Exceptionally high magnetization of stoichiometric Y₃Fe₅O₁₂ epitaxial films grown on Gd₃Ga₅O₁₂

Y₃Fe₅O₁₂ (YIG) is one of the most thoroughly studied magnetic materials and has been widely used in microwave applications in the past several decades due to its exceptionally low magnetic damping.¹ In recent years, YIG has played a central role in the emerging fields of ferromagnetic resonance (FMR) spin pumping and thermally driven spin caloritronics.^2–9 Previous studies and applications almost exclusively used bulk YIG crystals or μm-thick YIG films synthesized by liquid phase epitaxy. More recently, high quality thin YIG films of a few to hundreds of nm thickness grown by pulsed laser deposition^10,11 and sputtering^3,12,13 have attracted much attention and revealed exciting phenomena, particularly in spin pumping.^2,12–14 The static and dynamic magnetic characteristics of the YIG thin films depend on crystalline ordering, stoichiometry, and defect level. These characteristics in turn determine the behavior of spin transport in YIG-based heterostructures. Despite the extensive use of YIG thin films for these studies, a thorough characterization of the magnetization is generally lacking. Here, we report a systematic study of high quality YIG films grown by off-axis sputtering using complementary characterization techniques, which exhibit a surprisingly high magnetization.

YIG epitaxial films, 4 to 250 nm thick, were deposited on Gd₃Ga₅O₁₂ (GGG) (111) substrates using an ultrahigh vacuum off-axis sputter deposition system.^12,13 A sputtering gas of Ar + 1.05% O₂ with a total pressure of 11.5 mTorr was used. EPI-polished single crystal GGG substrates with a surface roughness of <5 Å were purchased from MTI Corporation. The GGG substrates were heated to 750 °C for YIG deposition and rotated at 10°/s. The growth rate was 16 nm/h at a radio-frequency power of 60 W.

We extensively characterized the quality and purity of the YIG films. These studies revealed highly ordered films essentially free of defects and impurities. The structural quality of the YIG films was examined by X-ray diffraction (XRD) using a Bruker D8 triple-axis X-ray diffractometer. Figure 1 shows the 2θ-ω scans for five YIG films 16, 24, 40, 80, and 164 nm thick, all of which exhibit distinct Laue oscillations, indicating that the films are highly crystalline, ordered, and uniform. Although the YIG(444) peak is overshadowed by the GGG(444) peak, the YIG(444) peak position can be accurately determined from the Laue oscillation satellite peaks. The out-of-plane spacing between adjacent YIG (111) planes is 7.175, 7.169, 7.161, 7.154, and 7.153 Å, corresponding to YIG cubic lattice constants of 12.427, 12.417, 12.403, 12.391, and 12.390 Å for the 16, 24, 40, 80, and 164 nm films, respectively. Given the dislocation-free, full epitaxy shown below by STEM images, the in-plane lattice constant of the YIG films should equal that of GGG (12.383 Å), resulting in minimal epitaxial strain with very small tetragonal distortions between 0.36% (16 nm) and 0.057% (164 nm).

The crystalline ordering of the 164 nm YIG film was further characterized by high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) using an FEI probe-corrected Titan³ 80–300S/TEM. Figure 2(a) shows a large-area STEM image of the (111)-oriented YIG/GGG viewed along the ⟨110⟩ direction, which demonstrates the high uniformity of the YIG film without any detectable defects. It directly measures the thickness of the film (164 nm). We also performed energy-dispersive X-ray (EDX) spectroscopy over the area marked by the yellow dashed box, which gives an atomic (at. %) composition of Y: 14.9 ± 1.2 at. %, Fe: 25.0 ± 3.4 at. %, and O: 60.1 ± 3.9 at. % using experimentally determined Cliff-Lorimer k-factors from a standard of equal thickness. This confirms proper stoichiometry (3:5:12 = 15%:25%:60%) within the instrument sensitivity. A high-resolution STEM image in Fig. 2(b) reveals clear atomic ordering of Y and Fe in the garnet lattice. In HAADF-STEM or “Z-contrast” (Z: atomic number) imaging, scattering is Rutherford-like in nature leading to an intensity that is approximately proportional to Z²: the most intense columns are pure Y (Z = 39), the least intense are pure Fe (Z = 26), and the intermediate-intensity columns contain alternating Y/Fe atoms. Thus, we identify the alternating pure Y and pure Fe columns along the blue dashed lines, while the green box marks a triplet of (Y/Fe)-Fe-(Y/Fe), which matches the overlaying ⟨110⟩ projection of the YIG lattice.

The STEM image of the YIG/GGG interface shown in Fig. 2(c) demonstrates a smooth transition from GGG to YIG without any visible transition layer or detectable defects such as dislocations. This high quality epitaxy arises from the fact that YIG and GGG are nearly perfectly matched with a lattice mismatch of only 0.057%, which is also why GGG is the ideal substrate for YIG growth. It clearly shows the atomic ordering of Gd/Ga in the GGG and Y/Fe in the YIG. The yellow box in Fig. 2(c) highlights a chain of -Ga-Gd-Fe-Y- atoms across the interface. The atomic ordering of YIG near the interface is the same as anywhere else deep in the YIG film.

In stoichiometric YIG, all Fe atoms should be Fe³⁺ where oxygen deficiency can lead to the presence of Fe²⁺ ions. To test for oxygen deficiency, we used electron energy loss spectroscopy (EELS) to measure the valence state of Fe in the YIG film. Figure 2(d) shows an EELS scan of the Fe L_2,3 edge in the YIG film, where only the Fe³⁺ L₃ (L₂) peak is present with the maximum at 709.5 eV (722.6 eV) and no Fe²⁺ at 707.8 eV (720.4 eV) is detected.^15,16 Quantitative analysis of the L_2,3 edge gives 99.0 ± 3.9% Fe³⁺, indicating a stoichiometric oxidation state. To probe whether there is interdiffusion at the YIG/GGG interface, we performed EDX line scans across the interface as indicated by the red dashed line in Fig. 2(c). Figure 2(e) shows the atomic percentages of Y, Fe, Gd, and Ga as a function of distance from the interface, which provides evidence of an interfacial transition region (from 0 to full intensity) of 1.4, 4.9, 2.8, and 4.8 nm, respectively. There is no detectable Gd and Ga in the YIG film beyond a few nm from the interface. The widths of the interfacial transition region may be due to delocalization of the X-ray emission signal or interdiffusion. As shown below, since the 4 nm YIG film exhibits high magnetization (2052 G) similar to that of the thicker films, the interdiffusion layer should be much thinner than 4 nm; thus, the widths of the EDX transition region are mostly due to delocalization of the X-ray emission.

Ferromagnetic resonance is a precise spectroscopic technique for quantitative measurement of magnetization and magnetic anisotropy. The angular dependencies of the FMR absorption for all of the YIG samples were measured in a microwave cavity using an X-band Bruker electron paramagnetic resonance (EPR) spectrometer. Figure 3(a) shows the derivative FMR absorption spectra for the 16 nm YIG film at a resonance frequency f = 9.61 GHz with the orientation of the applied magnetic field varying from in-plane (θ_H = 90°) to out-of-plane (θ_H = 0°) [see Fig. 3(b) for the experimental setup]. The in-plane linewidth is $ΔH$ = 4.3 G as shown in Fig. 3(c), which is very narrow for a 16 nm YIG film on GGG and indicates high magnetic uniformity. By plotting the angular dependence (θ_H) of the FMR resonance field (H_res), we can determine the effective saturation magnetization, $4πMeff =4πMs +H2⊥$⁠, where $Ms$ is the saturation magnetization and $H2⊥$ is the out-of-plane uniaxial anisotropy. The free energy for a cubic crystal structure in the presence of an applied magnetic field can be calculated using,^13,17

where $H4⊥$ is the out-of-plane cubic anisotropy, $H4||$ is the in-plane cubic anisotropy, $H2||$ is the in-plane uniaxial anisotropy, and θ and ϕ are the angles describing the orientation of the equilibrium magnetization (M) with respect to the film normal and in-plane easy axes, respectively. The equilibrium orientation (⁠ $θ, ϕ$⁠) at each θ_H can be obtained by minimizing $E$ in Eq. (1)^13,18

where $γ$ is the gyromagnetic ratio, from which the effective saturation magnetization can be extracted. Figures 3(d) and 3(e) show the angular dependencies of H_res for the 16 and 164 nm YIG films at room temperature, which give $4πMeff$ = 2172 ± 13 and 2141 ± 32 G, respectively. The saturation magnetization (⁠ $Ms$⁠) can be calculated by subtracting $H2⊥$ from $4πMeff$⁠. Previously, we studied the magnetocrystalline anisotropy as a function of the tetragonal distortion of YIG films grown on Y₃Al₅O₁₂ (YAG).¹³ From this dependence and the tetragonal distortion of the YIG films reported here—between 0.36% and 0.057%—the induced uniaxial anisotropy term would be rather small: 166 G for the 16 nm YIG films and 38 G for the 164 nm film. Thus, $4πMeff$ nearly equals $4πMs$⁠, especially for the thicker films. The values of $4πMeff$ obtained from the angular dependencies of H_res for YIG films from 4 to 250 nm thick are shown in Fig. 3(f), ranging between 2052 G (4 nm) and 2261 G (250 nm) at room temperature. All of these values are significantly higher than the previously reported saturation magnetization of 1797 G for YIG single crystals,¹⁹ motivating further investigation to confirm these results.

A second method to determine the YIG saturation magnetization is through the frequency dependence of H_res. We measured FMR absorption of the YIG films at frequencies ranging from 4 to 20 GHz using a microwave stripline. For each measurement, the magnetic field was swept with the microwave frequency fixed. The FMR signal was detected by applying a small modulation to the magnetic field and measuring the differential reflected microwave power with a Stanford Research 850 Lock-In amplifier after passing the reflected microwave signal through a DC-blocked, zero-biased Schottky diode detector. $4πMeff$ can be determined from the frequency dependence of H_res by fitting to the Kittel formula,^20,21  $ω=γHres(Hres+4πMeff)$⁠. Figures 4(a) and 4(b) show two representative f vs. H_res plots for the 16 and 164 nm YIG films, from which we obtain $4πMeff$ = 2273 ± 8 and 2156 ± 12 G, respectively. The values of $4πMeff$ for YIG films of 8–250 nm thickness, obtained from the frequency dependence of H_res, are also shown in Fig. 3(f). All of these (2156 to 2347 G) are again well above the reported value of 1797 G for YIG single crystals,¹⁹ even after subtraction of the out-of-plane anisotropy field. From the frequency dependence of the FMR linewidth, $ΔH$⁠, we can determine the Gilbert damping constant, $α$⁠, of the YIG films using,^9,21  $ΔH=ΔHinh+4παf3γ$⁠, where $ΔHinh$ is the inhomogeneous broadening. Figures 4(c) and 4(d) show the $ΔH$ vs. f plots for the 16 and 164 nm YIG films, yielding α = 6.6 × 10⁻⁴ and 9.4 × 10⁻⁴, respectively, which are representative for all of our YIG films. The inhomogeneous broadening of the YIG films ranges from 1.6 to 4.4 G. These low values of α and ΔH_inh are additional verification of the quality of these YIG films and well controlled oxidation states since oxygen deficiency increases damping.^9,21

To further confirm the surprisingly large magnetization of our YIG films obtained from the angular and frequency dependencies of H_res, we measured the saturation magnetization (⁠ $4πMs$⁠) of the 164 and 250 nm YIG films using a LakeShore vibrating sample magnetometer (VSM) at room temperature. Given the large paramagnetic background of the GGG substrate, these two thick films give the highest accuracy in the magnetization measurements. Figure 5(a) shows the room temperature in-plane hysteresis loop for the 164 nm YIG film after subtraction of the paramagnetic background, which gives $4πMs$ = 2020 ± 50 G. Similarly, the 250 nm YIG film was found to have $4πMs$ = 2085 ± 50 G. Both are considerably higher than the 1797 G reported for single crystal YIG at room temperature, confirming a surprisingly large saturation magnetization of our YIG films. In addition, the YIG films exhibit very small coercivity (H_c) with sharp magnetic reversal, such as in our earlier report of YIG films with H_c = 0.35 Oe and a nearly ideal square hysteresis loop, further indicating the high magnetic uniformity and low defect density of the YIG films.²² Figure 5(b) shows an out-of-plane magnetic hysteresis loop of the 164 nm YIG film, where the saturation field, H_sat = 2070 G, equals the effective saturation magnetization, corroborating the values obtained from the FMR measurements.

We also measured the temperature dependence of saturation magnetization for the 164 and 250 nm films in the VSM, as shown in Figs. 5(c) and 5(d), which exhibit a Curie temperature of 530 and 520 K, respectively, slightly below the value of 559 K reported for single crystal YIG.¹⁹ In addition, the angular dependence of the FMR was measured at low temperatures down to 20 K and the results are shown in Figs. 5(c) and 5(d). Despite the small differences between the saturation magnetizations obtained from the angular dependence of H_res, in-plane VSM, and out-of-plane VSM measurements, all of the data show low temperature saturation magnetization around 3000 G. This is well above the value of 2470 G reported for bulk YIG at 4.2 K,¹⁹ and more surprisingly, clearly higher than the maximum theoretical value of 2459 G at 0 K for Y₃Fe₅O₁₂.

Similarly, high magnetization has been previously reported for YIG films grown by pulsed-laser deposition.^11,23 For example, Kelly et al. obtained $4πMs$ = 2100 G for 20 and 7 nm YIG films grown on GGG,²³ which was attributed to an off-stoichiometry in their YIG films. However, our STEM, EDX, and EELS results demonstrate that our YIG films on GGG are stoichiometric without any detectable Gd or Ga in YIG and all Fe atoms are in the 3+ state (no Fe²⁺) within the resolution of the techniques. Thus, off-stoichiometry is not the cause of the high magnetization measured by multiple techniques in our YIG films over a broad range of thicknesses, but the underlying mechanism for this interesting phenomenon remains a tantalizing puzzle deserving further study. To elucidate whether the GGG substrate affects the YIG magnetization, we grew a 160 nm YIG film on the Y₃Al₅O₁₂ (YAG) (001) substrate. The measured magnetization of the YIG/YAG sample at various temperatures using VSM is shown in Fig. 5(c), which is clearly lower than that of the YIG films on GGG. A possible explanation for this decrease is the lower quality of YIG on YAG due to the larger lattice mismatch (3%). However, the XRD scan in the inset to Fig. 1 for this YIG/YAG sample demonstrates that the 160 nm YIG film is still of high crystalline quality with clear Laue oscillations and fully relaxed with a lattice constant of 12.386 Å. Thus, the surprisingly high magnetization observed in YIG/GGG could be due to some unexpected effect of the GGG substrate on the YIG films. Future characterization of these YIG films with high magnetization, such as element-specific magnetic moment measurements, and theoretical insights will be needed to reveal the underlying mechanism for this surprising observation. Nevertheless, the ability to tune the magnetization of a technologically important magnetic material such as YIG via epitaxy can potentially open opportunities for microwave and spintronic applications.

This work was primarily supported by National Science Foundation under Grant No. DMR-1507274 (sample growth and characterization, ISHE measurements and analysis). This work was supported in part by U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, under Award No. DE-FG02–03ER46054 (FMR measurements and modeling) and the Center for Emergent Materials, an NSF-funded MRSEC, under Grant No. DMR-1420451 (STEM characterization).