Figure 1(b) depicts the X-ray diffraction (XRD) patterns of all specimens, which are well-explained by the Fe13Ge8-type structure (refer to the simulated pattern in Fig. 1(b)). Further, no evident impurity phase is detected via scanning electron microscopy (SEM) images (Figs. S1(c) to S1(g) in the Supplemental Information). The hexagonal lattice parameters a and c are obtained with the help of a Rietveld refinement program15,16 and are summarized in Table 2. These parameters are plotted as a function of the Ge content x in Fig. 1(c) and reveal that the a-axis length reduces while the c-axis expands with increasing x. The c/a ratio is also calculated for each sample, as displayed in Fig. 1(d). The result illustrates a systematic increase of c/a as the Ge atom replaces the Ga atom gradually. We have also investigated the solubility limit of the Ge atom in Co6.2Ga3.8−xGex (see also Figs. S1(a), S1(b), S1(h), and S2 in the Supplemental Information). On the Ge-rich side, although the x = 3.5 sample does not show any noticeable impurity phase in the SEM image, the XRD pattern cannot be fully explained by the Fe13Ge8-type structure. An impurity phase appears on reducing the Ge content below x = 2.4, which is evident in the x = 2.0 sample. In the x = 2.3 sample, we cannot detect the impurity phase in the XRD pattern and the SEM image, but the magnetization curves measured at temperatures in the paramagnetic state of the Fe13Ge8-type structure have revealed the presence of the ferromagnetic impurity phase (Fig. S3(c) in the Supplemental Information).
Table 2
Lattice parameters a and c, TC, µeff, θW, Hc at 2 K, and room temperature ρ value ρ (RT) of Co6.2Ga3.8-xGex (x = 2.4 to 3.2).
x
|
a
|
c
|
TC
|
µeff
|
θW
|
Hc at 2 K
|
ρ (RT)
|
|
(Å)
|
(Å)
|
(K)
|
(µB/Co)
|
(K)
|
(kOe)
|
(µΩcm)
|
2.4
|
7.906(3)
|
4.970(1)
|
60.3
|
1.78
|
50
|
44
|
185
|
2.6
|
7.900(3)
|
4.977(1)
|
46.4
|
1.77
|
41
|
26
|
186
|
2.8
|
7.894(4)
|
4.984(2)
|
13.2
|
1.97
|
-83
|
9.3
|
209
|
3.0
|
7.875(2)
|
4.985(1)
|
5.8
|
1.95
|
-116
|
1.4
|
126
|
3.2
|
7.857(4)
|
4.992(2)
|
< 2
|
2.15
|
-309
|
0.24
|
227
|
The temperature-dependent dc magnetic susceptibility χdc of each sample exhibits an enhancement of χdc in the low-temperature range, which suggests a ferromagnetic ordering, as shown in Fig. 2(a). The χdc value at 2 K is heavily reduced by increasing x, and the TC systematically decreases. The temperature at which the minimum temperature derivative of χdc occurs defines TC, shown in Table 2 for each sample and represented in Figs. 2(b) and 2(c). The x = 3.2 sample would possess TC below 2 K. The temperature dependences of inverse χdc are demonstrated in Fig. 2(d). In each sample, 1/χdc follows the Curie-Weiss law expressed by χdc = C/(T-θW) at high temperatures, as indicated by the solid line. The effective magnetic moment µeff obtained from the C value and the Weiss temperature θW are presented in Table 2. All µeff values are smaller than that of an isolated Co2+ or Co3+ ion (3.87 or 4.90 µB/Co), which suggests an itinerant character of d-electrons. For the x = 2.6 or 2.4 sample, the positive θW is nearly identical to TC, indicating a ferromagnetic ordering. However, in the x = 2.8 ~ 3.2 samples, negative θW values are present, indicating the dominance of AFM interaction. The magnetization curves exhibit hysteresis loops, which are characteristic of FM compound. Therefore, the samples with x ≧ 2.8 undergo ferrimagnetic ground states. Furthermore, it is notable that the frustration index f, defined as |θW|/TC, significantly increases from 6.3 to over 155 as x increases from 2.8 to 3.2 in the ferrimagnetic state. This increase strongly supports the presence of spin frustration, which is consistent with the geometrically frustrated Kagome and triangular lattices depicted in Fig. 1(a). Hence, the notable characteristic of Co6.2Ga3.8−xGex is its capacity for chemical manipulation of spin frustration.
The isothermal magnetization curves (where M is the magnetization and H is the external field) for all samples, spanning − 70 kOe to 70 kOe, are presented in Figs. 3(a) through 3(e). The high field M at 2 K displays a sudden drop as x increases from 2.6 to 2.8, which is indicative of spin compensation in the ferrimagnetic samples with x = 2.8 ~ 3.2. However, even in the ferromagnetic samples with x = 2.4 or 2.6, the highest M value is relatively smaller than µeff, implying the existence of a canted ferromagnetic structure. Notably, the x = 2.4 and 2.6 samples exhibit a giant coercivity of 44 kOe and 26 kOe, respectively, at 2 K. The x = 2.3 sample (TC=65 K) with a small amount of impurity phase shows a larger Hc of 46 kOe at 2 K (see Figs. S3 (a) and S3(b) in the Supplemental Information). In the x = 2.4 or 2.6 sample, Hc increases significantly as the temperature drops below TC, and the initial magnetization curve at 2 K, exhibiting a small slope, undergoes an abrupt jump at approximately Hc. This magnetization process is a typical characteristic of domain wall pinning17. The ferrimagnetic samples also demonstrate hysteresis loops at low temperatures, and the corresponding Hc values at 2 K are provided in Table 2.
Figure 4 displays the temperature dependencies of ρ in all the samples. The values of ρ are normalized by the corresponding room temperature values listed in Table 2. The metallic nature of the samples is evident from the order of magnitude of ρ in each one. The ferrimagnetic samples exhibit a negative temperature coefficient of resistivity below around 150 K, which could be indicative of carrier localization and/or a partial opening of the gap at the Fermi surface.
We aim to investigate the correlation between Co bond length and magnetism. The Bethe-Slater curve, widely used for analysing magnetism in magnetic metals, suggests that longer and shorter interatomic distances between magnetic atoms favour FM and AFM interactions, respectively18. This tendency has been observed in various intermetallic compounds19,20. The selected Co interatomic distances are listed in Table 3, and, taking into account the multiplicity (2 for Co1-Co1 and Co2-Co2, 6 for Co1-Co3, and 4 for Co2-Co3), Co1-Co3 and Co2-Co3 bonding likely determine the magnetic ordering type. The x-dependence of θW in Co6.2Ga3.8−xGex strongly suggests the coexistence of FM and AFM interactions. Co1-Co3 and Co2-Co3 bonds could lead to AFM and FM interactions, respectively, although further investigation is necessary. When x exceeds 2.8, the Co1-Co3 and Co2-Co3 bond lengths considerably decrease, consistent with the rapid predominance of AFM interaction as reflected by θW.
Table 3
Selected Co interatomic distances in Co6.2Ga3.8-xGex (x = 2.4 to 3.2). The multiplicities are 2 for Co1-Co1, 6 for Co1-Co3, 2 for Co2-Co2, and 4 for Co2-Co3, respectively.
x
|
Co1-Co1
|
Co1-Co3
|
Co2-Co2
|
Co2-Co3
|
|
(Å)
|
(Å)
|
(Å)
|
(Å)
|
2.4
|
2.485
|
2.536
|
2.485
|
2.631
|
2.6
|
2.489
|
2.535
|
2.489
|
2.630
|
2.8
|
2.492
|
2.534
|
2.492
|
2.630
|
3.0
|
2.493
|
2.530
|
2.493
|
2.625
|
3.2
|
2.496
|
2.526
|
2.496
|
2.621
|
It should be noted that the layered hexagonal perovskite Sr5Ru4.1O15, known for its giant coercive properties4, shares the same space group P63/mmc (194) as Co6.2Ga3.8−xGex. This metallic compound exhibits a highly anisotropic crystal structure with c/a = 4.106, wherein Ru acts as the magnetic atom and partially forms a triangular lattice. The analysis through Curie-Weiss fitting suggests the presence of itinerant d-electrons of Ru. The saturation moment of 0.05 µB/Ru is much smaller than the µeff value of the Ru ion, implying weak ferromagnetism. The giant coercivity of Sr5Ru4.1O15 arises from the large magnetocrystalline anisotropy with the geometrical frustration4. Co6.2Ga1.4Ge2.4 and Co6.2Ga1.2Ge2.6, both of which are also metallic, have a c/a ratio much smaller than 1.0 (as seen in Fig. 1(d)), indicating an anisotropic crystal structure. The Co atoms form Kagome and triangular lattices, and the Co magnetic moment is itinerant. Co6.2Ga1.4Ge2.4 and Co6.2Ga1.2Ge2.6 exhibit relatively low saturation moments, likely originating from a canted ferromagnetic structure. Thus, the overall behaviour of Co6.2Ga1.4Ge2.4 and Co6.2Ga1.2Ge2.6 is quite similar to the magnetic and transport properties of Sr5Ru4.1O15. Therefore, we speculate that the giant coercivity in rare-earth-free magnets with the space group P63/mmc can be attributed to the itinerant d-electrons in geometrically frustrated metals and canted spin structure, in addition to the anisotropic crystal structure.
As mentioned in the introduction, CaBaCo4O7 is the rare example of a rare-earth-free Co-based bulk inorganic compound exhibiting a giant Hc10. This cobaltite also features Co-Kagome layers despite its distorted orthorhombic crystal structure. While its low saturation moment (~ 0.7 µB/f.u.) is akin to that of Co6.2Ga3.8−xGex, the unique dielectric behaviour is different from the metallic transport of Co6.2Ga3.8−xGex (x = 2.4 and 2.6). It is thus appropriate to classify Co6.2Ga3.8−xGex (x = 2.4 and 2.6) as a new category of rare-earth-free Co-based inorganic compounds that exhibit giant coercivity.
A comparison of magnetic properties between Co6.2Ga3.8−xGex and isostructural Fe3Ga0.35Ge1.65 would be of great significance. Fe3Ga0.35Ge1.65 exhibits FM ordering below 341 K, and even at 50 K, no noticeable hysteresis loop is detected13. At 50 K, the saturation magnetization is 80 emu/g, equivalent to approximately 1.47 µB/Fe. Thus, it is likely that the itinerant nature of d-electrons is weakened in Fe3Ga0.35Ge1.65, and the itinerant magnetic moment is essential for the manifestation of giant coercivity in transition-metal magnets with the P63/mmc space group.