Energy-efficient spintronic memories and oscillators require a large spin-orbit torque (SOT) and low effective damping for exciting magnetic precession. Conventional
SOT-driven bilayers, consisting of a heavy metal and an ultrathin ferromagnet (e.g., ~1 nm), suffer from high damping due to interfacial spin pumping and scattering. Recently, SOTs have
been reported in thicker (~10 nm) single-layer ferromagnetic films with vertical compositional gradients [1-3]. We hypothesize that thick vertically graded ferromagnets can also enable
low damping, potentially coexisting with substantial SOTs. Here, we examine the impact of intentional compositional gradients on damping and SOTs, specifically in graded films
consisting of two ferromagnetic elements: Fe with low intrinsic damping [4] and Ni with sizable spin-orbit coupling [5]. We grew 10-nm-thick graded and homogeneous Fe-Ni films by continuously tuning the sputtering powers on Fe and Ni sources [Fig. 1(a-c)]. The targeted vertical compositional and
magnetic gradients are confirmed and quantified by polarized neutron reflectometry. In-plane broadband ferromagnetic resonance (FMR) [Fig. 1(d)] points to low ef ective damping
parameters of ≈0.0045 for the graded films, comparable to ≈0.0038 for the homogenous film. Out-of-plane FMR [Fig. 1(e)] reveals intrinsic damping parameters of ≈0.0032 for both the
graded and homogenous Fe-Ni films. These FMR results indicate that low damping is maintained despite the steep, intentional vertical inhomogeneity. From spin-torque FMR
measurements on a graded sample, we detect a modest (at most ≈2%) linear change in the FMR linewidth with a DC current density of 1×1011 A/m2
[Fig. 2], suggesting a small dampinglike SOT. Our findings constitute a step toward understanding and engineering low-damping single-layer ferromagnetic films for SOT-driven applications. 
**References** [1] Liu, L., Yu, J., Gonzalez-Hernandez, R., Phys Rev. B., Vol. 101, p. 220402 (2020) 
[2] Tang, M., Shen, K., Xu, S., Advanced Materials, Vol. 32, p. 2002607 (2020) 
[3] Zhu, L., Ralph, D. C., & Buhrman, R. A. Advanced Functional Materials p. 2103898 (2021) 
[4] Wu, S., Smith, D.A., Nakarmi, P., et. al., Phys Rev. B., Vol, 105, p. 174408 (2022) 
[5] Du, C., Wang, H., Yang, F., et. al., Phys Rev. B., Vol. 90, p. 140407 (2014) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/5c298ab0a08d5d203c251d6f15a04437.png) 
Fig. 1: (a,b) Schematics of (a) FeNi graded, (b) NiFe graded, and (c) FeNi homogeneous films. (d,e) Frequency dependence of (d) in-plane and (e) out-of-plane FMR linewidth for homogeneous and graded Fe-Ni films. 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/4fc66015f32a2a8a2709c1a39348e0fb.png) 
Fig. 2: DC bias current dependence of spin-torque FMR linewidth for 10-μm-wide graded NiFe strip at 7 GHz, magnetized at in-plane angle (a) 50o and (b) 230o

Single Layer Vertically Graded Fe

Electrically conductive metals are typically good transmitters or absorbers of pure spin currents. Here, we report evidence that an interface of two conductive elemental metals – namely, Cu and Cr – constitutes a good spin-current reflector. Our study was initially motivated by the question of whether the elemental antiferromagnet Cr acts as a spin transmitter (akin to electrically insulating NiO [1]) or a spin absorber (akin to metallic IrMn [2]). To this end, we have performed ferromagnetic resonance (FMR) spin pumping measurements on spin-valve-like stacks of NiFe(10)/Cu(5)/Cr(tCr)/(Co)Fe(4), where the FMR-driven NiFe layer pumps an AC pure spin current. Any spin current transmitted through the Cu/Cr spacer would be absorbed by the (Co)Fe sink, generating additional Gilbert damping, △α, for the NiFe source. Thus, △α is proportional to how much a spin current is transmitted or absorbed across the Cr interlayer. In Figure 1, the sharp decline of △α with increasing Cr thickness indicates a remarkable trend: The introduction of Cr suppresses spin transmission and absorption – i.e., the spin current is largely reflected by the Cu/Cr spacer. However, our complementary element-selective X-ray FMR measurements confirm that the spin current is transmitted through the Cr spacer in NiFe/Cr/CoFe. We therefore identify the Cu/Cr interface, rather than the Cr bulk, as the source of the strong spin reflection. Figure 2 shows that △α varies only weakly with decreasing temperature (increasing antiferromagnetic order in Cr), which suggests that antiferromagnetism in Cr is not responsible for the spin-reflective behavior. Our finding points to the possibility that other electrically conductive metals can form effective spin reflectors, thereby offering new avenues in the fundamental studies and engineering of pure spin currents across interfaces.


![](https://assets.underline.io/uploads/markdown_image/1/image/e7884bfa3e9da4b8fbfbd64553b2d860.jpg)


[Fig. 1] △α vs. Cr layer thickness tCr in NiFe/Cu/Cr(tCr)/(Co)Fe measured at room temperature. Both the epitaxial and polycrystalline series show decaying with tCr, due to spin reflection at the Cu/Cr interface.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc5e03a64fe9cbcdaa9a866583d3cb89.jpg)


[Fig. 2] △α vs. temperature, showing that spin transport is affected only weakly even as Cr develops stronger antiferromagnetic order at lower temperatures.

Spin-Reflective Metallic Cu/Cr Interface

Advancing the understanding of magnetic relaxation, often discussed in terms of “damping,” is essential for energy-efficient spintronic memories, oscillators, and spin-wave circuits. BCC Fe is an elemental ferromagnet with attractive properties for these applications. Here, we examine magnetic relaxation – i.e., intrinsic and extrinsic damping – in two series of sputter-grown, polycrystalline Fe thin films with distinct structural properties: (1) strongly textured, smooth Fe films grown on Cu and (2) weakly textured, rough Fe films grown on Ag. Out-of-plane ferromagnetic resonance (FMR) measurements reveal intrinsic Gilbert damping parameters of ≈ 0.0024 for all Fe films thicker than 4 nm, regardless of their structural properties, as shown in Fig. 1. This damping parameter range is in quantitative agreement with that for epitaxial Fe [1]. The remarkable invariance with microstructure strongly suggests that intrinsic Gilbert damping is a local property, averaged over a short length scale of a few nm, with limited impact from grain boundaries and film roughness. The in-plane FMR linewidths of the Fe films exhibit pronounced nonlinear frequency dependencies, indicating the presence of strong extrinsic damping. Figure 2 shows the extrinsic linewidth obtained by subtracting the intrinsic Gilbert contribution ΔHG (isotropic for Fe [1,2]) from the total in-plane linewidth ΔHIP. To fit our experimental data, we have used a grain-to-grain two-magnon scattering model [3-5] with two types of correlation functions proposed for modeling self-affine and mounded surfaces [6], which capture inhomogeneities in the film. However, neither of the two correlation functions is able to reproduce the data quantitatively. Our finding points to the need to further examine the fundamental impact of film microstructure on extrinsic damping.

![](https://assets.underline.io/uploads/markdown_image/1/image/1036e2b51a2ec70732f50783b672e744.jpg)


Fig. 1. Out-of-plane Gilbert damping αOOP as a function of film thickness.

![](https://assets.underline.io/uploads/markdown_image/1/image/0dd999a01cf02f7a52d306323d0872e3.jpg)


Fig. 2. In-plane extrinsic FMR linewidth vs frequency for (a) Cu/Fe (8 nm) film and (b) Ag/Fe (25 nm) film. Black squares represent experimental linewidth data. Dashed blue and solid red curves represent the fitted curves using correlation functions proposed for modeling self-affine and mounded surfaces, respectively.

Intrinsic and Extrinsic Damping in Polycrystalline Fe Thin Films

Identifying the origins of ferromagnetic resonance (FMR) linewidth broadening is essential for the fundamental understanding of magnetic relaxation, often discussed in terms of “damping”. It is not yet well understood how inhomogeneity and structural disorder contribute to magnetic relaxation in polycrystalline thin films, even though they are widely used in device applications. In this presentation, we systematically examine the impact of inhomogeneity and disorder on the FMR linewidth of sputter-grown polycrystalline Fe and Fe80V20 films with thickness 2-25 nm and different seed layers. A highly nonlinear frequency dependence of FMR linewidth is observed for Fe films on Cu/Ti seed layers. As shown in Fig. 1, all linewidth vs frequency data are quantitatively reproduced with a two-magnon scattering model [1, 2, 3] that accounts for a random distribution of the effective anisotropy field among grains in the polycrystalline film. The fit results indicate that a larger grain size is correlated with stronger two-magnon scattering, which – somewhat counterintuitively – may be accompanied by a lower Gilbert damping parameter. Films with the strongest two-magnon scattering contribution (cf. 10-nm-thick Fe/Cu/Ti, Fig. 1) exhibit the highest coercivity, pointing to a connection between magnetic inhomogeneity and the observed non-Gilbert relaxation. In addition, it is found that two-magnon scattering is reduced by changing the seed layer or alloying Fe with V (Fig. 2). We will discuss the possible mechanisms that lead to narrower FMR linewidths in polycrystalline Fe(V) films. The fundamental understanding gained from our study enables a coherent approach to develop low-loss polycrystalline magnetic media for power-efficient spintronic devices.References: [1] R. McMichael and P. Krivosik, IEEE Trans. Mag., Vol. 40, p.2 (2004) [2] S. Kalarickal, P. Krivosik and J. Das, Phys. Rev. B, Vol. 77, p.054427 (2008) [3] W. Peria, T. Peterson and A. McFadden, Phys. Rev. B, Vol. 101, p.134430 (2020) 


Two-magnon Scattering in Polycrystalline Fe and FeV Alloy Thin Films

GOE: Magnetization Dynamics V

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A3: Magnetization Dynamics and Damping I: Damping and Ferromagnetic Resonance

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Shuang Wu

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Presentations

Single Layer Vertically Graded Fe

Spin-Reflective Metallic Cu/Cr Interface

Intrinsic and Extrinsic Damping in Polycrystalline Fe Thin Films

Two-magnon Scattering in Polycrystalline Fe and FeV Alloy Thin Films

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