Modelling data for Predicting New Iron Garnet Thin Films with Perpendicular Magnetic Anisotropy

These data include detailed calculations and graphs based on our manuscript submitted to Journal of Magnetism and Magnetic Materials, entitled “Predicting New Iron Garnet Thin Films with Perpendicular Magnetic Anisotropy”. These data are organized in two parts; first, we present the calculated plots of sensitivity of magnetic anisotropy field and anisotropy energy density for 49 epitaxial rare earth iron garnet (REIG) film/substrate pairs (a total of 98 plots, Figs. 1–15). In the second part, we present in Table 1 the complete details on the calculations for total magnetic anisotropy and all material constants used for each of 50 film/substrate pairs. The comparison with the previous experimental demonstrations is also shown in Table 1 (last column) and 2 with an accompanying discussion confirming the reliability of our model.


Data
This data article provides a detailed calculation of effective magnetic anisotropy energy density of 50 different rare earth iron garnet/substrate pairs. Figs. 1e15 demonstrate the sensitivity of total magnetic anisotropy energy density (left column) and magnetic anisotropy field (right column) on strain and saturation magnetization variabilities. Variation of effective magnetic anisotropy energy density and anisotropy field, respectively, are shown for  Table   Subject Materials Science Specific subject area Electronic, optical, and magnetic materials Type of data Table  Figure Text How data were acquired Effective magnetic anisotropy energy density terms and anisotropy field were calculated from K eff ¼ À 3 2 l 111 Y 1 À v ε jj þ 2pMs 2 þ K 1 , and H A ¼ 2 K eff Ms formulae; required parameters for calculations were used from tabulated values, or calculated individually using relevant formulae and filled in Table 1.
The plots of Figs. 1e15 were obtained using MATLAB. Data format Raw: tabulated intrinsic materials data Analysed: anisotropy terms calculated based on raw data Descriptive: effective magnetic anisotropy behaviour based on analysed data Parameters for data collection We used the intrinsic room temperature material properties (bulk saturation magnetization, magnetostriction constants, first-order magnetocrystalline anisotropy K 1 ) from experimental references. We used the same Poisson's ratio and Young's moduli for all REIG chemistries in our calculations.

Description of data collection
We collected our raw data from tabulated experimental intrinsic material parameters (lattice parameter, bulk saturation magnetization, Poisson's ratio, Young's modulus, magnetostriction constant, first-order magnetocrystalline anisotropy). Next, we calculated the analysed data (in-plane strain, stress, shape anisotropy K shape , magnetoelastic anisotropy K indu ) using the intrinsic material parameters. Finally, we used our analysed magnetic anisotropy data to calculate the effective anisotropy K eff and its classification as in-plane or perpendicular magnetic anisotropy (PMA Value of the Data The development of magnetic iron garnets with perpendicular magnetic easy axis (PMA) has been a major materials research area, which enabled researchers to start expanding the physics of spintronics and spin wave devices. Spintronic devices, especially emerging spin-orbit torque memory and logic devices, are expected to benefit from the development of rare earth iron garnets with tunable magnetic properties, magnetic anisotropy, crystal strain and structure and magnetooptical properties. There is no previous research in the literature that systematically investigates the ways in which one can change the composition of rare earth iron garnet thin films to tune magnetic anisotropy and achieve room temperature PMA. The PMA rare earth iron garnet films presented in this article are expected to be of interest for materials scientists working on magnetic oxides and devices, spintronic device researchers working on spin Seebeck effect, spin wave devices, spin logic, spin-orbit torques, all-optical switching, current-controlled magnetism, tunneling magnetoresistance studies, tunnel junctions and other spintronic effects involving unique transport and magnetooptical properties of thin film garnets. These predicted films offer materials scientists multiple material options to test under a variety of growth and postprocessing conditions. This article will be of interest also for spintronics, complex oxide, magnetooptics, spin logic and magnetism researchers.   Table 1 shows the theoretical, measured and calculated parameters of effective magnetic anisotropy energy density (K eff ). Table 2 includes the comparison of magnetic anisotropy state predicted by our model with previous experimental demonstrations.

Analytical calculation method of magnetic anisotropy energy density and field
In order to calculate the effective anisotropy energy density we used K eff ¼ K indu þ K shape þ K 1 equation to calculate the total anisotropy energy density for 50 thin film rare earth iron garnet/substrate pairs. Figs. 1e15 exclude the Gadolinium Iron Garnet (GdIG) film on substituted Gadolinium Gallium Garnet (SGGG) substrate because there is no lattice mismatch between the film and the substrate. Each anisotropy term consist of the following parameters: First-order magnetocrystalline anisotropy, K 1 , is an intrinsic temperature-dependent constant reported for each REIG material. Young's modulus (Y), Poisson's ratio (n) and magnetostriction constant (l 111 ) parameters evolving in the magnetoelastic anisotropy energy density term (first term) are considered to be constant according to the values previously reported. For shape anisotropy energy calculations (second term), bulk saturation magnetization (M s ) for each film was used. Since each film may exhibit variability in M s with respect to bulk, the model presented here yields the most accurate predictions when the experimental film M s , l 111 , Y, n and K 1 , and in-plane strain values are entered for each term. Table 1 shows the theoretical, measured and calculated parameters of anisotropy energy density terms and contributing parameters. In Table 2, we present a comparison of our model's predictions with the previous experimental studies. Anisotropy fields were calculated using H A ¼ 2 K eff Ms formula. The original Microsoft Excel and MATLAB files used for generating the data for Figs. 1e15 are also presented.

Predictive capability and validity of our model
We tested the prediction accuracy of our model by going through each available experimental demonstration of garnet thin film/substrate anisotropy characterization and comparing their measured anisotropy with the predictions of our model. Below, we show the prediction accuracy and cases where experiments are different from our predictions.
As shown in the table above, our model is able to predict the magnetic anisotropy state of almost all garnet/substrate combinations.