High-quality thulium iron garnet films with tunable perpendicular magnetic anisotropy by off-axis sputtering – correlation between magnetic properties and film strain

Thulium iron garnet (TmIG) films with perpendicular magnetic anisotropy (PMA) were grown on gadolinium gallium garnet (GGG) (111) substrates by off-axis sputtering. High-resolution synchrotron radiation X-ray diffraction studies and spherical aberration-corrected scanning transmission electron microscope (Cs-corrected STEM) images showed the excellent crystallinity of the films and their sharp interface with GGG. Damping constant of TmIG thin film was determined to be 0.0133 by frequency-dependent ferromagnetic resonance (FMR) measurements. The saturation magnetization (Ms) and the coercive field (Hc) were obtained systematically as a function of the longitudinal distance (L) between the sputtering target and the substrate. A 170% enhancement of PMA field (H⊥) was achieved by tuning the film composition to increase the tensile strain. Moreover, current-induced magnetization switching on a Pt/TmIG structure was demonstrated with an ultra-low critical current density (jc) of 2.5 × 106 A/cm2, an order of magnitude smaller than the previously reported value. We were able to tune Ms, Hc and H⊥ to obtain an ultra-low jc of switching the magnetization, showing the great potential of sputtered TmIG films for spintronics.

Utilizing the electron's second fundamental characteristic-spin, advances in spintronic research such as spin-transfer torque (STT) and spin-orbit torque (SOT) have recently attracted enormous attention. Especially, the manipulation of the magnetization of a ferromagnet in using a pure spin current generated by large spin-orbit coupling materials is a fascinating topic for both fundamental research and technological application. A pure spin current injected to a ferromagnet will induce two types of SOTs, i.e., a damping-like torque (DLT) directed along ˆ× m (ˆσ × m ) and a field-like torque (FLT) along ˆm σ × , where m and σ represent the unit vectors of magnetization M and spin polarization, respectively. SOTs have been experimentally verified to perform the magnetization switching 1 , which paves the way to realize all-electrical control of the magnetization.
Among various ferromagnets, ferrimagnetic insulators (FIs) of rare earth iron garnets have attracted a great deal of interests because of their unique properties. Yttrium iron garnet (YIG) [2][3][4][5] and lutetium iron garnet (LuIG) 6 possess ultra-low intrinsic damping constants, which benefits spin transport studies such as long-range spin wave propagation, efficient spin pumping, SOT and spin-torque ferromagnetic resonance (ST-FMR). Moreover, thulium iron garnet (TmIG) films grown on (111)-oriented gadolinium gallium garnet (GGG) substrates were reported to show stress-induced PMA 7,8 . Recently, SOT-driven magnetization switching has been demonstrated in Pt/TmIG hetero-structures 9 . The pure spin currents injected to TmIG exert a torque and reverse the magnetization at low current densities. The pure spin currents can be induced not only by spin Hall effect (SHE) in Pt/TmIG hetero-structures, but also by Rashba-Edelstein effect (REE) in TI/TmIG hetero-structures. A charge current directed in the plane of TI induces nonequilibrium spin polarization by REE and leads to a torque acting on the magnetization of the magnetic layer 10 . A higher efficiency is expected because of the spin-momentum locking features of topological surface states. PMA can reduce the threshold switching current and maintain high thermal stability of the magnetization; the electrically insulating property of TmIG also circumvents the shunting effect. High-quality TmIG films pave the way towards ultra-low current-induced SOT for magnetization manipulation in ferromagnetic hetero-structures with high SOT efficiency, thus realizing the magnetization switching, magnetic oscillation and ultrafast chiral domain wall motion. These can be applied to data storage, magnetic random access memory, logic/memory utilizing domain wall 9 .
It was reported that TmIG films had been grown mostly by pulsed laser deposition (PLD) [7][8][9]11,12 . However, the small deposition area is the major shortcoming of PLD, limiting its application in industry. As an alternative way to deposit oxide thin films, we have successfully utilized off-axis magnetron sputtering to grow high-quality TmIG films with excellent crystallinity and PMA on GGG(111) 13 and observed a negative magnetoresistance in TI/ TmIG hetero-structures, revealing time-reversal symmetry breaking in TI 14 . The advantage of off-axis sputtering includes fewer ion bombardments and applications of large-scale growth. In this work, we perform the systematic study on the magnetic and structural properties of films with different Tm/Fe ratios. We have examined the excellent crystallinity of TmIG films by spherical aberration-corrected scanning transmission electron microscope (Cs-corrected STEM), and determined the damping constant of the TmIG thin films by frequency-dependent ferromagnetic resonance (FMR) measurements. Off-stoichiometric TmIG films with Fe-rich composition possess smaller lattice constants and larger in-plane tensile strains on GGG(111). We further demonstrated the tunability of PMA by varying the film composition, which verified that PMA in TmIG films was manipulated by the film strain, and is originated from the magnetostriction effect. Remarkably, the notable enhancement of perpendicular magnetic anisotropy field (H ⊥ ) was achieved by increasing the in-plane tensile strain. Moreover, the current-induced magnetization switching of Pt/TmIG with the ultra-low critical current density 2.5 × 10 6 A/ cm 2 was reported. We also estimated the real part G r and the imaginary part G i of spin mixing conductance in Pt/TmIG to be 1.1 × 10 15 Ω −1 m −2 and 1.2 × 10 14 Ω −1 m −2 , respectively from the transverse resistance of Hall measurements, which implied the efficient spin transfer at the interface between Pt and TmIG. Our work of high-quality, highly tunable PMA TmIG films provides a new route to tailoring rare earth iron garnet films for spintronic application.

Results and Discussion
TEM and STEM images of TmIG thin film. Figure 1 shows the structural and magnetic properties of the optimized off-axis sputtered TmIG thin film on GGG(111) with a longitudinal distance of 7 cm 13 . The cross-sectional TEM image and the energy-dispersive X-ray spectroscopy (EDS) element mapping images shown in Fig. 1(a) show the uniform composition distribution in each layer and show no obvious chemical intermixing at the interface of the TmIG/GGG thin film. Figure 1(b,c) are the cross-sectional high-angle annular dark-field (HAADF) images of Cs-corrected STEM with atomic resolution, showing excellent crystallinity of the TmIG. The spots with brighter contrast denote the heavier atoms in the samples, and the spots match very well with the purple dots representing heavier atoms of Gd in GGG and Tm in TmIG thin films plotted by a crystallographic program. Furthermore, a sharp and nearly perfect interface between the TmIG and GGG layers was observed, showing no visible interfacial defect and dislocation. The STEM results show that the TmIG film was epitaxially grown on the GGG substrate with exactly the same crystal structure and the same orientation with the sharp interface. The STEM results are in agreements with the XRD results showing the extended Pendellosung fringes.
Damping constant of TmIG thin film. We conducted the frequency-dependent ferromagnetic resonance (FMR) measurements on the TmIG films to extract the damping constant. The linewidth of the FMR spectrum (ΔH) increased linearly as a function of the microwave frequency with the magnetic field applied out of plane, and in the plane as in Fig. 1(d,e), respectively. The damping constants α was extracted by fitting ΔH as a function of frequencies (f = ω/2π), where γ denotes the gyromagnetic ratio and ΔH 0 denotes the film inhomogeneity line broadening. The damping constant α of TmIG film was then determined to be 0.0133 with the field out of plane, and 0.0146 with the field in the plane. The slightly larger α value measured with the magnetic field applied in the plane than the out-of-plane might be an indication of the two-magnon scattering (TMS) [15][16][17] . The TMS is due to the film inhomogeneity (such as grain boundaries and voids) and makes significant contributions when the applied magnetic field is not along the film normal direction. The contribution of TMS to α is minimized when the field is normal to the sample plane when conducting the FMR measurements.
TmIG film composition tuning: tensile strain and magnetic properties. The surface normal XRD scans of the samples A, B, C, D and E are shown in Fig. 2(a). Note that these five TmIG films were sputtered at longitudinal distance L of 5, 6, 7, 8, and 9 cm, respectively, varying the composition and the strain in the films. Clear Pendellosung fringes in all TmIG films exhibited the excellent film quality. Out-of-plane lattice constants of samples A, B, C and E were 12.274 Å, 12.289 Å, 12.299 Å and 12.302 Å, respectively. The gradual increase of the out-of-plane lattice constant reflected a Tm-richer composition as L increased, consistent with the previous composition investigation 13 . The Tm: Fe ratio of samples are determined by Rutherford backscattering spectrometry (RBS) and X-ray photoelectron spectroscopy (XPS) in the Supplementary information S1. For a reference TmIG sample grown at L = 7 cm, the Tm: Fe ratio was measured as 0.57 by RBS.  8 . We calculated and summarized the out-of-plane lattice constants and the in-plane strain in Fig. 2(b). We show that the in-plane tensile strain can be tuned systematically from 0.353% to 0.476% with decreasing L by off-axis sputtering without altering the substrates.
Enhancement of perpendicular magnetic anisotropy field by tensile strain. The   In the Fe-rich films, the Fe would occupy the Tm site and reduce the total moment, because of the larger moment of Fe than that of Tm 18 . As for the Tm-rich films, we observed the moment decreasing. The tetrahedral sites are much smaller than the octahedral sites for the Tm to occupy. However, if Tm ions occupied the octahedral sites, the total moment would increase. Based on our results, the magnetization seems not to be dominated by the occupation of Tm ions on the octahedral sites. On the other hand, in Tm-rich films, there is another possibility that Fe vacancies appear 19 . The Fe vacancies on the tetrahedral sites reduce the magnetic moments while Fe vacancies on the octahedral sites increase the magnetic moments. They further reported that the Fe vacancies on the tetrahedral sites remained relatively constant than that on octahedral sites, which implied that the Fe vacancies on the tetrahedral sites may dominate in slightly off-stoichiometric iron garnets. Our Tm-rich film is only off-stoichiometric to a smaller amount than their reported iron garnets. Therefore, we infer that the reduction of the magnetic moment in our Tm-rich films could be the results of domination of Fe vacancies on the tetrahedral sites. For H c , pinning of domain walls increases the H c ; nucleation process decreases the H c . The H c above 2.4 Oe might be due to the pinning of domain walls, possibly induced by the point defects such as element substitutions and vacancies often present in off-stoichiometric films [20][21][22][23] . TmIG films with low H c require less current-induced effective field to switch the magnetization. We have measured the reduced current density of magnetization switching. The low H c indicates higher magnetization switching efficiency although it may have less thermal stability. However, our ability to tune the H c from 2.4 Oe to 54 Oe by off-axis sputtering offer a clear advantage when balancing between thermal stability and magnetization switching efficiency. Figure 3(a) shows the FMR results. The resonance fields (H res ) of all the samples were summarized as a function of θ H . The out-of-plane resonance fields of the samples are always smaller than the in-plane resonance fields, showing the PMA in the TmIG films. Figure 3(a) shows the well-fitted experimental data from angle-dependent FMR measurements, exhibiting the gradually varying 4πM eff with respect to samples of different L. The effective magnetization 4πM eff was determined by fitting the data in Fig. 3(a). The H ⊥ was extracted from M s and 4πM eff , according to 4πM eff = 4πM s − H ⊥ 24 . Figure 3(b) shows the calculated H ⊥ of samples A to E by fitting the measured data in Fig. 3(a,c) displays the tensile strain dependence of H ⊥ for samples with different Tm: Fe ratios. The H ⊥ was enhanced significantly from 1429 Oe to 2439 Oe (170%). The results have revealed the enhancement of H ⊥ with larger tensile strain by tuning the film composition, in excellent agreement with the results obtained by changing the substrate lattice constant 7,8,11 . The ability to tune M s , H c and H ⊥ of TmIG by off-axis sputtering showed a great potential for ultralow-dissipation spintronic devices based on FIs.

Current-induced magnetization switching.
For the current-induced magnetization switching experiment, a Pt/TmIG bilayer was patterned into a Hall bar for the Hall effect measurements, as shown in Fig. 4(a). The Hall resistance as a function of the out-of-plane magnetic field H Z in Fig. 4(b) shows that the magnetization of TmIG switched by the out-of-plane magnetic field. The measured Hall resistance R H after applying the electric pulses are plotted as a function of the injected current density (j) with the low in-plane field H X = 5 Oe, as shown in Fig. 4(c). The magnetization was switched with an ultralow critical current density j c ~ 2.5 × 10 6 A/cm 2 , one order of magnitude smaller than the first reported value (j c ~ 1.8 × 10 7 A/cm 2 ) with an in-plane field H X = 500 Oe in Pt/TmIG by Avci et al. 9 . Our result was also comparable to the switching current density (j c ~ 6.0 × 10 6 A/cm 2 ) with a >35 Oe in-plane field later reported by Avci et al. 20 . In order to explain our low critical current density, we adopted the spin Hall magnetoresistance theory 25 to characterize the spin transfer at the interface between Pt and TmIG by examining the spin mixing conductance, and presented the calculation in details in Supplementary Information S2. Assuming the spin Hall angle and the spin diffusion length of Pt to be 0.08 26 and 1.4 nm 25 respectively, we estimated the real part G r and the imaginary part G i of the spin mixing conductance to be 1.1 × 10 15 Ω −1 m −2 and 1.2 × 10 14 Ω −1 m −2 , respectively, larger than the previously reported values in Pt/TmIG 9,27 . This may support the more efficient spin transmission at the interface and lead to the smaller current for the switching. The effective torque field was measured by harmonic Hall measurements. The second-harmonic Hall voltages (V 2ω ) were measured and plotted as a function of the in-plane transverse field (H T ), as shown in Fig. 4(d). The V 2ω is given by the formula 9,28 .

Conclusion
We have grown high-quality TmIG films with PMA on GGG(111) by off-axis sputtering. Excellent crystallinity of TmIG films was observed from Cs-corrected STEM images with a sharp interface and synchrotron radiation XRD. Damping constant of the TmIG thin film was measured to be 0.0133. We have demonstrated the enhancement of H ⊥ from 1429 Oe to 2439 Oe (170%) by adjusting the TmIG film composition to be Fe rich, thereby increasing the tensile strain. Moreover, we also have demonstrated current induced switching with a very low

Methods
Sample preparation. The TmIG films were grown on GGG(111) substrates by off-axis RF sputtering and the detailed sputtered parameters were given in ref. 13 . We have prepared five TmIG films as samples A, B, C, D, and E with respective longitudinal distance L (between the target and the substrates) of 5, 6, 7, 8, and 9 cm in order to vary the film Tm: Fe compositional ratio and tune the strain to achieve the best magnetic properties. The O 2 /Ar ambient pressure was at 3.5 mtorr and the RF power was at 40 Watt.
Structural characterization. The cross-sectional samples for TEM were prepared by conventional mechanical polishing. The element mappings were conducted by EDS. The cross-sectional HAADF images of TmIG thin films were obtained by Cs-corrected STEM to show the crystallinity and the interface of TmIG/GGG. The STEM investigations were conducted on a JEOL-2100F microscope with a CEOS spherical-aberration corrector, so that we can obtain the high-quality STEM images with an atomic resolution. The HAADF images taken from very high angle are highly sensitive to the variations in the atomic number of atoms in the sample. XRD using synchrotron radiation has been employed to study crystallography and the strain of the sputtered TmIG films epitaxially grown on GGG.
Magnetic characterization. The magnetic properties, such as the M s , the H c were measured using AGM.
The damping constants α and H ⊥ were measured using a series of X-band TE 102 mode microwave cavities.

Current-induced magnetization switching measurements.
To conduct the current-induced magnetization switching experiments 9 , an e-beam evaporated Pt thin film 3.2 nm thick was grown on a TmIG thin film 9 nm thick. The sample was patterned into a Hall bar with dimension 800 μm × 100 μm for Hall effect measurements. An in-plane magnetic field H X of 5 Oe was applied along the direction of applied current. Electric pulses with 5 milliseconds duration were applied by Keithley 2400. Second-harmonic measurements using SR830 lock-in amplifier were performed with a frequency of 500 Hz and an applied current density of 1.88 × 10 6 A/cm 2 .
Data availability statement. The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.