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Wei et al., Sci. Adv. 2021; 7 : eabc5053 20 January 2021

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Ultralow magnetic damping of a common metallic ferromagnetic filmYanping Wei1,2*, Wenjing Zhang1, Bing Lv2, Xia Xu1, Shibo Xi3, Zijun Ma1

For most magnetic materials, ultralow damping is of key importance for spintronic and spin-orbitronic applications, but the number of materials suitable for charge-based spintronic and spin-orbitronic applications is limited be-cause of magnon-electron scattering. However, some theoretical approaches including the breathing Fermi surface model, generalized torque correlation model, scattering theory, and linear response damping model have been presented for the quantitative calculation of transition metallic ferromagnet damping. For the Fe-Co alloy, an ultralow intrinsic damping approaching 10−4 was first theoretically predicted using a linear response damping model by Mankovsky et al. and then experimentally observed by Schoen et al. Here, we experimentally report a damping parameter approaching 1.5 × 10−3 for traditional fundamental iron aluminide (FeAl) soft ferromagnets that is comparable to those of 3d transition metallic ferromagnets and explain this phenomenon based on the principle of minimum electron density of states.

INTRODUCTIONUltralow magnetic damping has been always desired for meeting the energy and speed requirements of devices for spintronic and spin- orbitronic applications. At first glance, ultralow magnetic damping contradicts the charge current requirement for most spintronic and spin-orbitronic applications because such a charge current causes high damping due to magnon-electron scattering (1). Nevertheless, yttrium-iron-garnet (YIG) materials that are ferrimagnetic insulators with low damping are good candidates for achieving low-energy consumption and high speed required for spintronic device appli-cations. Furthermore, in the past several years, several theoretical approaches for the evaluation of magnetic damping of a transition metallic ferromagnet such as the breathing Fermi surface model, gen-eralized torque correlation model, scattering theory, and linear re-sponse damping model have been implemented by many groups for the quantitatively accurate calculations of low magnetic damping in metallic systems (2–6). Moreover, ultralow intrinsic damping ap-proaching 10−4 was experimentally observed by Schoen et al. (1) for the Fe-Co alloy owing to the unique features of its band structure and density of states (DOS).

Compared to 3d transition metal ferromagnets (e.g., Fe-Co, Fe-Ni, Fe-V, and Ni-Co alloys), research on the magnetic damping of tra-ditional fundamental iron aluminide (FeAl) soft ferromagnets with excellent mechanical and functional properties and particularly low cost has been rare (7–9). A comparably low magnetic damping achieved for an FeAl metallic system will make it a promising material for spintronic and spin-orbitronic applications. Motivated by the goal of matching the low magnetic damping of a transition metal ferro-magnet, and by the fact that magnetic damping is related to the DOS at the Fermi level and the crystallization quality of the materials con-trolled by the preparation process (1, 10), here, we examine the elec-tronic structure of Fe1−xAlx using density functional theory (DFT) calculations carried out with the Vienna Ab initio Simulation Package (VASP) and the generalized gradient approximation (GGA) for the

exchange and correlation potential (11–13). Furthermore, we grew high-quality single-crystalline Fe1−xAlx alloy films with a thickness of 20 nm and a 3-nm-thick capping Al layer on MgO(100) by molec-ular beam epitaxy (MBE) and studied the compositional dependence of the damping parameter in the Fe1−xAlx alloys. In situ reflection high-energy electron diffraction (RHEED) and high-resolution x-ray diffraction (HRXRD) demonstrated that Fe1−xAlx films have single- domain texture. Frequency sweeps with various fixed–magnetic field ferromagnetic resonance (FMR) measurements found a low mag-netic damping parameter approaching 1.5 × 10−3 at the Al concen-tration of 25%; this magnetic damping parameter value is lower than that obtained for polycrystalline Co25Fe75 (14).

RESULTSDFT calculationsWe use eight body-centered cubic (bcc) unit cells with 16 Fe atoms to construct a supercell for the pure Fe DOS calculations and for Fe1−xAlx with different concentrations x where Fe on various sites are replaced by Al atoms. We obtained several representative DOS of Fe1−xAlx and found that they exhibit a minimum at the Fermi level at the Al concentration of 25% (Fig. 1), with minimal magnet-ic damping found at the same alloy concentration as that found by Schoen et al. (1).

Characterization of crystalline structureFor the growth of the samples, the chamber pressure of our custom- designed MBE was below 10−9 mbar, which is favorable for the fab-rication of high-quality single-crystalline Fe1−xAlx alloy films under nonequilibrium conditions. The chemical composition of the sample based on its deposition rate was monitored in situ by a quartz crys-tal microbalance. The nucleation and growth of the FeAl films were monitored in situ by RHEED. The RHEED patterns (fig. S1) show that a pure Fe1−xAlx(100)[011]‖MgO(100)[010] single-orientation relationship was obtained. The dependence of the fine crystal struc-ture of the Fe1−xAlx films of the Al concentration was assessed by HRXRD. Figure 2A shows the results of -2 scans for the films with various Al concentrations. The (200) peaks at 65.021° for the prepared films correspond to bcc lattice constants of 2.867 Å of pure Fe and the Fe(100)‖MgO(100) out-of-plane orientation relationship.

1College of Science, Gansu Agricultural University, Lanzhou 730070, China. 2Key Lab for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou Uni-versity, Lanzhou 730000, China. 3Institute of Chemical and Engineering Sciences, Agency for Science, Technology and Research, Singapore Synchrotron Light Source, National University of Singapore, 5 Research Link, Singapore 117603, Singapore.*Corresponding author. Email: [email protected]

Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).

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As the Al concentration increases, a solid solution of Al in Fe is formed up to approximately 20 atomic % (at %) (15) and is named as the A2 structure. The (200) peaks shift to 64.256° when Al concentration is 19 at %, indicating that the bcc lattice constant is 2.895 Å with A2 structure, which is larger than that of pure Fe. Furthermore, at an Al concentration of 25%, a new DO3 phase is formed with the (200) and (400) peaks at 30.840° and 63.256°, respectively, corresponding to the face-centered cubic lattice constant of 5.790 Å (see A2, B2, and DO3 in fig. S2). Figure 2B shows the skew-geometry scan of the MgO{202} (black line) and DO3-Fe3Al{202} planes that exhibits the expected fourfold symmetry of MgO(100) and Fe3Al(100) with a cubic lattice system. However, the Fe3Al {202} peak is shifted to 45° from its position at 0° for the MgO {202} peak, indicating the Fe1−xAlx(100)[110]‖MgO(100)[100] in-plane orientation relation-ship observed by in situ RHEED. The thickness and roughness of the films are assessed by x-ray reflectometry scan, and the fitting results are depicted in Fig. 2C. These results indicate that the thick-ness of the obtained Fe3Al is 20 nm with the roughnesses of 0.7 and 0.4 nm for MgO and Fe3Al, respectively.

Characterization of basic magnetizationTo elucidate the easy and hard magnetizing directions of the Fe1−xAlx films, we measured angle-remanent curves using a vibrating sample magnetometer (VSM). Figure 3A shows the angular remanent magneti-zation (Mr) dependence for the FexAl1−x alloy films with several different Al concentrations in zero field after applying a saturation field of 500 Oe. It is obvious that an in-plane cubic anisotropy and an inter-face-induced uniaxial anisotropy (16) coexist in the Fe1−xAlx alloy films because Mr is lower at 90o than at 0o. Here, 0° is the starting point along the MgO[010] direction in our experiment with the second minimum Mr indicating that the hard magnetization direction corresponds to the Fe1−xAlx [011], and Mr reaches its maximum value at 45o corresponding to the easy magnetization direction along the Fe1−xAlx [010] (schematic of the measurement geometry as shown in fig. S3). Figure 3B shows the results of the examination of the dependence of the magnetic hysteresis loops of Fe1−xAlx along the easy and hard magnetization axes on Al concentration. The saturation magnetization (Ms) of Fe1−xAlx changes from 1500 to 663 emu/cc as the Al concentrations varies

from 0 to 25% (corresponding 0Msare also shown in fig. S4), while for the hard magnetization direction, the saturation field decreases with increasing Al concentration, indicating that the magnetocrystalline anisotropy become weaker with increasing Al content. The quantitative value of the magnetic anisotropy of Fe1−xAlx at the Al concentration of 25% where the DOS exhibits a minimum at the Fermi level was determined by angular-dependent FMR measurements. The external

Fig. 1. Several calculated representative electron DOS of Fe1−xAlx (x = 0, 19, 25, and 50). Eight bcc unit cells with 16 Fe atoms are used to construct a supercell for pure Fe DOS calculations and for Fe1−xAlx with different concentrations x where Fe on various sites are replaced by Al. The energies are given relative to the Fermi energy, Ef = 5.87 eV, for comparison, and inset numerical values are those of the DOS at the Fermi energy for FeAl with various compositions labeled.

Fig. 2. High-resolution x-ray diffractometry and reflectometry of Fe1−xAlx alloy films on MgO. (A) Longitudinal HRXRD -2 scans of the Fe1−xAlx alloy films with various Al concentrations grown on the MgO(100) substrate. The asterisked peak is the reflection of Al2O3 substrate for loading samples during testing. The slight changes in the diffraction angle of the samples account for distortion of the lattice, and the lattice changes are indicated by the comparison to the red dashed line. For Fe3Al, an obvious new diffraction peak (200) appears at 30.7o. a.u., arbitrary units. (B) Azimuthal HRXRD Ф scans of the Fe3Al{202} and MgO{202} planes. For the Fe3Al/MgO scan, four reflections at 45o intervals are observed, indicating an in-plane fourfold symmetry and a relative 45o rotation epitaxial growth of the Fe3Al films on the MgO substrate. (C) High-resolution x-ray reflectometry scans of the Fe3Al /MgO films where a corresponding fit (brown) gives a thickness of 20 nm for Fe3Al and a roughness of 0.7 and 0.4 nm for MgO and Fe3Al, respectively. Inset: HRXRD rocking curve of the Fe3Al (202) peak gives a full width at half-maximum of 0.49°.


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field [i.e., the resonant field (Hres)] for the various angles for the derivative spectra of the FMR absorption of Fe3Al was obtained at a microwave frequency of 9.4 GHz as shown in Fig. 3C. The resonant field decreases when the angle of the external field is at 30o (near 45o) but becomes largest for the angle of 90o, suggesting the results that are consistent with the easy and hard magnetization directions as shown in Fig. 3A. To obtain the magnetic anisotropy value, we examined a series of resonant fields as a function of the angle by angular-dependent FMR measurements, and the obtained results were fitted according to

f r =

 ─ 2  [ H res + 4 M s − 2 K 2∥ ─ M s

cos 2 φ + K 4∥ ─ 2 M s

(3 + cos4φ ) ] 1/2

× [ H res − 2 K 2∥ ─ M s

cos2φ + 2 K 4∥ ─ M s

cos4φ ] 1/2

(1)

where H2∥(H2∥ = 2K2∥/Ms) and H4∥(H4∥ = 2K4∥/Ms) are the in-plane uniaxial and cubic anisotropies, respectively, φ is the in-plane angle for the magnetization (M) with respect to the easy axis, and is the magnetogyric ratio. The results are shown in Fig. 3D, and the fitted H2∥ and H4∥ are 80 and 100 Oe, respectively, in agreement with the value (100 Oe) determined from the saturation field in the

hard magnetization direction of the magnetic hysteresis loops in Fig. 3B.

Measurement of Gilbert dampingThe damping parameter is determined from the linewidth depen-dence of the frequency according to (17)

H = H 0 + 4f ─ ∣∣ (2)

or frequency width dependence of the frequency according to (17).

f = (∣ ∣ H 0 + 4f ) √ ___________

1 + ( 0 M s ─ 4f  )

2 (3)

where is the Gilbert damping parameter, H0 is the inhomogeneous linewidth, f is the FMR frequency, and is the magnetogyric ratio. Here, we choose Eq. 3 to fit the Gilbert damping parameter since it is easy to vary a fixed field with a vector network analyzer (VNA) instrumentation with frequency sweeps at a fixed field. Figure S5 depicts the obtained VNA transmission data and fits to the real and imaginary parts of the complex permeability spectra for the Fe1−xAlx films as a function of the Al concentration. In the absence of an ex-ternal field, the resonance frequency fr changes from 10.5 to 2.3 GHz

Fig. 3. The angular dependence of the remanent magnetization and FMR and the dependence of magnetocrystalline anisotropy on Al content. (A) 0° is the starting point along the MgO[010] direction in the measured angle-remanent curves showing second minimum Mr that indicates the hard magnetization direction cor-responding to the Fe1−xAlx [011], and Mr reaches its maximum value at 45o corresponding to the easy magnetization direction along the Fe1−xAlx [010]. The dashed line is a guide for identifying the first and second minimum Mr. (B) Magnetic hysteresis loops along the easy and hard magnetization axes of the Fe1−xAlx showing the dependence on Al concentration. The saturation field along the easy magnetization direction labeled with 45o remains constant and the hard magnetization direction labeled with 0o decreases as the Al concentrations increases, indicating that the magnetocrystalline anisotropy of Fe1−xAlx becomes weaker with increasing Al content. (C) Derivative FMR absorption spectra for Fe3Al from 0o (corresponding to the MgO[010] direction) to 180o at a microwave frequency of 9.4 GHz. (D) Series of resonant fields fitted by the experimental data for the extraction of H2∥ and H4∥.


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with increasing Al concentration. On the basis of the Landau-Lifshitz- Gilbert equation and theory of FMR, 0 = H eff , where 0 is the intrinsic circular frequency, is the magnetogyric ratio, and H eff is the effective field. It is found that with increasing Al concentration, the effective field H eff of the Fe1−xAlx films become weaker, result-ing a lower resonance frequency of 2.3 GHz at the Al concentration of 25%.

To obtain the Gilbert damping parameter, the frequency width dependence of the frequency must be found, and therefore, we mea-sured field-dependent FMR absorption using a VNA instrument by performing frequency sweeps for the Fe75Al25 and Fe81Al19 films. As shown in Fig. 4, the resonance frequency fr shifts to higher values as the external field increases for the Fe75Al25 films. The width of the imaginary component of the complex permeability spectra reveals the energy absorption capacity that is related to the value of the Gilbert damping parameter and becomes narrower when the resonance fre-quency increases with increasing external field. Figure 4 (B and C) shows the results for the frequency width dependence of the frequency for the Fe75Al25 and Fe81Al19 samples. For Eq. 3, the 0 𝑀 s values of 0.83 and 0.99 T were obtained by stationary magnetic characterization (see the Supplementary Materials), and the /2 value of 2.79 GHz/kOe

was obtained for the angular dependence of the FMR (see Fig. 3D). Therefore, H0 and the Gilbert damping parameter can be fitted by Eq. 3, obtaining the values of 0.2 GHz and 1.5 × 10−3, respectively, for the Fe75Al25 films, and of 0.1 GHz and 2.3 × 10‐3 for the Fe87Al13 films, where Η0 is the inhomogeneous broadening that is not re-lated to the resonance frequency fr.

DISCUSSIONThe measured value of the Gilbert damping parameter for the Fe75Al25 films is comparable to the values reported in previous stud-ies such as the low for YIG, Co2FeAl, NiMnSb, and CoFe (1, 18–20); the lowest was reported by Lee et al. (14) for the Co25Fe75 films with a single-crystal structure. Notably, YIG is a ferrimagnetic insu-lator, Co2FeAl and NiMnSb are Heusler alloys, and CoFe is a 3d tran-sition metallic ferromagnet. However, for the FeAl systems, which are traditional fundamental iron aluminides with soft ferromagnetism, and for the Al fraction of 25%, the Gilbert damping parameter reaches 1.5 × 10−3, approaching the value obtained for the Co25Fe75 films. Our measured Gilbert damping parameter for the Fe75Al25 films represents the total damping including the contributions of radiative damping and spin pumping damping that are small and can be ignored. Therefore, the intrinsic damping of our Fe75Al25 films should approach the 10−4 regime. This raises a question as to why the Gilbert damping parameter of the traditional fundamental iron aluminides is so low for the Al fraction of 25%. To answer this question, we performed electronic structure calculations to obtain the partial DOS (PDOS) of Fe and Al. The representative PDOS results are shown in Fig. 5 (A and B) and indicate that the total DOS (TDOS) of Fe3Al are mainly due to the contributions of the Fe d states. Compared to Fe, the peak in the DOS below Ef (d states) shifts to lower energies with increasing proportion of Al and reaches the lowest energy value at 25% Al (see Figs. 1 and 5C). On the basis of the hybridization of the atoms occupying the cubic sublattice of Fe3Al (21), a set of bonding a1 orbitals and a set of antibonding t2 orbitals form because

Fig. 4. Determination of Gilbert damping. (A) The resonance frequency shifts higher as external field increases, and the frequency width dependence of the frequency was obtained by frequency sweeps for the Fe75Al25 films. (B and C) Corresponding frequency width dependence of the frequency for the Fe75Al25 and Fe81Al19 films. Gilbert damping parameter values were fitted by Eq. 3 and were = 1.5 × 10−3 and = 2.3 × 10−3, respectively.

Fig. 5. Representative results of PDOS for Fe3Al. (A and B) PDOS for the Fe and Al atoms that sum to TDOS of Fe3Al, with the main contributions arising from the d states of Fe atoms. Inset in (A): TDOS of Fe3Al. (C) The d-state DOS of pure Fe and Fe3Al. The peak position in the DOS below Ef shifts to lower energies by 2.05 eV for the Al content of 25%. (D) DOS of eg and t2g orbitals.


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of the hybridization of the s and p states in the [FeAl] substructure. The Fe 3dx2-y2 and 3dz2 states split into the lower t2g orbital, and the 3dxy, 3dxz, and 3dyz states split into the higher eg orbital owing to the crystalline field of a Fe3Al cubic system. The newly formed eg and t2g hybrid orbitals from Fe 3d states couple with each other, give rise to the doubly degenerate bonding and antibonding eg orbitals, and tri-ply degenerate nonbonding t2g orbital (the DOS of eg and t2g orbital as shown in Fig. 5D). Compared to the peak in the DOS below Ef (d states) in Fe3Al, the sharp peak of the DOS of eg and t2g below Ef shifts to a lower energy position that tends to be occupied by valence electrons and results in the minimum DOS observed at Ef.

In conclusion, we observe ultralow magnetic damping of 1.5 × 10−3 in traditional fundamental FeAl soft highly crystalline ferromagnets at an Al concentration of 25%, offering new opportunity for the se-lection of low-cost materials not limited to 3d transition metallic elements for spintronic and spin-orbitronic applications. These re-sults were obtained on the basis of the principle of minimum DOS proposed by Schoen et al. (1) and further verify that magnetic damp-ing is proportional to the DOS at the Fermi level in the same alloy with corresponding concentration. This work provides a new ap-proach for the screening of materials for spintronic and spin- orbitronic applications and verifies the explanation proposed by Schoen et al. to enable the screening of a broader range of low-damping materials.

MATERIALS AND METHODSDFT calculationDFT calculation framework was performed with the VASP, and the exchange and correlation potential was taken within the GGA of Perdew- Burke-Ernzerhof. The Monkhorst-Pack scheme of a 20 × 20 × 20 grid was used for integration in the Brillouin zone. The cutoff energy for the plane waves was set to 500 eV, and the difference between two steps was set to below 10−5 eV per atom to ensure the convergence of the total energy. The calculation was performed on the basis of the experimental lattice parameters.

Sample preparationA set of 20-nm-thick high-quality single-crystalline Fe1−xAlx alloy films were grown at room temperature on MgO(100) substrate at a rate of 0.97 and 1.36 Å/min for Fe and Al, respectively, using MBE equipped with solid-source crucible evaporation cells for Fe and Al. In situ, 3 nm of Al as a capping layer was deposited on the surface of Fe1−xAlx films to avoid oxidizing. Before growth of Fe1−xAlx films, the MgO substrate was chemically cleaned in an ultrasonic cleaner at 60°C, with trichloromethane, acetone, methanol, and deionized water in turn for 5 min. Then, it was sealed in deionized water and dried by N2 flow before loading into the growth chamber, therein, further thermally cleansed at 600°C. The nucleation and chemical composition of the sample based on its deposition rate were moni-tored in situ by RHEED and quartz crystal microbalance equipped on MBE.

CharacterizationsThe crystal structures and epitaxial relationship were investigated by RHEED and HRXRD, and the films thickness and roughness were assessed by x-ray reflectometry scans. The basic magnetization of samples was measured by VSM, and the quantitative value of the magnetic anisotropy was determined by angular-dependent FMR

measurements with absorption derivative versus field profile at 9.4 GHz (fixed frequency scanning field). The Gilbert damping parameter was determined by VNA-FMR measurements since it is easy to vary a fixed field in VNA instrumentation with frequency sweeps at a fixed field.

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/7/4/eabc5053/DC1

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Acknowledgments Funding: This work was supported by National Natural Science Foundation of China (grant no. 21961001), Basic Scientific Research Business Expenses of the Central University and Open Project of Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education (LZUMMM2018011), and Scientific Research Foundation for the Talents Introduction of Gansu


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Agricultural University (2017RCZX-39). Author contributions: Y.W. and Z.M. designed this study. B.L. examined the electronic structure of samples, and Y.W. prepared Figs. 1 and 5. W.Z. and X.X. prepared Figs. 2 and 3, respectively. S.X. prepared Fig. 4. Y.W. wrote the main manuscript text and revised the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and references. Data that support the findings of this report are available from the corresponding author upon request.

Submitted 1 June 2020Accepted 24 November 2020Published 20 January 202110.1126/sciadv.abc5053

Citation: Y. Wei, W. Zhang, B. Lv, X. Xu, S. Xi, Z. Ma, Ultralow magnetic damping of a common metallic ferromagnetic film. Sci. Adv. 7, eabc5053 (2021).


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Ultralow magnetic damping of a common metallic ferromagnetic filmYanping Wei, Wenjing Zhang, Bing Lv, Xia Xu, Shibo Xi and Zijun Ma

DOI: 10.1126/sciadv.abc5053 (4), eabc5053.7Sci Adv

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