Determination of yttrium iron garnet superexchange parameters as a function of oxygen and cation stoichiometry

In this work, we describe the consequences of oxygen and metal-ion deficiency for the magnetic properties of a magnetic oxide in bulk and thin-film form. The influence of the off stoichiometry on valence of the iron atoms and the local structural configuration of these atoms is investigated in correlation with the magnetic Curie temperatures and the associated microscopic parameters, such as the exchange integrals. Combining both structural information obtained by x-ray absorption spectroscopy at Fe K edge and exchange integrals as determined from temperature-resolved magneto-optical magnetometry, we show that the electron-transfer integrals, underlying the superexchange interaction, control the global dependence of the Curie temperature on stoichiometry as should be expected. The determination of the electron-transfer integrals allows also the confirmation that metal-ion deficiencies in off-stoichiometric yttrium iron garnet (OS YIG) films lead to a significant increase in the magnetization (as observed experimentally). That can only be explained when considering a preferential site occupation of the iron vacancies on octahedral sites in agreement with our earlier work on OS YIG films [Y. Dumont et al., Phys. Rev. B 76, 6 (2007)]. Furthermore, the combination of the experimentally determined iron valence with the Fe(a)-O-Fe(d) bonding angle and the exchange integrals allows for the direct determination of the crystal electric field parameter and the Coulomb repulsion energy as a function of the stoichiometry of the YIG films.