Figure 1. Alignments of magnetic domains in the absence and presence of a magnetic field. (a,b): Alignment of the magnetic domain in the absence and presence of a magnetic field (Microsoft Bing), respectively. (c,d): Images of the magnetic domain in the presence and absence of a magnetic field, respectively, acquired by a Lorentz electron microscope [3] (Published with permission of SPIE).

Conventionally used ferromagnetic materials exhibit some limitations, such as a low hardness, which hinders their application and has necessitated the development of better ferromagnetic materials [8]. When ferromagnetism was unexpectedly observed in Ge, Mn, and Te, several studies were conducted on inorganic nonmetallic materials, and many ferromagnetic materials were successfully discovered. Traditionally, ferromagnetism was believed to be demonstrated by elements with partially filled d or f orbitals. In contrast, when researchers revealed that an element without partially filled d or f orbitals could also exhibit ferromagnetism, it opened up a completely new realm in the field of ferromagnetism. Reducing one of the dimensions limits the electronic transition, promoting column interactions and increasing the bandwidth ratio. This increase in material–column interactions and bandwidth ratio induces magnetism in these materials [9]. Numerous materials with either partially filled f or d orbitals were both theoretically and experimentally analyzed. Nonmagnetic elements that show ferromagnetism in their oxide compounds or other forms are referred to as d⁰ ferromagnetic substances, and the corresponding ferromagnetism is termed d⁰ ferromagnetism. d⁰ Ferromagnetism was discovered for the first time in HfO₂ when the O-rich surface of Hf with no magnetic ions in HfO₂ exhibited ferromagnetism [10]. Thereafter, the ferromagnetic properties of oxides of other elements of the same period, including ZnO, Cu₂O, and TiO₂, were examined, and these oxides were found to demonstrate ferromagnetism; furthermore, numerous other nonmagnetic d-block elements, such as Sc, Cr, Mn, Zr, and Nb, were reported to exhibit ferromagnetism upon doping with some specific type of impurities [11]. Similarly, oxides of f block elements, such as CeO₂ doped with Co and Mn, were investigated to further explore this [12]. Moreover, the oxides of nonmagnetic elements without d or f orbitals, including Al₂O₃, In₂O₃, and CaO, demonstrated ferromagnetic properties, implying that these properties can be modified within elements [13]. Subsequently, the non-oxide nonmagnetic compound BN, C structures, and rock salts were also reported to possess considerable ferromagnetism [14]. Accordingly, it was concluded that modification of the internal environment of a nonmagnetic element or a ferromagnetic nonmetal by defects, such as valency complexes, vacancies, and impurities, arising from the integration of the element with another element, can induce magnetic properties [15]. Thus, the phenomenon of ferromagnetism is universal, and is demonstrated not only by magnetic elements, but also their impurities and non-magnetic elements by doping with oxide or other inorganic elements [16]. Furthermore, the drawbacks that limit the use of traditional magnetic elements have been overcome by mixing these elements with other compounds; for example, B [8]. Many modern medical procedures, such as varicose treatment, hyperthermia, and endovenous thermal ablation require local heating of the human body. However, it is challenging to convert electrical power into heat flux and directly transfer this heat flux to the required area without harming the surrounding tissue. Heating catheters composed of biocompatible magnetic composites with low-frequency induction heating (LFIH) is an effective solution in this regard [17]. Cu–Mn–Ga-based ferromagnetic shape memory single crystals were fabricated for the first time by annealing their cast polycrystalline alloys. Their functional properties have also been reported. The obtained results should be highly significant for the development of brittle ferromagnetic Cu–Mn–Ga alloys [18]. Numerous studies have been performed on the advancement of ferromagnetism, which have resulted in the discovery of numerous ferromagnetic compounds.

Boride compounds are gaining considerable attention because of their mechanical properties and high conductivities. They are widely used to overcome the hardness limitations of magnetic elements [8]. B, as an electron-deficient element, facilitates the trapping of electrons from other metal species by forming a strong B bond with these species. They produce either divalent-metal hexaborides or divalent hexaborides with alkaline-earth metals [19]. The hexaborides of alkaline-earth metals, including SrB₆, BaB₆, and CaB₆, are extremely sensitive to stoichiometry because of their high impurity contents and inferior physical properties. When these compounds were doped with Th and La, the resulting compounds demonstrated weak ferromagnetism at high temperatures [20]. Although these compounds lack d or f orbitals, their ferromagnetism has attracted significant research attention [11]. Divalent hexaborides (MB₆, M = Sr, Ba, Ca) crystallize in CsCl-type cubic structures, and their physical properties are substantially similar to those of Group IIA elements, that is, alkaline-earth metals [21]. The structure of a divalent hexaboride comprises a central metal ion surrounded by hexaboride ions (Figure 2). In the CaB₆ prototype structure, a single metal atom is surrounded by eight octahedra of B atoms, each centered on the corner of the cube. There are five B atoms in an octahedron, with four adjacent atoms and one along one of its axes. Moreover, 24 B atoms are coordinated at the center of the atom; nevertheless, no valence bonds are formed between them [22]. In contrast, the B atoms are covalently bonded to each other and are responsible for several physical and chemical properties of these compounds [23]. A cubic B sublattice is inherently electron-deficient because the B atoms must distribute their three valence electrons over five bonds. This implies that a sublattice cannot exist, even with the donation of electrons from the metals. Hexaborides must contain a metal cation with a charge of at least +2 to be electronically stable [24]. KB₆ with a low K content has been synthesized in controlled environments [25]. Consequently, considering that the B sublattice forms a semi-rigid “cage,” alkaline-earth, rare-earth, and some actinide cations are the only candidates in this regard based on their sizes and valences.