# Spinel Magnetic Iron Oxide Nanoparticles: Properties, Synthesis and Washing Methods
## 2 Crystal Structure and Magnetic Properties of Spinel Iron Oxide
### Magnetic Properties  
#### 2.2.1 General Information on Magnetism  
The magnetic materials are characterized by three main parameters:  
* Their magnetic moments (\(\overrightarrow{\mathrm{\mu}}\)) which can be assimilated at electric dipoles from orbital atomic moments and spin of materials. Under the effect of an imposed external magnetic field (\(\overrightarrow{H}\)), they tend to line up in the direction of the field which induces a magnetization within the material.
* Their magnetic susceptibility (\(\chi\)) representing the trend of magnetic moments of the material to be aligned by the presence of an external magnetic field and which can be defined by the magnetization ratio on the external field \(\overrightarrow{M}\)\(\overrightarrow{H}\).
* Their saturation magnetization (\(\mathrm{M_{s}}\)) representing the maximum value of the magnetization that a material can reach when the external magnetic field increases: it is given for a defined temperature.  
Generally, the field is expressed in Oersted, the magnetic susceptibility is not unity and the magnetization is expressed in emu (electromagnetism unit) per gram of sample.  
Two big families of magnetic materials exist: the unordered magnetic materials (non-cooperative magnetism) and the ordered magnetic materials (cooperative magnetism).  
In the first case, considering the unordered magnetic materials (non-cooperative magnetism), there is no spontaneous arrangement of their magnetic moments and therefor there is neither magnetic order nor spontaneous magnetization. We then differentiate:  
* The diamagnetism which is an intrinsic property of the matter such as \(\chi<0\). The magnetic moments with the application of an external field will tend to align in the opposite direction of this field.
* The paramagnetism which is a property due to free electrons of materials or unpaired electrons of ions such as \(\chi>0\). The magnetic moments will tend to align in the direction of an applied external field.  
In the second case of ordered magnetic materials (cooperative magnetism), there is a spontaneous arrangement of their magnetic moments \(\mu\) even in the absence of an external field. This spontaneous arrangement can be:  
* Parallel (ferromagnetism); this results in an overall measurable magnetization for the material even in the absence of an external magnetic field.
* Antiparallel with compensation of magnetic moments (antiferromagnetism); there exist two populations of magnetic moments aligned antiparallel to one another. The two populations of magnetic moments fully compensate and there is no overall magnetization measurable in the absence of an external magnetic field in this type of material.
* Antiparallel without compensation of magnetic moments (ferrimagnetism); a global magnetization is measurable for the material even in the absence of an external magnetic field.  
A schematic representation of the five types of magnetic behavior is presented Figure 3.  
In the three types of cooperative magnetisms, the susceptibility is positive and higher in absolute value than for paramagnetic materials. It should also be noted that the long distance magnetic order is only present for a temperature below a critical value called the Curie temperature (T\({}_{\text{C}}\)) for the ferromagnetism and ferrimagnetism compounds or for a temperature below at the Neel temperature (T\({}_{\text{N}}\)) for the antiferromagnetism materials. If the temperature is higher than one of these two critical temperatures, the thermal agitation becomes enough to suppress spontaneous magnetization and the material then becomes paramagnetic.  
Magnetite and maghemite present a ferrimagnetic behavior [5] for the temperatures below the Curie temperature, around 480 \({}^{\circ}\)C and 645 \({}^{\circ}\)C respectively. The saturation magnetization (M\({}_{\text{S}}\)) are around 92 emu/g for the magnetite and 74 emu/g for the maghemite [6]. These numeric values are reported for massive materials of magnetite and maghemite.