The understanding of a coercivity mechanism in high performance Nd–Fe–B permanent magnets relies on the analysis of magnetic properties of all phases present in magnets. By adding Cu in such compounds, a new Nd6Fe13Cu grain boundary phase is formed; however, the magnetic properties of this phase and its role in the magnetic decoupling of matrix Nd2Fe14B grains are still insufficiently studied. In this work, we have grown Nd6Fe13Cu single crystals by the reactive flux method and studied their magnetic properties in detail. It is observed that below the Néel temperature (TN = 410 K), Nd6Fe13Cu is antiferromagnetic in zero magnetic field; whereas when a magnetic field is applied along the a-axis, a spin-flop transition occurs at approximately 6 T, indicating a strong competition between antiferromagnetic and ferromagnetic interactions in two Nd layers below and above the Cu layers. Our atomistic spin dynamics simulation confirms that an increase in the temperature and/or magnetic field can significantly change the antiferromagnetic coupling between the two Nd layers below and above the Cu layers, which, in turn, is the reason for the observed spin-flop transition. These results suggest that the role of an antiferromagnetic Nd6Fe13Cu grain boundary phase in the coercivity enhancement of Nd–Fe–B–Cu magnets is more complex than previously thought, mainly due to the competition between its antiferro- and ferromagnetic exchange interactions.

Modern Nd–Fe–B-based permanent magnets are one of the most powerful hard magnetic materials that dominate today's market.1–3 The microstructure of a high-performance Nd–Fe–B magnet should consist of micro- or nanometer-sized Nd2Fe14B hard magnetic grains, isolated (i.e., magnetically decoupled) by a paramagnetic Nd-rich grain boundary phase,4–7 regardless of the synthesis techniques. Nevertheless, it is known that besides such a “classical” microstructure, Nd–Fe–B-based magnets can contain additional magnetic phases located either inside the 2:14:1 grains8 or as grain boundary phases,9,10 and the coercivity of such magnets remains at a high level.

It is known that a small amount of Cu or Ga improves the wettability of a grain boundary rare-earth rich phase in the Nd–Fe–B-based permanent magnets, showing a pronounced effect on increasing the coercivity.11–13 At the same time, a new grain boundary phase Nd6Fe13Cu (or Nd6Fe13Ga) is present.14,15 However, the exact magnetic state of this grain boundary phase (paramagnetic, ferromagnetic, or antiferromagnetic) and its role in the formation of a high coercive state are still under discussion.16–18 This situation is mostly related to the lack of information in the literature on the intrinsic magnetic properties of the 6:13:1 phase.

The system RE6Fe13−xTMx (RE = Nd, Pr, and Sm; TM = Cu, Ag, Au, Si, Ge, Al, Sn, and Ga) was investigated by many groups in the past few years.19–23 Still, there is a strong debate on the magnetic order of the 6-13-1 phase. Kajitani et al., de Groot et al., and Goll et al. reported the compound to be antiferromagnetic;10,21,24 whereas Hu et al. and Yan et al. stated that it has to be ferrimagnetic,19,20 and Weitzer et al. reported it to be ferromagnetic.22 Although the magnetic order is discussed for various compositions, the Nd6Fe13Cu (or Pr6Fe13Cu) phase is the most interesting for permanent magnet applications; nevertheless, the information about the magnetic properties of this compound is sometimes controversial. Knoch et al. studied Nd6Fe13Cu polycrystalline powder and reported it with a ferrimagnetic spin structure. Furthermore, it was reported that there was a spin reorientation transition upon cooling at around 4.2 K from ferri- to ferromagnetic order.23 Hautot et al. investigated the Nd6Fe13Cu compound and reported it as antiferromagnetic order with the Néel temperature (TN) at 408 K,25 whereas for the same composition, Kajitani et al. reported TN = 420 K,21 Knoch et al. claimed that TC = 463 K,23 and Weitzer et al. showed TC = 430 K.22 Such discrepancies can be explained by the fact that the magnetic measurements in the literature were done on polycrystalline samples, containing a small amount of the Nd2Fe17 phase with TC = 327 K.26 

From theory, first-principle calculations show that the hypothetical binary Nd6Fe14 compound has a ferromagnetic ordering (FM), while the substitution of Ga for Fe atoms in Nd6Fe13−xGaX makes the antiferromagnetic (AFM) state stable due to the anti-parallel coupling between the neighboring Nd–Fe blocks separated by Ga atoms.27 This AFM–FM competition leads to a metamagnetic transition occurring at low temperatures in the Nd6Fe13−xTMX compounds with TM = Ga,28 Al,27 Au,29 Sn,30 and Pd,31 where a relatively high external magnetic field can change the magnetic ordering from the AFM to FM states. The presence of a metamagnetic transition has also been reported for the Nd6Fe13Cu phase, but the critical field of such a metamagnetic transition varies from 1.5 (Ref. 23) to 10 T,24 and sometimes the abrupt change in magnetization was interpreted as a spin reorientation transition caused by temperature dependencies of anisotropy constants of Nd-ions.32 It is known that the critical field of metamagnetic transition strongly depends on the orientation of the crystals with respect to the external magnetic fields; however, none of these works have studied the magnetic properties in Nd6Fe13−xTMX single crystals, which is necessary for unambiguous determination of the intrinsic magnetic properties (Table I).

TABLE I.

Summary of magnetic properties of Nd6Fe13Cu single crystals.

M(14 T) at 300 K (Am2/kg) M(14 T) at 10 K (Am2/kg) TN (K)
a-axis  45.11  68.47  410 
c-axis  41.39  34.40  410 
M(14 T) at 300 K (Am2/kg) M(14 T) at 10 K (Am2/kg) TN (K)
a-axis  45.11  68.47  410 
c-axis  41.39  34.40  410 

In this study, to precisely investigate the intrinsic magnetic properties of Nd6Fe13Cu, we grow single crystals of 1 × 1 × 0.1 mm3 in size and measure the magnetic properties along different crystallographic directions in a wide range of external magnetic fields and temperatures. It is shown that Nd6Fe13Cu has an AFM structure with a Néel temperature of 410 K, which is further confirmed by our atomistic spin dynamics (ASD) simulation predicting an antiferromagnetic ground state with a Néel temperature of around 440 K. At temperatures below 150 K, an external magnetic field of 6–7 T applied along the a-axis induces a spin-flop transition, indicating a strong competition between the antiferro- and ferromagnetic exchange interactions between the Nd and Fe sublattices. Our experimental results are supported by the atomistic spin dynamics simulation showing that the increasing temperature and/or magnetic field provide extra driving forces to compete with the antiferromagnetic exchange couplings between the two Nd layers below and above the Cu layers, which, in turn, is the reason for the observed spin-flop transition. Moreover, the competing behavior in the exchange couplings can be well interpreted according to the calculated exchange coupling parameters based on density functional theory (DFT).

The reactive flux technique was applied to grow Nd6Fe13Cu single crystals.33,34 The Nd6Fe13Cu phase crystallizes in the peritectic reaction Liq. + Nd2Fe17 Nd6Fe13Cu at ∼900 K and turned out to be stable below this temperature. According to the ternary phase diagram, we designed the optimal composition Nd73Fe9Cu18 and prepared the master bulk alloy by induction melting under an argon atmosphere. The obtained ingot was broken into pieces, placed in a ZrO2 crucible and sealed in quartz ampule under vacuum. The heat treatment consisted of dwelling the sample at 600 °C for 1 h, then a slow cooling (15 K/h) to 570 °C, then further cooling with 0.5 K/h to 500 °C with subsequent quenching in water. In order to check the stability of the Nd6Fe13Cu phase at temperatures used for the heat treatment of the Nd–Fe–B magnets, several single crystals were selected, wrapped in tantalum foil, sealed in the quartz tube, and then annealed by heating up from room temperature to 600 °C (300 K/h), dwelled at this temperature for 1 h and cooling with furnace to room temperature.9,10

To analyze the microstructure, phase analysis was performed using a Tescan VEGA 3 scanning electron microscope (SEM) with a backscattered electron (BSE) detector. In addition, energy dispersive x-ray spectroscopy (EDX) was performed to quantify the local composition. The quality of the grown crystals was checked with a backscattering Laue diffractometer. Suitable crystals were oriented for measurements of the intrinsic magnetic properties. Temperature and field dependencies of magnetization were performed using a PPMS-VSM (Quantum Design PPMS-14) and magnetic property measurement system (Quantum Design MPMS).

To understand the spin texture evolution with respect to the temperature, as well as with respect to external magnetic fields, we performed atomistic spin dynamics (ASD) simulations using the Uppsala Atomistic Spin Dynamics (UppASD) software,35 implemented based on the Landau–Lifshitz–Gilbert (LLG) equation. As inputs for the ASD simulations, the exchange coupling parameters Jij were calculated using the post-processing code “jx”36 provided by OpenMX37 after an LDA + U self-consistent calculation.38 In the self-consistent calculation, the energy cutoff and energy convergence criteria were set to 400 Ry and 1.0 × 10–8 Hartree, respectively. 6 × 6 × 6 and 8 × 8 × 8 k-meshes were adopted for self-consistent and Jij calculations, respectively.

Figure 1(a) shows the BSE image of the Nd73Fe9Cu18 alloy after the single crystal growth. The ingot contains three different phases: oblong grains of desired Nd6Fe13Cu (dark), which were extracted by short time etching in water solution of citric and acetic acid (2%–4%). Other phases, which are shown in Fig. 1(a), are the square-like NdCu phase (gray) and the Nd-rich phase (light, the composition of the area marked in square is eutectic Nd84.5Fe3.6Cu11.9). Figure 1(b) shows the BSE image of an extracted single crystal of the Nd6Fe13Cu phase. It can be seen that the Nd6Fe13Cu crystal has a layered structure, but the mechanical stability of the crystal is good. The backscattered Laue diffraction was performed to ensure the quality of the crystal and to determine the orientation of the principal crystallographic direction. Figure 1(c) shows a diffraction pattern obtained from a flat surface of the crystal (out-of-plane), showing that this orientation is (001).

FIG. 1.

(a) BSE image of the ingot after single crystal growing, (b) extracted single crystal of the Nd6Fe13Cu phase, and (c) Laue x-ray back-scattered diffraction of the Nd6Fe13Cu single crystal.

FIG. 1.

(a) BSE image of the ingot after single crystal growing, (b) extracted single crystal of the Nd6Fe13Cu phase, and (c) Laue x-ray back-scattered diffraction of the Nd6Fe13Cu single crystal.

Close modal

The magnetic properties of the Nd6Fe13Cu single crystal were measured in two different directions: in-plane (along the a-axis) and out-of-plane (along the c-axis). Figure 2(a) shows the temperature dependencies of magnetization measured along the a direction in magnetic fields 1, 3, 5, and 7 T. A kink around 410 K corresponds to the Néel temperature TN. Similar results were also shown in the work of Isnard, where instead of Cu, Si was used to stabilize the 6:13:1 phase.39 In our case, in the temperature range below the TN, the M(T) curves of the Nd6Fe13Cu single crystal demonstrate a non-typical behavior for the “pure” antiferromagnetic phase: instead of a continuous decrease in the magnetization with the temperature, the magnetic moment of the sample first rises under cooling, indicating that an inter-sublattice antiferromagnetic exchange interaction weakens with decreasing temperature. The M(T) curves show a well-defined second kink at temperatures below 200 K, which gradually shifts toward low temperatures in a high magnetic field. (A dotted line is added to the figure to show the evolution of this transition with the magnetic field.)

FIG. 2.

(a) a-axis (in-plane) and (b) c-axis (out-of-plane) M(T) curves measured under different external fields (1, 3, 5, and 7 T); and (c) a-axis (in-plane) and (d) c-axis (out-of-plane) M(H) curves. The insets in (c) and (d) show M(H) curves measured on additionally annealed single crystal.

FIG. 2.

(a) a-axis (in-plane) and (b) c-axis (out-of-plane) M(T) curves measured under different external fields (1, 3, 5, and 7 T); and (c) a-axis (in-plane) and (d) c-axis (out-of-plane) M(H) curves. The insets in (c) and (d) show M(H) curves measured on additionally annealed single crystal.

Close modal

Figure 2(b) shows the M(T) curves measured along the c-axis of the crystal in magnetic fields of 1, 3, 5, and 7 T. It can be seen that at low temperatures, the M(T) curves measured in the a-axis (in-plane) differ greatly from the c-axis (out-of-plane) M(T) dependencies, showing that the magnetic properties of Nd6Fe13Cu are highly anisotropic below TN. The low-temperature kink in the M(T) curves measured along the a-axis is still visible, but it is not as pronounced as in the case of a magnetic field applied along the c-axis.

The field dependencies of magnetization M(H) measured in a magnetic field up to 14 T at various temperatures are shown in Fig. 2(c) (the magnetic field is along the c-direction) and in Fig. 2(d) (H is parallel to the crystallographic axis a). It can be seen that when the magnetic field is applied along the c-direction, at temperatures below 250 K, a field-induced spin-flop transition occurs, and the jump in magnetization becomes more noticeable at temperatures below 150 K. At 10 K, the spin-flop transition is accompanied by magnetic hysteresis, which indicates the first-order nature of the transition. In contrast, when the magnetic field is applied along the a-axis, there is no spin-flop transition in the magnetic field up to 14 T, and the magnetization gradually increases with the field, demonstrating a typical magnetization behavior of an antiferromagnetic material. Thus, we can suppose that the antiferromagnetic exchange interactions depend strongly on the crystallographic orientation, and the magnetic anisotropy of Nd ions seems to play an important role in the formation of the antiferromagnetic structure.

Obviously, the magnetic state of the Nd6Fe13Cu phase in the field up to 6 T is always antiferromagnetic, and there is no experimental evidence for ferrimagnetic or canted magnetic structures in the low fields. At the same time, in the work of Knoch et al.23 it was shown that the magnetic order is ferromagnetic at around 4.2 K for this compound. To understand this apparent contradiction with our results, we performed an additional low-temperature annealing (600 °C) of our single crystal to study how such heat treatment can affect the magnetic state of the Nd6Fe13Cu phase. The insets in Figs. 2(c) and 2(d) show the M(H) dependencies measured on additionally annealed single crystals. Certainly, such annealing slightly changes the magnetic properties of the Nd6Fe13Cu single crystals, and a scanty “ferromagnetic”-like kink appears at the low field part of the M(H) curves measured at 50 and 10 K. This can be ascribed to the appearance of the local areas in the sample where antiferromagnetic order is not fully compensated and the large angle canted magnetic structure with the non-zero net magnetic moment is presented in the single crystal. All of this indicates that the Nd6Fe13Cu phase is not very stable at temperatures around 600 °C, and this fact must be taken into account when considering the coercivity mechanism of Nd–Fe–B magnets containing the 6:13:1 phase.

ASD simulations are then performed to better understand the magnetic transition below TN under the external magnetic field along the a-axis (in-plane) magnetization direction. First, the TN is evaluated to be around 440 K based on the obtained magnetic susceptibility variation with temperature under no external magnetic field according to the ASD simulation results, which agrees rather well with the experiments (TN = 410 K). Next, we employ ASD simulations under external magnetic fields of 1, 7, and 14 T, respectively, to gain insight into the in-plane magnetic transitions below TN as illustrated in Fig. 2.

In the ASD simulations, we assume easy-plane anisotropy as demonstrated by the experiments. The calculated exchange coupling parameters and the predicted ground-state spin configuration are displayed in Figs. 3(a) and 3(c), respectively. As can be seen from Fig. 3(c), the Nd–Fe interface in the unit cell of Nd6Fe13Cu always prefers an AFM coupling (dashed arrows) between the spin moments, as suggested by the strongly negative Jij values for the first few nearest neighbors of Nd and Fe atoms [see Fig. 3(a)]. In addition, the two Nd layers below and above the Cu layers also prefer an AFM spin configuration, which can be attributed to the negative Jijs between the Nd–Nd atom pairs. Note that the ASD simulations do not account for the orbital moments. According to Hund's rule and the self-interaction-corrected relativistic DFT calculations,40 the orbital moments of Nd atoms are antiparallel to their spin moments, and the magnitude of the orbital moments is larger than that of the spin moments. Taking the orbital moments into consideration, the directions of the total magnetic moments corresponding to each atomic layer are illustrated using the solid arrows in Fig. 3(c).

FIG. 3.

(a) Exchange coupling parameters Jij as a function of atomic distance Rij in Nd6Fe13Cu. The Jijs between the dominating atom pairs of Nd1(16l)-Fe, Nd2(8f)-Fe, Nd1(16l)-Nd, and Nd2(8f)-Nd are demonstrated. 16l and 8f are the Wyckoff positions of Nd having coordinates of (0.164, 0.336, 0313) and (0.0, 0.0, 0.108), respectively. (b) Evolution of averaged spin moments with respect to temperature under external out-of-plane/in-plane magnetic fields of 1, 7, and 14 T. (c) Predicted ground state spin configuration (denoted by dashed arrows) and ground state magnetic configuration (denoted by solid arrows) if orbital moments are included.

FIG. 3.

(a) Exchange coupling parameters Jij as a function of atomic distance Rij in Nd6Fe13Cu. The Jijs between the dominating atom pairs of Nd1(16l)-Fe, Nd2(8f)-Fe, Nd1(16l)-Nd, and Nd2(8f)-Nd are demonstrated. 16l and 8f are the Wyckoff positions of Nd having coordinates of (0.164, 0.336, 0313) and (0.0, 0.0, 0.108), respectively. (b) Evolution of averaged spin moments with respect to temperature under external out-of-plane/in-plane magnetic fields of 1, 7, and 14 T. (c) Predicted ground state spin configuration (denoted by dashed arrows) and ground state magnetic configuration (denoted by solid arrows) if orbital moments are included.

Close modal

More importantly, according to the simulated spin moment curves under various temperatures with the magnetic fields aligned along the in-plane and out-of-plane directions [see Fig. 3(b)], it is observed that there is a spin-flip transition as indicated by an abrupt increase in the spin moments when the external magnetic field is along the in-plane direction. A careful examination is then adopted in order to figure out the origin of such a spin flip. By plotting out the distributions of the in-plane spin moments at different temperatures and external magnetic fields, we find that with the facilitation of the external magnetic field, at T = 360 K and M i n plane = 7 T, the Nd spin moments, which previously aligned along the direction of the external magnetic fields [atomic layers marked by red dashed arrows in Fig. 3(c)], show an apparent tendency to point toward the opposite direction [see Fig. 4(b)]. A similar transition happens at a lower temperature (∼300 K) with a larger external magnetic field [14 T, see Fig. 4(c)]. This phenomenon can be understood from the energy point of view. The increasing temperature and magnetic field provide an extra driving force to be competitive with the antiferromagnetic exchange couplings between the two Nd layers below and above the Cu layers.

FIG. 4.

Evolution of the distribution, ns of Nd spin moments along the in-plane (a-axis) direction with temperature at an external magnetic field equal to (a) 0, (b) 7, and (c) 14 T.

FIG. 4.

Evolution of the distribution, ns of Nd spin moments along the in-plane (a-axis) direction with temperature at an external magnetic field equal to (a) 0, (b) 7, and (c) 14 T.

Close modal

It is noted that it is challenging for the ASD simulations to reproduce the exact experimental measurements. For instance, with a magnetic field of 7 T at 10 K (see Fig. 2), the spin-flip already occurs, while under the same magnetic field, the ASD simulation captures such a process at a temperature slightly higher than 340 K. Such discrepancy can be due to the following reasons. First, our ASD simulations utilize a spin Hamiltonian and accordingly predict spin moment evolution as a function of temperature and external magnetic fields, meaning that the contribution from the orbital moments is not explicitly incorporated.41 Second, in this work, we assume an in-plane magnetic anisotropy constant favoring magnetization along the y direction of −0.05 mRy for both Fe and Nd elements. We have to admit that this assumption is quantitatively rough. However, evaluating the element-resolved magnetic anisotropy based on ab initio methods is challenging in rare-earth-transition-metal-based systems, not to mention its temperature dependence.42 In addition, the exchange coupling parameters are also calculated at 0 K, in which the temperature effect is missing as well. Nevertheless, the qualitatively good description of the magnetic field and temperature effects can provide already insightful understanding of the magnetic properties of the 6:13:1 phase, consistent with the experimental observations.

To sum up, single crystals of the Nd6Fe13Cu intermetallic compound were grown by the reactive flux technique. It is found that in fields below 6 T, Nd6Fe13Cu has an antiferromagnetic structure with a Néel temperature of 410 K. The magnetic fields can significantly affect the magnetic state of the single crystals; as below 150 K, an external magnetic field of approximately 6 T applied along the a-axis induces a spin-flop transition, which indicates the competition between the exchange interactions of the Nd and Fe sublattices and their single-ion magnetocrystalline anisotropy.43,44 When the magnetic field is applied along the c-axis (the hard axis of magnetization), no spin-flop transition is observed up to 14 T, which is typical for classical two-sublattice collinear antiferromagnets with relatively weak magnetic anisotropy.45,46

In the 6:13:1 structure, the Fe, Nd, and Cu layers are stacked in the direction of the c-axis, and the directions of Fe and Nd moments change through the Cu layer.21,32 Atomistic spin dynamics simulations confirm that the Nd spin moments are aligned along the a-axis (in-plane), but an increase in the temperature and/or magnetic field can significantly change the antiferromagnetic coupling between the two Nd layers below and above the Cu layers, which, in turn, is the reason for observed spin-flop transition.

Our results are valuable for the understanding of the coercivity mechanism in Cu-doped Nd–Fe–B magnets, where the Nd6Fe13Cu phase is a grain boundary phase and the microcrystalline grain of the matrix Nd2Fe14B phase must be exchange coupled.47,48 However, the 6–13-1 phase would hardly provide sufficient exchange-bias effect at the grain boundary49–51 or operate as a shell-antiferromagnet phase52–54 due to the strong competition between its antiferromagnetic and ferromagnetic interactions. For this reason, it is very unlikely that the 6:13:1 phase enhances the coercivity of the Nd–Fe–Cu–B magnets.

The authors acknowledge the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project ID No. 405553726, TRR 270, subprojects A10, A05, and A01. The authors also thank the Lichtenberg High-Performance Center of TU Darmstadt for providing computational resources.

The authors have no conflicts to disclose.

Jianing Liu: Conceptualization (equal); Investigation (equal); Writing – original draft (equal). Ruiwen Xie: Conceptualization (equal); Formal analysis (equal); Methodology (equal); Writing – original draft (equal). Alex Aubert: Investigation (equal); Supervision (equal); Writing – review & editing (equal). Lukas Schäfer: Methodology (equal); Writing – review & editing (equal). Hongbin Zhang: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal). Oliver Gutfleisch: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal). Konstantin P. Skokov: Conceptualization (equal); Methodology (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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