The characteristic microstructure of Sm(Co,Fe,Cu,Zr)z (z=6.79.1) alloys with SmCo5 cell walls in Sm2Co17 cells, all intersected by Zr-rich platelets, makes them some of the best performing high-temperature permanent magnets. Plentiful research has been performed to tailor their microstructure at the nanoscale; but due to its complexity, many questions remain unanswered about the effect of the individual phases on the magnetic performance at different temperatures. Here, we explore this effect for three different Sm(Co,Fe,Cu,Zr)z alloys by deploying high-resolution magnetic imaging via in situ transmission electron microscopy and three-dimensional chemical analysis via atom probe tomography. We show that their microstructures differ in terms of SmCo5 cell-wall and Z-phase size and density as well as the Cu concentration in the cell walls and demonstrate how these features influence the magnetic domain size and density, thus forming different micromagnetic spin structures. Moreover, we illustrate that the dominant coercivity mechanism at room temperature is domain-wall pinning and show that magnets with a denser cell-wall network, a steeper Cu gradient across the cell-wall boundary, and thinner Z-phase platelets have a higher coercivity. We also show that the coercivity mechanism at high temperatures is domain-wall nucleation at the cell walls. Increasing the Cu concentration inside the cell walls decreases the temperature of transition between pinning and nucleation, significantly decreasing the coercivity with increasing temperature. We, therefore, provide a detailed explanation of how the microstructure on the atomic to nanoscale directly affects the magnetic performance and provide detailed guidelines for an improved design of Sm(Co,Fe,Cu,Zr)z magnets.

Sm(Co,Fe,Cu,Zr)z (z=6.79.1) alloys are one of the best commercially available permanent magnets for high-temperature applications, owing to their high Curie temperature and large magnetic coercivity.1–3 Their microstructure, which has been nanoengineered over decades of extensive research,4–7 forms as a result of a carefully designed aging and heat-treatment process. It comprises Sm2Co17 cells, SmCo5 cell walls, and Zr-rich platelets called the Z phase. The platelets are oriented perpendicular to the c-axis of the cells, which is also the easy axis of the magnetocrystalline anisotropy. The intertwined structure of the cells with high saturation magnetization and the cell walls with high magnetocrystalline anisotropy significantly improves the magnetic properties and makes them highly tunable.8,9 Specifically important is the enhancement of coercivity due to domain-wall (DW) pinning, which arises from the difference in the DW energy between the cells and the cell walls because of their different magnetocrystalline anisotropy.10–17 This has been well-documented experimentally by Lorentz transmission electron microscopy (LTEM), magnetic force microscopy, and Kerr microscopy.18–24 

Due to the complexity of the microstructure, many questions about the role of certain microstructural features in the magnetic properties of the magnet remain elusive. It has been proposed that the Z-phase platelets act as diffusion pathways for the formation of SmCo5 cell walls, aiding the segregation of Cu inside the cell walls.25 However, the magnetic properties of the lamellar Z phase are not well studied, because they differ from their bulk values. A recent study showed that the Z phase has an insignificant magnetic anisotropy compared to the other two phases and proposed that increasing the thickness of the Z phase would decrease the coercivity of the magnet.26 Furthermore, the size of the Sm2Co17 cells affects the coercivity and the remanence, because it determines the chemical composition of the cell walls.27 The presence of Cu in the cell walls increases the DW-pinning strength and thus the coercivity.28–30 Simultaneously, this decreases the Curie temperature of the cell walls as well as the overall remanence, so the effect of Cu and cell size on the high-temperature magnetic properties remains unclear. Finally, magnetization reversal can start with DW nucleation at the cell walls or Z phase,26,31,32 meaning that the magnetization processes in Sm(Co,Fe,Cu,Zr)z can be either DW pinning or nucleation, or both. In order to fully understand the behavior of Sm(Co,Fe,Cu,Zr)z magnets, it is necessary to investigate how the aforementioned microstructural features give rise to DW pinning and nucleation and what determines one of them being the dominant magnetization process. So far, the limited resolution of magnetic imaging techniques has hindered direct observations and therefore the ability to answer these questions.

Here, we present a systematic study of three Sm(Co,Fe,Cu,Zr)z magnets with different chemical compositions manufactured using the same heat-treatment process (described in the Methods section). We correlate the magnetic performance of these magnets at different temperatures using high-resolution imaging of their microstructure and micromagnetic spin structure. The microstructure has been imaged by energy-dispersive x-ray (EDX) spectroscopy in the scanning TEM (STEM) mode and atom probe tomography (APT), while the spin structure has been imaged by in situ heating LTEM and off-axis electron holography (EH). By correlating these methods and comparing the magnets in detail, we identify the mechanisms of how the microstructure gives rise to complex spin structures, such as closed magnetic loops and dense networks of magnetic domains. We also show that the dependence of coercivity on temperature is dominated by DW pinning at low temperatures and nucleation at high temperatures and explain how these magnetization processes arise from different microstructural features. Finally, we propose how the microstructure should be modified to improve the performance of Sm(Co,Fe,Cu,Zr)z magnets.

The three magnetic samples that were studied, namely, SmLCuL (low Sm, low Cu), SmLCuH (low Sm, high Cu), and SmHCuH (high Sm, high Cu), have different chemical compositions, as shown in Table I. SmLCuH has a higher Cu content than SmLCuL at the expense of Co. Similarly, SmHCuH has a higher Sm content than SmLCuH at the expense of Co. The z number, i.e., the ratio of transition metals to Sm, is 7.7 for SmLCuL, and SmLCuH and 7.3 for SmHCuH.

TABLE I.

Chemical compositions of the samples investigated in this work; z describes the ratio of transition metals to Sm.

SampleSm (at. %)Co (at. %)Fe (at. %)Cu (at. %)Zr (at. %)z
SmLCuL 11.5 60.9 18.8 6.2 2.5 7.7 
SmLCuH 11.6 59.4 18.8 7.7 2.5 7.7 
SmHCuH 12.0 58.7 18.9 7.8 2.5 7.3 
SampleSm (at. %)Co (at. %)Fe (at. %)Cu (at. %)Zr (at. %)z
SmLCuL 11.5 60.9 18.8 6.2 2.5 7.7 
SmLCuH 11.6 59.4 18.8 7.7 2.5 7.7 
SmHCuH 12.0 58.7 18.9 7.8 2.5 7.3 

The microstructure of the samples was imaged by STEM EDX spectroscopy on TEM lamellae with the c-axis in-plane to ensure identical imaging conditions. The average thickness of the lamellae, as measured by electron energy-loss spectroscopy (EELS), varies between 95 and 145 nm, and the thickness variations are greater within the same lamella than among different lamellae. We imaged locations with different thicknesses and verified that the thickness variation does not affect the measurements qualitatively or quantitatively. Figure 1 reveals that the samples have a typical microstructure of high-performance Sm(Co,Fe,Cu,Zr)z magnets with Sm2Co17 cells, zig-zag SmCo5 cell walls, and the Z phase. It is difficult to perform a statistical analysis of microstructural features, such as the cell-wall separation (the distance between adjacent cell walls with the same direction, i.e., the cell width), the cell-wall thickness, the Z-phase separation (the distance between adjacent Z-phase platelets), and the Z-phase thickness, because the boundaries between the phases are not well-defined and their values vary significantly within the sample. In the following, we discuss the average values measured in the images, and the error analysis is omitted because the measurement error is at least an order of magnitude smaller than the variations within the same sample. Here, it is important to note that TEM measurements are two-dimensional projections of a three-dimensional system. For example, the cell walls and Z-phase platelets may intersect the lamella plane at an angle that would make their thickness appear bigger than the actual values. However, due to the similar thickness and the same crystal orientation of the lamella, as analyzed in Fig. 1 in the supplementary material, these measurements represent a reliable quantitative comparison between the samples.

FIG. 1.

EDX chemical analysis. HRSTEM EDX element maps of Zr and Cu for (a) and (d) SmLCuL, (b) and (e) SmLCuH, and (c) and (f) SmHCuH, where bright contrast represents Z-phase platelets and SmCo5 cell walls.

FIG. 1.

EDX chemical analysis. HRSTEM EDX element maps of Zr and Cu for (a) and (d) SmLCuL, (b) and (e) SmLCuH, and (c) and (f) SmHCuH, where bright contrast represents Z-phase platelets and SmCo5 cell walls.

Close modal

Zr and Cu concentration maps, extracted from the EDX data and indicating the morphology of the Z phase and cell walls, respectively, are shown in Figs. 1(a) and 1(d) for SmLCuL, Figs. 1(b) and 1(e) for SmLCuH, and Figs. 1(c) and 1(f) for SmHCuH. The average Z-phase separation is 44 nm in SmLCuL, 67 nm in SmLCuH, and 91 nm in SmHCuH. Because the amount of Zr is the same in all samples, the difference in Z-phase separation is compensated by Z-phase thickness, which is on average 23 nm in SmLCuL, 28 nm in SmLCuH, and 59 nm in SmHCuH. The reason for such a difference in the Z-phase morphology may be due to the fact that the Z phase acts as a diffusion pathway for the formation of Sm-rich cell walls,25 thus reflecting the difference in the Sm content between the samples, where the sample with the highest Sm content has the thickest Z phase.

In all samples, the two directions of the zig-zag cell walls are symmetrical with respect to the c-axis and make an angle between 55° and 65° with each other. The average cell-wall separation (cell width) is 104 nm in SmLCuL, 107 nm in SmLCuH, and 81 nm in SmHCuH. Since the Sm content and cell-wall separation are almost identical in SmLCuL and SmLCuH and lower in SmHCuH, it can be concluded that the cell-wall separation decreases with increasing amount of Sm, which favors the formation of Sm-rich cell walls. The average cell-wall thickness is 15 nm in SmLCuL, 27 nm in SmLCuH, and 36 nm in SmHCuH. This may be explained by considering three factors. First, increasing the amount of Sm favors the formation of Sm-rich cell walls. Second, Cu segregates inside the cell walls, so a higher Cu content may lead to thicker cell walls. Third, the Z phase acts as a diffusion pathway for the formation of cell walls during the annealing process, so the cell-wall thickness may increase with the Z-phase thickness. This is why SmHCuH, with the highest Sm and Cu content and the thickest Z phase, has the thickest cell walls.

The segregation of Cu inside the cell walls plays an important role in DW pinning, but this cannot be reliably quantified in EDX due to the fact that a TEM image is a two-dimensional projection of a three-dimensional structure. For example, if the cell walls intersect the lamella plane at an angle, this may distort an observed Cu concentration profile, making the cell walls appear wider and the Cu concentration lower than the real values. Particularly important is the Cu gradient at the interface between the cells and the cell walls, which can only be resolved with atomic-resolution measurements in three dimensions. For this reason, an APT analysis, as shown in Fig. 2, was performed. The three-dimensional reconstruction of the samples [Figs. 2(d)2(f)] confirms a typical microstructure with Sm2Co17 cells, SmCo5 cell walls, and a Zr-rich Z phase. Proxigrams (proximity histograms) were extracted from the reconstruction, which show the concentration of individual elements as a function of distance from a predefined interface. Here, the predefined interface corresponds to all surfaces with a Cu concentration of 15%, which represent the boundaries of the cell walls. This provides statistically relevant information, because the concentration profiles are averaged over all cell walls. The proxigrams shown in Fig. 2 reveal that the Cu concentration profile inside the cell walls is bell-shaped. The Cu concentration at 2.5 nm from the interface is 38.6±0.2% in SmLCuL [Fig. 2(a)], 42.2±0.3% in SmLCuH [Fig. 2(b)], and 34.0±0.2% in SmHCuH [Fig. 2(c)]. Although SmHCuH has the highest Cu content (see Table I), it has the lowest Cu concentration inside the cell walls, because it has the most numerous and thickest cell walls, over which Cu has to be distributed. Figure 2(g) compares the Cu profiles of the samples, which were obtained by normalizing the local Cu concentration with respect to its value at 2.5 nm from the interface. SmLCuH has the steepest profile, with a gradient of 49.2% nm-1 at the inflection point, followed by SmLCuL and SmHCuH, with gradients of 43.0 and 37.0% nm-1 at the inflection points, respectively. The steepness of the Cu profile has a profound effect on the DW-pinning strength, which will be discussed below.

FIG. 2.

APT chemical analysis. Concentration proxigrams of individual elements plotted against the distance from the cell-wall boundaries and APT reconstructions showing SmCo5 cell walls (pink) and Z-phase platelets (yellow) for (a) and (d) SmLCuL, (b) and (e) SmLCuH, and (c) and (f) SmHCuH. (g) Cu concentration normalized with respect to its value at 2.5 nm from the cell-wall boundary, revealing the steepness of the Cu gradient for each sample.

FIG. 2.

APT chemical analysis. Concentration proxigrams of individual elements plotted against the distance from the cell-wall boundaries and APT reconstructions showing SmCo5 cell walls (pink) and Z-phase platelets (yellow) for (a) and (d) SmLCuL, (b) and (e) SmLCuH, and (c) and (f) SmHCuH. (g) Cu concentration normalized with respect to its value at 2.5 nm from the cell-wall boundary, revealing the steepness of the Cu gradient for each sample.

Close modal

The APT data were also used to measure the Zr distribution in the Z phase, which is almost identical in all samples, as shown in Fig. 2 in the supplementary material. The thickness of the Z phase is 3.1±0.7 nm for SmLCuH and 4.4±1.5 nm for SmHCuH. These data confirm the discussion above that EDX measurements overestimate the thickness of the measured features due to a two-dimensional projection of three-dimensional objects across thick TEM lamellae. Nonetheless, the APT measurements validate the relative comparison obtained by EDX, confirming that the Z phase is thicker in SmHCuH than in SmLCuH. The thickness was not measured for SmLCuL, because the APT reconstruction was not big enough to provide statistically relevant data, as visible in Fig. 2(d).

The aforementioned nanoscale microstructural features interact with the micromagnetic spin structure and the associated magnetization processes because they are comparable in size to the fundamental magnetic length scales in Sm(Co,Fe,Cu,Zr)z magnets. For example, the theoretical DW width of Sm(Co,Fe,Cu,Zr)z magnets is between 2.6 and 5.7 nm, and the exchange length, which defines the length scale of magnetization collinearity, is between 5.2 and 8.0 nm.33 The micromagnetic spin structure of the samples was imaged using LTEM in the Fresnel mode, where DWs create alternating bright and dark (convergent and divergent) contrast at defocus (see Methods). Figure 3 shows that the DWs have a typical zig-zag shape resulting from pinning at the SmCo5 cell walls. As was the case with the microstructural features, average values will only be discussed in the following due to large variations in the size of the micromagnetic spin structures within the same sample. In SmLCuL [Fig. 3(a)], the domains are significantly elongated; their length can span over a micrometer, and the separation between adjacent DWs, i.e., the width of the domains, is on average 310 nm. In SmLCuH [Fig. 3(b)], the domains are smaller, their length spans between 400 and 600 nm, and the DW separation is 187 nm on average. In SmHCuH [Fig. 3(c)], the domains are significantly smaller, with their length typically spanning between 150 and 250 nm, and the DW separation is 65 nm on average. From this, we can conclude that the DW separation increases with increasing cell-wall separation, so that the DWs are most numerous in SmHCuH, just like the SmCo5 cell walls. However, this is not the only factor impacting the DW separation, because SmLCuL and SmLCuH have approximately the same cell-wall separation, but their DW separation is not the same. This may be explained by considering the concentration of Cu in the cell walls, which will be discussed below.

FIG. 3.

Micromagnetic spin structure. Fresnel images at 300 μm overfocus of the thermally demagnetized state of (a) SmLCuL, (b) SmLCuH, and (c) SmHCuH, showing the density of DWs in each sample. Magnetic induction maps of (d) SmLCuL, (e) SmLCuH, and (f) SmHCuH, with white arrows demonstrating magnetization curling, which in panel f results in a closed magnetic loop. The contour spacing in the maps is π.

FIG. 3.

Micromagnetic spin structure. Fresnel images at 300 μm overfocus of the thermally demagnetized state of (a) SmLCuL, (b) SmLCuH, and (c) SmHCuH, showing the density of DWs in each sample. Magnetic induction maps of (d) SmLCuL, (e) SmLCuH, and (f) SmHCuH, with white arrows demonstrating magnetization curling, which in panel f results in a closed magnetic loop. The contour spacing in the maps is π.

Close modal

The micromagnetic spin structure was further analyzed by performing off-axis electron holography (EH) measurements, which provide quantitative information on the in-plane component of the magnetic induction in the lamellae. The magnetic induction maps extracted from EH are shown in Figs. 3(d)3(f). The direction of the contours and their color represent the direction of the magnetic field (as indicated by the color bar), while the density of the contour lines represents the magnetic field strength. The contour spacing, i.e., the phase change of the electron wave between adjacent contours, is π in all induction maps presented in this paper. Conventionally, only π DWs are expected in high-anisotropy magnets,34 but the arrows in Fig. 3(d) illustrate that π/2 DWs are also present in SmLCuL. Figure 3(e) shows that the spin structure is even more complex in SmLCuH, with a high degree of magnetization curling, resulting in DWs not having a well-defined angle. This is demonstrated with arrows in Fig. 3(e), where the change in the magnetic field direction across the same DW varies abruptly. The spin structure is the most complex in SmHCuH, where magnetization curling is so strong that in some cases it leads to closed magnetic loops. An example of such a magnetic loop is marked with arrows in Fig. 3(f). The density of the magnetic field lines varies within all samples. Since electron holography can only detect the in-plane component of the magnetic field, a lower density of field lines indicates the presence of a significant out-of-plane component of the magnetic field. One such region can be seen in the top corner of Fig. 3(d), where the contour spacing is almost flat. Finally, for each sample an external magnetic field of 1.5 T was applied by the objective lens perpendicular to the lamella and no change in the micromagnetic spin structure was found, which indicates very strong DW pinning.

The microstructural analysis was directly correlated with magnetic imaging in order to identify the mechanisms by which the microstructural features and micromagnetic spin structures are related. In Figs. 4(a)4(c), an EDX Cu concentration map indicating the positions of cell walls [Fig. 4(a)], an LTEM image indicating the positions of DWs [Fig. 4(b)], and a magnetic induction map indicating the direction of the magnetic field [Fig. 4(c)] are compared for the same area in SmLCuL. As indicated by white arrows, the DWs are pinned at the SmCo5 cell walls. However, the shape of the DWs does not match exactly the cell-wall morphology, which gives evidence for DWs being situated in the Sm2Co17 cells (repulsive pinning). Please note that the wave-like contrast visible in Fig. 4(b) does not come from ion-beam curtaining but is a fringe contrast from the interference, because the image was recorded in EH mode. Figures 4(d) and 4(e) compare for the same area in SmHCuH an electron-wave amplitude map (extracted from EH), indicating the positions of cell walls with bright contrast [Fig. 4(d)], and a magnetic induction map, indicating the direction of the magnetic field [Fig. 4(e)]. The DWs are pinned at the cell walls and follow them closely. At the intersections between two cell walls, as shown by yellow arrows, the DWs follow one cell wall and then curl in order to start following the other cell wall. Such curling can result either in DWs not having a very well-defined angle of rotation or in the formation of closed magnetic loops. This finding explains that SmHCuH has the most complex and heterogeneous micromagnetic spin structure (as shown in Fig. 3), because it has the densest network of cell walls with numerous intersections. Therefore, by comparing the microstructure and the spin structure directly, it has been observed how complex micromagnetic spin structures are formed in Sm(Co,Fe,Cu,Zr)z magnets, enriching our current understanding of magnetic phenomena in permanent magnets.

FIG. 4.

Correlation of the microstructure and micromagnetic spin structures. (a) An EDX concentration map of Cu; (b) a Fresnel image at 200 μm overfocus; and (c) a magnetic induction map of the same area in SmLCuL, with white arrows revealing repulsive DW pinning at a cell wall. (d) An electron-wave amplitude map and (e) a magnetic induction map of the same area in SmHCuH, exemplifying by yellow arrows that magnetic loops form as a consequence of pinning at cell-wall intersections. The contour spacing in the induction maps is π. The color wheel indicates the direction of magnetic induction.

FIG. 4.

Correlation of the microstructure and micromagnetic spin structures. (a) An EDX concentration map of Cu; (b) a Fresnel image at 200 μm overfocus; and (c) a magnetic induction map of the same area in SmLCuL, with white arrows revealing repulsive DW pinning at a cell wall. (d) An electron-wave amplitude map and (e) a magnetic induction map of the same area in SmHCuH, exemplifying by yellow arrows that magnetic loops form as a consequence of pinning at cell-wall intersections. The contour spacing in the induction maps is π. The color wheel indicates the direction of magnetic induction.

Close modal

In situ heating LTEM experiments were performed with and without an external magnetic field to investigate the magnetization processes in Sm(Co,Fe,Cu,Zr)z at high temperatures. There is no observed change in the microstructure when the samples are heated from room temperature (RT) to 400 °C, which is the temperature at which the magnets are stabilized in the annealing process. This means that any observed change in the micromagnetic spin structure in this temperature range is due to a change in the magnetic properties and not due to a change in the microstructure. When the samples are heated without an external magnetic field, there is no change in the micromagnetic spin structure from RT to 400 °C. This excludes the possibility that there is a change from repulsive to attractive pinning with increasing temperature, because the shape of the DWs does not change. However, when the samples are heated in an external magnetic field of 1.5 T perpendicular to the lamella, the spin structure changes significantly. Figures 5(a)5(c) show LTEM images of the same area in SmLCuH at 20 °C [Fig. 5(a)], 200 °C [Fig. 5(b)], and 250 °C [Fig. 5(c)]. Some DWs are nucleated and their neighboring DWs are annihilated between 150 and 200 °C, as indicated by two yellow arrows comparing the same positions in Figs. 5(a) and 5(b). This is direct evidence of DW nucleation in Sm(Co,Fe,Cu,Zr)z magnets. As the temperature increases above 200 °C, the DWs are annihilated [Fig. 5(c)], because the coercivity decreases and the magnet becomes saturated perpendicular to the lamella plane (parallel to the external magnetic field). At 250 °C, most DWs have been annihilated, but some DWs survive even at 300 °C. The full in situ heating experiment is shown in Video 1 in the supplementary material.

FIG. 5.

DW nucleation and annihilation. In situ heating Fresnel images at 80 μm underfocus in an external magnetic field of 1.5 T perpendicular to the lamella at (a) 20 °C, (b) 200 °C, and (c) 250 °C, demonstrating DW nucleation (yellow arrows in panels a and b) and annihilation (panel c).

FIG. 5.

DW nucleation and annihilation. In situ heating Fresnel images at 80 μm underfocus in an external magnetic field of 1.5 T perpendicular to the lamella at (a) 20 °C, (b) 200 °C, and (c) 250 °C, demonstrating DW nucleation (yellow arrows in panels a and b) and annihilation (panel c).

Close modal

The observed micromagnetic spin structures and microstructural features are all nanoscopic, and in order to estimate their effect at the macroscopic scale, the bulk magnetic properties of the samples were measured and are presented in Fig. 6. All hysteresis loops have a shape typical for Sm(Co,Fe,Cu,Zr)z magnets, which does not change with temperature, as demonstrated for RT in Fig. 6(a) and for 400 °C in Fig. 6(b). When the external magnetic field is applied in the opposite direction to demagnetize the remanent state, there is an initial dip in magnetization (between 0 and 0.5 T), hypothesized to be due to the Z phase reversing its magnetization before the rest of the magnet.26Figure 6(c) shows the temperature dependence of the saturation magnetization (solid symbols) and remanence (hollow symbols) for all three samples. SmLCuH has the highest saturation magnetization below 100 °C, followed by SmLCuL and then SmHCuH. Above 100 °C, SmLCuL surpasses SmLCuH. Quantitatively, the reduction in the saturation magnetization from RT to 400 °C is 10.3% for SmLCuL, 15.4% for SmLCuH, and 14.8% for SmHCuH. Similarly, SmLCuL has the highest remanence, followed by SmLCuH and SmHCuH at all temperatures. Quantitatively, the reduction in the remanence from RT to 400 °C is 16.4% for SmLCuL, 15.9% for SmLCuH, and 21.3% for SmHCuH. Figures 6(d)6(f) show the dependence of the coercivity on temperature for each sample individually, revealing that at RT SmLCuH has the highest coercivity, followed by SmLCuL and SmHCuH. This changes at 400 °C, where all magnets have approximately the same coercivity. Quantitatively, the coercivity reduction from RT to 400 °C is 74.6% for SmLCuL, 76.7% for SmLCuH, and 71.2% for SmHCuH. The highest saturation magnetization and remanence and the lowest associated reduction with increasing temperature are expected for SmLCuL, because it has the highest amount of Co, an element with a high magnetic moment and Curie temperature. The opposite is valid for SmHCuH.

FIG. 6.

Bulk magnetic properties. Hysteresis loops of all samples at (a) RT and (b) 400 °C, having the same shape and revealing a magnetization dip before reversal. (c) Temperature dependence of saturation magnetization (solid symbols) and remanence (hollow symbols) for all samples. Theoretical coercivity values for DW pinning (green) and nucleation (red) are fitted to the experimental values, showing that the transition happens around (d) 175 °C for SmLCuL, (e) 125 °C for SmLCuH, and (f) 200 °C for SmHCuH.

FIG. 6.

Bulk magnetic properties. Hysteresis loops of all samples at (a) RT and (b) 400 °C, having the same shape and revealing a magnetization dip before reversal. (c) Temperature dependence of saturation magnetization (solid symbols) and remanence (hollow symbols) for all samples. Theoretical coercivity values for DW pinning (green) and nucleation (red) are fitted to the experimental values, showing that the transition happens around (d) 175 °C for SmLCuL, (e) 125 °C for SmLCuH, and (f) 200 °C for SmHCuH.

Close modal

The differences in the coercivity between the samples cannot be explained by considering only their bulk chemical compositions and microstructures, since there is no observed change in the microstructure with increasing temperature. The magnetic properties of the two phases depend on intrinsic material parameters, which change with increasing temperature. Specifically, DW pinning at the cell walls occurs due to the difference in the DW energy γ=4AK1 between the cells and cell walls, where A is the exchange constant and K1 is the first magnetic anisotropy constant. Using A=24.7pJm1 and K1=3.3MJm3 for the Sm2Co17 cells,35,36 one obtains γcell=36.1mJm2 at RT for all samples. The addition of Cu to the SmCo5 cell walls reduces A and K1, so that γcellwall of each sample is different due to different cell-wall Cu concentrations. Taking A=23.6pJm1 and K1=18.6MJm3 for pure SmCo536 and calculating the reduction for each Cu concentration,29 one obtains A=16.9pJm1, K1=6.9MJm3, and γcellwall=43.3mJm2 for SmLCuL; A=16.1pJm1, K1=5.8MJm3, and γcellwall=38.8mJm2 for SmLCuH; and A=17.8pJm1, K1=8.4MJm3, and γcellwall=49.0mJm2 for SmHCuH. Therefore, γcell<γcellwall at RT for all samples, meaning that the DWs are situated in the cells where the DW energy is lower (repulsive pinning).

Our results show that SmLCuH, which is the sample with the largest Cu gradient, has the highest coercivity at RT, while SmHCuH, the sample with the smallest Cu gradient, has the lowest coercivity (see Fig. 2). Importantly, SmLCuH has the lowest Δγ between the cells and the cell walls, meaning that it is not the total Cu concentration that determines the DW-pinning strength, but the steepness of the Cu gradient. Therefore, the DW-pinning strength does not only depend on the end-to-end Δγ but also on the rate of change of Δγ, which is the highest for SmLCuH and lowest for SmHCuH. Additionally, SmHCuH has the thickest Z phase, which is another contributing factor to its relatively low coercivity. The influence of the Z phase is further described in the context of Fig. 1 in the supplementary material.

With increasing temperature, γcell decreases slower than γcellwall,37 so that γcell>γcellwall at high temperatures, where the DWs are pushed into the cell walls (attractive pinning). The boundary between the cells and cell walls provides numerous nucleation sites, leading to DW nucleation at high temperatures (as shown in Fig. 5). The temperature dependence of A and K1 is not known, so it is not possible to directly calculate the temperature of transition from pinning to nucleation. However, it can be determined by fitting the theoretical values of the expected coercivity Hc for DW pinning and nucleation to our experimental data, as shown in Figs. 6(d)6(f). For DW pinning, the following expression is used:10 

Hc=H0cT/Ms,
(1)

where T is the temperature, Ms is the saturation magnetization, and the fitting parameters are H0, representing the extrapolated absolute-zero coercivity, and c, describing the DW energy. Equation (1) is an empirical equation and does not take into account the temperature dependence of intrinsic material parameters, such as A and K1. However, it can be used to qualitatively describe the temperature dependence of the coercivity, and it empirically matches our experimental data. For DW nucleation, the following expression is used:38 

Hc=aK1/MsnMs,
(2)

where K1 is the uniaxial magnetic anisotropy,39 and the fitting parameters are a, describing the defect type and dimensions, and n, representing the effect of dipolar interactions. Our fits demonstrate that the coercivity is dominated by DW pinning at low temperatures and DW nucleation at high temperatures. The transition between the two occurs between 150 and 200 °C for SmLCuL, between 100 and 150 °C for SmLCuH, and at 200 °C for SmHCuH.

It can be concluded that the sample with the highest Cu concentration has the lowest temperature of transition from pinning to nucleation, and vice versa. This can be explained by the fact that the Cu concentration reduces γcellwall, so that the temperature where γcell=γcellwall also reduces. Nucleation therefore happens at the cell walls and starts at lower temperatures with increasing Cu concentration inside the cell walls. Lowering the temperature where nucleation starts in turn decreases the coercivity with increasing temperature. These important results on the temperature behavior of Sm(Co,Fe,Cu,Zr)z magnets allow us to provide guidelines on how to directly improve their magnetic performance. Specifically, the Cu concentration should be carefully engineered so that the Cu gradient is as steep as possible to increase the coercivity while the total Cu concentration should be as low as possible to avoid coercivity reduction with increasing temperature.

By directly comparing atomic-resolution microstructural analysis and high-resolution magnetic imaging, we are able to identify key microstructural features that dominate the magnetic performance of composite Sm(Co,Fe,Cu,Zr)z magnets. The morphology of the SmCo5 cell walls determines the magnetization texture. The denser the cell-wall network, the denser the DW network with more magnetization curling, which can lead to the formation of closed magnetic loops. Increasing the Cu gradient at the cell walls strengthens DW pinning at the cell walls and thus increases the coercivity. Contrarily, increasing the Z-phase thickness decreases the coercivity. The coercivity mechanism in Sm(Co,Fe,Cu,Zr)z is DW pinning at low temperatures and DW nucleation at high temperatures, and the transition between the two occurs between 100 and 200 °C. DW nucleation happens at the cell walls, and increasing the Cu concentration inside the cell walls lowers the temperature where nucleation starts, which in turn increases the coercivity reduction with increasing temperature. From our results we conclude that, in order to improve the performance of Sm(Co,Fe,Cu,Zr)z magnets, the Z-phase thickness should be minimized and the Cu gradient at the cell-wall edges should be increased while keeping the total Cu concentration as low as possible. We provide a detailed understanding of the link between macroscopic magnetic properties and nanoscale microstructure, and thus give precise directions on how the microstructure should be modified to further tailor the performance of Sm(Co,Fe,Cu,Zr)z magnets.

The alloying elements were molten in an induction furnace in an argon atmosphere of 99.999% purity and cast in a metallic mold. The alloy was hammer-milled and then jet-milled to obtain a particle size of 4–8 μm. The resulting powder was transferred to a rubber mold, where it was aligned with magnetic pulses of field strength 5 T and then isostatically pressed at 300 MPa. This was sintered in vacuum at 1200–1220 °C, solution-annealed at 1170–1200 °C, and quenched to RT in an inert-gas atmosphere. The next steps were tempering at 850 °C, slow-cooling to 400 °C, and subsequent quenching to RT. All samples were produced by Arnold Magnetic Technologies. Table I shows the overall chemical compositions of the materials used in this study.

Electron-transparent lamellae for TEM measurements were made in a Helios 600i dual-beam focused ion beam (FIB) scanning electron microscope (SEM) workstation. Polished magnetic samples were Ga+ sputtered and the lamellae were prepared using the conventional lift-out method. A Fischione Nanomill system was used for low-energy (<1 keV) Ar+ milling, which significantly reduced ion-beam induced surface damage.

The lamella thickness was measured using the EELS log-ratio technique on an FEI Tecnai F30 field-emission gun (FEG) transmission electron microscope.

HRSTEM EDX maps were obtained at an accelerating voltage of 200 kV, using an FEI Talos F200X microscope equipped with a Super-X EDS system.

The micromagnetic spin structure of the lamellae was investigated in their thermally demagnetized (magnetically pristine) state in the zero magnetic field (Lorentz mode). The LTEM measurements were performed in the Fresnel mode, where electrons are deflected by the Lorentz force F=ev×B, with e the electron charge, v the velocity of the electrons, and B the in-plane magnetic induction in the sample. EH measurements were performed using a magnetic biprism40 at a voltage between 90 and 100 V, which resulted in 3-nm fringe spacing and 75% contrast. The room-temperature LTEM and EH images were obtained on a spherical aberration-corrected FEI Titan microscope at an accelerating voltage of 300 kV using a Gatan K2-IS direct-electron counting camera. The in situ heating LTEM experiments were performed on the aforementioned FEI Tecnai F30 microscope. All images were recorded deploying the Gatan Microscopy Suite software.

Magnetization cycles and in situ experiments were repeated several times for each sample to verify the reproducibility of the results.

The standard lift-out method on an FEI Helios Focused Ion Beam 600i workstation was used to prepare needle-shaped samples for the APT analysis, which were mounted to a flat-top microtip coupon provided by Cameca. An apex of <70 nm diameter was achieved by applying sequential annular milling and low-kV cleaning, resulting in <0.01 at. % Ga in the top 10 nm of the specimen. Data were collected between 5 and 9.5 kV on a LEAP 4000X-HR atom probe microscope at 54 K by applying 100 pJ laser pulses at a frequency of 200 kHz, which give a Co charge-state ratio Co++/Co+ between 5 and 10. These parameters and a chamber vacuum of 10-9 Pa resulted in a background level consistently below 20 ppm/ns. The atom-map reconstructions were validated by considering that the Z platelets are flat. Additionally, the lattice spacing was measured via spatial distribution maps along the easy axis, normal to the platelets, to validate the dimensional accuracy of the atom-map reconstruction.

A superconducting quantum interference device (SQUID), a part of quantum design’s magnetic property measurement system (MPMS3), was used to measure hysteresis loops along the easy axis of sample pieces with masses between 35 and 65 g at temperatures between RT and 400 °C.

An electron wave passing through a magnetized sample gains an electromagnetic phase shift, as described by the Aharonov–Bohm effect,41,42

φ(x,y)=φel(x,y)+φmag(x,y)=CelV(r)dzπΦ0Az(r)dz,
(3)

with the electrostatic and magnetic contributions to the phase shift φel(x,y) in the electrostatic potential V(r) and φmag(x,y) in the vector potential Az(r), the magnetic flux quantum Φ0=π/e, and the interaction constant Cel=γmeleλ/2, where γ is the Lorentz factor and λ is the electron wavelength. Here, the z-axis denotes the incident electron beam direction. The electrostatic contribution was assumed to be uniform throughout the sample, as compared to the magnetic contribution.

The magnetic induction maps shown in Figs. 3 and 4 were created in two steps. First, the cosine of the magnetic phase φmag was calculated to create contours, so that the phase difference between two neighboring contours is 2π. Second, the gradient of φmag was calculated to find the direction of the projected in-plane magnetic induction. This was visualized by superimposing a color scheme on the maps (as indicated by the color wheel in Figs. 3 and 4), where each color represents a specific direction.

See the supplementary material for the complete diffraction analysis of twinning, APT analysis of the Z phase, and the in situ heating LTEM experiment.

L.P., R.E.S., M.C., and J.F.L. gratefully acknowledge funding from the Swiss National Science Foundation (Grant No. 200021–172934). R.E.D.-B. and A.K. gratefully acknowledge funding from the German Research Foundation (Project-ID No. 405553726–TRR 270) and from the European Union’s Horizon 2020 Research and Innovation Programme (Grant No. 823717, project “ESTEEM3” and Grant No. 856538, project “3D MAGiC”). We also thank Joakim Reuteler for preparing the TEM lamellae and ScopeM, ETH Zurich for the access to its facilities.

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

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Supplementary Material