# Unexpected Ferromagnetism--A Review
## 2 Examples of \(d^{0}\) Ferromagnetism
### Non-Magnetic Oxides
#### 2.2.1 HfO\({}_{2}\)  
One of the most investigated materials in regard to its unexpected ferromagnetic behavior is hafnium oxide (HfO\({}_{2}\)). In 2004 it was discovered that HfO\({}_{2}\) exhibits ferromagnetic behavior at room temperature in the form of thin films without dopants, which came as a surprise, mainly because Hf\({}^{4+}\) and O\({}^{2-}\) are not magnetic ions [24].  
Over the last decade, there have been many theories regarding the unexpected ferromagnetic behavior, ranging from impurities to intrinsic defects, such as oxygen vacancies; however, there has not been a consistent conclusion. With the help of theoretical research, it was observed that the generation of magnetism is strongly related to highly concentrated defects that have a magnetic charge configuration. Due to the absence of 3D long-range order, amorphous materials tend to have higher concentrations of intrinsic defects than crystalline materials. Therefore, [PERSON] et al. fabricated amorphous nanostructured HfO\({}_{2}\) thin films using a glancing angle deposition technique in order to investigate its ferromagnetic behavior. Their results indicated that the obtained nanostructure exhibited room temperature ferromagnetism without doping which could have been attributed to oxygen vacancies. Moreover, it was observed that morphology strongly affects the intrinsic defects, enhancing the ferromagnetic behavior. Based on SEM and TEM analysis, it was determined that the films had a thickness of around 220 nm with a morphology-based on vertically aligned nano-helices structure. These structures had different screw pitches ranging from 0 to 210 nm; and based on the dimension of the screw pitch, it was observed that the number of spirals is inversely proportional--the smaller the pitch, the higher the number of spirals and the other way around. XPS analysis indicated that there is a difference between the spiral-containing samples and flat film samples. More specifically, the nanosamples with helix structures contained a higher proportion of oxygen deficiency-related peaks and lower proportions for the stoichiometric oxygen peak, correlating to a higher amount of oxygen vacancies than the flat films. Moreover, the analysis results indicated that the nanostructures have a higher bonding configuration for Hf. It was assumed that, due to the fact that the Hf\({}^{4+}\) ion has a high charge, it polarizes the neighboring oxygen shells; one electron from the oxygen vacancy would occupy the nearby Hf\({}^{4+}\) ion and yield Hf\({}^{3+}\) and F\({}^{+}\) center resulting in the generation of shallow and deep trap states. The authors proposed that this trapped electron that occupies an orbital overlapping with the unpaired electron of Hf\({}^{3+}\) is the origin of ferromagnetism in the studied nanostructures [25].  
Recent studies on different structures of HfO\({}_{2}\) based on first-principle numerical simulations have given some insight into the surface electronic and magnetic properties. The results indicated that there was a clear difference between non-stoichiometric Hf and O-rich surfaces. While both stoichiometric and Hf rich non-stoichiometric surfaces proved not to be magnetic, the O rich non-stoichiometric surfaces exhibited ferromagnetic behavior. Therefore, an O excess surface with asymmetric behavior may be needed to obtain ferromagnetism in simple non-magnetic oxides [26].