6.11.3 Garnets

Garnets are usually known as minerals. In the context of magnetic materials, garnets are represented by a general formula Y₃Fe₅O₁₂,  containing two magnetic ions, one typically being iron and another being rare earth. Here R, in addition to yttrium can be one of lanthanide atoms such as lanthanum, cerium, samarium etc.

The unit cell of Y₃Fe₅O₁₂  is cubic and contains 8 formula units i.e. 160 atoms, quite complex!
In garnet ferrites, orbital magnetic contribution of iron atoms is quenched due to shielding from crystal field while lanthanide ions contribute to both orbital and spin magnetic moment, thus contributing more to the total magnetic moment.

In this structure, R atoms are cubic coordinated i.e. 12-fold coordinated, 2 Fe atoms are octahedrally coordinated and the remaining three Fe atoms are tetrahedrally coordinated with antiparallel spin configuration of spins on tetrahedral and octahedral sites while orientation of spins on R-site is parallel to those on octahedral sites. We know that each Fe³⁺ ion  contributes 5μ_B which each lanthanide atom, R, contributes a moment of magnitude μ_Rμ_B where μ_R is the strength of moment of R ion. Hence the total picture looks like the following:

The value of μ_R is 7 for Gd while zero for Y.  As we see from the above schematic figure, net magnetic moment would be dominated by rate earth ions when  μ_R is greater than 5/3 .

This is dependent upon the temperature which governs the coupling between rare earth and Fe  ions. Typically the net magnetic moment drops as the temperature increases, especially for strongly magnetic ions like Gd, Tb and Dy. Gd-doped garnet of composition Y_1.2Gd_1.8 Fe₅O₁₂ has a rather stable saturation magnetization for a wide temperature range centered around ~50°C .

Garnets can be quite useful materials in microwave applications because of their high electrical resistivity and hence lower losses around microwave frequencies. The material is also easy to synthesize in either of bulk polycrystalline ceramic, single crystal or thin film forms. The structural parameters as well as magnetic properties can be tuned by tailoring the composition of the material.