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[Jhantu Pradhan](https://orcid.org/0009-0004-9427-7007), [M. S. Devapriya](https://orcid.org/0009-0004-2754-9383), [Rohiteswar Mondal](https://orcid.org/0000-0003-4543-5588), [Jun Uzuhashi](https://orcid.org/0000-0003-2023-8158), [Tadakatsu Ohkubo](https://orcid.org/0000-0003-3548-1951), [Shinya Kasai](https://orcid.org/0000-0001-7149-4800), [Chandrasekhar Murapaka](https://orcid.org/0000-0002-0283-7037), [Arabinda Haldar](https://orcid.org/0000-0002-0490-9719)

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Copyright 2024 Author(s). This article is distributed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) License.[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

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[Ultra-low Gilbert damping and self-induced inverse spin Hall effect in GdFeCo thin films](https://mdr.nims.go.jp/datasets/94136826-a6e0-4fb6-830b-f4e290ecd8e2)

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Ultra-low Gilbert damping and self-induced inverse spin Hall effect in GdFeCo thin filmsJhantu Pradhan,1 M. S. Devapriya,1 Rohiteswar Mondal,2 Jun Uzuhashi,3 Tadakatsu Ohkubo,3 Shinya Kasai,3 Chandrasekhar Murapaka,2 and Arabinda Haldar1,a)1Department of Physics, Indian Institute of Technology Hyderabad, Kandi, 502284 Telangana, India2Department of Materials Science and Metallurgical Engineering, Indian Institute of Technology Hyderabad, Kandi, 502284,Telangana, India3Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science (NIMS), Tsukuba 305-0047, Japana) Author to whom correspondence should be addressed: arabinda@phy.iith.ac.inABSTRACTFerrimagnetic materials have garnered significant attention due to their broad range of tunabilities and functionalities in spintronics applications. Among these materials, rare earth-transition metal GdFeCo alloy films have been the subject of intensive investigation due to their spindependent transport properties and strong spin–orbit coupling. In this report, we present self-induced spin-to-charge conversion in singlelayer GdFeCo films of different thicknesses via an inverse spin Hall effect. A detailed investigation of spin dynamics was carried out using broadband ferromagnetic resonance measurements. The anisotropy constant and the effective g-factor are found to decrease with thickness,and they become nearly constant for thicknesses beyond 25 nm. A remarkably low damping constant of 0.0029 ± 0.0003 is obtained in the 43 nm-thick film, which is the lowest among all previous reports on GdFeCo thin films. Furthermore, we have demonstrated a self-induced inverse spin Hall effect, which has not been reported so far in a single-layer of GdFeCo thin films. Our analysis shows that the inverse spin Hall effect becomes increasingly dominant over the spin rectification effect with increasing film thickness. The in-plane angular-dependent voltage measurement of the 43 nm-thick film reveals a spin pumping voltage of 1.64 μV. The observation of spin-to-charge current conversioncould be due to the high spin–orbit coupling element Gd in the film as well as the interface between GeFeCo/Ti and substrate/GdFeCo of the films. Our findings underscore the potential of GdFeCo as a prime ferrimagnetic material for emerging spintronic technologies.I. INTRODUCTIONThe study of interconversion between spin current and charge current is one of the primary requirements for realizing pure spin current based spintronic devices. The phenomenon by whichcharge current is converted to spin current is known as the spin Hall effect (SHE).1 On the other hand, the conversion of spin current to charge current occurs due to the inverse spin Hall effect (ISHE).2 The underlying physical mechanism involves the presence of a strong spin–orbit coupling (SOC) for such interconversion between spin and charge. In this context, heavy metals (HMs) and topological materials have been found to be promising for their large SOC.3–5 A popular method of injecting spin current within the HM is known as the spin pumping effect, where large precession in the FM layer at ferromagnetic resonance (FMR) injects a spin current from the FM layer to the HM layer.6 Recently, a single-layer of ferromagnetic material has been shown to exhibit spin-to-charge conversion under FMR excitation.7 The voltage drop across the film is primarily attributed to the selfinduced ISHE, which is found to be more significant in relatively thicker films. The self-induced ISHE does not require a bi-layer heterostructure, simplifying the fabrication process and eliminating the interface effects such as spin backflow and spin memory loss.8 In the context of self-induced ISHE, ferrimagnets (FiMs) are emerging as promising contenders, offering an alternative to traditional FM layers.9 FiM materials integrate the advantages of both FMs and AFMs.10 Furthermore, it possesses two distinct points: the magnetization compensation point,11 at which the total　magnetization becomes zero, and the angular momentum compensation point, at which the net angular momentum vanishes.12 These inherent properties render FiMs promising candidates for future spintronics applications. The rare earth-transition metal (RE-TM) GdFeCo alloy is a typical FiM material studied extensively due to its vast diversity in magnetic properties. Recently, ultrafast spin dynamics, 13 SOC-induced effects (spin–orbit torque, chiral spin textures, etc.),14–19 the existence of the anomalous Hall effect (AHE),20,21 bulk perpendicular magnetic anisotropy,18,20,22,23 etc. have been reported in GdFeCo thin films. The substantial SOC associated with the 5d element Gd in GdFeCo films allows the interplay between charge, spin, and orbital transport. It has also been shown that the GdFeCo alloy hosts ample self-induced spin–orbit torque.15 Moreover, Kim et al.24 and Bainsla et al.25 have recently reported a relatively low Gilbert damping in GdFeCo thin films, a crucial parameter for generating spin current. Building upon these findings, Sun et al. proposed a phenomenological theory elucidating the ISHE signal output in FiM/HM bilayer structures.26 Despite these theoretical advancements, experimental investigations into ISHE in FiMs employing the FMR technique remain scarce.27,28 Here, we have demonstrated self-induced ISHE in Gd12.5Fe76.1Co11.4 thin films as a function of its thickness. The Gilbert damping parameter (αeff) diverges around compensation points,27 and a large damping leads to negligible spin current, resulting in insignificant ISHE as spin current is proportional to 1 (αeff)2.29 To ensure significant spin current generation, we have chosen a composition away from the compensation point, where the damping constant remains relatively low, facilitating efficient spin pumping and subsequent spin-to-charge conversion. To extract the precise value of the Gilbert damping parameter, we have systematically conducted in-plane angle dependent FMR measurement at a fixed frequency of excitation and frequency dependence FMR response along the easy axis of magnetization. Our investigations reveal ultra-low Gilbert damping in thicker films exceeding 30 nm, alongside inverse spin Hall voltage detection. In-plane angle dependent measurements are carried out to discern the contributions from ISHE and spin rectificationeffects (SREs) in the measured voltage. A spin pumping voltage of 1.64 μV is estimated in a 43 nm-thick sample.II. EXPERIMENTAL METHODGd12.5Fe76.1Co11.4 (tGdFeCo nm) thin films are grown with varying thicknesses (tGdFeCo = 11, 19, 27, 35, and 43 nm) using dc magnetron sputtering of a single GdFeCo target with the specified composition. The base pressure in the deposition chamber was better than 5 × 10−7 mbar. The films were deposited in an Ar atmosphere at a pressure of 5 × 10−3 mbar. The alloy films were grown at room temperature on naturally oxidized Si (100) substrates. The film thickness is determined using the atomic force microscopy (AFM) technique. A 3 nm-thick titanium (Ti) capping layer was deposited on top of the GdFeCo films to prevent oxidation of the magnetic layer. Substrate rotation at a constant speed of 10 rpm ensured uniformity in film thickness during deposition. Structural characterization was performed using grazing incidence xray diffraction (GIXRD) with Cu–Kα radiation. Scanning electron microscopy equipped with energy dispersive x-ray spectroscopy (SEM-EDS) was employed to cross-verify the film composition. Cross-sectional scanning transmission electron　microscopy equipped with energy dispersive x-ray spectroscopy (STEM-EDS) was performed to identify the composition profile of the films. The 50-nm-thick TEM lamella was prepared by a thickness-controllable program30 using focused-ion-beam (FIB)-SEM dual-beam Helios5UX with AutoScript program (Thermo Fisher Scientific) while considering FIB-damage becomes minimized.31 The STEM investigation was carried out at 300 kV accelerating voltage using Spectra Ultra S/TEM (Thermo Fisher Scientific). Static magnetic properties were assessed via vibrating sample magnetometry (VSM), whereas dynamic properties were investigated utilizing a lock-in-based broadband FMR technique. The sample was placed on the co-planar wave-guide (CPW) in a flip-chip manner. Angulardependent measurements were conducted by varying the in-plane magnetic field direction [wH , defined as the angle between the applied external magnetic field (H) and the easy axis of magnetization] through sample rotation for a fixed excitation frequency (f = 10 GHz). The frequency dependence FMR response data were recorded along the easy axis (=0°). To measure ISHE voltage, copper wires were used to make contacts using silver paste at the edges of the samples. A schematic of the voltage measurement is shown in Fig. 1(a). The voltage was detected using the lock-in-based technique.III. RESULTS AND DISCUSSIONFigures 1(b) and 1(c) present a cross-sectional STEM image alongside the EDS elemental line profile of a 35 nm-thick GdFeCo film. The line profile reveals a uniform distribution of Gd, Fe, and Co across the film thickness, with some deviations at the interfaces. Furthermore, the nano-beam electron diffraction (NBED) pattern of the 35 nm-thick GdFeCo film [Fig. 1(d)] indicates the presence of both nanocrystalline (spotty patterns) and amorphous (halo pattern) phases. Grazing incidence x-ray diffraction (GIXRD) measurements also reveal no significant peaks, except for one at 2θ = 69.1°, corresponding to the Si (400) reflection (see Fig. S1 in the supplementary material). SEM-EDS measurements provide the relative atomic percentages of Gd, Fe, and Co as 12.2%, 76.05%, and 11.7%, respectively, closely matching the composition of our GdFeCo target (see Fig. S2 in the supplementary material). Figure 1(e) depicts the magnetization hysteresis (M–H) characteristics of a 43 nm-thick sample measured using VSM. We have estimated the magnetic dead layer (MDL) by plotting the arealsaturation magnetization (Ms  tGdFeCo) as a function of tGdFeCo as shown in Fig. 1(f). The inclination of the linear regression line provides the intrinsic magnetization at saturation, while the x axis intercept yields the MDL thickness. The Ms value and MDL thickness are determined to be 1000 emu/cm3 and 1.56 nm, respectively. The presence of the MDL is likely attributable to intermixing at the interface between GdFeCo and the capping layer. In order to reveal the thickness-dependent anisotropy of the films, we have carried out the in-plane angle dependent FMR measurement. FMR spectra were recorded by sweeping the external magnetic field (0–3000 Oe) for a fixed microwave excitation frequency (f = 10 GHz), and angular measurement was carried out by rotating the sample from 0–360° in steps of 15°. Figure 2(a) shows the derivative of FMR spectra of all samples along the easy axis at 10 GHz, which were fitted to the sum of symmetric and antisymmetric components of the Lorentzian function,32 enabling the estimation of resonance field (Hr) and linewidth (ΔH). The Hr values along the easy axis of magnetization are determined to be 936, 905, 892, 889, and 867 Oe for samples of thicknesses 11, 19, 27, 35, and 43 nm, respectively. The angular dependence of Hr for all the samples is depicted in Fig. 2(b). The error bar is the same as the symbol size. Notably, Hr exhibits a minimum along 0° and 180° (easy axis) and maximum along 90° and 270° (hard axis), indicating the presence of twofold uniaxial anisotropy in all samples. To estimate the anisotropy field (Hk), the experimental data are fitted with the following form of the Kittel formula:32–34 (1)     where γeff is the effective gyromagnetic ratio, and 4πMeff is the effective saturation magnetization. The effective g-factor is related to the gyromagnetic ratio by the formula , where μB is the Bohr magneton and h is the Planck constant. There are three coupled adjustable fitting parameters geff, 4πMeff, and Hk that are not orthogonal to each other during the least-squares non-linear fitting process. To eliminate the mutual dependency among parameters and extract the exact fitting values, we have measured the FMR spectra of all the samples along the easy axis () for f = 6–18GHz in steps of 1 GHz. The variations of Hr with f are shown in Fig. 2(c). Initially, we set  and fitted the  vs Hr data by using Eq. (1). Subsequently, the Hr vs f plot was fitted with the same equation (), keeping the Hk value fixed from the previous step. This iterative process continued until convergence of all fitting parameters was achieved. The thickness dependency of Hk, 4πMeff, and geff is illustrated in Figs. 3(a)–3(c). The anisotropy field is higher in thinner films and nearly constant at around 10 Oe in thicker films above 30 nm. The values of 4πMeff are found to increase monotonously from ∼9900 to ∼13600 G with the increase in thickness of GdFeCo films, and its positive value implies in-plane magnetization. The smaller value of 4πMeff observed in thinner films can be attributed to the formation of an MDL at the interfaces.35 Additionally, recent findings indicate that the effective composition of the RE element is slightly larger in thinner films below a certain critical thickness.36,37 Therefore, larger values of the effective composition of Gd in thinner films can lead to a decrease in effective saturation magnetization with the decrease in film thickness. The value of geff for the 11 nm-thick sample is 2.21, and it decreases gradually to 2.004 in 43 nm-thick film as shown in Fig. 3(c). Note that the variations in composition lead to a change in geff.38 We believe that the augmented effective Gd-content in our thinner films can also lead to the elevated value of geff . To study the effect of thickness on the Gilbert damping constant (αeff), we have analyzed ΔH vs f data [Fig. 2(d)] along the easy axis () by using the following expression:25　　　   (2)where  is the inhomogeneous linewidth broadening, which appears due to magnetic inhomogeneity in the sample. The value of  (or ), extracted from the simultaneous fitting of  vs  data and  vs  data by using Eq. (1), is utilized in Eq. (2) to estimate the precise value of the damping constant. The estimated values of  with film thickness is illustrated in Fig. 3(d). All the samples showed minor nonlinearity in the linewidth plot in the low-frequency regime (<10 GHz). While the exact origin of this nonlinearity is not entirely clear, it is plausible that extrinsic mechanisms, such as two-magnon scattering (TMS), may contribute to this nonlinearity. The origin of this TMS could be the presence of both nanocrystalline and amorphous phase in our films as obtained from the NBED (Fig. 1(d)). To minimize the influence of these effects and provide a more accurate assessment of the intrinsic damping, we have fitted the data at high field regions (f ≥ 10 GHz), where the linewidth displays a linear dependence. The extracted damping, using only this linear regime, is shown in Fig. 3(d) by blue square symbols. The damping constant of the 43-nm-thick film is found to be 0.0029±0.0002, which is remarkably low. We have also fitted full frequency range data to highlight the deviation in the damping parameter estimation in Fig. 3(d) as circular symbols. The lower values of αeff in thicker films could be associated with a reduced surface contribution.39 We have observed a relatively large values of ΔH0 in our films, which may arise due to coexistence of nanocrystalline and amorphous phases resulting in magnetic inhomogeneity inside the films. The ΔH0 values for 11, 19, 27, 35, and 43 nm-thick films are 45, 72, 76, 64, and 112 Oe, respectively. The existence of large SOC element Gd could lead to considerable spin-to-charge conversion in the GdFeCo thin film. Additionally, the thicker GdFeCo films show a low damping constant (, which promotes to have a significant self-induced ISHE. The ISHE results in a voltage transverse to the spin flow direction. Figure 4(a) shows the voltage () measured at  for a 43-nm-thick sample where  is defined as the angle between the voltage measurement direction and perpendicular to the magnetic field direction (Please see Fig. 1(a)).  mainly contains the voltage generated by ISHE as well as the contribution from the spin rectification effect (SRE). The voltage drops due to the pure ISHE signal only generate symmetric components, whereas SRE has both symmetric and antisymmetric components. Therefore, the  can be written as40. (3)To disentangle the symmetric (Vsym) and antisymmetric (Vasym) components to the voltage, we have fitted the data using Eq. (3). Individual Vsym (green line) and Vasym (blue line) fits are also included in Fig. 4(a). The ratio Vsym / Vasym for the 43 nm-thick sample is 2.22 ± 0.11, which implies that the voltage drop due to ISHE is relatively stronger than that of the SRE. This result is comparable with the previous report on self-induced ISHE in an Fe film.41 Figure 4(b) shows the Vmeas data of a 43 nm-thick sample at 0° and 180°. It is observed that Vsym changes its polarity when the sample is rotated to 180°. This is one of the key characteristics of the ISHE signal, which validates the existence of self-induced ISHE in the GdFeCo film.42 We have measured Vmeas for all the samples at ψ ¼ 0_. Figure 4(c) depicts the Vmeas obtained in 27, 35, and 43 nm-thick samples and corresponding fit lines. Vmeas could not be identified due to low signal-to-noise ratio in 11 and 19 nm-thick samples. The absence of Vmeas in 11 and 19 nm-thick samples could be due to relatively larger values of Gilbert damping constants of the films. The Vsym / Vasym ratio for 27, 35, and 43 nm-thick samples are 0.79 ± 0.08, 1.63 ± 0.10, and 2.22 ± 0.11, respectively. Therefore, ISHE contribution is dominant over SRE contribution in 35 and 43 nm-thick GdFeCo films. To calculate the spin pumping voltage (Vsp) arising due to ISHE and voltage originated from SRE [which has contributions from anisotropic magnetoresistance (AMR) and anomalous Hall effect (AHE)], we have performed　in-plane angle dependent Vmeas for the 43 nm-thick sample. The angular dependent Vsym and Vasym data are plotted in Fig. 4(d). The Vsym data are fitted using the equation42               (4)and the Vasym data are fitted using the equation42                                     (5)where θ is the angle between the magnetic and electric fields of the microwave and ψ0 is the correction factor of the sample misalignment during measurement. The value of θ is 90° in our case. Therefore,  (anomalous Hall voltage) contributes only to antisymmetric voltage.  and  are the perpendicular (parallel) components of AMR voltage to symmetric and antisymmetric voltage, respectively. The effective perpendicular (parallel) components can be calculated using the following formula:42               (6)The estimated values of Vsp and VAHE are -1.64 ± 0.13 and 0.64 ± 0.034 μV, respectively.  contribution is calculated to be around 0.84±0.15 µV. On the other hand, a significantly small  (≈0.19±0.09 µV) is obtained in the films. A recent study of self-induced ISHE40 in La0.67Sr0.33MnO3 films of different thicknesses has reported a  of 1-2 µV, which is comparable to the values obtained in GdFeCo films  in this work. Our  range is also comparable with some of the well-known FM/HM bilayer structures.40,43,44 The origin of self-induced ISHE in our GdFeCo thin films might be the high SOC of 5d band introduced by Gd. It has been found that the Gd metal shows well-defined Rashba surfaces,45 which is a common character of RE metals. Furthermore, recent studies of current-induced spin torque in GdFeCo reported that the dominant source of self-torque in GdFeCo is the interface between GdFeCo/light metal.15 Therefore, the GdFeCo/Ti interface, the substrate/GdFeCo interface, or both in our study could be a source of observed ISHE.IV. CONCLUSIONIn conclusion, we have reported self-induced ISHE in ferrimagnetic GdFeCo films. Thickness-dependent spin dynamic properties of these films are investigated using a lock-in-based FMR system. We have observed an ultra-low damping constant of 0.0029 for the 43 nm-thick GdFeCo film, which is the lowest reported value so far for any GdFeCo film. Self-induced ISHE is observed in films with thicknesses exceeding 25 nm, and an efficient spin-to-charge conversion is demonstrated in single-layer GdFeCofilms. Our analysis indicates that the contribution from selfinduced ISHE becomes dominant as the film thickness increases, surpassing contributions from phenomena such as the AHE and AMR. The Vsp value of 1.64 μV is estimated in the 43 nm-thick sample through in-plane angular ISHE measurements. Our findings, showcasing low Gilbert damping constant and the occurrence of self-induced ISHE, underscore the potential of GdFeCo as a promising ferrimagnetic material for future spintronic devices.SUPPLEMENTARY MATERIALSee the supplementary material for the GIXRD and SEM-EDS results and analysis of our GdFeCo film.ACKNOWLEDGMENTSA.H. would like to acknowledge funding under the DAE-YSRA (No. 59/20/05/2021-BRNS), Board of Research in Nuclear Sciences (BRNS), India. C.M. would like to acknowledge funding from SERB-Core Research Grant (No. CRG/2022/005472). We acknowledge the DST–FIST facility, VSM at the Department of Physics, IIT Hyderabad (Project No. SR/FST/PSI 215/2016). J.P. acknowledges funding from the Council of Scientific & Industrial Research (CSIR), India. J.U., T.O., and S.K. acknowledge JSPSKAKENHI (Grant No. JP24K00952), Japan. 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(b) In-plane angle ( dependent resonance field () for all the samples at a frequency of 10 GHz. Data are fitted with Eq. (1). (c) Frequency () vs. resonance field () plot and corresponding fit to Eq. (1) with =0. (d) Linewidth () vs. frequency () plot. The solid lines correspond to the fit to Eq. (2) from 10 to 18 GHz.FIG. 3. The variation of a) in-plane anisotropy field (), (b) Effective saturation magnetization (), (c) Effective g-factor (), and (d) Effective Gilbert damping constant () with . The circle and square symbols represent the results obtained from fitting the whole frequency range and high frequency range (≥ 10GHz), respectively.FIG. 4. (a) Measured dc voltage  vs. applied external field H plot for 43-nm-thick sample at 10 GHz along , where  is the angle between voltage measurement direction and perpendicular to the applied magnetic field (H) direction as shown in inset. The solid magenta line is the best fit to Eq. (3). The green and blue lines correspond to symmetric and antisymmetric contributions to the measured voltage. (b)  of 43-nm-thick sample at  and  and their corresponding fits to Eq. (3). (c)  of 27, 35, and 43-nm-thick samples at . (d) The plot of the symmetric () and antisymmetric () components of  vs. for 43-nm-thick sample. Magenta and blue solid curves are the best fit for  and , using Eqs. (4) and (5), respectively.image4.tiffimage1.tiffimage2.tiffimage3.tiff