor decrease of approximately −0.04% to −0.87% along the c-axis, except for the irregular expansion of V-doped atomic layers, which increases by about 0.40%. According to the significant difference in the interface width between the 1:5/2:17_H and 1:5/2:17_R interfaces induced by elemental doping, we can see that element doping may unavoidably induce extra interfacial stress to facilitate from the 2:17_H to 2:17_R phase.

3.2. Thermodynamic Stability of Typical Elements-Doped 1:5/2:17_H/R Interfaces

We systematically investigate the formation energies of 1:5/2:17 _H/R interfaces by substituting Sm or Co sites with (Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Al, Si, and Ga) and to demonstrate their site preferences in the interface (Figure 3). Higher negative formation energies indicate the greater thermodynamic stability of the interface, and it increases the likelihood of doping elements to occupy that specific crystal site.

The 1:5/2:17_R interface (Figure 3a) shows a preference for alloy elements with a larger atomic radius (Ti, V, Fe, and Ni) to occupy the spacious Co18f site on the 2:17_R side. Conversely, Si, Zn, and Al are situated in the narrow position of the Co9d, Co18h, and Co6c site within the 2:17_R phase, owing to their small atom radii. Elements with a medium atomic radius like Cu, Cr, Mn, and Ga tend to occupy the more confined Co2c or Co3g site of the 1:5 phase. Figure S6 in the Supplementary Materials shows the local structures of different Co crystal site and intuitively displays their space size. However, Cr doping is less likely due to its higher formation energy.

It is noteworthy that the system exhibits relatively lower formation energy when doping low-melting-point elements (Zn, Al, and Ga), which indicates a high solubility. When doped with high-melting-point elements, such as Ti, V, Cr, Mn, Fe, Ni, and Cu, the higher formation energies suggest a lower solubility in the 1:5/2:17_R interface. Interestingly, nonmetal element Si doping has lower formation energy despite it having a high melting point.

For the 1:5/2:17_H interface, the distribution of alloy elements fluctuates significantly. As shown in Figure 3b, Ti, V, Zn, Cr, and Al prefer the Co12k site within the 2:17_H phase, but Cr substitution is unstable with a positive formation energy compared to the other dopants. Fe, Si, and Ga preferably reside in the Co12j site. Mn, Ni, and Cu elements are predominantly found in the Co2c site of the 1:5 phase. Obviously, the site preferences of doping elements at the high-temperature phase are unrelated to their atomic radius. Si, Ga, and Fe have tendencies to accumulate at the interface. Additionally, the substitution of Co with low-melt-point elements becomes more practical, as certain high-melt-point elements like Ti, Ni, and Cu exhibit lower formation energy. These disparities in the distribution of elements result in distinct interfacial interactions, varying local atomic coordination environments, and ultimately impact the stability of interface and its magnetic properties.

It is known that the 1:5_H phase is precipitated from the 2:17_H precursor during the heat treatment process. But recent in situ observations confirmed that the 1:5/2:17_H phase may coexist in the early stage of the heating process [28]. Thus, if the 1:5/2:17_H and 1:5/2:17_R interface are regarded as the high-temperature phase and room-temperature phase of the 2:17 type, respectively, the site preference behaviors of alloy elements in the 1:5/2:17_H and 1:5/2:17_R interface could be categorized into four distinct types (Figure 3) from high temperature to room temperature. Type I alloy elements, such as Cu and Mn, always segregate at the 1:5_H phase. Type II alloy elements, such as Ti, V, Fe, Zn, Al and Si, always segregate at the 2:17 phase. Type III alloy elements, such as Ni, tend to diffuse from 1:5_H to 2:17_R. Type IV alloy elements, such as Ga, tend to reverse diffuse from 2:17_H to 1:5_H. The results suggest that Cu, Mn, and Ga elements would benefit to generate 1:5_H precipitation, which could improve coercivity in Sm-Co magnets.

3.3. The Binding Strengths of Pristine and Doped 1:5/2:17_H/R Interfaces

To examine the influence of doping elements on interfacial binding strength, we calculate the interfacial separation work for both the SmCo₅/Sm₂Co₁₇-R and SmCo₅/Sm₂Co₁₇-H interfaces. Interfacial separation work is a crucial physical quantity that plays an essential role in determining the interface stability. This metric represents the energy per unit area required to separate an interface into two independent surfaces. The degrees of freedom related to deformation and diffusion are neglected to calculate an ideal interfacial separation work. The equation [29] for calculating interfacial separation work is as follows:

E_sep = (E_SmCo5 + E_Sm2Co17 − E_inter)/A,

where E_sep refers to the interfacial separation work; E_SmCo5, E_Sm2Co17, E_inter denote the total energies of the optimized SmCo₅ surface, Sm₂Co₁₇ surface, and SmCo₅/Sm₂Co₁₇ interface, respectively. A represents the interface area. A higher value of interfacial separation work corresponds to a more stable interface.

The results presented in Figure 4 show that the perfect 1:5/2:17_R interface has a higher interfacial separation work of 0.261 eV/Ų, compared to the 1:5/2:17_H interface with the value of 0.220 eV/Ų. It indicates that the former interface possesses stronger interfacial binding strength. In the case of doping with Cr, Mn, Ni, and Cu in the 1:5/2:17_R interface, the interface interactions are expected to be weakened, as evidenced by relatively lower interfacial separation work values of 0.249, 0.248, 0.231, and 0.255 eV/Ų, respectively. Conversely, doping with Ti, V, Fe, Zn, Al, Si, and Ga increases the interfacial separation work compared to the pristine 1:5/2:17_R interface. This behavior can be attributed to the lower electronegativity of Ti, V, Fe, Zn, Al, Si, and Ga compared to Co. The weak electron attraction abilities between these dopants and Co result in the redistribution of charges at the interface and enhancing the interface interaction that can be obviously observed from the differential charge density in Figure S7 of Supplementary Materials. However, for the high-temperature phase 1:5/2:17_H interface, most of the doped elements decrease the interfacial separation work (Figure 4). Therefore, dopant elements have a weak influence on the interface binding strength of the high-temperature phase.

3.4. Magnetic Properties of Pristine and Doped 1:5/2:17_H/R Interfaces

Figure 5 displays the magnetic moment of the interfaces 1:5/2:17_H and 1:5/2:17_R with/without dopants. Doping with Mn and Fe in the 1:5/2:17_R interface leads to an increase in the magnetic moment by 1.626 and 0.425 μ_B, respectively (Figure 5a). This is because Mn and Fe have a larger local magnetic moment compared to the Co atom (1.882 μ_B) by 0.565 and 0.585 μ_B, respectively, increasing the saturation magnetization of the Sm₂Co₁₇-type cellular structure magnet at room temperature. The addition of Ti, V, Zn, Al, and Si as dopants reduces the total magnetic moment since their local magnetic moment is antiparallel to the Co atom or belongs to nonmagnetic elements. The Ni atom has a diminished local magnetic moment (0.387 μ_B), which leads to an overall reduction in the total magnetic moment. Cu doping has a minor effect on the total magnetic moment (140.57 μ_B) although it has a minor local magnetic moment of −0.049 μ_B. Similarly, the total magnetic moment for Ga-doped interface increases by 0.3 μ_B, despite being nonmagnetic itself with a negligible magnetic moment of −0.054 μ_B. The reason is that a small quantity of nonmagnetic dopants may increase the local magnetic moment of the Co atoms next to dopants. As shown in Figure S7 in the Supplementary Materials, the differential charge density between the Ga-doped and pristine 1:5/2:17_R interfaces demonstrate that the excess electrons are induced around the neighboring Co atoms after Ga doping, resulting in the enhancement of the Ga-Co and Co-Co exchange interaction. Similarly, inducing Mn and Fe elements also strengthens the Co-Co electron exchange interaction [Figure S7 in Supplementary Materials]. Hence, Mn, Fe, and Ga can be suitable dopants for improving the saturation magnetization in Sm₂Co₁₇-type cellular structure magnet.

For the SmCo₅/Sm₂Co₁₇-H interface, Mn and Fe dopants increase total magnetic moment (1.6 and 0.1 μ_B, respectively) due to their larger local magnetic moment compared to Co. Other dopants reduce the total magnetic moment because of antiferromagnetic coupling or nonmagnetic features. Therefore, Mn and Fe doping are deemed as the suitable dopants for improving the saturation magnetization of the 1:5/2:17_H/R interface.

4. Discussion

According to the aforementioned results on interfacial stacking, site preference, and interfacial expansion induced by the addition of dopants, we can comprehensively revisit the elemental substitution of the Sm-Co interfacial structure. The interface spacing of the 1:5/2:17_R is 0.092 Å larger than that of 1:5/2:17_H interface, implying that there is extra stress induced by the phase transform from 2:17_H to 2:17_R. Moreover, the various stacking interface configurations possess a different total energy; it suggests that the interface stress originates not only from the lattice misfit between the 1:5_H and 2:17_H/R phase, but also from the atomic stacking interaction in the interface interval. The site preferences behaviors of alloy elements in the 1:5/2:17_H and 1:5/2:17_R interfaces are very different, and their influence on magnetic moment also displays an obvious change. This suggests that the dopants would play a key role in coercivity in Sm-Co magnets, which requires more research in the future. The weaker interfacial interaction of 1:5/2:17_H interfaces are more likely to serve as the diffusion pathway for crystal defects (dislocations, stacking faults, or point defects) as mentioned in previous studies [30,31,32]. Thus, the alloy elements or dopants segregate in the interfacial zone would influence defect diffusion or phase precipitation. In subsequent works, further interactions between the interfaces and defects need to be investigated experimentally to clarify the microstructures and microchemistry in order to enhance the performance of SmCo-type magnets.

5. Conclusions

In summary, we adopt first-principles calculations and thoroughly study the atomic structure, elemental site preference, interfacial binding strength, and magnetic properties of both SmCo₅/Sm₂Co₁₇-R and SmCo₅/Sm₂Co₁₇-H interfaces with and without dopants. The following conclusions are drawn:

(1)

The SmCo-Co (Co-SmCo) termination with hollow-Sm stacking is the most stable configuration for the 1:5/2:17_R (1:5/2:17_H) interface. This stacking mode easily forms the basal stacking faults gliding along the a/3 [$1\stackrel{-}{1}00$] partial dislocations direction. The 1:5/2:17_R and 1:5/2:17_H interfaces exhibit completely opposite behaviors in terms of elemental doping. The doped 1:5/2:17_H interface along the c-axis is expanded by about 1.98~3.28%, while the 1:5/2:17_R interface slightly shrinks by about −0.04~−0.87% along the c-axis. This great difference between doped 1:5/2:17_R and 1:5/2:17_H interfaces may induce the extra interfacial stress and facilitates the phase transformation from 2:17_H to 2:17_R.

(2)

The site preferences of the alloys in the 1:5/2:17_H and 1:5/2:17_R interfaces are categorized into four distinct types. The type I (Cu, Mn) and type IV (Ga) elements prefer to segregate at 1:5_H in the 1:5/2:17 interfaces. Type II (Ti, V, Fe, Zn, Al, Si) and type III (Ni) tend to segregate at the 2:17 phase in the 1:5/2:17 interfaces.

(3)

The relationship between interface distances, interfacial binding strength, and elemental doping is complex, and there is no obvious relation for different alloy-doped 1:5/2:17_H/R structures. Mn, Fe, and Ga doping are beneficial in improving the saturation magnetization strength in SmCo₅/Sm₂Co₁₇-R magnets due to improving the Co-Co exchange interaction. This work provides a new insight to uncover the effect of elemental doping on SmCo₅/Sm₂Co₁₇ cellular structures.