# Unexpected Ferromagnetism--A Review
## 1 Conventional vs. \(d^{0}\) Magnetism  
It is commonly known that, in order for a material to exhibit magnetic behavior, one of the most important requirements is to have partially filled \(d\) or \(f\) bands. The magnetic order is achieved by the exchange interactions among the above-mentioned partially filled bands. However, challenging to the common knowledge of how magnetism works, it has been discovered that some nanomaterials, with either entirely empty or full \(d\) and \(f\) bands, exhibit unexpected magnetic behavior. Unexpected magnetism can be induced by reducing one, or more, of the materials' dimensions. Reducing at least one dimension leads to the restriction in the electrons' tendency to \"jump\" from one atomic site to the other, also known as \"electron hopping\". Therefore, the kinetic energy of the electrons is diminished while increasing the ratio between the electrostatic interactions in electric charges and the kinetic energy (Coulomb interactions/bandwidth ratio); this enhances the possibility of reduced scale materials to exhibit magnetism [1]. Nanomagnetism is a field that studies the magnetic behavior of certain materials at a nanometric scale. Because of the increased surface-to-volume ratio, the magnetic features of nanomaterials can be fully contrasting from those of the bulk material, which have an identical chemical composition. Due to extensive research on the topic, the magnetic characteristics of bulk ferro- and antiferro-magnetic materials contrast with the corresponding material at the nanometer scale. Moreover, it has been observed that some nanomaterials may exhibit ferromagnetism at room temperature, in spite of the fact that the initial material is not magnetically active at all. There are several structural and geometrical features that control the magnetism behavior of a certain material: The distance between atoms, ligancy (coordination number), and symmetry. There are several consequences to modifying the structure of a nanomaterial. The modification of the local environment of the atoms can be attained through defect introduction, such as impurities, vacancies, and vacancy complexes. By reducing the ligancy and changing the symmetry, the energy levelbands are expected to narrow. This is the reason for the enhancement of magnetism in materials with ferromagnetic behavior; and could also explain why some non-magnetic materials exhibit magnetic behavior [2]. The main difference between non-magnetic and magnetic materials is that, for the first type, without the interference of an external magnetic field, the magnetization density is zero, whereas, for the latter, in the same conditions, the magnetization density is finite. Whereas the magnetic materials are attracted to an external magnetic field, many other materials are repelled by this kind of field, thus having a diamagnetic behavior. There are also paramagnetic materials that are weakly attracted by an external magnetic field, yet, unlike the ferromagnets, their magnetization vanishes when the field is removed due to the thermal motion, which causes random orientation of uncoupled spins. In order for an element to be in a ferromagnetic state, it has to have unpaired electrons and mechanisms that drive the ferromagnetic coupling of the mentioned unpaired electrons. However, even though the electrons of an atom have a magnetic field, this does not translate to the fact that the atom itself has a magnetic field. In order for this to happen, the unpaired electrons must be located in the outer shells. An example of an atom with a strong magnetic field is iron due to its four unpaired electrons found on the outer shell. However, even though the existence of unpaired electrons is necessary for ferromagnetism, it is not enough. The electrons found in higher orbitals have higher kinetic energy and, therefore, lower potential energy. This correlates to the need for unpaired electrons on low energy levels, meaning they are closer to the nucleus [2].