# Unexpected Ferromagnetism--A Review
## 2 Examples of \(d^{0}\) Ferromagnetism  
### Alkaline-Earth Hexaborides  
Borides are a class of compounds which is highly attractive due to their crystal structure and bonding. The boron atoms are held together by strong covalent bonds (also described as \"covalent cage structure\"), which result in the materials' hardness, having an outcome of high melting temperatures. However, their mechanical features are not the reason why they attracted such attention. Their unique properties come from their electronic conductivity. Hexaborides have a deficiency in charge in their sub-lattice; however, they can gain electrons by \"trapping\" metal atoms due to the strong boron bonds. Both from an experimental and a theoretical point of view, it has been determined that they can gain two electrons; therefore, generating semiconducting divalent hexaborides and metallic trivalent hexaborides. Among all the properties exhibited by hexaborides, the one that has raised questions is the magnetic behavior of the alkaline-earth hexaborides (MB\({}_{6}\), where M = Ca, Ba, or Br). The reason for this is that, as mentioned above, in order for a material to exhibit magnetism, the main requirement is to have partially-filled \(d\) or \(f\) bands; however, alkaline-earth hexaborides, such as CaB\({}_{6}\), do not have electros on either \(d\) or \(f\) bands [13; 14]. An example of the crystal structure for CaB\({}_{6}\) is presented in Figure 1.  
The first ferromagnetic behavior in alkaline-earth hexaborides was reported by [PERSON] et al. in 1999 [15]. In this study, lanthanum-doped calcium hexaborides (CaB\({}_{6}\)) exhibited weak ferromagnetic behavior, where some La atoms were replaced by Ca atoms in the structure. It was initially considered that the main reason for this behavior was due to the supplementary electrons introduced by La, generating an excitonic insulator state. Though, later studies reported that weak ferromagnetic behavior was observed even in undoped CaB\({}_{6}\); and was attributed to Ca vacancies generated during synthesis [16]. Undoped CaB\({}_{6}\), SrB\({}_{6}\), and BaB\({}_{6}\) were investigated either as single crystals or as thin films, and they all exhibited weak ferromagnetic behavior at room temperature, which is believed to be a result of intrinsic defects [17; 18; 19]. [PERSON] et al. reported the synthesis of alkaline-earth hexaborides and investigated, amongst other features, their magnetic properties. They reported a single-step synthesis route for the fabrication of nanocrystalline hexaborides with tunable particle size. Their results indicated that all samples exhibited weak ferromagnetic behavior at room temperature. Moreover, their high-resolution transmission electron microscopy analysis suggested that one main factor determining magnetism was their intrinsic defects [20]. Recent studies on ternary alkaline earth hexaborides were made to correlate the local structure's deviations with the exhibited ferromagnetism. Using X-ray scattering measurements, Raman spectroscopy, and high-resolution transmission electron microscopy, the local structure of CaSrB\({}_{6}\), CaBaB\({}_{6}\), and SrBaB\({}_{6}\) were investigated. Local symmetry breaking in the B\({}_{6}\) sub-lattice was observed because of displacement disorder, as well as nano-domain generation due to rapid synthesis. The result suggested that the changes in the B\({}_{6}\) sub-lattice may help understand the weak ferromagnetic behavior exhibited by these hexaborides [21]. When discussing CaB\({}_{6}\) specifically, many theoretical points of view have been made in regard to its ferromagnetic behavior. Yet, amongst these, the one standing out is the one that the weak displayed magnetism in CaB\({}_{6}\) is a result of structural defects, such as vacancies in the B\({}_{6}\) lattice. Moreover, there have been studies on the surface of CaB\({}_{6}\) crystals which suggested that ferromagnetism may be determined by magnetic impurities, such as iron.