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Low Gilbert damping and linewidth in magnetostrictive FeGa thin films
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
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Research articles
Low Gilbert damping and linewidth in magnetostrictive FeGa thin films a,b,⁎
a,b
Sujan Budhathoki , Arjun Sapkota , Ka Ming Law ⁎ Shambhu KCa,b, Tim Mewesa,b, Adam J. Hausera,b, a b
a,b
, Bhuwan Nepal
a,b
, Smriti Ranjit
T
a,b
,
Center for Materials for Information Technology (MINT), The University of Alabama, Tuscaloosa, AL 35487, USA Department of Physics and Astronomy, The University of Alabama, Tuscaloosa, AL 35487, USA
A B S T R A C T
Fabrication of voltage tunable high-frequency devices using magnetostrictive ferromagnet-piezoelectric hybrid structures requires materials with low damping and narrow linewidth to achieve low microwave loss. Galfenol exhibits superior magnetostriction, stability over a wide range of temperatures, and is free of rare earth elements, making it an economical and promising candidate, if the microwave losses can be minimized. We report the fabrication, structural and magnetic characterization, and study of dynamic properties of epitaxial FeGa thin films exhibiting an ultra-low residual linewidth, ΔH0 = 13 ± 1 Oe – a requirement for low +0.0028 microwave loss and effective damping parameter, α eff , as low as 0.0065+−0.0005 0.0001 for the 16 nm thick film. Similarly, we found α eff = 0.0039−0.0007 and ΔH0 = 71 ± 1 Oe for the 24 nm thick film, demonstrating its potential for applications in magnetic memory and high frequency devices.
1. Introduction The effective manipulation of magnetization is the key to realize energy-efficient spintronic devices. There has been strong research interest across the scientific community concerning electrical field [1–3] or strain mediated [4–6] manipulation of magnetization for writing information onto magnetic materials used in data storage. These effects can be achieved in magnetoelectric composite materials, for example; the strong magneto-electric coupling across magnetostrictive ferromagnet-piezoelectric hybrid structures can be exploited to fabricate magnetic memory [7,8] and spin wave-based magnetic logical [9,10] devices. The realization of these devices requires magnetic thin films with very high magnetostriction to enable voltage-induced switching of magnetization when combined with a piezostrictive element. Favorable performance requires narrow ferromagnetic resonance (FMR) linewidth and fast magnetization switching speeds dictated by the effective damping parameter [11]. These properties are strongly affected by the inhomogeneity of the magnetostrictive ferromagnetic structure when fabricated in thin-film forms. Transition metal ferromagnets (for eg; Fe, Co, Ni) exhibit significant magnetostriction, but binary alloys such as galfenol and ternary alloys such as terfenol-D outnumber them [12,13]. Galfenol (Fe100 − x Gax , 12 at. % ⩽ x ⩽ 30 at.%) is a rare-earth-free binary alloy that has been widely studied in recent years due to its large magnetostriction coefficient (λ s∼350 ppm in bulk [14] and λ s∼400 ppm for single crystals [15]), superior thermal-stable magnetization close to critical temperature [16] and low saturation and switching fields [15,16] suitable for applications in sensors, mechanical actuators and spintronic devices [17–19,7]. ⁎
There are different structural variants of Fe-Ga alloys in which Ga content influences the magnitude of magnetostriction [20–23]. Previous studies have shown that disordered bcc α -Fe phase (A2) exhibits maximum magnetostriction, whereas cubic D03 (Fe3 Ga) is detrimental to magnetostriction [24,25]. The single crystal galfenol thin films exhibit magnetostriction comparable to that of bulk [26], however, single-crystal epitaxial growth of galfenol thin film is challenging due to possible poly-crystalline nature [27]. In addition, the large FMR linewidth of 450–700 Oe [28,29] at X-band limits its use in microwave devices. This large residual linewidth can be tuned by doping metalloid elements such as Boron but one has to compromise the magnitude of magnetostriction and hence the strength of magnetoelectric coupling [29,11,30]. In this work we report the fabrication, structural characterization and dynamic magnetic properties of phase pure, epitaxial Fe19 Ga81 thin films grown via sputter beam epitaxy method [31–36]. Despite a relatively large lattice mismatch, the films exhibit low coercivity, ultra-low Gilbert damping constant, and a narrow residual FMR linewidth term, likely the result of improved film quality that has proven elusive to date. The results suggest potential for incorporation of galfenol thin films in low-loss spin-torque oscillators and spin-wave based logic devices. 2. Experiment The use of a single composite sputter target with stoichiometry matching the desired film is problematic: Positional stoichiometry inevitably varies due to variance in the ejection angle probabilities for
Corresponding authors. E-mail addresses: [email protected] (S. Budhathoki), [email protected] (A.J. Hauser).
https://doi.org/10.1016/j.jmmm.2019.165906 Received 1 August 2019; Received in revised form 10 September 2019; Accepted 26 September 2019 Available online 04 October 2019 0304-8853/ © 2019 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
S. Budhathoki, et al.
small-angle XRR (Fig. 2(a)): The pronounced, narrow oscillations are due to the thickness of the FeGa film, while the much longer period oscillation is from the much thinner Al cap layer. The recursive Parratt formalism [38] was employed to fit the observed XRR pattern using GENX software [39] which gave FeGa thickness to be 16.3 nm and 24 nm with respective Al cap thicknesses of 2.3 and 2.7 nm. Taken together, the XRR and fitting indicate atomically abrupt, smooth interfaces between substrate and film, film and Al cap and the Al cap and the air (surface). From EDX analysis of the FeGa thin films, the Fe content was found to be 81% (±3%) and 80% (±3%) for the 16 nm and 24 nm thick films respectively which were confirmed by RBS. Fig. 2(b) shows the on-axis XRD pattern for the 16 nm thick film. Fig. 2(c) shows the off-axis XRD pattern of the (1 1 0) crystal orientation of the film. The full width at half maximum for the 16 nm (Fig. 2(b) inset) thick film is found to be 0.8° and the out of plane lattice constant is found to be 2.841 ± 0.002 Å, which is 2.03% lower than the bulk 2.900 Å[40] value. By using the lattice spacing deduced from the FeGa (1 1 0) peak position in conjunction with the out-of-plane (2 0 0) value, the in-plane lattice constant is found to be 2.933 ± 0.003 Å, which is 1.14% larger than the bulk value, confirming the in-plane tensile strain implied by the smaller out-of-plane lattice constant. Although, it does appear that significant relaxation has already taken place, the volume of the film unit cell is within 0.2% of the bulk value with tetragonality of 0.969 ± 0.001 Å. Both in-plane and out-of-plane XRD measurements indicate phase pure, epitaxial films with no film impurity peaks detected. The expected epitaxial relationship between the FeGa film and MgO(1 0 0) substrate as shown in Fig. 1 is confirmed by the fourfold symmetry of FeGa(1 1 0) peaks with a 45° rotation to MgO(2 2 0) peaks as observed from the ϕ -scan in Fig. 2(d). The in-plane (along the ϕ = 0° ([1 1 0]) and ϕ = 45° ([1 0 0]) inplane directions) magnetic hysteresis loop, at room temperature, of the 16 and 24 nm thick films is shown in Fig. 3. The observed hysteresis profile as shown in Fig. 3(b) suggests that ϕ = 45° ([1 0 0]) is the easy axis of magnetization with lower relative coercivity. The ferromagnetic saturation magnetization for 16 and 24 nm thick FeGa film is determined to be Ms = 1550 ± 90 emu/cc (2.0 ± 0.1 μB /f.u) and Ms = 1540 ± 65 emu/cc (2.0 ± 0.1 μB /f.u) respectively which is ∼15 % higher than observed for poly-crystalline FeGa films by Gopman et al. [41] and in close agreement with epitaxial FeGa films measured by Weston et al. [42] and Tacchi et al. [43]. The coercivity (Hc ) is found to be 25.2 Oe and 35.1 Oe for the 16 and 24 nm thick FeGa film respectively, Fig. 3(b), lower that the values observed by Gopman et al. [41] and Weston et al. [42], though their films were significantly thicker and may account entirely for the difference. Regardless, the films are undoubtedly soft ferromagnets of potential use for low loss applications. We also note that thinner films exhibit homogeneous strain transfer compared to thicker films [44] and can be exploited for non-volatile magnetization switching in nanoscale magnetoelectric memory cells [45,26,46]. The values for Hc and remanent magnetization (Mr ) are summarized in Table 1.
different elements, and is exacerbated by element-dependent scattering of ejected atoms off process gas at pressures above 2–5 mTorr. In addition, while conventional on-axis sputtering is a sufficiently fast method for growing thin-film alloys, higher growth energetics result in higher defect rates of the crystal/atomic ordering and altered film properties. Defects from film growth must be addressed first, as they obfuscate the intrinsic nature and delay understanding of the material. Epitaxial FeGa films were grown on MgO (1 0 0) substrates at a base pressure of 5 × 10−9 Torr via “sputter beam epitaxy”-an ultra-high vacuum (UHV) custom hybrid system built by AJA International, Inc. comprising the low energetic and stoichiometry control of MBE [31,32], elemental flexibility, homogeneity over a larger area, faster deposition rate, low-cost, and industry-friendly attributes of directcurrent (DC) combinatorial magnetron sputtering [31,33,34] with offaxis geometry [35,36]. Each gun has a wedge-shaped shutter producing a uniform sputter beam at the off-axis angle range utilized, with a flux difference of less than 1% across a 2-inch wafer before substrate rotation. The substrate holder then rotates at 80 rpm to ensure maximum uniformity even under rapid growth conditions. Co-deposition fluxes of stoichiometric Fe64 Ga36 and elemental Fe targets were tuned by quartz crystal microbalance pre-growth to produce Fe81Ga19 thin films. The MgO substrates were in situ annealed at 700 °C for 30 min in UHV to remove water and carbon contaminants from the surface [37] followed by film deposition at a substrate temperature of 250 °C and the Al layer was deposited below 100 °C to prevent the oxidation of films. The optimal growth temperature and Ar pressure (20 mTorr) were determined by the simultaneous observation of (1) maximal film peak intensity in X-ray diffraction (XRD) patterns and (2) the most pronounced Kiessig oscillations in X-ray reflectometry (XRR). Stoichiometry of FeGa films was determined using energy dispersive X-ray (EDX) spectroscopy and confirmed by Rutherford Backscattering. Crystal structure and epitaxial quality were determined by XRD using a Philips X-pert system. XRR was employed to measure the thickness of each film, as well as the relative roughness of the films during optimization. MgO (a = 4.212 Å) is an excellent substrate to grow FeGa thin films as it has a reasonable lattice match (lattice mismatch ∼2.63%, tensile strain) as shown in Fig. 1(a), the crystal structure of disordered bcc α -Fe phase (A2) and its expected epitaxial relationship on MgO substrate with a 45° rotation in Fig. 1(b). The static and dynamic properties of FeGa films were studied using the VSM module in a Quantum Design Physical Property Measurement System (PPMS) and Ferromagnetic Resonance (FMR) spectroscopy. The in-plane angular dependent measurements at a fixed frequency of 25 GHz were carried out as well using FMR spectroscopy, to obtain information about the magnetic anisotropy of the sample.
3. Structural and magnetic characterization Fig. 2 shows the XRD scans of epitaxial FeGa thin films grown on MgO(1 0 0) substrates. We observe two overlaid Kiessig oscillations in
4. Ferromagnetic resonance studies The dynamic magnetic properties of FeGa thin films were studied using broadband ferromagnetic resonance (FMR) spectroscopy. The measurements were carried out using a custom design coplanar waveguide structure capable of operating up to 64 GHz [47]. The microwave power absorbed by the sample at a fixed frequency is measured as a function of the applied field using a Schottky diode and lock-in detection [48]. As can be seen in Fig. 4(a) this approach provides an excellent signal-to-noise ratio for the FMR signal for the thin films of this study. The dynamics of the magnetization M is captured by the LandauLifshitz-Gilbert (LLG) equation [49,50]:
Fig. 1. (a) FeGa (A2) crystal structure (b) The epitaxial relationship between MgO(1 0 0) and FeGa(1 0 0) demonstrated by a 2 × 2 construction with a 45° rotation on MgO(1 0 0) plane.
dM 1 dM = −γM × H eff + M × α eff dt Ms dt 2
(1)
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
S. Budhathoki, et al.
Fig. 2. XRD scans of phase-pure epitaxial FeGa thin films grown on MgO(1 0 0) by sputtering in pure Ar of 20 mTorr. (a) A small-angle X-ray reflectometry scan of FeGa(2 0 0) film demonstrates pronounced Kiessig oscillations. (b) 2θ -ω XRD scan of 16 nm thick FeGa(2 0 0) film. Inset: Rocking curve scan of FeGa(2 0 0) peak showing FWHM = 0.8°. Asterisks (*) indicate substrate peaks (c) 2θ -ω XRD scan of 16 nm thick FeGa film to determine in-plane lattice parameter. (d) ϕ -scan of the (1 1 0) peak at a tilt angle ψ = 45° for 16 nm thick FeGa(2 0 0) film demonstrate epitaxial relationship between the film and the MgO substrate. gμ
where γ = ℏB is the gyromagnetic ratio, Ms is the saturation magnetization, and H eff is the effective field, which includes all external and internal fields including exchange, anisotropy, and dipolar fields. FMR measurements were carried out along easy and hard axes of the FeGa films with the external magnetic field applied in-plane but perpendicular to the in-plane microwave field. Fig. 4(a) shows a raw ferromagnetic resonance signal for a FeGa thin film measured along its hard axis at 20 GHz, and the corresponding fit using a Lorentzian lineshape [51] to extract the resonance field Hres and peak-to-peak linewidth ΔHpp . The FMR condition can be found using Kittel’s general formula [52]:
f = γ ′ {[Hz + (Ny + N ye − Nz ) Mz ] × [Hz + (Nx + N xe − Nz ) Mz ]}1/2
1/2
H H f = γ ′ ⎧ ⎡Hres + 4 cos (4ϕH ) ⎤ ⎡Hres + 4 (3 + cos (4ϕH )) + 4πMeff ⎤ ⎫ ⎨ 2 8 ⎦⎣ ⎦⎬ ⎭ ⎩⎣
(3) where, for H4 > 0 , ϕH = 0° and 45° represent the easy and hard axis respectively, whereas for H4 < 0 the situation is reversed. When the external magnetic field is applied along the easy and hard axis of the fourfold anisotropy; the assumption ϕH = ϕM , is fulfilled for sufficiently large fields. Therefore, the broadband ferromagnetic resonance data measured along these two directions is fitted using a combined fit based on equation [3] with ϕH = 0° and ϕH = 45° respectively, see Fig. 4(b). The gyromagnetic ratio γ ′ was found to be K⊥ 3.05 ± 0.03 GHz/kOe and the effective magnetization M eff = Ms + 2πM s was 1622±42 emu/cm3 for the 16 nm thick FeGa film. This effective magnetization is in close agreement to the observed saturation magnetization as expected for a vanishing perpendicular anisotropy K⊥. Similar values of γ ′ = 3.08 ± 0.03 GHz/kOe and M eff = 1601 ± 39 emu/ cm3 were found for the 24 nm thick FeGa film. A significant fourfold 4K anisotropy H 4 = M 4 = −742 ± 15 Oe was observed for the 24 nm thick s FeGa film whereas it was −1000 ± 24 Oe for the 16 nm thick FeGa film from Kittel fit. The negative sign for H4 indicates that ϕH = 0° i.e [1 1 0] crystal direction is the hard axis of the film and its easy axis is along ϕH = 45° i.e along [1 0 0] crystal direction consistent with the observed hysteresis profile.
(2)
where Ny and Nx are demagnetization factors (corresponding to the shape anisotropy) and N ye and N xe are effective demagnetization factors (determined from an equivalent field derived from the magnetocrystalline anisotropy energy). This general formula assumes a static magnetic field applied in the z-direction and an alternating microwave field in the x-direction. In the case of FeGa thin films, a fourfold in-plane anisotropy is expected, and one can derive an approximate expression for the dependence of the resonance frequency on the resonance field Hres by assuming that the magnetization is aligned with the applied external field direction, i.e. ϕH = ϕM [53,54] 3
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
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Fig. 3. Magnetic hysteresis loop along in-plane direction (a) at wide-field range along ϕ = 0° ([1 1 0]) (b) and at narrow field range (± 200 Oe) along ϕ = 0° ([1 1 0]) and ϕ = 45° ([1 0 0]) to show remanent magnetization and coercivity, at room temperature for the 24 and 16 nm thick FeGa films. Fig. 4. (a) In-plane Ferromagnetic resonance signal (black line) and fit (red line) at 20 GHz along the hard axis for FeGa film. The FMR resonance field Hres and peak to peak linewidth ΔHpp determined from the fit are indicated as dashed lines. (b) Broadband FMR resonance field data along the hard ϕH = 0° (red symbols) and easy ϕH = 45° (blue symbols) axes. The blue and red solid lines represent a combined Kittel fit using equation [3] along the easy and hard axes respectively for the 16 nm thick FeGa thin film. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The magnetization relaxation is interpreted using the Gilbert damping formulation, assuming that a sufficiently high field is applied to avoid field dragging of the magnetization. In this case, one expects a linear dependence of the FMR peak-to-peak linewidth on the microwave frequency [49,55,56]:
ΔH (f ) = ΔHo +
f 2 α eff γ′ 3
(4)
where ΔH0 is the residual linewidth at zero frequency attributed to inhomogeneities or defects [56] that can change the internal magnetic field locally. The second term quantifies the Gilbert like contributions to the linewidth. We use the term “effective Gilbert damping parameter” or α eff to indicate that besides the intrinsic damping due to spin-
orbit coupling other damping mechanisms like spin pumping [57], eddy currents [58] and two-magnon scattering [59,60] can lead to contributions that scale linearly or approximately linearly with frequency. The experimental data were fitted using equation [4] to extract ΔH0 and
Table 1 Summary of gyromagnetic ratio, effective magnetization, damping parameter, linewidth, coercivity, and remanent magnetization for the 16 and 24 nm thick FeGa films. As the error margins indicate the hard axis data provides the most accurate values for the effective damping parameter. Sample [nm]
γ ′ [GHz/kOe]
Meff [emu/cm3]
αeff
ΔH0 [Oe]
Hard axis
Easy axis
Hard axis
Easy axis
Hc [Oe] Hard axis
Mr [kemu/cc] Hard axis
16
3.05 ± 0.03
1622 ± 42
0.0005 0.0065+ −0.0001
0.0087 0.0043+ −0.0002
13 ± 1
203 ± 4
25.2
1.10
24
3.08 ± 0.03
1601 ± 39
0.0028 0.0039+ −0.0001
0.0137 0.0012+ −0.0005
71 ± 1
316 ± 8
35.1
1.14
4
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
S. Budhathoki, et al.
Fig. 5. Linewidth as a function of frequency, fitted using equation (4) to extract the effective damping parameter (solid lines) for the 16 nm thick FeGa film. The dashed lines are the steepest slope that have ΔH0 = 0 and are consistent with the data sets, they are used to determine a conservative upper limit for the effective damping parameter, see text for details.
the effective damping parameter, as shown in Fig. 5. The residual linewidth was found to be ΔH0 = 13 ± 1 for the 16 nm thick FeGa film whereas it was 71 ± 1 Oe for the 24 nm thick FeGa film along the hard axis which is significantly lower than reported by Kuanr et al. [61], Butera et al. [28] and Lou et al. [29] indicative of the high quality of the epitaxial films in our study. The increase in linewidth can be attributed to an expected increase in defects or inhomogeneities with film thickness. The effective damping parameter was found to be α eff = 0.0065+−0.0005 0.0001 for the 16 nm thick film which is one order magnitude lower than the previously reported values for FeGa thin films [41,26]. The upper limit of the error margin was estimated assuming that the damping is solely caused by Gilbert type damping at the highest microwave frequency whereas the lower limit of the error margin is based on the statistical error of the slope for the hard axis data [62]. While this parameter is generally assumed to be dominated by the intrinsic damping contribution, we note that two-magnon scattering can also lead to a linewidth contribution that is approximately linear in frequency [49] and therefore cannot be excluded as a possible source. The values for linewidth, damping parameter and effective magnetization are summarized in Table1. In-plane angle-dependent FMR measurements were also carried out at a fixed frequency of 25 GHz to corroborate the cubic anisotropy in FeGa films. In Fig. 6(a) the in-plane angular dependence of Hres field clearly demonstrates a fourfold anisotropy as expected based on the crystal symmetry. The fourfold anisotropy field H4 determined by fitting the data to equation [3] was found to be −795 ± 1 Oe, consistent with the corresponding value H4 = −786 ± 15 Oe determined from the combined Kittel plot (not shown) within the error margins for the 24 nm thick FeGa film. In addition to this, a strong fourfold anisotropy of the linewidth was observed as well, with the maxima (minima) of the linewidth coinciding with the minima (maxima) of the resonance field. For the in-plane angular dependence of the linewidth, contributions from misalignment between the magnetization and the applied field direction (field drag) and linewidth broadening due to mosaicity, for a system with a fourfold anisotropy one expects the linewidth to have an eightfold symmetry [63]. Two-magnon scattering from misfit dislocations [60] and inhomogeneities of the crystalline anisotropy [64] are possible mechanisms that will have the same symmetry as the crystal lattice, consistent with the observed fourfold symmetry of the linewidth. Therefore the in-plane angular dependence of the FMR linewidth is fitted using [65,62]:
ΔH = ΔHiso + ΔH2mcos 2 [2(ϕH − ϕ0)]
Fig. 6. In-plane angular dependence of (a) resonance field data (black symbols) demonstrating fourfold anisotropy. The data is fitted (red solid line) using equation [3] to extract fourfold anisotropy term H4 and (b) the linewidth (black symbols) also demonstrating a fourfold anisotropy. The data is fitted (red solid line) using equation [5] to extract the isotropic linewidth contribution ΔHiso and the strength anisotropic two-magnon scattering linewidth contribution ΔH2m for the 24 nm thick FeGa film. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
where, ΔHiso is the isotropic contribution from Gilbert damping and inhomogeneous broadening, ΔH2m is the anisotropic contribution from two-magnon scattering and ϕ0 = 45°. From the measurement ΔH2m was found to be 293±4 Oe. This value is significantly larger than ΔHiso = 104±2 Oe, indicating that the FMR linewidth is dominated by anisotropic two-magnon scattering.
5. Conclusion We have investigated the structural and dynamic properties of phase pure, epitaxial FeGa thin films grown on MgO(1 0 0) substrates using the combinatorial sputter beam epitaxy method which results in high quality thin films. Structural characterization confirmed the cubic structure of the film, in agreement with dynamic FMR studies revealing fourfold magnetic symmetry. FMR measurements showed an ultra-low in homogenous linewidth contribution of 13 ± 1 Oe and effective 0.0005 damping parameter as low as 0.0065+ −0.0001 for the 16 nm thick film suitable for potential application in high-frequency microwave devices.
Declaration of Competing Interest
(5)
None. 5
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
S. Budhathoki, et al.
Acknowledgment
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A.S. would like to acknowledge NSF-CAREER Award No. 1452670. References [1] C. Grezes, F. Ebrahimi, J. Alzate, X. Cai, J. Katine, J. Langer, B. Ocker, P. Khalili Amiri, K. Wang, Ultra-low switching energy and scaling in electric-field-controlled nanoscale magnetic tunnel junctions with high resistance-area product, Appl. Phys. Lett. 108 (2016) 012403 . [2] D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura, H. Ohno, Magnetization vector manipulation by electric fields, Nature 455 (2008) 515. [3] D. Chiba, M. Yamanouchi, F. Matsukura, H. Ohno, Electrical manipulation of magnetization reversal in a ferromagnetic semiconductor, Science 301 (2003) 943. [4] N. Tiercelin, Y. Dusch, A. Klimov, S. Giordano, V. Preobrazhensky, P. Pernod, Room temperature magnetoelectric memory cell using stress-mediated magnetoelastic switching in nanostructured multilayers, Appl. Phys. Lett. 99 (2011) 192507 . [5] J. Cui, J.L. Hockel, P.K. Nordeen, D.M. Pisani, C.-Y. Liang, G.P. Carman, C.S. Lynch, A method to control magnetism in individual strain-mediated magnetoelectric islands, Appl. Phys. Lett. 103 (2013) 232905 . [6] M. Buzzi, R. Chopdekar, J. Hockel, A. Bur, T. Wu, N. Pilet, P. Warnicke, G. Carman, L. Heyderman, F. Nolting, Single domain spin manipulation by electric fields in strain coupled artificial multiferroic nanostructures, Phys. Rev. Lett. 111 (2013) 027204 . [7] V. Novosad, Y. Otani, A. Ohsawa, S. Kim, K. Fukamichi, J. Koike, K. Maruyama, O. Kitakami, Y. Shimada, Novel magnetostrictive memory device, J. Appl. Phys. 87 (2000) 6400. [8] H. Boukari, C. Cavaco, W. Eyckmans, L. Lagae, G. Borghs, Voltage assisted magnetic switching in Co50Fe50 interdigitated electrodes on piezoelectric substrates, J. Appl. Phys. 101 (2007) 054903 . [9] A. Khitun, M. Bao, K.L. Wang, Magnonic logic circuits, J. Phys. D: Appl. Phys. 43 (2010) 264005 . [10] A. Khitun, K.L. Wang, Non-volatile magnonic logic circuits engineering, J. Appl. Phys. 110 (2011) 034306 . [11] J. Lou, D. Reed, C. Pettiford, M. Liu, P. Han, S. Dong, N. Sun, Giant microwave tunability in FeGaB/lead magnesium niobate-lead titanate multiferroic composites, Appl. Phys. Lett. 92 (2008) 262502 . [12] M. Wun-Fogle, J. Restorff, A. Clark, Magneto mechanical coupling in stress-annealed Fe-Ga (Galfenol) alloys, IEEE Trans. Magn. 42 (2006) 3120. [13] T.A. Duenas, G.P. Carman, Large magnetostrictive response of Terfenol-D resin composites, J. Appl. Phys. 87 (2000) 4696. [14] A.E. Clark, M. Wun-Fogle, J.B. Restorff, T.A. Lograsso, J.R. Cullen, Effect of quenching on the magnetostriction on Fe1 − x Gax (0.13 < x < 0.21), IEEE Trans. Magn. 37 (2001) 2678. [15] A.E. Clark, M. Wun-Fogle, J.B. Restorff, T.A. Lograsso, Magnetostrictive properties of galfenol alloys under compressive stress, Mater. Trans. 43 (2002) 881. [16] T. Ma, J. Gou, S. Hu, X. Liu, C. Wu, S. Ren, H. Zhao, A. Xiao, C. Jiang, X. Ren, et al., Highly thermal-stable ferromagnetism by a natural composite, Nat. Commun. 8 (2017) 13937. [17] J. Atulasimha, A.B. Flatau, A review of magnetostrictive iron-gallium alloys, Smart Mater. Struct. 20 (2011) 043001 . [18] A.E. Clark, J.B. Restorff, M. Wun-Fogle, T.A. Lograsso, D.L. Schlagel, Magnetostrictive properties of body-centered cubic Fe-Ga and Fe-Ga-Al alloys, IEEE Trans. Magn. 36 (2000) 3238. [19] L. Shu, G. Wu, D. Chen, M.J. Dapino, Modeling of galfenol bending actuator considering nonlinear hysteresis and dynamic real-time control strategy, Smart Mater. Struct. 25 (2016) 035046 . [20] Q. Xing, Y. Du, R. McQueeney, T. Lograsso, Structural investigations of Fe-Ga alloys: phase relations and magnetostrictive behavior, Acta Mater. 56 (2008) 4536. [21] G. Petculescu, R. Wu, R. McQueeney, Magnetoelasticity of bcc Fe-Ga alloys, Handbook of Magnetic Materials, vol. 20, Elsevier, 2012, pp. 123–226. [22] G. Petculescu, K. Hathaway, T.A. Lograsso, M. Wun-Fogle, A. Clark, Magnetic field dependence of galfenol elastic properties, J. Appl. Phys. 97 (2005) 10M315. [23] J. Cullen, P. Zhao, M. Wuttig, Anisotropy of crystalline ferromagnets with defects, J. Appl. Phys. 101 (2007) 123922 . [24] M. Huang, T.A. Lograsso, A. Clark, J. Restorff, M. Wun-Fogle, Effect of interstitial additions on magnetostriction in Fe-Ga alloys, J. Appl. Phys. 103 (2008) 07B314. [25] J. Gaudet, T. Hatchard, S. Farrell, R. Dunlap, Properties of Fe-Ga based powders prepared by mechanical alloying, J. Magn. Magn. Mater. 320 (2008) 821. [26] D. Parkes, L. Shelford, P. Wadley, V. Holý, M. Wang, A. Hindmarch, G. Van Der Laan, R. Campion, K. Edmonds, S. Cavill, Magnetostrictive thin films for microwave spintronics, Scientific Rep. 3 (2013) 2220. [27] J. Dean, M. Bryan, N. Morley, G. Hrkac, A. Javed, M. Gibbs, D. Allwood, Numerical study of the effective magneto crystalline anisotropy and magnetostriction in polycrystalline FeGa films, J. Appl. Phys. 110 (2011) 043902 . [28] A. Butera, J. Gómez, J. Weston, J. Barnard, Growth and magnetic characterization of epitaxial Fe81Ga19 /MgO (100) thin films, J. Appl. Phys. 98 (2005) 033901 . [29] J. Lou, R. Insignares, Z. Cai, K.S. Ziemer, M. Liu, N.X. Sun, Soft magnetism, magnetostriction, and microwave properties of FeGaB thin films, Appl. Phys. Lett. 91 (2007) 182504 . [30] J. Lou, M. Liu, D. Reed, Y. Ren, N.X. Sun, Giant electric field tuning of magnetism in novel multiferroic FeGaB/lead zinc niobate-lead titanate (PZN-PT) heterostructures, Adv. Mater. 21 (2009) 4711. [31] M. Ohring, Materials Science of Thin Films, Elsevier, 2001. [32] A.Y. Cho, J.R. Arthur, Molecular Beam Epitaxy, Prog. Solid State Chem. 10 (1975) 157.
6
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Research articles
Low Gilbert damping and linewidth in magnetostrictive FeGa thin films a,b,⁎
a,b
Sujan Budhathoki , Arjun Sapkota , Ka Ming Law ⁎ Shambhu KCa,b, Tim Mewesa,b, Adam J. Hausera,b, a b
a,b
, Bhuwan Nepal
a,b
, Smriti Ranjit
T
a,b
,
Center for Materials for Information Technology (MINT), The University of Alabama, Tuscaloosa, AL 35487, USA Department of Physics and Astronomy, The University of Alabama, Tuscaloosa, AL 35487, USA
A B S T R A C T
Fabrication of voltage tunable high-frequency devices using magnetostrictive ferromagnet-piezoelectric hybrid structures requires materials with low damping and narrow linewidth to achieve low microwave loss. Galfenol exhibits superior magnetostriction, stability over a wide range of temperatures, and is free of rare earth elements, making it an economical and promising candidate, if the microwave losses can be minimized. We report the fabrication, structural and magnetic characterization, and study of dynamic properties of epitaxial FeGa thin films exhibiting an ultra-low residual linewidth, ΔH0 = 13 ± 1 Oe – a requirement for low +0.0028 microwave loss and effective damping parameter, α eff , as low as 0.0065+−0.0005 0.0001 for the 16 nm thick film. Similarly, we found α eff = 0.0039−0.0007 and ΔH0 = 71 ± 1 Oe for the 24 nm thick film, demonstrating its potential for applications in magnetic memory and high frequency devices.
1. Introduction The effective manipulation of magnetization is the key to realize energy-efficient spintronic devices. There has been strong research interest across the scientific community concerning electrical field [1–3] or strain mediated [4–6] manipulation of magnetization for writing information onto magnetic materials used in data storage. These effects can be achieved in magnetoelectric composite materials, for example; the strong magneto-electric coupling across magnetostrictive ferromagnet-piezoelectric hybrid structures can be exploited to fabricate magnetic memory [7,8] and spin wave-based magnetic logical [9,10] devices. The realization of these devices requires magnetic thin films with very high magnetostriction to enable voltage-induced switching of magnetization when combined with a piezostrictive element. Favorable performance requires narrow ferromagnetic resonance (FMR) linewidth and fast magnetization switching speeds dictated by the effective damping parameter [11]. These properties are strongly affected by the inhomogeneity of the magnetostrictive ferromagnetic structure when fabricated in thin-film forms. Transition metal ferromagnets (for eg; Fe, Co, Ni) exhibit significant magnetostriction, but binary alloys such as galfenol and ternary alloys such as terfenol-D outnumber them [12,13]. Galfenol (Fe100 − x Gax , 12 at. % ⩽ x ⩽ 30 at.%) is a rare-earth-free binary alloy that has been widely studied in recent years due to its large magnetostriction coefficient (λ s∼350 ppm in bulk [14] and λ s∼400 ppm for single crystals [15]), superior thermal-stable magnetization close to critical temperature [16] and low saturation and switching fields [15,16] suitable for applications in sensors, mechanical actuators and spintronic devices [17–19,7]. ⁎
There are different structural variants of Fe-Ga alloys in which Ga content influences the magnitude of magnetostriction [20–23]. Previous studies have shown that disordered bcc α -Fe phase (A2) exhibits maximum magnetostriction, whereas cubic D03 (Fe3 Ga) is detrimental to magnetostriction [24,25]. The single crystal galfenol thin films exhibit magnetostriction comparable to that of bulk [26], however, single-crystal epitaxial growth of galfenol thin film is challenging due to possible poly-crystalline nature [27]. In addition, the large FMR linewidth of 450–700 Oe [28,29] at X-band limits its use in microwave devices. This large residual linewidth can be tuned by doping metalloid elements such as Boron but one has to compromise the magnitude of magnetostriction and hence the strength of magnetoelectric coupling [29,11,30]. In this work we report the fabrication, structural characterization and dynamic magnetic properties of phase pure, epitaxial Fe19 Ga81 thin films grown via sputter beam epitaxy method [31–36]. Despite a relatively large lattice mismatch, the films exhibit low coercivity, ultra-low Gilbert damping constant, and a narrow residual FMR linewidth term, likely the result of improved film quality that has proven elusive to date. The results suggest potential for incorporation of galfenol thin films in low-loss spin-torque oscillators and spin-wave based logic devices. 2. Experiment The use of a single composite sputter target with stoichiometry matching the desired film is problematic: Positional stoichiometry inevitably varies due to variance in the ejection angle probabilities for
Corresponding authors. E-mail addresses: [email protected] (S. Budhathoki), [email protected] (A.J. Hauser).
https://doi.org/10.1016/j.jmmm.2019.165906 Received 1 August 2019; Received in revised form 10 September 2019; Accepted 26 September 2019 Available online 04 October 2019 0304-8853/ © 2019 Elsevier B.V. All rights reserved.
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
S. Budhathoki, et al.
small-angle XRR (Fig. 2(a)): The pronounced, narrow oscillations are due to the thickness of the FeGa film, while the much longer period oscillation is from the much thinner Al cap layer. The recursive Parratt formalism [38] was employed to fit the observed XRR pattern using GENX software [39] which gave FeGa thickness to be 16.3 nm and 24 nm with respective Al cap thicknesses of 2.3 and 2.7 nm. Taken together, the XRR and fitting indicate atomically abrupt, smooth interfaces between substrate and film, film and Al cap and the Al cap and the air (surface). From EDX analysis of the FeGa thin films, the Fe content was found to be 81% (±3%) and 80% (±3%) for the 16 nm and 24 nm thick films respectively which were confirmed by RBS. Fig. 2(b) shows the on-axis XRD pattern for the 16 nm thick film. Fig. 2(c) shows the off-axis XRD pattern of the (1 1 0) crystal orientation of the film. The full width at half maximum for the 16 nm (Fig. 2(b) inset) thick film is found to be 0.8° and the out of plane lattice constant is found to be 2.841 ± 0.002 Å, which is 2.03% lower than the bulk 2.900 Å[40] value. By using the lattice spacing deduced from the FeGa (1 1 0) peak position in conjunction with the out-of-plane (2 0 0) value, the in-plane lattice constant is found to be 2.933 ± 0.003 Å, which is 1.14% larger than the bulk value, confirming the in-plane tensile strain implied by the smaller out-of-plane lattice constant. Although, it does appear that significant relaxation has already taken place, the volume of the film unit cell is within 0.2% of the bulk value with tetragonality of 0.969 ± 0.001 Å. Both in-plane and out-of-plane XRD measurements indicate phase pure, epitaxial films with no film impurity peaks detected. The expected epitaxial relationship between the FeGa film and MgO(1 0 0) substrate as shown in Fig. 1 is confirmed by the fourfold symmetry of FeGa(1 1 0) peaks with a 45° rotation to MgO(2 2 0) peaks as observed from the ϕ -scan in Fig. 2(d). The in-plane (along the ϕ = 0° ([1 1 0]) and ϕ = 45° ([1 0 0]) inplane directions) magnetic hysteresis loop, at room temperature, of the 16 and 24 nm thick films is shown in Fig. 3. The observed hysteresis profile as shown in Fig. 3(b) suggests that ϕ = 45° ([1 0 0]) is the easy axis of magnetization with lower relative coercivity. The ferromagnetic saturation magnetization for 16 and 24 nm thick FeGa film is determined to be Ms = 1550 ± 90 emu/cc (2.0 ± 0.1 μB /f.u) and Ms = 1540 ± 65 emu/cc (2.0 ± 0.1 μB /f.u) respectively which is ∼15 % higher than observed for poly-crystalline FeGa films by Gopman et al. [41] and in close agreement with epitaxial FeGa films measured by Weston et al. [42] and Tacchi et al. [43]. The coercivity (Hc ) is found to be 25.2 Oe and 35.1 Oe for the 16 and 24 nm thick FeGa film respectively, Fig. 3(b), lower that the values observed by Gopman et al. [41] and Weston et al. [42], though their films were significantly thicker and may account entirely for the difference. Regardless, the films are undoubtedly soft ferromagnets of potential use for low loss applications. We also note that thinner films exhibit homogeneous strain transfer compared to thicker films [44] and can be exploited for non-volatile magnetization switching in nanoscale magnetoelectric memory cells [45,26,46]. The values for Hc and remanent magnetization (Mr ) are summarized in Table 1.
different elements, and is exacerbated by element-dependent scattering of ejected atoms off process gas at pressures above 2–5 mTorr. In addition, while conventional on-axis sputtering is a sufficiently fast method for growing thin-film alloys, higher growth energetics result in higher defect rates of the crystal/atomic ordering and altered film properties. Defects from film growth must be addressed first, as they obfuscate the intrinsic nature and delay understanding of the material. Epitaxial FeGa films were grown on MgO (1 0 0) substrates at a base pressure of 5 × 10−9 Torr via “sputter beam epitaxy”-an ultra-high vacuum (UHV) custom hybrid system built by AJA International, Inc. comprising the low energetic and stoichiometry control of MBE [31,32], elemental flexibility, homogeneity over a larger area, faster deposition rate, low-cost, and industry-friendly attributes of directcurrent (DC) combinatorial magnetron sputtering [31,33,34] with offaxis geometry [35,36]. Each gun has a wedge-shaped shutter producing a uniform sputter beam at the off-axis angle range utilized, with a flux difference of less than 1% across a 2-inch wafer before substrate rotation. The substrate holder then rotates at 80 rpm to ensure maximum uniformity even under rapid growth conditions. Co-deposition fluxes of stoichiometric Fe64 Ga36 and elemental Fe targets were tuned by quartz crystal microbalance pre-growth to produce Fe81Ga19 thin films. The MgO substrates were in situ annealed at 700 °C for 30 min in UHV to remove water and carbon contaminants from the surface [37] followed by film deposition at a substrate temperature of 250 °C and the Al layer was deposited below 100 °C to prevent the oxidation of films. The optimal growth temperature and Ar pressure (20 mTorr) were determined by the simultaneous observation of (1) maximal film peak intensity in X-ray diffraction (XRD) patterns and (2) the most pronounced Kiessig oscillations in X-ray reflectometry (XRR). Stoichiometry of FeGa films was determined using energy dispersive X-ray (EDX) spectroscopy and confirmed by Rutherford Backscattering. Crystal structure and epitaxial quality were determined by XRD using a Philips X-pert system. XRR was employed to measure the thickness of each film, as well as the relative roughness of the films during optimization. MgO (a = 4.212 Å) is an excellent substrate to grow FeGa thin films as it has a reasonable lattice match (lattice mismatch ∼2.63%, tensile strain) as shown in Fig. 1(a), the crystal structure of disordered bcc α -Fe phase (A2) and its expected epitaxial relationship on MgO substrate with a 45° rotation in Fig. 1(b). The static and dynamic properties of FeGa films were studied using the VSM module in a Quantum Design Physical Property Measurement System (PPMS) and Ferromagnetic Resonance (FMR) spectroscopy. The in-plane angular dependent measurements at a fixed frequency of 25 GHz were carried out as well using FMR spectroscopy, to obtain information about the magnetic anisotropy of the sample.
3. Structural and magnetic characterization Fig. 2 shows the XRD scans of epitaxial FeGa thin films grown on MgO(1 0 0) substrates. We observe two overlaid Kiessig oscillations in
4. Ferromagnetic resonance studies The dynamic magnetic properties of FeGa thin films were studied using broadband ferromagnetic resonance (FMR) spectroscopy. The measurements were carried out using a custom design coplanar waveguide structure capable of operating up to 64 GHz [47]. The microwave power absorbed by the sample at a fixed frequency is measured as a function of the applied field using a Schottky diode and lock-in detection [48]. As can be seen in Fig. 4(a) this approach provides an excellent signal-to-noise ratio for the FMR signal for the thin films of this study. The dynamics of the magnetization M is captured by the LandauLifshitz-Gilbert (LLG) equation [49,50]:
Fig. 1. (a) FeGa (A2) crystal structure (b) The epitaxial relationship between MgO(1 0 0) and FeGa(1 0 0) demonstrated by a 2 × 2 construction with a 45° rotation on MgO(1 0 0) plane.
dM 1 dM = −γM × H eff + M × α eff dt Ms dt 2
(1)
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
S. Budhathoki, et al.
Fig. 2. XRD scans of phase-pure epitaxial FeGa thin films grown on MgO(1 0 0) by sputtering in pure Ar of 20 mTorr. (a) A small-angle X-ray reflectometry scan of FeGa(2 0 0) film demonstrates pronounced Kiessig oscillations. (b) 2θ -ω XRD scan of 16 nm thick FeGa(2 0 0) film. Inset: Rocking curve scan of FeGa(2 0 0) peak showing FWHM = 0.8°. Asterisks (*) indicate substrate peaks (c) 2θ -ω XRD scan of 16 nm thick FeGa film to determine in-plane lattice parameter. (d) ϕ -scan of the (1 1 0) peak at a tilt angle ψ = 45° for 16 nm thick FeGa(2 0 0) film demonstrate epitaxial relationship between the film and the MgO substrate. gμ
where γ = ℏB is the gyromagnetic ratio, Ms is the saturation magnetization, and H eff is the effective field, which includes all external and internal fields including exchange, anisotropy, and dipolar fields. FMR measurements were carried out along easy and hard axes of the FeGa films with the external magnetic field applied in-plane but perpendicular to the in-plane microwave field. Fig. 4(a) shows a raw ferromagnetic resonance signal for a FeGa thin film measured along its hard axis at 20 GHz, and the corresponding fit using a Lorentzian lineshape [51] to extract the resonance field Hres and peak-to-peak linewidth ΔHpp . The FMR condition can be found using Kittel’s general formula [52]:
f = γ ′ {[Hz + (Ny + N ye − Nz ) Mz ] × [Hz + (Nx + N xe − Nz ) Mz ]}1/2
1/2
H H f = γ ′ ⎧ ⎡Hres + 4 cos (4ϕH ) ⎤ ⎡Hres + 4 (3 + cos (4ϕH )) + 4πMeff ⎤ ⎫ ⎨ 2 8 ⎦⎣ ⎦⎬ ⎭ ⎩⎣
(3) where, for H4 > 0 , ϕH = 0° and 45° represent the easy and hard axis respectively, whereas for H4 < 0 the situation is reversed. When the external magnetic field is applied along the easy and hard axis of the fourfold anisotropy; the assumption ϕH = ϕM , is fulfilled for sufficiently large fields. Therefore, the broadband ferromagnetic resonance data measured along these two directions is fitted using a combined fit based on equation [3] with ϕH = 0° and ϕH = 45° respectively, see Fig. 4(b). The gyromagnetic ratio γ ′ was found to be K⊥ 3.05 ± 0.03 GHz/kOe and the effective magnetization M eff = Ms + 2πM s was 1622±42 emu/cm3 for the 16 nm thick FeGa film. This effective magnetization is in close agreement to the observed saturation magnetization as expected for a vanishing perpendicular anisotropy K⊥. Similar values of γ ′ = 3.08 ± 0.03 GHz/kOe and M eff = 1601 ± 39 emu/ cm3 were found for the 24 nm thick FeGa film. A significant fourfold 4K anisotropy H 4 = M 4 = −742 ± 15 Oe was observed for the 24 nm thick s FeGa film whereas it was −1000 ± 24 Oe for the 16 nm thick FeGa film from Kittel fit. The negative sign for H4 indicates that ϕH = 0° i.e [1 1 0] crystal direction is the hard axis of the film and its easy axis is along ϕH = 45° i.e along [1 0 0] crystal direction consistent with the observed hysteresis profile.
(2)
where Ny and Nx are demagnetization factors (corresponding to the shape anisotropy) and N ye and N xe are effective demagnetization factors (determined from an equivalent field derived from the magnetocrystalline anisotropy energy). This general formula assumes a static magnetic field applied in the z-direction and an alternating microwave field in the x-direction. In the case of FeGa thin films, a fourfold in-plane anisotropy is expected, and one can derive an approximate expression for the dependence of the resonance frequency on the resonance field Hres by assuming that the magnetization is aligned with the applied external field direction, i.e. ϕH = ϕM [53,54] 3
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
S. Budhathoki, et al.
Fig. 3. Magnetic hysteresis loop along in-plane direction (a) at wide-field range along ϕ = 0° ([1 1 0]) (b) and at narrow field range (± 200 Oe) along ϕ = 0° ([1 1 0]) and ϕ = 45° ([1 0 0]) to show remanent magnetization and coercivity, at room temperature for the 24 and 16 nm thick FeGa films. Fig. 4. (a) In-plane Ferromagnetic resonance signal (black line) and fit (red line) at 20 GHz along the hard axis for FeGa film. The FMR resonance field Hres and peak to peak linewidth ΔHpp determined from the fit are indicated as dashed lines. (b) Broadband FMR resonance field data along the hard ϕH = 0° (red symbols) and easy ϕH = 45° (blue symbols) axes. The blue and red solid lines represent a combined Kittel fit using equation [3] along the easy and hard axes respectively for the 16 nm thick FeGa thin film. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The magnetization relaxation is interpreted using the Gilbert damping formulation, assuming that a sufficiently high field is applied to avoid field dragging of the magnetization. In this case, one expects a linear dependence of the FMR peak-to-peak linewidth on the microwave frequency [49,55,56]:
ΔH (f ) = ΔHo +
f 2 α eff γ′ 3
(4)
where ΔH0 is the residual linewidth at zero frequency attributed to inhomogeneities or defects [56] that can change the internal magnetic field locally. The second term quantifies the Gilbert like contributions to the linewidth. We use the term “effective Gilbert damping parameter” or α eff to indicate that besides the intrinsic damping due to spin-
orbit coupling other damping mechanisms like spin pumping [57], eddy currents [58] and two-magnon scattering [59,60] can lead to contributions that scale linearly or approximately linearly with frequency. The experimental data were fitted using equation [4] to extract ΔH0 and
Table 1 Summary of gyromagnetic ratio, effective magnetization, damping parameter, linewidth, coercivity, and remanent magnetization for the 16 and 24 nm thick FeGa films. As the error margins indicate the hard axis data provides the most accurate values for the effective damping parameter. Sample [nm]
γ ′ [GHz/kOe]
Meff [emu/cm3]
αeff
ΔH0 [Oe]
Hard axis
Easy axis
Hard axis
Easy axis
Hc [Oe] Hard axis
Mr [kemu/cc] Hard axis
16
3.05 ± 0.03
1622 ± 42
0.0005 0.0065+ −0.0001
0.0087 0.0043+ −0.0002
13 ± 1
203 ± 4
25.2
1.10
24
3.08 ± 0.03
1601 ± 39
0.0028 0.0039+ −0.0001
0.0137 0.0012+ −0.0005
71 ± 1
316 ± 8
35.1
1.14
4
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
S. Budhathoki, et al.
Fig. 5. Linewidth as a function of frequency, fitted using equation (4) to extract the effective damping parameter (solid lines) for the 16 nm thick FeGa film. The dashed lines are the steepest slope that have ΔH0 = 0 and are consistent with the data sets, they are used to determine a conservative upper limit for the effective damping parameter, see text for details.
the effective damping parameter, as shown in Fig. 5. The residual linewidth was found to be ΔH0 = 13 ± 1 for the 16 nm thick FeGa film whereas it was 71 ± 1 Oe for the 24 nm thick FeGa film along the hard axis which is significantly lower than reported by Kuanr et al. [61], Butera et al. [28] and Lou et al. [29] indicative of the high quality of the epitaxial films in our study. The increase in linewidth can be attributed to an expected increase in defects or inhomogeneities with film thickness. The effective damping parameter was found to be α eff = 0.0065+−0.0005 0.0001 for the 16 nm thick film which is one order magnitude lower than the previously reported values for FeGa thin films [41,26]. The upper limit of the error margin was estimated assuming that the damping is solely caused by Gilbert type damping at the highest microwave frequency whereas the lower limit of the error margin is based on the statistical error of the slope for the hard axis data [62]. While this parameter is generally assumed to be dominated by the intrinsic damping contribution, we note that two-magnon scattering can also lead to a linewidth contribution that is approximately linear in frequency [49] and therefore cannot be excluded as a possible source. The values for linewidth, damping parameter and effective magnetization are summarized in Table1. In-plane angle-dependent FMR measurements were also carried out at a fixed frequency of 25 GHz to corroborate the cubic anisotropy in FeGa films. In Fig. 6(a) the in-plane angular dependence of Hres field clearly demonstrates a fourfold anisotropy as expected based on the crystal symmetry. The fourfold anisotropy field H4 determined by fitting the data to equation [3] was found to be −795 ± 1 Oe, consistent with the corresponding value H4 = −786 ± 15 Oe determined from the combined Kittel plot (not shown) within the error margins for the 24 nm thick FeGa film. In addition to this, a strong fourfold anisotropy of the linewidth was observed as well, with the maxima (minima) of the linewidth coinciding with the minima (maxima) of the resonance field. For the in-plane angular dependence of the linewidth, contributions from misalignment between the magnetization and the applied field direction (field drag) and linewidth broadening due to mosaicity, for a system with a fourfold anisotropy one expects the linewidth to have an eightfold symmetry [63]. Two-magnon scattering from misfit dislocations [60] and inhomogeneities of the crystalline anisotropy [64] are possible mechanisms that will have the same symmetry as the crystal lattice, consistent with the observed fourfold symmetry of the linewidth. Therefore the in-plane angular dependence of the FMR linewidth is fitted using [65,62]:
ΔH = ΔHiso + ΔH2mcos 2 [2(ϕH − ϕ0)]
Fig. 6. In-plane angular dependence of (a) resonance field data (black symbols) demonstrating fourfold anisotropy. The data is fitted (red solid line) using equation [3] to extract fourfold anisotropy term H4 and (b) the linewidth (black symbols) also demonstrating a fourfold anisotropy. The data is fitted (red solid line) using equation [5] to extract the isotropic linewidth contribution ΔHiso and the strength anisotropic two-magnon scattering linewidth contribution ΔH2m for the 24 nm thick FeGa film. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
where, ΔHiso is the isotropic contribution from Gilbert damping and inhomogeneous broadening, ΔH2m is the anisotropic contribution from two-magnon scattering and ϕ0 = 45°. From the measurement ΔH2m was found to be 293±4 Oe. This value is significantly larger than ΔHiso = 104±2 Oe, indicating that the FMR linewidth is dominated by anisotropic two-magnon scattering.
5. Conclusion We have investigated the structural and dynamic properties of phase pure, epitaxial FeGa thin films grown on MgO(1 0 0) substrates using the combinatorial sputter beam epitaxy method which results in high quality thin films. Structural characterization confirmed the cubic structure of the film, in agreement with dynamic FMR studies revealing fourfold magnetic symmetry. FMR measurements showed an ultra-low in homogenous linewidth contribution of 13 ± 1 Oe and effective 0.0005 damping parameter as low as 0.0065+ −0.0001 for the 16 nm thick film suitable for potential application in high-frequency microwave devices.
Declaration of Competing Interest
(5)
None. 5
Journal of Magnetism and Magnetic Materials 496 (2020) 165906
S. Budhathoki, et al.
Acknowledgment
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