###### Abstract  
A series of charge-balanced Si\({}^{4+}\)-M\({}^{1+,2+}\) (M = Mg\({}^{2+}\), K\({}^{+}\), Li\({}^{+}\)) substitution compositions with the chemical formulae of SrFe\({}_{12-2}\)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\({}_{0.6}\))\({}_{x}\)O\({}_{19}\) (\(x\) = 0.05, 0.1, 0.2, 0.4, 0.6) were prepared using conventional ceramic processes. While the sole doping of Si with \(x\) = 0.1 (SrFe\({}_{12-y}\)Si\({}_{x}\)O\({}_{19}\) (\(x\) = 0.1)) causes a noticeable Fe\({}_{2}\)O\({}_{3}\) phase formation, the co-doping of Si-Mg and Si-Li allow a single M-type phase formation with x up to \(x\) = 0.1 and \(z\) = 0.4, respectively. Notably, a 2.6% increase in the saturation magnetization was obtained for Si-Li-substituted SrM with \(z\) = 0.05--that is, SrFe\({}_{11.95}\)Si\({}_{0.03}\)Li\({}_{0.03}\)O\({}_{19}\). Enhancement of the magnet performance can also be achieved when anisotropic permanent magnets are fabricated based on the substitution composition SrFe\({}_{11.95}\)Si\({}_{0.03}\)Li\({}_{0.03}\)O\({}_{19}\). The remnant magnetic flux density was improved by 2.5% compared to that of the unsubstituted SrM (from 4207 to 4314 G). The maximum energy product (BH\({}_{\text{max}}\)) value also increased from 4.24 to 4.46 M-G-Oe. The enhancement in permanent magnet performance is attributed to the increase in the M\({}_{\text{S}}\) of SrM by the optimal Si-Li substitution. This is a promising result because enhanced permanent magnet performance is achieved with intrinsic magnetic property improvement. M +
Footnote †: journal: Applied  
It has been reported that La-Zn [4; 5] or Mn-Zn [6] substitution into SrM increases the M\({}_{\rm S}\) because the non-magnetic Zn\({}^{2+}\) ions selectively replace Fe\({}^{3+}\) ions with spin directions that are antiparallel to the net magnetization direction. It has also been proven that La-Ca-Co co-substitutions into SrM are one of most successful approaches leading to significant improvement in the uniaxial magnetocrystalline anisotropy constant (K\({}_{\rm u}\)) without decreasing the M\({}_{\rm S}\). Thus, La-Ca-Co-substituted SrM has been commercialized into high-grade magnet products [7; 8; 9]. However, the doping of cobalt, a highly expensive element, significantly drives up its price. Therefore, reducing material costs without compromising the magnetic properties is an important concern in the research and development of permanent magnets. Recently, improved hard magnetic properties have been reported in hexaferrite nanomagnets prepared by sol-gel-based methods [16; 17; 18]. In these studies, a large coercivity (H\({}_{\rm C}\)) > 6 kOe was achieved owing to the nanocrystallization of hexaferrire grains. It is well-known that the coercivity of a single grain (\(h_{\rm C}\)) increases as its size decreases until it reaches the upper limit of the critical grain diameter for a single domain (\(d_{cri}\)). This exhibits a close reciprocal dependence of on grain size (\(d\)) as expressed in the below Equation [19]. \[h_{\rm C}=d_{cri}/d^{1.08} \tag{1}\]  
However, for the real application of sintered magnets, a process capable of mass production through a solid-state reaction method is required rather than a chemical synthesis, such as sol-gel. The successful development of a ferrite magnet requires not only improvement of the intrinsic hard-magnetic parameters (such as M\({}_{\rm S}\) and K\({}_{\rm u}\)) but also successful process control. The improvement of intrinsic magnetic properties can be achieved through the proper cation substitution. In process control, grain growth suppression and densification must be simultaneously performed during the sintering process. SiO\({}_{2}\) is a sintering additive that plays a crucial role in suppressing grain growth.