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 $\text{Fe}K$ 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 ${\text{Fe}}_a{\text{-O-Fe}}_d$ 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.

Figure 1

Variation in the (a) average lattice parameter and (b) Curie temperature of bulk YIG as a function of cation stoichiometry. The corresponding values for bulk stoichiometric (BS) YIG are given for comparison.

Figure 2

Variation in the (a) average lattice parameter as a function of the oxygen pressure during the deposition and in (b) Curie temperature as a function of the lattice parameter. The corresponding values for BS YIG are given for comparison.

Figure 3

Absorption spectrum of a YIG thin film prepared at 15 mTorr of oxygen pressure. The curve was normalized for the incoming x-ray intensity. The pre-edge background has been adjusted.

Figure 4

Shift of absorption pre-edge with respect to ${\text{Fe}}^{2+}$ and ${\text{Fe}}^{3+}$ references for (a) bulk YIG and (b) YIG thin films.

Figure 5

Back-transformed $\left(1–4.5\text{Å}\right)$ experimental EXAFS spectrum (dots) for a YIG thin film (prepared at 15 mTorr of oxygen pressure) compared to fit (line). Also reported (lines, shifted) are the contribution of the coordination shells included in the minimization procedure: ${\text{Fe}}_{d,a}\text{-O}$, ${\text{Fe}}_{d,a}\text{-Y}$, and ${\text{Fe}}_d{\text{-Fe}}_a$.

Figure 6

(Color online) Local distances in bulk YIG lattice with variable cation stoichiometry. ${\text{Fe}}_{d,a}$ stands for the iron atom in, respectively, tetrahedral or octahedral oxygen coordination. Dashed line represents the corresponding interatomic distance calculated from Refs. 16, 17.

Figure 7

(Color online) Local distances in thin-film YIG lattice with variable oxygen stoichiometry. ${\text{Fe}}_{d,a}$ stands for the iron atom in, respectively, tetrahedral or octahedral oxygen coordination. Dashed line represents the corresponding calculated interatomic distance (Refs. 16, 17).

Figure 8

Angle ${\text{Fe}}_d{\text{-O-Fe}}_a$ (a) for bulk YIG with variable cation stoichiometry and (b) for thin YIG films with variable oxygen stoichiometry. The corresponding $\alpha$, Y/Fe, and $a$ values for BS YIG are given for comparison.

Figure 9

(Color online) Schematic representation of superexchange coupling between two iron magnetic moments in (a) stoichiometric YIG. Variation in the ${\text{Fe}}_{d,a}\text{-O}$ distances and ${\text{Fe}}_d{\text{-O-Fe}}_a$ angles in the case of nonstoichiometry in (b) cations and (c) oxygen. The dashed lines and pale circles represent stoichiometric YIG from (a).

Figure 10

(Color online) (a) Thermal variation in the Faraday rotation (solid circles), the magnetization (triangles), the resulting fits of the magnetization modeling (see text) and the calculated sublattice magnetizations ($n_a$ and $n_d$—dashed-dotted and dashed lines, respectively). (b) Variation in $T_C$, of the experimentally determined magnetization $n_{exp}$ and the sublattice magnetizations, $n_a$ and $n_d$, with the lattice parameter. (c) Variation in the three exchange integrals, $j_{aa}$, $j_{dd}$, and $j_{ad}$ compared to the calculated variation in the crystal-field parameter $D_q$ as a function of the lattice parameter.