Effects of La-Co Co-Substitution and Magnetic Field Pressing on the Structural and Magnetic Properties of SrM Hexaferrites

Abstract

We carefully investigated the effects of La-Co co-substitution and magnetic field pressing (MFP) on the structural and magnetic properties of SrM hexaferrites. Samples composed of Sr_1−xLa_xFe_12−xCo_xO₁₉ were sintered at 1230 °C for 2 h in air with sintering additives composed of 0.7 wt% CaCO₃ and 0.7 wt% SiO₂. A single M-type phase was confirmed to exist up to x = 0.3. Rietveld refinement revealed a slight decrease in lattice parameter a and the unit cell volume (V_cell) with an increasing x, while parameter c showed a significant decrease. The saturation magnetization (M_s) values increased from 70.90 to 72.40 emu/g with an increasing x from 0.0 to 0.15 and then decreased to 71.38 emu/g with further increasing of x to 0.3, while the anisotropy field (H_a) increased from 17.7 to 25.9 kOe, leading to a continuous increase in the intrinsic coercivity (H_ci), from 3.52 to 5.00 kOe, respectively. Using the MFP process, the c-axis of M-type hexaferrite grains could be effectively aligned to the applied field direction, which significantly affected the microstructures and, thus, magnetic properties of samples. Unlike non-MFP samples, exhibiting a significant increase in the average grain size (d_avg) but almost unaltered average thickness (t_avg) with an increasing x from 0.0 to 0.3, MFP-processed samples exhibited almost unaltered d_avg values but a continuous decrease in t_avg. Consequently, the variation in remanent flux density (B_r) versus x followed that of M_s versus x and thus exhibited the highest B_r of 4.05 kG for x = 0.15, leading to the highest maximum energy product {(BH)_max} of 3.62 MGOe. With an increasing x from 0.0 to 0.3, the H_ci values continuously increased from 3.14 to 3.84 kOe mainly due to a continuous increase in H_a, although they were significantly lowered in comparison with those of non-MFP samples because of a large increase in B_r for a given composition x. A higher M_r/M_s ratio always resulted in a larger (BH)_max in our samples regardless of x. A careful comparison of the microstructures and magnetic properties between MFP and non-MFP samples provided valuable insights into a broad area of permanent magnet optimization.

1. Introduction

M-type (MeFe₁₂O₁₉ Me: Ba, Sr) hexaferrites have been applied for ceramic permanent magnets due to their cost-effectiveness, chemical stability, and notable hard magnetic characteristics, including high M_S and high H_a [1,2,3]. Thus, these permanent magnets have been used for the motor components of automobiles, household washing machines, air conditioners, etc. Among various fabrication processes employed to prepare M-type hexaferrites [1,4], the solid-state reaction is a commonly employed method in industrial manufacturing due to its cost-effectiveness and suitability for mass production. The performance of a permanent magnet is normally evaluated on the basis of its B_r, H_ci, and (BH)_max values, which are closely related to intrinsic properties, such as M_s and H_a [1,2,3,5].

The intrinsic properties of M_S and H_a for M-type hexaferrites depend on the cation substitution composition and site occupancy in the unit cell [1,3,4,5]. M-type hexaferrites consist of the stacked structures of spinel (S, Fe₆O₈) and hexagonal (R, MFe₆O₁₁) blocks, represented as SRSR, where the asterisk (*) denotes a 180° rotation around the c-axis. The crystallographic sublattices of Fe³⁺ in the M-type structure are categorized into five sublattices: 2a, 2b, 4f₁, 4f₂, and 12k sites. The spin magnetic moments of Fe³⁺ ions at the 12k, 2a, and 2b sites align parallel to the c-axis, while those at the 4f₁ and 4f₂ sites align antiparallel to it. Consequently, this arrangement results in a net magnetic moment of 20 μ_B per unit cell at 0 K [1,6]. The M_S value can be improved through the substitution of cations like Co²⁺ [7], Zn²⁺ [8], Al³⁺ [9], and Ti⁴⁺ [10] for the Fe³⁺ sites. On the other hand, H_a can be increased by substituting rare earth elements for the Sr site, such as La [11], Nd [12], and Sm [12]. While a simultaneous improvement of both M_S and H_a values via a single element substitution has never been reported [1,8,9,10,11,12,13], among various substituents explored, La-Co co-substitution has been reported to be very effective for the enhancement of H_a without a significant reduction in M_S [14,15,16,17,18,19,20].

The magnetic properties of M-type bulk magnets can be influenced by various factors, such as the sintering density, the average grain size and distribution, and the c-axis alignment of grains, in addition to chemical compositions [21]. The magnetic properties of sintered samples are largely influenced by the sintering additives [22,23], sintering temperature and time [24], and atmosphere [25,26]. High sintered density and high grain alignment along the c-axis dominantly contribute to an increase in B_r, while the size and distribution of grains with multiple domains have an inverse relationship with H_ci. The sintering additives of SiO₂ and CaCO₃ have been commonly used for M-type hexaferrites not only to achieve high sintered density through a liquid-phase sintering but also to suppress grain growth [22,23].

Meanwhile, the MFP process is a highly effective technique for the fabrication of high-performance permanent magnets. This is achieved by aligning the magnetic easy axes of individual particles parallel to the external magnetic field during the pressing process [3,27]. The c-axis alignment of M-type hexaferrite particles via the MFP method significantly improves the squareness of the demagnetization curve of a sintered bulk sample, resulting in a marked enhancement in both B_r and (BH)_max. The effectiveness of the MFP method extends to the industrial production of various permanent magnets, such as M-type hexaferrite [28], SmCo₅ [29], Sm₂TM₁₇ [30], and Nd-Fe-B magnets [31]. Although the MFP process has been widely used in the industry, previous reports on M-type hexaferrites for permanent magnets mainly focus on non-MFP polycrystalline samples with randomly oriented grains, making it hard to find a comprehensive study for the effect of c-axis alignment on magnetic properties [17,18,32]. Therefore, it is critical to conduct a comparative study between non-MFP and MFP samples—as such studies are hardly found in the previous literature—in order to understand their relationship in microstructures and extrinsic magnetic properties, such as H_ci, B_r, and (BH)_max. For this purpose, we carefully investigated the lattice parameters, microstructures, and magnetic properties of both non-MFP and MFP samples. In this study, we carefully investigated the lattice parameters, microstructures, and magnetic properties of La-Co co-substituted Sr M-type hexaferrites with compositions of Sr_1−xLa_xFe_12−xCo_xO₁₉ (0.0 ≤ x ≤ 0.3) for a comparative study between bulk samples prepared with and without applying the MFP process.

2. Experimental

The La-Co-co-substituted Sr M-type hexaferrites with the nominal compositions of Sr_1−xLa_xFe_12−xCo_xO₁₉, (0.0 ≤ x ≤ 0.4) were prepared via a solid-state reaction in air. We measured the weights of SrCO₃ and Fe₂O₃ (purity 99.9%, Gojundo, Uiwang-si, Republic of Korea) to have the compositional ratio of Sr:Fe = (1 − x):(12 − x), added 0.3 wt% SiO₂ additive, and ball-milled the powder mixture with zirconia balls in ethanol for 24 h. The powder mixture was dried in an oven at 60 °C for 3 h. Then, the powder mixture was calcined at 1280 °C for 2 h in air. The substituents of La₂O₃ and Co₃O₄ powders (99.9% purity, Gojundo, Uiwang-si, Republic of Korea) and the additives of 0.7 wt% CaCO₃ and 0.4 wt% SiO₂ were added to as-calcined powder. The mixed powders were wet-milled with zirconia balls in ethanol for 24 h, dried in an oven at 60 °C for 3 h, and then pelletized with a uniaxial press (10 mm diameter) at a pressure of 220 MPa (Jeil Hydraulics, Seoul, Republic of Korea) to produce randomly oriented samples (Non-MFP1 samples). Also, ball-milled powders were mixed with a distilled water and pelletized with the uniaxial press at 1.5 tons, while applying the external magnetic field of 15 kOe to produce c-axis-aligned samples (MFP samples). We also prepared uniaxially pressed samples (1 inch diameter) at a pressure of 220 MPa and followed by CIP (cold isostatic pressing) with 1.5 tons of non-MFP2 samples. The resulting pellets were sintered at 1230 °C for 2 h, in air.

Powder X-ray diffraction (XRD, D8 Advance, Bruker, Billerica, MA, USA) was performed using a Cu Kα source (λ = 0.15406 nm). Phase identification was conducted with a divergence slit width of 0.2 mm, a voltage of 40V, a current of 40A, and a scanning speed of 2°/min. The lattice parameters were calculated based on the refined XRD data, using a Rietveld refinement analysis (Bruker TOPAS, V6, software). The microstructure and composition of the samples were analyzed using field emission scanning electron microscopy (FE-SEM, MERLIN Compact, Zeiss, Oberkochen, Germany) with an energy-dispersive spectrometer (EDS). The average grain size was evaluated by applying an intercept line method to the SEM micrographs. To observe the grain boundary, polished samples were thermally etched in a muffle furnace at 1130 °C for 0.5 h, in air. Magnetic hysteresis curves were measured at room temperature, using a vibrating sample magnetometer (VSM-7410, Lakeshore, Westerville, OH, USA) up to the maximum applied field of ±26 kOe. The samples were cut into a cube shape with the dimensions of 2.0 × 2.0 × 2.0 mm for the M-H measurement. The M_s and H_a values were determined using the law of approach to saturation (LAS) by fitting the initial curves. The B-H hysteresis curves were measured for the samples of 1 inch in diameter at room temperature using a B-H tracer (Permagraph C-300, Magnet-Physik, Cologne, Germany).

3. Results and Discussion

3.1. Characteristics of Randomly Oriented Polycrystalline Samples

3.1.1. Lattice Parameters and Microstructures

The powder XRD patterns of the Sr_1−xLa_xFe_12−xCo_xO₁₉ (0.0 ≤ x ≤ 0.4) samples sintered at 1230 °C for 2 h in air are shown in Figure 1. The diffraction peaks corresponding to the M-type hexaferrite phase are indexed with reference to the ICDD cards [00-033-1340]. From this figure, one can see that the M-type single phase is obtainable from x values up to 0.35. Previous studies have demonstrated that La and Co ions exhibit solubility in SrM in the x region of 0.0–0.35 [14,16]. However, the sample with x = 0.4 exhibits minor peaks of Fe₂O₃ [ICDD card 04-008-7623], LaFeO₃ [ICDD card 00-037-1493], and CoFe₂O₄ [ICDD card 00-022-1086], evidencing that this nominal composition is above the solubility limit of La-Co co-substitution in SrM and hence the M-type single phase composed of x = 0.4 is unobtainable at the sintering conditions of 1230 °C for 2 h in air.

Although a secondary phase is undetectable in the XRD pattern of the sample with x = 0.35 in Figure 1, we performed a SEM-EDS analysis for this sample to further identify whether it is composed of the M-type single phase or not. Figure 2 presents SEM backscattered electron (BSE) images, along with corresponding EDS element mapping micrographs illustrating the distribution of O, Fe, La, and Sr in the Sr_0.65La_0.35Fe_11.65Co_0.35O₁₉ (x = 0.35) samples. In Figure 2, a secondary phase exhibits a brighter contrast compared to the primary phase (SrM). Within this secondary phase, the Fe content is notably lower, while the Sr content is higher compared to the main phase. The phases are presumed to be (La, Sr), (Fe,Co)O₃, and CoFe₂O₄, although it was undetectable in the XRD patterns of the x = 0.35 sample shown in Figure 1. The solubility limit of La-Co in the SrM is believed to exist between x = 0.3 and 0.35 at 1230 °C, in air, from Figure 1 and Figure 2. Therefore, the secondary phases observed for the sample x = 0.4 in Figure 1 are presumed not to be Fe₂O₃, LaFeO₃, and CoFe₂O₄ but to be (Fe,Co)₂O₃, (La, Sr)(Fe,Co)O₃, and CoFe₂O₄ since Sr and Co can substitute for the La and Fe sites, respectively, except the spinel phase of CoFe₂O₄. No secondary phase was observed in the SEM-EDS analysis for samples with x ≤ 0.3, suggesting that the M-type single phase is achievable from the samples of x ≤ 0.3. The solubility limit of La-Co in the SrM is believed to exist between x = 0.3 and 0.35 at 1230 °C, in air, from Figure 1 and Figure 2.

Rietveld refinement was used to calculate the lattice parameters a and c, with R_wp (weighted profile R-value) < 9% and χ²(reduced Chi-squared value) smaller than 1.4 accuracy. The lattice parameters a and c were calculated from the d_hkl values obtained from powder XRD patterns based on the following equation [14],

$$d_{hkl}={\left\{\frac{4(h^2+hk+k^2)}{3a^2}+\frac{l^2}{c^2}\right\}}^{-1/2}$$

(1)

where d_hkl is the inter-planer spacing; and h, k, and l are the Miller indices. The cell volume (V_cell) was calculated from a²csin120°. The lattice parameters of Sr_1−xLa_xFe_12−xCo_xO₁₉ (0.0 ≤ x ≤ 0.30) samples are shown in Figure 3.

As shown in Figure 3, the lattice parameter a gradually decreases with the increasing x in Sr_1−xLa_xFe_12−xCo_xO₁₉ from 0.0 to 0.25, and then it turns to slightly increase with a further increasing x, up to 0.30, while the lattice parameter c monotonously decreases up to x = 0.30. The unit cell volume (V_cell) monotonously decreases with the increasing x from 0 to 0.3, as illustrated in Figure 3b. Notably, La³⁺ (1.22 Å) and Co²⁺ (0.75 Å) can substitute for Sr²⁺ (1.31 Å) and Fe³⁺ (0.65 Å) sites, respectively [33]. The ionic radius of La³⁺ is smaller than that of Sr²⁺, while the ionic radius of Co²⁺ is larger than that of Fe³⁺. As La-Co is co-substituted into SrM, and Fe²⁺ (0.78 Å) is formed due to a local substitution imbalance between La³⁺ and Co²⁺ [34,35,36]. According to Loan et al. [34], with an increasing x, there is a corresponding increase in the concentration of Co²⁺ occupying the 2a site of Fe³⁺ for x < 0.15. Furthermore, it can be inferred that the occupation of Co²⁺ at the 2a site results in the formation of Fe²⁺ at the 2a site.

Figure 3. The lattice parameters (a, c) (a) and unit cell volumes (V_cell) and the c/a ratio (b) for the Sr_1−xLa_xFe_12−xCo_xO₁₉ (0.0 ≤ x ≤ 0.3) samples sintered at 1230 °C (filled square) and post-annealed at 1230 °C (open triangle) for samples in Ref. [37].

Figure 3. The lattice parameters (a, c) (a) and unit cell volumes (V_cell) and the c/a ratio (b) for the Sr_1−xLa_xFe_12−xCo_xO₁₉ (0.0 ≤ x ≤ 0.3) samples sintered at 1230 °C (filled square) and post-annealed at 1230 °C (open triangle) for samples in Ref. [37].

In our previous study on La-Co-co-substituted SrM hexaferrites [37], the M-type single phase could be synthesized at 1300 °C for 2 h in air, without sintering additives. For a comparison with the present results, we performed additional post-annealing at 1230 °C for 2 h in air for those as-sintered samples in Ref. [37]. The lattice parameters a and c of the post-annealed samples are also represented in Figure 3a. Compared with post-annealed samples without sintering additives, the lattice parameter a showed no significant change, while the decrease in parameter c became more pronounced with the increasing x, particularly up to x = 0.25. Consequently, as shown in Figure 3b, the c/a ratio exhibited a significant decrease with an increasing x up to x = 0.25, while the V_cell values are somewhat peculiar variation. It is known that Si and Ca, used as sintering additives, can substitute for Fe and Sr sites, respectively [22,38], which most probably caused the above difference in the lattice parameter c. However, a negligible variation in c for x = 0.3 with sintering additives may be due to a reduced effect of the sintering additives on c at a much higher La-Co concentration relative to the amounts of sintering additives.

Consistent with previous reports on the Sr_1−xLa_xFe_12−xCo_xO₁₉ samples with sintering additives of SiO₂ and CaCO₃ [19,20], the lattice constant c continuously decreases while the lattice constant a negligibly changes with the increasing x. Iida et al. [19] and Ogata et al. [20] commonly attribute the variations in the lattice parameters only to differences in ionic radii between La³⁺ and Co²⁺ substituents and Sr²⁺ and Fe³⁺ ions in SrM, respectively, but not take the effect of sintering additives into account. However, since the sintering additives of SiO₂ and CaCO₃ contribute to the increase in the lattice parameter c up to x = 0.25, we argue that, when the sintering additives are used, their effects should be taken into account to understand the variation in the lattice parameters as a function of x if they substitute for the cation sites.

Figure 4 shows the SEM micrographs of the Sr_1−xLa_xFe_12−xCo_xO₁₉ samples (0.0 ≤ x ≤ 0.3). The average grain size (d_avg) and its standard deviation (SD) are listed in

Table 1. The average grain sizes corresponding to the average length of the hexagonal plate (d_avg) and the average thickness of the hexagonal plate (t_avg), its standard deviation (SD), average aspect ratio, average volume (V_avg), sintered density (D), and relative density (D/D_th) for the non-MFP1 Sr_1−xLa_xFe_12−xCo_xO₁₉ (0.0 ≤ x ≤ 0.3) samples sintered 1230 °C for 2 h in air.

	x = 0.0	x = 0.1	x = 0.15	x = 0.2	x = 0.25	x = 0.3
davg (μm)	1.20 ± 0.15	1.42 ± 0.54	1.66 ± 0.34	1.72 ± 0.66	1.81 ± 0.66	1.96 ± 0.87
tavg (μm)	1.10 ± 0.40	0.99 ± 0.34	0.97 ± 0.36	0.89 ± 0.31	0.91 ± 0.39	0.86 ± 0.30
Aspect ratio	1.09 ± 0.38	1.43 ± 0.40	1.71 ± 0.71	1.93 ± 0.24	1.99 ± 0.45	2.28 ± 0.35
Vavg (μm3)	1.03	1.30	1.74	1.71	1.94	2.15
D (g/cm3)	4.82	4.72	4.87	4.82	4.82	4.78
D/Dth	94.5	92.4	95.3	94.3	94.3	93.5

. The values of both d_avg and SD increase from 1.20 ± 0.15 μm to 1.96 ± 0.87 μm as x increases from 0.0 to 0.3, while the average thickness of the hexagonal plate (t_avg) of 0.95 ± 0.34 μm insignificantly changed. To determine the d_avg and t_avg values from the SEM micrographs composed of randomly oriented grains, we selected about 150 grains with a hexagonal plate shape and also about 150 grains with a rectangular shape, respectively. For this purpose, many different SEM micrographs were used for each composition x. The t_avg values from the rectangular grains are surely somewhat overestimated since the cross-sectional cut along the c-axis of each grain is less probable. However, although we take this overestimation into account, this t_avg evaluation of randomly oriented grains is very meaningful to compare with that of MFP-processed samples later. For this purpose, many SEM micrographs were used. As shown in Figure 4a, the sample of x = 0.0 exhibits a relatively smaller grain size and more uniform size distribution. However, the grain grows, and its size distribution becomes less uniform with the increasing x, as shown in Figure 4b–f. During the sintering process, a solid-state reaction leads to grain growth and densification, while a liquid-phase sintering can cause a rapid growth and densification even at a relatively lower sintering temperature [39]. The solid-state reaction of SrCO₃ and Fe₂O₃ to form SrFe₁₂O₁₉ is typically completed at the sintering temperature of 1200 °C [23]. Sintering additives such as SiO₂ and CaCO₃ are utilized to create a liquid phase during sintering, which might accelerate the formation of the M-type phase. Kang et al. [40] demonstrated that the grain growth behavior in polycrystalline ceramics can be explained by the relative values between the critical driving force and the maximum driving force for growth. The maximum and critical driving forces are influenced by factors such as the grain size, dopants, sintering atmosphere, and temperature. According to Moon et al. [41], the addition of Co₃O₄ to SrM as a sintering additive promotes the grain growth of M-type hexaferrite [41]. Therefore, the increase in the number of relatively larger grains shown in Figure 4b–f can be attributed to the compositional effect of La-Co substitution on these driving forces.

3.1.2. Magnetic Properties of Random Polycrystalline Samples

The initial magnetization curves and hysteresis loops of the Sr_1−xLa_xFe_12−xCo_xO₁₉ (0.0 ≤ x ≤ 0.3) samples are shown in Figure 5a,b, respectively. From the initial magnetization curves shown in Figure 5a, the M_S and H_a values of the samples were calculated using the law of approach to saturation (LAS) from the following equation [42]:

$$M=M_s\left(1-\frac{A}{H}-\frac{B}{H^2}\right)+{\chi }_{p}H$$

(2)

where M represents magnetization induced by an applied magnetic field, H; A is the inhomogeneity parameter associated with the material’s inhomogeneity; χ_p is the high field susceptibility; and B is the anisotropy parameter linked to magnetocrystalline anisotropy. The reported value for A is approximately 250 Oe in BaM [42], and the parameter χ_p becomes negligible in high magnetic fields. Therefore, Equation (2) can be approximated by the following equation:

$$M=M_s\left(1-\frac{A}{H}-\frac{B}{H^2}\right)$$

(3)

For a hexagonal crystal structure exhibiting uniaxial anisotropy, B can be expressed as follows:

$$B=\frac{H_a^2}{15}$$

(4)

The determination of M_S involves analyzing the linear portion of the M vs. 1/H² curves, with the condition that R² is greater than or equal to 0.999. The values for A and H_a can be calculated by fitting Equation (3) to the measured initial magnetization curves. It is important to note that R² is a statistical parameter reflecting the quality of the curve fit, and for reliable results, it should be at least 0.99. The A, M_S, and H_a values, along with their R² values calculated from Figure 5a and the intrinsic coercivity, H_ci, values from Figure 5b, for all samples are listed in

Table 2. The M_s, H_a, M_r, H_ci, A, field region for fitting, and R² values for the Sr_1−xLa_xFe_12−xCo_xO₁₉ (0.0 ≤ x ≤ 0.3) samples sintered 1230 °C for 2 h in air. The calculated values are presented with the error range.

x	Ms (emu/g)	Ha (kOe)	Mr (emu/g)	Hci (kOe)	A (Oe)	Field Region for Fitting (kOe)	R2
0.0	70.90 ± 0.01	17.7 ± 1.3	33.16	3.517	239	11–26	0.9944
0.1	71.28 ± 0.03	20.2 ± 1.4	36.30	3.645	230	12–26	0.9916
0.15	72.40 ± 0.04	21.1 ± 1.3	37.25	4.294	241	13–26	0.9912
0.2	71.91 ± 0.04	20.9 ± 1.1	36.03	4.295	227	13–26	0.9917
0.25	71.97 ± 0.05	22.7 ± 1.3	33.87	4.385	238	15–26	0.9976
0.3	71.38 ± 0.06	25.9 ± 1.5	36.17	5.001	240	17–26	0.9918

.

Figure 6 shows the dependencies of M_S, H_ci, and H_a on x from the data in Table 2. The M_S values increase from 70.90 to 72.40 emu/g as x increases from 0.0 to 0.15, and then they decrease to 71.38 emu/g up to x = 0.3. On the other hand, the H_a values increase from 17.7 to 25.9 kOe as x increases from 0.0 to 0.3. The H_ci values increase from 3.517 to 4.294 kOe as x increases from 0.0 to 0.15. The H_ci values increase slightly to 4.385 kOe at x = 0.2 and then increase to 5.001 kOe at x = 0.3.

In order to understand the effect of sintering additives on the intrinsic magnetic properties of M_s and H_a, we also evaluated those of La-Co-co-substituted SrM bulk samples without additives [37] and post-annealed at the same sintering conditions of 1230 °C for 2 h. Though not presented here, M_s values for present samples with additives are lower, i.e., below x = 0.15, but the difference in M_s becomes insignificant above x = 0.15. In the case of H_a, for the present samples with additives, it is lower only at x = 0.0, but the difference in H_a becomes negligible above x = 0.10. The conspicuous difference in both M_s and H_a at x = 0 most likely originates from the substitution of Ca and Si additive cations for the Sr and Fe sites, respectively. As x increases, the influence of sintering additives on M_s and H_a seems to become smaller because La-Co substituents affect them dominantly.

The M_s and H_a values evaluated using LAS have been reported for Sr_1−xLa_xFe_12−xCo_xO₁₉ samples by a few research groups [16,19]. Unfortunately, it is difficult to compare our M_s values with their values because detailed M_s evaluation procedures are not described in their papers. Nevertheless, our M_s values from x = 0.0 to 3.0, in Table 2, are in good agreement with those reported by Iida et al. [19], who employed the sintering additives of 0.4 wt% SiO₂ and 1.4 wt% CaCO₃. However, our M_s values were higher than those of Sr_1−xLa_xFe_12−xCo_xO₁₉ samples reported by X. Liu et al. [16], who employed SiO₂, CaCO₃, and Al₂O₃ (unknown wt%) as the sintering additives below x = 0.1; the difference becomes negligible above x = 0.1. On the other hand, our H_a values coincide with those reported only by Iida et al. [19] for the x values ranging from 0.10 to 0.25. Our H_a value is smaller for x = 0.0 but it becomes larger for x = 0.30, which may be due to the difference in the amounts of sintering additives.

As shown in Figure 6, H_ci increases with the increase in x. This variation in H_ci with x can be understood with the following relationship [43,44]:

$$H_{ci}=\alpha H_a-N(M_r+M_s)$$

(5)

The effect of the microstructure on H_ci is characterized by two factors: α and N. The first term in Equation (5) represents the magnetic field required to nucleate a reverse domain, and α increases as the grain size decreases. The second term includes N, M_r, and M_s. Here, N is the demagnetization factor, which increases as the grains become more platelet-shaped (i.e., with a higher aspect ratio). As shown in Table 1, increasing x results in larger average grain sizes and higher aspect ratios, causing a reduction in α and an increase in N, respectively. On the other hand, the combined value of M_r and M_s in Table 2 slightly increases up to x = 0.15 and then slightly decreases. Therefore, if H_a remains constant with x, the H_ci values should be continuously decreased, according to Equation (5). However, as shown in Table 2 and Figure 6, the H_ci values significantly increase with the increase in x, suggesting that such an increase in H_ci originates from the increase in H_a. The increase in H_a with the increasing x is ascribed to a continuous decrease in the crystal symmetry [14].

3.2. Characteristics of MFP-Processed Samples

3.2.1. Grain Alignments and Microstructures

The magnetic easy axis (c-axis) of M-type hexaferrite grains is aligned parallel to the applied field direction by the MFP process. Figure 7 shows the bulk surface XRD patterns of the MFP-processed Sr_1−xLa_xFe_12−xCo_xO₁₉ (x = 0.0, 0.15, 0.2, and 0.3) samples. From this figure, one can see that the bulk surface exhibits grain alignment primarily along the c-axis because the peaks of the (0 0 6), (0 0 8), and (0 0 14) planes are much larger than the main peak of the (1 1 4) plane. However, other peaks, such as the (1 0 7), (1 1 4), and (2 0 11) planes, are not negligible, implying that the c-axis alignment is insufficient.

The degree of orientation along the c-axis, w(00l), was calculated according to the following formula [45]:

$$w\left(00l\right)=\frac{\frac{\sum I\left(00l\right)}{\sum I\left(hkl\right)}-\frac{{\sum I\left(00l\right)}^{\mathsf{\theta }}}{{\sum I\left(hkl\right)}^{\mathsf{\theta }}}}{1-\frac{{\sum I\left(00l\right)}^{\mathsf{\theta }}}{{\sum I\left(hkl\right)}^{\mathsf{\theta }}}}$$

(6)

where the X-ray-integrated intensities of the (00l) plane and the (hkl) plane are represented by ∑I(00l) and ∑I (hkl), respectively. Similarly, the X-ray-integrated intensities of the (00l) plane and the (hkl) plane of the non-oriented powder sample are denoted by ∑I(00l)^θ and ∑I(hkl)^θ, respectively. The w(00l) values evaluated for the MFP samples using Equation (6) are presented in Figure 7. As shown in this figure, the w(00l) increases from 42.4 to 55.9% with the increasing of x from 0.0 to 0.3.

Figure 8 shows the SEM micrographs of the MFP-processed Sr_1−xLa_xFe_12−xCo_xO₁₉ (x = 0.0, 0.15, 0.2, and 0.3) samples. Figure 8a–d show the plane view perpendicular to the applied field, while Figure 8e–h show cross-sectional view parallel to the applied field. Consequently, the grains shown in Figure 8a–d predominantly represent the basal planes of hexaferrites, while those in Figure 8e–h represent cross-sectional views of hexagonal plates. Non-MFP1 samples exhibit non-uniform grains due to the random orientations of adjacent grains (see Figure 4).

The average grain sizes (d_avg), corresponding to the average length of the hexagonal plate, and the average thickness of the hexagonal plate (t_avg) were determined from the micrographs shown in Figure 8. The values and their standard deviation (SD) of d_avg and t_avg are listed in

Table 3. The average grain sizes corresponding to the length of the hexagonal plate (d_avg) and the thickness of the hexagonal plate (t_avg), its standard deviation (SD), average aspect ratio, average volume (V_avg), sintered density (D) and relative density (D/D_th) for the Sr_1−xLa_xFe_12−xCo_xO₁₉ (x = 0.0, 0.15, 0.2, and 0.3) MFP samples sintered 1230 °C for 2 h in air.

	x = 0.0	x = 0.15	x = 0.2	x = 0.3
davg (μm)	1.30 ± 0.35	1.34 ± 0.33	1.37 ± 0.27	1.38 ± 0.20
tavg (μm)	1.18 ± 0.21	0.92 ± 0.09	0.82 ± 0.08	0.77 ± 0.05
Aspect ratio	1.10±0.31	1.46±0.20	1.67±0.22	1.79±0.12
Vavg(μm3)	1.30	1.07	0.99	0.95
D(g/cm3)	4.92	4.93	4.93	4.92
D/Dth	96.2	96.5	96.5	96.2

. The average aspect ratio calculated by d_avg/t_avg and the average volume (V_avg) are also listed in Table 3, together with the measured sintered density (D) and evaluated relative density (D/D_th). As shown in Table 3, the d_avg value slightly increases from 1.30 to 1.38 μm as x increases from 0.0 to 0.3, while the SD values are decreased from ± 0.35 to 0.20 μm. Also, the t_avg values of samples decreased from 1.18 to 0.77 μm with the increasing x value, and their SD values also decreased from ± 0.21 to 0.05 μm.

M-type grains have been reported to have a hexagonal plate shape, with the basal plane perpendicular to the c-axis [1], which can also be observed in the planar microstructure in Figure 8. To grow into a hexagonal plate shape, the a-axis growth rate must be faster than the c-axis growth rate. Grain growth occurs via the diffusion of components through the liquid phase formed at the grain boundary during the sintering stage. Through the MFP process, the c-axis of the plate-shaped M-type grains can be dominantly aligned parallel to the applied field. Since the basal plane orientation is in the same direction as other grains during sintering, growth may be hindered, resulting in a slight increase in x.

The d_avg, t_avg, and aspect ratios listed in Table 1 and Table 3 are represented as a function of x for non-MFP1 and MFP samples, respectively, in Figure 9. Interestingly, as shown in Figure 9a,b, with the increasing x, while the d_avg values continuously increase and the t_avg values slightly decreases for non-MFP1 samples, the d_avg values remain almost constant, and t_avg values continuously decrease for the MFP samples. In addition, except for x = 0.0, both the d_avg and t_avg values of the MFP samples become smaller than those of the non-MFP1 samples with the increasing x. These differences result in an opposite variation in the average grain volumes with the increasing x, as shown in Figure 9c, while the aspect ratios of MFP samples are relatively lower than those of non-MPF1 samples; however, both increase with the increasing x, as shown in Figure 9c.

3.2.2. Magnetic Properties of MPF-Processed Samples

Figure 10a–c show the demagnetization (second quadrant of 4πM-H and B-H) curves and plots of B vs. (BH)_max for Sr_1−xLa_xFe_12−xCo_xO₁₉ samples (x = 0.0, 0.15, 0.2, and 0.3) processed with and without MFP process and sintered at 1230 °C for 2 h. Here, the direction in which the magnetic field is applied during the B-H measurement coincides with the applied field direction during MFP. The 4πM_r, H_ci, and (BH)_max values for these samples are listed in

Table 4. The 4πM_r, H_c, (BH)_max, and squareness Q values for the Sr_1−xLa_xFe_12−xCo_xO₁₉ (x = 0.0, 0.15, 0.2, and 0.3) samples sintered at 1230 °C with and without MFP process.

	MFP Samples					Non-MFP2 Samples
x	4πMr (kG)	Hci (kOe)	Hcb (kOe)	(BH)max (MGOe)	Q	4πMr (kG)	Hci (kOe)	Hcb (kOe)	(BH)max (MGOe)	Q
0.0	3.74	3.14	2.72	3.11	0.68	2.24	3.36	1.93	0.93	0.14
0.15	4.05	3.59	2.98	3.62	0.65	2.42	4.09	1.95	1.08	0.12
0.2	3.91	3.61	3.02	3.39	0.65	2.35	3.93	1.75	1.04	0.12
0.3	3.75	3.84	3.15	3.27	0.74	2.18	4.57	1.74	0.88	0.09

. Squareness, Q, is defined by Q = H_k/H_ci, where H_k is the knee field corresponding to a magnetization of 90% of B_r. As shown in Table 4, the highest induction remanence (B_r or 4πM_r) and the largest (BH)_max of 4.05 G and 3.62 MGOe, respectively, are obtainable from the MFP sample of x = 0.15.

The increase in H_ci for MFP samples listed in Table 4 is primarily influenced by the increase in H_a listed in Table 2, according to Equation (5). While the increment in H_a from x = 0.2 to 0.3 is about twice as much as that from x = 0.0 to 0.15, the increment in H_ci for MFP samples is reduced by about 0.76. Therefore, it is difficult to explain the variation in H_ci solely by the variation in H_a. According to Equation (5), H_ci is dependent on the magnetic properties, such as H_a, M_s, and M_r, as well as the microstructure factors of α and N. Meanwhile, the MFP process can largely enhance the grain alignment, and thereby M_r is abruptly increased, which may cause a significant decrease in H_ci, according to Equation (5) for a given composition, x. Interestingly, however, after MFP, the 4πM_r(or B_r) values increase from x = 0.0 to 0.15 and then decrease to x = 0.3, while H_ci continuously increases with the increasing x, suggesting that the 4πM_r increase is not always accompanied by an H_ci decrease for different x values. Furthermore, as shown in Figure 9, after MFP, the increase in aspect ratio with x leads to an increase in N and decrease in α, which is presumably responsible for the additional reducing effect on H_ci. Consequently, since the increasing effect of H_a is dominant compared with the decreasing effects of M_r and the microstructure factors α and N, H_ci is considered to increase with the increasing x for MFP samples.

Figure 11 shows the H_ci values versus x in (a) and also versus 4πM_r in (b) for Sr_1−xLa_xFe_12−xCo_xO₁₉ samples (x = 0.0, 0.15, 0.2, and 0.3) with and without the MFP process. As shown in Figure 11a, H_ci increases from 3.14 to 3.84 kOe in the MFP samples with increasing x from 0.0 to 0.3. This increasing tendency of H_ci with x is also commonly observed for non-MFP samples in this figure. However, the H_ci values for a given x decrease with increasing grain alignment. The w(00l) values for non-MFP2 samples evaluated by Equation (6) were 33.4, 35.3, 33.9, and 41.2% for x = 0.0, 0.15, 0.20, and 0.30, respectively, while those could not be evaluated for non-MFP1 samples. Somewhat enhanced grain alignments for non-MFP2 samples might be induced by the higher pressure of the CIP. As shown in Figure 11b, with the increasing grain alignment for a given composition, x, the increase in M_r always results in the decrease in H_ci for all compositions according to Equation (5).

The serious decease in H_ci with improving the grain alignment have also been reported for M-type [46] and Nd-Fe-B [47] magnets. Since it has been suggested that H_ci can be enhanced through simulations on grain boundary diffusion in SrM [48], it may be possible to further improve the H_ci values of MFP samples by using more appropriate sintering additives to ensure smaller average grains and also the presence of a secondary phase at the grain boundary.

Figure 12 shows the B_r, H_ci, and (BH)_max values versus x and also B_r versus M_r/M_s for MFP-processed Sr_1−xLa_xFe_12−xCo_xO₁₉ samples (x = 0.0, 0.15, 0.2, and 0.3). The data of MFP-processed samples from Refs. [16,19] are also plotted on this figure for a comparison. As shown in Figure 12a, our B_r values are comparable to those from Liu et al. [16], who used different sintering additives (SiO₂, CaCO₃, and Al₂O₃), but much smaller than those from Iida et al. [19], who employed the same kinds of sintering additives but different amounts (0.4 wt% SiO₂ and 1.4 wt% CaCO₃); however, their M_s values are almost identical to our M_s values. As previously mentioned, the degree of grain alignment can be evaluated by several different parameters, such as degree of c-axis orientation, w(00l); squareness, Q; and the M_r/M_s ratio. All of these parameters are proportional to B_r for a given x. However, for different compositions, only the M_r/M_s ratio is proportional to B_r.

Thus, the much higher B_r values reported by Iida et al. are attributable to the higher degree of alignment indicated by higher M_r/M_s values in Figure 12d. Figure 12b shows that our H_ci values are much lower compared with those of previous reports, which are primarily due to the much larger average grain size in our samples. As shown in Figure 10 and Table 4, the highest (BH)_max was achievable from the sample of x = 0.15 among all of our MFP samples. Compared with the previously reported (BH)_max values in Figure 12c, we can see that our values are similar to those from Liu et al. [16] but much lower than those from Iida et al. [19], and this is also the case for B_r values. Consequently, the highest (BH)_max is obtainable from the highest B_r. As shown in Figure 12d, both the B_r and (BH)_max values are also proportional to the M_r/M_s ratio for all samples with different compositions. Consequently, in comparison with previous reports on MFP-processed Sr_1−xLa_xFe_12−xCo_xO₁₉ samples [16,19], our MFP samples exhibit relatively lower values of B_r, H_ci, and (BH)_max, and this is largely due to the fact that the processing conditions, such as particle size and distribution, sintering additives, and defoamer, which are closely related to c-axis grain alignment, have never been optimized yet in such a study. Particularly, K. Iida et al. [19] reported the highest (BH)_max value of 4.86 MGOe for x = 0.3, suggesting that the (BH)_max values in Table 4 could be enhanced by improving the grain alignment through a processing optimization.

4. Summary

Highly dense La-Co-co-substituted SrM samples could be prepared using the sintering additives of 0.7 wt% SiO₂ and 0.7 wt% CaCO₃ and the sintering conditions of at 1230 °C for 2 h, in air. The M-type single phase was obtainable up to x = 0.3 in Sr_1−xLa_xFe_12−xCo_xO₁₉. The lattice parameters a, c, and V_cell decrease with an increasing x.

For non-MFP samples, both H_a and H_ci showed an increase from 17.7 to 25.9 kOe and from 3.5 to 5.0 kOe, respectively, with an increasing x up to 0.3, while M_s increases from 70.90 to 72.40 emu/g with an increasing x from 0.0 to 0.15 and then decreases to 71.38 emu/g up to x = 0.3. The increase in H_a with an increasing x, due to a decrease in the lattice symmetry, is the primary reason for a continuous increase in H_ci. For the undoped sample of x = 0, there exists a significant difference in H_a and H_ci values between the present sample and the post-annealed sample without sintering additives, which is surely due to the effect of Ca and Si substitution for the Sr and Fe sites in SrM. However, with an increasing x, these values tend to converge. On the other hand, H_a can increase due to a gradual decrease in the lattice symmetry with an increasing x.

MFP-processed samples possess much higher B_r and (BH)_max values compared with non-MFP samples, and these values are attributable to significantly enhanced grain alignment along the c-axis. Unlike non-MFP samples, exhibiting a significant increase in d_avg and its standard deviation from 1.20 ± 0.15 μm to 1.96 ± 0.87 μm, but almost unaltered average thickness(t_avg) of ~0.95 ± 0.34 μm with increasing x from 0.0 to 0.3, MFP-processed samples exhibited an almost-unaltered d_avg of ~1.35 ± 0.29 µm but a continuous decrease in t_avg from 1.18 ± 0.21 to 0.77 ± 0.05 µm. Furthermore, while H_ci values are lowered due to MFP for a given x, they increased with the increasing x, which is similar to the behavior of non-MFP samples. For the samples with the same composition x, both B_r and (BH)_max are proportional to the degree of c-axis orientation w(00l), squareness Q, and M_r/M_s ratio. However, for the samples with different x values, those depend only on the M_r/M_s ratio.

In conclusion, compared with non-MFP samples, while the B_r and (BH)_max values of MFP samples are greatly enhanced due to grain alignment along the c-axis (i.e., easy axis), the H_ci values are decreased mainly due to the increase in B_r. In addition, referring to previous reports, although the highest (BH)_max value of 3.62 MGOe could be achieved from the MFP sample of x = 0.15 in this study, further improvement in B_r, H_ci, and (BH)_max is expected not only for this composition but also other compositions by optimizing the MFP process and sintering conditions, and hence leading to a highly dense microstructure consisting of better grain alignment and refined uniform grains. Consequently, the comparative study between MFP and non-MFP samples provides us valuable insights into a broad area of permanent magnet optimization.