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[Madhav M. Bhat](https://orcid.org/0009-0006-1544-1337), [K. Simalaotao](https://orcid.org/0000-0002-6098-4422), [H. Suto](https://orcid.org/0000-0003-4387-5862), A. Perumal, A. Srinivasan, [Y. Sakuraba](https://orcid.org/0000-0003-4618-9550)

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[Atomic order induced reduction of Gilbert damping constant and enhancement of half-metallicity in off-stoichiometric Co2FeGa0.5Ge0.5 Heusler alloy thin films](https://mdr.nims.go.jp/datasets/134fac5c-4210-41b6-b418-fabc029da9cb)

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Atomic order induced reduction of Gilbert damping constant and enhancement of half-metallicity in off-stoichiometric Co2FeGa0.5Ge0.5 Heusler alloy thin filmsViewOnlineExportCitationRESEARCH ARTICLE |  JULY 23 2025Atomic order induced reduction of Gilbert damping constantand enhancement of half-metallicity in off-stoichiometricCo2FeGa0.5Ge0.5 Heusler alloy thin films Madhav M. Bhat  ; K. Simalaotao  ; H. Suto   ; A. Perumal  ; A. Srinivasan  ; Y. Sakuraba J. Appl. Phys. 138, 043904 (2025)https://doi.org/10.1063/5.0268776Articles You May Be Interested InEnhancement of magnetoresistance by inserting thin NiAl layers at the interfaces inCo2FeGa0.5Ge0.5/Ag/Co2FeGa0.5Ge0.5 current-perpendicular-to-plane pseudo spin valvesAppl. Phys. Lett. (March 2016)Phase stability and half-metallic character of off-stoichiometric Co2FeGa0.5Ge0.5 Heusler alloysJ. Appl. Phys. (November 2022)Growth of [001]-oriented polycrystalline Heusler alloy thin films using [001]-textured Ag buffer layer onthermally oxidized Si substrate for spintronics applicationsJ. Appl. Phys. (September 2024) 28 August 2025 03:13:19https://pubs.aip.org/aip/jap/article/138/4/043904/3355780/Atomic-order-induced-reduction-of-Gilbert-dampinghttps://pubs.aip.org/aip/jap/article/138/4/043904/3355780/Atomic-order-induced-reduction-of-Gilbert-damping?pdfCoverIconEvent=citejavascript:;https://orcid.org/0009-0006-1544-1337javascript:;https://orcid.org/0000-0002-6098-4422javascript:;https://orcid.org/0000-0003-4387-5862javascript:;https://orcid.org/0000-0002-4048-8739javascript:;https://orcid.org/0000-0003-3729-2572javascript:;https://orcid.org/0000-0003-4618-9550https://crossmark.crossref.org/dialog/?doi=10.1063/5.0268776&domain=pdf&date_stamp=2025-07-23https://doi.org/10.1063/5.0268776https://pubs.aip.org/aip/apl/article/108/10/102408/30132/Enhancement-of-magnetoresistance-by-inserting-thinhttps://pubs.aip.org/aip/jap/article/132/18/183902/2837732/Phase-stability-and-half-metallic-character-of-offhttps://pubs.aip.org/aip/jap/article/136/12/123906/3313731/Growth-of-001-oriented-polycrystalline-Heuslerhttps://e-11492.adzerk.net/r?e=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&s=d4MpZUAT5hcPdFlESCiDlGmpNWAAtomic order induced reduction of Gilbertdamping constant and enhancementof half-metallicity in off-stoichiometricCo2FeGa0.5Ge0.5 Heusler alloy thin filmsCite as: J. Appl. Phys. 138, 043904 (2025); doi: 10.1063/5.0268776View Online Export Citation CrossMarkSubmitted: 4 March 2025 · Accepted: 1 July 2025 ·Published Online: 23 July 2025Madhav M. Bhat,1,2 K. Simalaotao,2,3 H. Suto,2,a) A. Perumal,1 A. Srinivasan,1,b) and Y. Sakuraba1,2,3AFFILIATIONS1Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, India2Research Center for Magnetic and Spintronic Materials, NIMS, Tsukuba 305-0047, Japan3Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571, Japana)Author to whom correspondence should be addressed: SUTO.Hirofumi@nims.go.jpb)E-mail: asrini@iitg.ac.inABSTRACTThe development of energy-efficient spintronic devices with enhanced magnetoresistance demands materials with low Gilbert damping cons-tant (α) and high half-metallicity. In this study, we report a very low α in sputter-deposited off-stoichiometric Co2FeGa0.5Ge0.5 (CFGG)Heusler alloy thin films and investigate the relation between α and atomic ordering and half-metallicity. CFGG thin films with a compositionof Co44.3Fe30.7Ga13.9Ge11.1 were epitaxially deposited on MgO (001) substrates by magnetron sputtering followed by in situ annealing. Thedensity of states calculations revealed that this composition has higher half-metallicity than the stoichiometric composition, owing to Fermienergy tuning. As-deposited and 400 °C-annealed samples exhibited B2-type partially disordered structure, while annealing above 500 °Cinduced a L21-type ordered structure. The improvement in atomic order resulted in the reduction of α, as demonstrated by ferromagneticresonance measurement, and enhancement in half-metallicity, as revealed by anisotropic and ordinary magnetoresistance measurements.The 600 °C-annealed samples exhibited an intrinsic α of (3.5 ± 0.3) × 10−4, the low value reported for metallic ferromagnetic materials,demonstrating the potential for its use in energy-efficient spintronic devices.© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0268776I. INTRODUCTIONThe development of energy-efficient spintronic devicesdemands materials with low Gilbert damping constant (α), becausethe critical current density for device operation is directly related toα of the active layer material.1 Extensive studies have been con-ducted to realize low α materials, and CoFe is one of the conven-tional magnetic materials with low α with reported αint of(5.0 ± 1.8) × 10−4 and αtotal of (2.1 ± 0.1) × 10−3.2 Note that theexperimentally measured αtotal is a sum of intrinsic (αint) andextrinsic (αext) contributions, where the former represents thematerial parameter and the latter represents the effect of the mea-surement setup. As different approaches, doping and interfacialmodification have been reported to affect α.3–8 Half-metallicHeusler alloys, which have a novel electronic structure with electronof only one type of spin at the Fermi energy level (EF), are promis-ing low α materials. Because αint is considered to be proportionalto the density of states (DOS) at EF,9–11 the presence of only onetype of electronic spin (either up or down) DOS at EF in half-metallic material can result in small DOS at EF leading to low α.Furthermore, the part of spin scattering channels, such as spin-flipscattering, is forbidden due to half-metallicity, leading to a furtherreduction in damping. There have been several attempts to mini-mize α in Heusler alloys by enhancing the half-metallicity,12,13 andreported αtotal values ranging from 4.1 × 10−4 to 7.0 × 10−4,14,15which are lower than those of 3d transition magnetic materials.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 043904 (2025); doi: 10.1063/5.0268776 138, 043904-1© Author(s) 2025 28 August 2025 03:13:19https://doi.org/10.1063/5.0268776https://doi.org/10.1063/5.0268776https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0268776http://crossmark.crossref.org/dialog/?doi=10.1063/5.0268776&domain=pdf&date_stamp=2025-07-23https://orcid.org/0009-0006-1544-1337https://orcid.org/0000-0002-6098-4422https://orcid.org/0000-0003-4387-5862https://orcid.org/0000-0002-4048-8739https://orcid.org/0000-0003-3729-2572https://orcid.org/0000-0003-4618-9550mailto:SUTO.Hirofumi@nims.go.jpmailto:asrini@iitg.ac.inhttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1063/5.0268776https://pubs.aip.org/aip/japHalf-metallicity is also advantageous for obtaining large mag-netoresistance (MR) output and high spin-transfer torque (STT)efficiency of the devices,16 and studies on these properties havebeen extensively carried out on various Heusler alloys. Amongthem, Co2Fe based Co2FeGa0.5Ge0.5 (CFGG) has gathered consider-able attention with the demonstration of enhanced MR ratio inthe current-perpendicular-to-plane giant magnetoresistance(CPP-GMR) device17–19 due to high spin polarization (P) and aCurie temperature (TC) of 1080 K.20 Similarly, Co2Mn basedHeusler alloys are known for high P and have demonstrated signifi-cant MR ratios in CPP-GMR devices.21–25 However, the finite solu-bility of Mn in Ag spacer reduces the MR.26,27 These findings havefocused research interest on CFGG. Goto et al.28 have shown thatthe stoichiometric CFGG alloy has Co–Fe disorder arising from Coatoms occupying Fe sites. This disorder introduces minority DOSin the half-metallic gap, thereby decreasing the half-metallicity.Chen et al.29 have conducted a comprehensive study on the effectof CFGG composition on phase stability and half-metallicity andnoted that Co39.4Fe29.3Ga13.4Ge17.9 exhibits a single-phase withL21-type structure and increased half-metallicity due to reducedCo–Fe disorder. Based on these findings, α is expected to bereduced by using Co-deficient and Fe-rich off-stoichiometric com-position as α is closely related to half-metallicity. However, onlythe bulk α value (∼0.008) is available in the literature,20 and thusdetailed studies on α of CFGG thin films have been demanded.In this study, we report a very low α in CFGG thin films,focusing on Co-deficient and Fe-rich off-stoichiometric composi-tion, and investigate the relation of α of the film with atomicordering and half-metallicity. Epitaxial off-stoichiometric CFGGthin films deposited under ambient conditions were annealed atdifferent temperatures (Tan) to induce various degrees of atomicordering, which were examined by x-ray diffraction (XRD). Thechange in the half-metallicity was assessed by anisotropic magneto-resistance (AMR) and ordinary magnetoresistance (OMR) mea-surements. An increase in the magnitude of the negative AMRratio and an increase in the OMR ratio with an increase in Tanindicate an enhancement in half-metallicity of the films due toimprovement in atomic ordering. The αint of CFGG determined byferromagnetic resonance measurement decreased with increasingTan, achieving a very low αint of (3.5 ± 0.3) × 10−4 at Tan = 600 °C.These results illustrate the relation between αint and half-metallicityand demonstrate the potential of off-stoichiometric CFGG as a lowα and high spin polarization material.II. EXPERIMENTAL AND CALCULATION METHODSOff-stoichiometric CFGG epitaxial thin films were depositedon single-crystal MgO (001) substrates using a high (˃99.9%)purity alloy target of composition Co46.5Fe24.1Ga13.7Ge15.7. Thedeposition was carried out at room temperature using an ultrahighvacuum radio frequency magnetron sputtering system (EikoES-350) with a deposition rate of ∼1.2 nm/min. Prior to deposition,the sputtering chamber was evacuated to a base pressure of∼10−7 Pa. High-purity (∼99.999%) argon gas at a pressure of∼4 × 10−1 Pa was used as the sputtering gas. During the deposition,a target-to-substrate distance of 100 mm was maintained. Theas-deposited thin films were then annealed in situ in the vacuumchamber at 400, 500, and 600 °C for 30 min each to improve theatomic ordering. A 2 nm aluminum capping layer was deposited onthe annealed films after cooling down. All the CFGG thin filmswere deposited under the same sputtering condition, and the com-position estimated by x-ray fluorescence spectroscopy was in therange of Co44.3±0.7Fe30.7±1.2Ga13.9±0.3Ge11.1±0.2, indicating the smallcomposition difference among the samples. The atomic order wasdetermined from XRD patterns recorded with Rigaku Smartlabequipped with Cu-Kα radiation (λ = 1.5406 Å) in parallel beamgeometry. Using x-ray reflectivity measurement, the thickness androughness of the samples were found to be ∼24 ± 1 and ∼0.7 nm,respectively. For quantitative analysis of half-metallicity in thesamples, temperature dependent AMR and OMR measurementswere carried out using the DC four-probe method in the tempera-ture range of 10–300 K with a physical property measurementsystem (PPMS, Quantum Design USA). During AMR measure-ment, 0.2 mA direct current was passed along the 〈110〉 directionof the sample, while changing the saturation magnetization direc-tion within the sample plane over 360° by applying a magneticfield of 1 T. The AMR ratio was evaluated by Δρ/ρ0, withΔρ = ρw− ρ⊥. Here, ρw and ρ⊥ are the electrical resistivity at anangle w and 90° between the magnetization and the current direc-tion, respectively. During the OMR measurement, 0.1 mA directcurrent was passed along the 〈110〉 direction of the sample, whilevarying the magnetic field from 0 to 14 T oriented in a sampleplane and perpendicular to the current direction. OMR ratio wasevaluated by Δρ/ρ0, with Δρ = ρH− ρ0, where ρH and ρ0 are theelectrical resistivity in the presence and absence of magnetic field,respectively. The Gilbert damping parameter α was evaluated fromin-plane ferromagnetic resonance (FMR) measurements in the fre-quency range from 16 to 36 GHz using a Phase FMR-40 broadbandFMR setup connected to the PPMS. The obtained FMR spectrawere fitted to the equation,30dIdH¼ A1ΔH/2ð Þ2 � (H � Hr)2� �(ΔH/2)2 þ (H �Hr)2� �2 þ A22(H � Hr)(ΔH/2)(ΔH/2)2 þ (H �Hr)2� �2 :(1)This fitting allowed for the extraction of the resonance field(μ0Hr) and linewidth (μ0ΔH), which were used to calculate α. InEq. (1), dI/dH represents the first derivative of the microwaveabsorption signal with respect to an applied external magnetic field(H). The values A1 and A2 represent the coefficients of the symmet-ric and antisymmetric components of the FMR signal, respectively.Density-functional theory (DFT) calculations were performed byusing Vienna ab initio simulation package (VASP).31 These calcula-tions estimated the DOS near EF to assess the half-metallicity ofthe synthesized Co44.3Fe30.7Ga13.9Ge11.1 alloy composition. Theresults were compared with those of the stoichiometricCo50Fe25Ga12.5Ge12.5 alloy. Projector-augmented wave (PAW)32pseudopotentials were used to describe the interaction betweenvalence electrons and ion cores. The exchange-correlation energywas evaluated within the generalized gradient approximation(GGA),33 without considering the Coulomb interaction. The exper-imental lattice parameter (a = 5.725 Å), obtained from the XRDpattern, was used in all calculations. The Brillouin zone wasJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 043904 (2025); doi: 10.1063/5.0268776 138, 043904-2© Author(s) 2025 28 August 2025 03:13:19https://pubs.aip.org/aip/japsampled using a 25 × 25 × 25-point Monkhorst–Pack grid34 toachieve sufficient k-point density. Chemical disorder between Coand Fe atoms, as well as Ga and Ge atoms in the L21-type structure,was modeled using the virtual crystal approximation (VCA).35 Itshould be noted that previous studies29,36,37 reported that VCA cancorrectly treat disorder only for elements that are neighbors in theperiodic table. Therefore, VCA is appropriate for calculating theDOS for CFGG alloys, which exhibit disorder between Co and Fe,as well as Ga and Ge. The ideal CFGG L21 structure consists of twoface-centered cubic sublattices with four atomic positions: two Coatoms at (0.25, 0.25, 0.25) and (0.75, 0.75, 0.75), one Fe atom at(0.5, 0.5, 0.5), and Ga and Ge atoms in a 50:50 ratio at (0, 0, 0).For the off-stoichiometric Co44.3Fe30.7Ga13.9Ge11.1 alloy, the atomicsite occupancies were modified as follows: Co and Fe occupied the(0.25, 0.25, 0.25) and (0.75, 0.75, 0.75) sites in an 88.6%:11.4%ratio, Fe occupied the (0.5, 0.5, 0.5) site, and Ga and Ge occupiedthe (0, 0, 0) site in a 55.6%:44.4% ratio.III. RESULTS AND DISCUSSIONA. First-principles calculationsFirst, we examined the DOS of CFGG with stoichiometric com-position, along with the Co-deficient and Fe-rich off-stoichiometriccomposition used in the experiments. Figure 1(a) shows the calcu-lated spin resolved total DOS for Co50Fe25Ga12.5Ge12.5 andCo44.3Fe30.7Ga13.9Ge11.1 compositions. In the off-stoichiometric com-position, the DOS shifts horizontally and EF is located closer to themiddle of the gap, while the overall DOS shape is maintained. As aresult, the spin polarization increased from 35% to 58%. We addi-tionally calculated the sp-partial DOS, as shown in Fig. 1(b), becausethe electrons in the s and p bands are the primary contributors toelectric conduction due to their high Fermi velocities. The estimatedspin polarization of the sp-partial DOS is high, being 96% for stoi-chiometric CFGG and 94% for off-stoichiometric CFGG. Regardingthe sum of majority and minority DOS at EF, which is related to α,the same value of 1.166 states/eV was obtained for both stoichiometricand off-stoichiometric CFGG. However, Co–Fe disorder, which areexpected to occur in stoichiometric CFGG, is known to give rise to anin-gap state in the minority band at EF.28,38 This in-gap state canincrease α by increasing the sum of majority and minority DOS at EFand disturbing the half-metallicity, from which we predict that off-stoichiometric CFGG can achieve lower α.Figures 2(a) and 2(b) show the spin resolved band structuresfor Co50Fe25Ga12.5Ge12.5 and Co44.3Fe30.7Ga13.9Ge11.1 compositions,respectively. In both the compositions, a pseudo-gap is observed inthe minority-spin channel around EF, characterized by a substantialreduction in band dispersion and the absence of band crossingsnear EF. In contrast, the majority-spin bands are metallic, withseveral bands crossing EF, indicating metallic conduction in thatchannel. This behavior is consistent with that observed in the spinresolved total DOS. However, since the band structure does notexhibit a complete gap in the minority-spin channel, 100%half-metallicity is not realized. The presence of a pseudo-gapimplies that the system lies near the half-metallic regime, but smallperturbations such as atomic disorder can introduce states at EFand significantly degrade the spin polarization. Notably, the off-stoichiometric composition exhibits a more pronounced separationof minority-spin bands near EF, suggesting enhanced spin polariza-tion and a system that more closely approaches half-metallicity, aspredicted from the DOS analysis.B. Structural characterizationFigures 3(a) and 3(b) show the out-of-plane (χ = 0°) and〈111〉-direction (χ = 54.7°) 2θ-ω XRD patterns of the as-depositedand annealed samples, respectively. The presence of the 002 and004 peaks in the out-of-plane XRD patterns indicate the epitaxialgrowth along the [001] direction in all the samples. Theas-deposited and 400 °C-annealed samples exhibit a B2-type par-tially disordered structure as evidenced by the presence of 002 andthe absence of 111 superlattice peaks. The samples annealed atTan = 500 °C reveal a L21-ordered structure as evidenced by theappearance of 111 superlattice peak. Figure 3(c) shows the degreeFIG. 1. (a) Spin resolved total DOS calculated for Co50Fe25Ga12.5Ge12.5 and Co44.3Fe30.7Ga13.9Ge11.1 composition. The inset in the figure provides an expanded view ofDOS near EF. (b) sp-DOS corresponding to Co50Fe25Ga12.5Ge12.5 and Co44.3Fe30.7Ga13.9Ge11.1 compositions.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 043904 (2025); doi: 10.1063/5.0268776 138, 043904-3© Author(s) 2025 28 August 2025 03:13:19https://pubs.aip.org/aip/japof B2 (SB2) and L21 (SL21 ) ordering expressed as39SB2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiIobs002/Iobs004Isim002 /Isim004s, (2)SL21 ¼23� SB2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiIobs111/Iobs004Isim111 /Isim004s, (3)where I002, I004, and I111 indicate the integrated intensities of the002, 004, and 111 XRD peaks, with the superscripts “obs” and“sim” correspond to the values observed in the experiments andsimulation by VESTA software, respectively, for the Co-deficientand Fe-rich off-stoichiometric composition. Since the surfaceroughness is small (∼0.7 nm), its influence on the experimentallyobserved XRD peak intensity is considered negligible in theanalysis. During the simulation, the site occupations of each elementfollow the same configuration as the ones considered in the theoreti-cal calculations. A high SB2 of 0.8 already obtained in theas-deposited sample increases slightly by increasing Tan. In contrast,SL21 which appears at Tan = 500 °C increases close to unity atTan = 600 °C. Note that the presence of Co–Fe disorder is difficult toidentify from standard XRD data because of the close atomic formfactor of Co and Fe. The XRD using synchrotron radiated x raysenables the detection of disorder between the elements with closeatomic form factor through the change in anomalous dispersionterm of atomic form factor at the absorption edges of the constituentelements. This method is called anomalous XRD. A previous studyof anomalous XRD on CFGG reported that substantial Co–Fe disor-der existed in the as-deposited sample and the amount of disorderdecreased with increasing Tan up to 500 °C.28 Based on this report,we speculate that a similar type of Co–Fe disorder exists in oursample annealed at Tan≤ 400 °C. Moreover, it can be inferred fromFIG. 2. Spin resolved band structures for (a) Co50Fe25Ga12.5Ge12.5 and (b) Co44.3Fe30.7Ga13.9Ge11.1 compositions. A pseudo-gap near EF is evident in the minority-spinchannel, consistent with the features observed in the DOS (see Fig. 1).FIG. 3. XRD patterns of 2θ-ω scans of as-deposited and annealed samples at tilt angles (a) χ = 0° and (b) χ = 54.7°. (c) Dependence of SB2 and SL21 parameters of thesample on annealing temperature Tan.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 043904 (2025); doi: 10.1063/5.0268776 138, 043904-4© Author(s) 2025 28 August 2025 03:13:19https://pubs.aip.org/aip/japChen et al.29 that the Co44.3Fe30.7Ga13.9Ge11.1 thin films annealed atTan≥ 500 °C can be presumed to be free of Co–Fe disorder.C. MagnetoresistanceTo investigate the variation in half-metallicity with improve-ment in atomic order achieved by annealing, the AMR ratio wasmeasured at measurement temperatures (T) from 50 to 300 K, with50 K intervals. Figure 4(a) shows the angular variation in AMR ratiomeasured at T = 50 K for the as-deposited and annealed samples. Allthe samples show negative AMR and the amplitude of the negativeAMR ratio increases with increasing Tan. Figure 4(b) shows the tem-perature dependence of ΔρAMR normalized by the value at T = 50 K.Here, ΔρAMR is defined as the difference in the electrical resistivitywhen the magnetic field and current directions are parallel and per-pendicular.29 The as-deposited sample shows the largest reduction inthe normalized ΔρAMR with increasing T. Such behavior is largelydecreased in the annealed samples, and ΔρAMR became almost cons-tant at Tan = 500 °C and 600 °C. The negative AMR ratio is consid-ered a signature of half-metallicity,40–42 as discussed below, though itis not conclusive evidence.38According to the two-current model for the evaluation ofΔρAMR in half-metallic ferromagnetic materials, only s↑ → d↓ ands↑ → d↑ types of scattering processes are taken into consideration(subscripts ↑ and ↓ refer to up and down spin, respectively).Hence, ΔρAMR can be expressed as38ΔρAMR � γ(ρs,"!d, # � ρs,"!d, " )/ D(d)" (EF) 1� D(d)# (EF)D(d)" (EF)" #: (4)Here, D↑(d)(EF) and D↓(d)(EF) represent the d-orbital DOS at EF forup and down spins, respectively. The temperature dependence ofΔρAMR originated primarily from the D↓(d)(EF) due to the thermallyexcited electrons governed by the Fermi–Dirac distribution func-tion. In the case of L21-ordered off-stoichiometric CFGG, D↓(d)(EF)is nearly zero with EF located near the middle of the gap, as seen inthe calculated d-orbital DOS in Fig. 4(c). This electronic structureindicates that near-zero D↓(d)(EF) is robust against temperatureincrease. Therefore, ΔρAMR is expected to be constant, as observedin the L21-ordered sample for Tan ≥ 500 °C. On the other hand, asubstantial D↓(d)(EF) in the gap due to the Co–Fe disorder isexpected in the as-deposited and 400 °C-annealed samples.28,38 Inthis scenario, Eq. (4) does not hold because of the existence ofother types of s-d scattering processes, such as s↓ → d↓ and s↓ → d↑along with s↑ → d↓ and s↑ → d↑, which explain the large tempera-ture dependence in ΔρAMR. The above analysis qualitatively con-firms an enhancement in half-metallicity with an improvement inthe atomic order in the samples by increasing Tan.Further, the enhancement in half-metallicity with theimproved atomic order was analyzed by OMR measurements.Figures 5(a)–5(d) show the variation of OMR ratio calculated byΔρOMR/ρ0 as a function of external magnetic field for theas-deposited and 400, 500, and 600 °C annealed samples, respec-tively. Here, ΔρOMR = ρH− ρ0 with ρH and ρ0 representing the elec-trical resistivity in the presence and absence of a magnetic field,respectively. In all the samples, the OMR ratio exhibits a negativeslope with respect to the magnetic field, and the slope increaseswith decreasing measurement temperature. In the comparisonamong the samples with different Tan, the slopes show an increas-ing trend with increasing Tan, as discussed below.In general, the electrical resistivity of a ferromagneticmaterial can be decomposed to three components, viz., ρ(T) = ρR + ρP(T) + ρM(T),43,44 where ρR, ρP(T), and ρM(T) are resis-tivity due to temperature independent electron-defect scattering,temperature-dependent scattering of electrons by phonons, andtemperature-dependent scattering of electrons by magnons, respec-tively. At room temperature, ρM(T) is sensitive to the magneticfield and decreases with increasing magnetic field due to the sup-pression of electron–magnon scattering, which leads to negativemagnetoresistance.45In half-metallic ferromagnets, the absence of minority DOS atEF results in an exponential suppression of ρM(T), i.e.,ρM(T)e�Δ/kBT ,43,44 where Δ represents the lowest excitation energyfor spin-flip process of majority charge carriers, as depicted inFig. 5(e), and kB is the Boltzmann constant. At low temperature,this additional factor suppresses ρM(T). Additionally, low tempera-ture reduces lattice vibration, diminishing ρP(T). In this scenario,ρR becomes dominant, where the Lorentz force causes electrons toFIG. 4. (a) Angular dependence of AMR ratio of the samples recorded at 50 K. (b) Measurement temperature dependence of normalized ΔρAMR for various samples withdifferent Tan. (c) d-orbital DOS of off-stoichiometric CFGG with L21 ordered structure.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 043904 (2025); doi: 10.1063/5.0268776 138, 043904-5© Author(s) 2025 28 August 2025 03:13:19https://pubs.aip.org/aip/japtravel longer paths in a magnetic field, leading to an increase inρ(T).46 Therefore, the OMR ratio increases with decreasing temper-ature. The OMR ratio at 10 K increases with increasing Tan, asshown in Fig. 5(f ), and this increase is attributed to the increase inΔ and resultant higher suppression of ρM(T). As Δ is directly linkedto half-metallicity, the increase in the OMR ratio signifies theimproved half-metallicity of the material with Tan.Goto et al.28 have shown an improvement in spin polariza-tion of CFGG as the B2 disorder changes to L21 order. Based onthis report, the enhancement in the L21 order by increasing Tanfrom 400 to 600 °C explains the improved half-metallicity.However, the improvement in the half-metallicity between theas-deposited and 400 °C-annealed samples cannot be explainedon this basis because both samples do not exhibit L21 ordering,suggesting the effect of the Co–Fe disorder. As reported in theanomalous XRD study, the Co–Fe disorder gives rise to theminority DOS at EF, deteriorating the half-metallicity.28,38 Sincethe amount of Co–Fe disorder decreases continuously withincreasing Tan and ultimately vanishes at Tan ≥ 500 °C, half-metallicity of the 400 °C-annealed samples improves from that ofthe as-deposited sample.D. Magnetodynamic propertiesTo investigate the relation between αint and half-metallicity,FMR measurements at room temperature were performed.Figure 6(a) shows the typical FMR spectrum with fitting by Eq. (1)to evaluate the resonance field (μ0Hr) and linewidth (μ0ΔH).30 Theobtained μ0Hr with the corresponding resonance frequency (f) wasplotted, as shown in Fig. 6(b), to evaluate the gyromagnetic ratio (γ)by fitting the data to the Kittel equation.47 The estimated γ was usedto evaluate the total Gilbert damping constant (αtotal) by fitting theμ0ΔH vs f plot [shown in Fig. 6(c)] with the relation,48μ0ΔH ¼ 4παtotalγf þ μ0ΔH0, (5)where μ0ΔH0 is the intrinsic linewidth. The experimentally obtainedαtotal from Eq. (5) is ∼(7.3 ± 0.3) × 10−4, which contains both intrin-sic (αint) and extrinsic (αext) components. αext consists of contribu-tions from two-magnon scattering (αTMS), spin pumping (αsp),radiative damping (αrad), and eddy current (αeddy).49 Here, αTMS isneglected because of the high frequencies used in the FMR measure-ments.10 Spin pumping is also neglected by considering the lowspin–orbit coupling of the Al capping layer and its thickness is lessthan the spin diffusion length. The third contribution αrad, arisingfrom the interaction between magnetization precession and theco-planar waveguide, is estimated to be ∼3.7 × 10−4, according to thereport by Schoen et al.50 The last contribution arises from the eddycurrent induced by alternating magnetic field is estimated to be∼1 × 10−5.49 By subtracting all the extrinsic contributions from αtotal,αint was determined. Figure 6(d) shows the Tan dependence of αtotaland αint. The αint value decreases with increasing Tan up to 500 °Cand decreases slightly upon further increasing Tan to 600 °C, reach-ing the very low value of (3.5 ± 0.3) × 10−4. This decreasing trend inαint coincides with that of the enhanced half-metallicity revealed inthe AMR and OMR measurements, supporting their relation.FIG. 5. Variation of OMR ratio with applied magnetic field measured at 10, 100, 200, and 300 K for (a) as-deposited, (b) Tan = 400 °C, (c) Tan = 500 °C, and(d) Tan = 600 °C samples. (e) Schematic of DOS vs energy plot of a half-metal. (f ) Tan dependence of OMR ratio measured with a field of 14 T at 10 K.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 043904 (2025); doi: 10.1063/5.0268776 138, 043904-6© Author(s) 2025 28 August 2025 03:13:19https://pubs.aip.org/aip/japSince αint is directly proportional to the sum of majority and minor-ity DOS at EF, its reduction by the enhanced half-metallicity leads toa reduction in αint. In comparison, non-conducting Yttrium IronGarnet exhibits much lower αtotal of (8.58 ± 0.21) × 10−5.51 However,achieving low αtotal in conducting materials is essential for charge-based spintronic devices. Among conducting materials, Co25Fe25showed αint of 5.0 × 10−4 and αtotal ranging from ∼1.4 × 10−3 to2.1 × 10−3,2,52,53 while NiFe and CoFeB exhibited αtotal of∼4.6 × 10−3 to 5.5 × 10−3 and 4.2 × 10−3, respectively.54,55These reported values are higher than the obtained α in thisstudy for Co44.3Fe30.7Ga13.9Ge11.1. Furthermore, we fabricatedCo51.5Fe24.75Ga13.25Ge10.5 films with a composition close to thestoichiometric CFGG. The αint of this CFGG film annealed atTan = 600 °C was found to be (6.9 ± 0.5) × 10−4, as shown inFig. 6(d), which is higher than that of the Co44.3Fe30.7Ga13.9Ge11.1film ((3.5 ± 0.3) × 10−4) annealed at the same Tan, highlighting itsadvantage for obtaining low α.IV. CONCLUSIONSIn summary, we studied α in off-stoichiometric Co-deficientand Fe-rich CFGG Heusler alloy thin films annealed at differentTan using FMR measurements and demonstrated very low α. Wealso investigated the relation of α with atomic ordering and half-metallicity. The CFGG thin films were prepared by magnetronsputtering and annealed in situ at Tan = 400, 500, and 600 °C toimprove the atomic ordering. Structural analysis confirmed thepresence of a B2-type disordered structure in the as-depositedsample. L21 ordering appeared at Tan = 500 °C and improved as Tanwas increased to 600 °C. The effect of atomic ordering on the half-metallicity was explored through AMR and OMR measurements,which indicated an improvement in half-metallicity with increasingTan due to the improved atomic ordering. The enhancement inhalf-metallicity is reflected in the low value of αint. The αint valuedecreased significantly with increasing Tan up to 500 °C, andfurther increasing Tan to 600 °C slightly decreased αint, achieving aFIG. 6. (a) Typical FMR spectrum of the off-stoichiometric CFGG thin film. (b) Variation of μ0Hr with resonance frequency along with fit to the Kittel equation. (c) Variationof μ0ΔH as a function of resonance frequency of the samples along with fit to Eq. (5). (d) Variation of αtotal and αint with Tan for Co44.3Fe30.7Ga13.9Ge11.1 along with αtotaland αint values for Co51.5Fe24.75Ga13.25Ge10.5 annealed at 600 °C.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 138, 043904 (2025); doi: 10.1063/5.0268776 138, 043904-7© Author(s) 2025 28 August 2025 03:13:19https://pubs.aip.org/aip/japremarkably low αint of (3.5 ± 0.3) × 10−4. These results demon-strated that off-stoichiometric CFGG is a promising material toreduce the critical current density and pave the way for the realiza-tion of highly energy-efficient spintronic devices.ACKNOWLEDGMENTSThe authors thank S. Kuramochi and N. Kojima, NIMS, fortheir support in the film preparation and characterizations. Thiswork was supported by the Advanced Storage ResearchConsortium (ASRC), JST CREST under Grant No. JPMJCR21O1,and the MEXT Initiative to Establish Next-generation NovelIntegrated Circuits Centers (X-NICS) under Grant No. JPJ011438.AUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose.Author ContributionsMadhav M. Bhat: Formal analysis (equal); Investigation (lead);Visualization (lead); Writing – original draft (lead). K. Simalaotao:Formal analysis (lead); Writing – review & editing (equal).H. Suto: Conceptualization (lead); Investigation (equal);Supervision (equal); Writing – review & editing (lead).A. Perumal: Conceptualization (equal); Supervision (equal);Writing – review & editing (equal). A. Srinivasan:Conceptualization (equal); Supervision (equal); Writing – review &editing (equal). Y. Sakuraba: Conceptualization (equal);Supervision (lead); Writing – review & editing (equal).DATA AVAILABILITYThe data that support the findings of this study are availablefrom the corresponding author upon reasonable request.REFERENCES1Y. Fan, J. Wang, A. Chen, K. Yu, M. Zhu, Y. Han, S. Zhang, X. Lin, H. Zhou,X. Zhang, and Q. Lin, “Thickness-dependent Gilbert damping and soft magne-tism in metal/Co-Fe-B/metal sandwich structure,” Nanomaterials 14, 596 (2024).2M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach,O. Eriksson, O. Karis, and J. M. 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