## 2 Materials and Methods  
M-type hexaferrites with nominal compositions of SrFe\({}_{12-2x}\)Si\({}_{x}\)Mg\({}_{x}\)O\({}_{19}\) (\(x\) = 0, 0.05, 0.1, 0.2), Sr\({}_{1-y}\)Fe\({}_{12-y}\)Si\({}_{y}\)K\({}_{y}\)O\({}_{19}\) (\(y\) = 0.05, 0.1, 0.2), and SrFe\({}_{12-z}\)(Si\({}_{0.6}\)Li\({}_{0.6}\))\({}_{2}\)O\({}_{19}\) (\(z\) = 0.05, 0.1, 0.2, 0.4, 0.6) were prepared using solid-state reaction routes. The precursor powders of 99.5% Fe\({}_{2}\)O\({}_{3}\) and 99.0% SiO\({}_{2}\) (industrial use), 99.9% SrCO\({}_{3}\), 99.9% Li\({}_{2}\)CO\({}_{3}\), 99.9% MgO, and 99.9% K\({}_{2}\)CO\({}_{3}\) (Kojundo Chemical Lab. Co., Ltd., Tokyo, Japan) were weighed according to the chemical formulae. The powder mixture was ball-milled in water for 24 h using a polypropylene jar (77 mm in diameter and 158 mm in height) and yttria-stabilized ZrO\({}_{2}\) balls with diameters of 3, 5, and 10 mm.  
The mixing ratios of the ZrO\({}_{2}\) balls with diameters of 3, 5, and 10 mm were approximately 50, 35, and 15 wt%, and their total weight was five times that of the total sample powder. The dried powder was placed in an alumina crucible and calcined at a temperature of 1100 \({}^{\circ}\)C in air for 4 h. The calcined powders were crushed, sieved, ball-milled again for 20 h, and dried. For samples with a selected composition, sintering additives, such as SrCO\({}_{3}\), CaCO\({}_{3}\), and SiO\({}_{2}\), were added in the second ball milling process before sintering.  
The milled hexaferrite powders were pressed in a mold with a diameter of 15 mm at a pressure of 16.7 MPa to produce disk-shaped green compact pellets. The pelletized samples were sintered in air in the temperature range of 1230-1250 \({}^{\circ}\)C for 2 h. During the sintering process, the heating rate was 5 \({}^{\circ}\)C/min, and the samples were then furnace-cooled to room temperature. For the selected composition of the samples, an anisotropic sintered magnet with a diameter of approximately 35 mm was fabricated at a ferrite magnet manufacturing site (Union Materials Corporation in Korea). Here, all process conditions except for the magnetic field molding process were performed in the same manner as for preparing an isotropic sintered body. During the molding process for anisotropic magnets, a magnetic field of 10 kOe was applied for the alignment of the hexaferrite particles, and the molding pressure was 3.92 MPa.  
The sample density was calculated based on the weight and geometric dimensions of the disk-shaped samples. X-ray diffraction (XRD, D8 Advance, Bruker) was performed for phase identification using a Cu K\(\alpha\) radiation source (\(\lambda\) = 0.15406 nm), and Rietveld refinement was performed on the selected samples. The fitting of the XRD patterns was conducted using the software TOPAS (Bruker, version 4.2). Field-emission scanning electron microscopy (FE-SEM, JSM-7610F, JEOL) was performed for phase identification.  
The average grain size was evaluated using a random intercept method applicable to the SEM micrographs. The magnetization curves were measured using a vibrating-sample magnetometer (VSM, Lakeshore 7410) at room temperature with a sweeping magnetic field within \(\pm\) 25 kOe for sintered samples with randomly oriented crystalline grains. The performance of the anisotropic magnets fabricated in a commercial magnet manufacturer (Union Materials Corp., Pohang, Republic of Korea) was characterized using a B-H loop tracer (BH-5501, Denshijiki Industry) at room temperature.