The bulk properties of RFe systems have been studied extensively for many years[25,26,27,28]. They show ferro- or ferrimagnetic structures in binary compounds. Their crystal structure is the cubic Laves Phase MgCu type, shown in Figure 6.1, and the iron atoms occupy corner-sharing tetrahedral networks with a (m) point symmetry and a threefold axis lying along one of the directions. This direction is the principal axis of the electric field gradient, . The rare earth atoms have a cubic (3m) site symmetry.
In the high temperature paramagnetic state the four iron sites are equivalent, giving a single Mössbauer spectrum. In the magnetically ordered state the number of sites which are magnetically equivalent or inequivalent depends upon the angle between the magnetisation and the axes of local symmetry along the 4 directions. If the magnetisation is parallel to the  direction (as in DyFe or HoFe) this makes an equivalent angle to all iron sites of 54.7. Again a single Mössbauer spectrum is observed.
If the magnetisation is parallel to the direction (as in YFe) there are two inequivalent types of iron site; one at an angle of 0 to the magnetisation and the remaining three at an angle of 70.5. The hyperfine interactions are different at the two sites due to the total hyperfine splitting at the nucleus being a function of the angle between the hyperfine field and the principal axis of the quadrupole interaction, , (Equation 2.21) and the angular dependence of dipolar fields on this same angle (Equation 2.20). Hence in a Mössbauer spectrum we would expect two components in a ratio of 3:1 and this is observed.
If the magnetisation is along an arbitrary direction then all the iron sites may be inequivalent, giving a Mössbauer spectrum with four components of equal intensity.
Dr John Bland, 15/03/2003