United States

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.&lt;br/&gt;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.&lt;br/&gt;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 Δ&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;G&lt;/sub&gt; (isotropic for Fe [1,2]) from the total in-plane linewidth Δ&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;IP&lt;/sub&gt;. 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.


2022 Joint MMM-INTERMAG

Intrinsic and Extrinsic Damping in Polycrystalline Fe Thin Films

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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MMM 2020

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.

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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Antiferromagnetic materials with non-collinear spin structures (NC-AFMs) offer significant potential for spintronic applications[1]. They have vanishingly small magnetization and ultrafast spin dynamics. In addition, they allow for the presence of important counterparts to the effects considered to be exclusive to materials with net magnetization, such as the anomalous Hall effect (AHE)[2], magneto-optical Kerr effect[3] or anomalous Nernst effect (ANE)[4]. One of the promising candidates of the NC-AFM class are Mn antiperovskites, with a typical representative being Mn3NiN. In this contribution we present ANE measurements on epitaxial thin films of Mn3NiN prepared on SrTiO3 substrate with spin structure lying in the (111) plane. Previous theoretical predictions suggest that despite the modest spin-orbit coupling, the magnitude of the ANE in Mn3NiN ought to exceed that of Mn3Sn NC-AFM due to the Berry phase boost[5]. We implement two complementary methods to detect the ANE response of the Mn3NiN films. First, the global Nernst response is measured using a micro-patterned Hall bar device with platinum resistive heaters generating an in-plane thermal gradient. The measured anomalous Nernst data (Fig.1(a)) are in good agreement with the AHE measurements[5], indicating a similar physical origin of the two effects. Second, to add a spatial resolution, scanning thermal gradient microscopy[4] is used. A laser beam incident on a micro-patterned device induces thermal gradients. The method reveals the sample’s domain structure. We find a signature of an ANE component that we can control with the external field due to the unsaturated moment present lying in the (111) plane, different from the previously measured Mn3Sn. This small moment provides a means for manipulating magnetic order, and even writing magnetic domain-like structures (Fig.1(b)). These two methods provide fruitful insight into the magnetic behaviour of NC-AFMs.

![](https://assets.underline.io/uploads/markdown_image/1/image/e3391f086f9d4953ae3f5db220e7247b.jpg)

Fig.1. Anomalous Nernst effect in Mn3NiN. (a) Global ANE as a function of the out-of-plane magnetic field at different base temperatures. (b) Scanning thermal gradient microscopy at T = 100 K. The domain-like structure was written by high-intensity laser beam and 500 mT in-plane magnetic field.

Anomalous Nernst effect in thin films of non-collinear antiferromagnet Mn3NiN

We combined XMLD, XMCD and MOKE measurements in order to follow the magnetic properties of epitaxial CoO(111)/Fe(110) [1] and NiO(111)/Fe(110) [2] bilayers. We find that in both studied cases FM sublayer plays a dominant role and determines the magnetic state of the neighboring AFM, however completely different interaction mechanisms are involved. In CoO/Fe bilayers the AFM spins are frozen and their orientation is imprinted by magnetization of Fe layer when the system passes the Neel temperature of CoO. Once the Fe layer grafts the particular magnetic anisotropy (MA) into the CoO overlayer, it later remains frozen and insensitive to external factors like external magnetic field or Fe magnetization direction [3]. Specifically, choice of particular magnetic state of Fe sublayer, when passing Néel temperature of CoO, determines both the axis and direction of interfacial antiferromagnetic spins after the sample is cooled and allows for imprinting their +/- 90° and 0/180° alignment within the sample plane. For example, particular direction of frozen AFM spins determines the corresponding sign of the shift field of exchange biased magnetic hysteresis loop (Fig.1). For NiO/Fe bilayers, due to the weak intrinsic MA of NiO, the AFM spins are rotatable and always follow the reorientation of Fe magnetization that can be controlled by external magnetic field or via the temperature and thickness driven SRT of Fe(110). Recently we showed that in a uniform thickness NiO(111)/Fe(110) system, two magnetic states with orthogonal spin orientations can be stabilized in antiferromagnetic NiO [2]. Field-free, reversible switching between these AFM states was demonstrated. Here we present results of systematic investigations of such field-free, temperature induced switching of AFM NiO spins. Fig. 2 shows temperature dependence of RL2 ratio for various thicknesses of Fe. Critical temperature of SRT in AFM NiO can be tuned in wide temperature window ~ (250 – 380 K) for field-free, reversible switching of AFM spins. XML(C)D-PEEM results obtained on individual self-organized NiO/Fe nanostripes will be also presented.

![](https://assets.underline.io/uploads/markdown_image/1/image/ea6cc84785bb0485bc069d8c09366d06.jpg)

Fig.1. Memory of frozen AFM spins in CoO(111)/Fe bilayer.

![](https://assets.underline.io/uploads/markdown_image/1/image/46723238dbaaa7708138289f718efd3d.jpg)

Fig.2. Temperature dependence of XMLD (RL2 ratio) for NiO/Fe [4].

Memory of frozen and rotatable antiferromagnetic spins in epitaxial CoO(111)/Fe and NiO(111)/Fe bilayers.

Synchronization of large spin Hall nano-oscillators (SHNO) arrays is an appealing approach toward ultra-fast non-conventional computing based on nanoscale coupled oscillator networks [1]. However, for large arrays, interfacing to the network, tuning its individual oscillators, their coupling, and providing built-in memory units for training purposes, remain substantial challenges. Here, we address all these challenges using memristive gating of W/CoFeB/MgO/AlOx based SHNOs. We use this type of stack as their substantial perpendicular magnetic anisotropy (PMA) can generate both localized and propagating spin waves [2]. In its high resistance state (HRS), the memristor modulates the perpendicular magnetic anisotropy (PMA) at the CoFeB/MgO interface purely by the applied electric field, which leads to both a voltage-controlled SHNO frequency and a voltage-controlled threshold current [3]. In its low resistance state (LRS), and depending on the voltage polarity, the memristor adds/subtracts a current Im to/from the SHNO drive. The operation in this LRS also affects the SHNO auto-oscillation mode and frequency, which can be tuned up to 28~MHz/V. This tuning allows us to reversibly turn on/off mutual synchronization in chains of four SHNOs and turn the chain into different partially synchronized states [4]. Memristor gating is, therefore, an efficient approach to input, tune, and store the state of the SHNO array for any non-conventional computing paradigm, all in one platform. Examples include SHNO based Ising Machines [5,6] and pattern recognition using memristive-controlled SHNO chains [4], which will both be discussed in detail in the presentation.

Memristor-controlled mutual synchronization of spin Hall nano-oscillator arrays for neuromorphic computing and spintronic Ising machines

Band inversion of electrons due to strong spin-orbit coupling (SOC) is commonly seen in magnetic materials. It characteristically appears in topological insulators (TIs) with inverted bandgaps [1] and Weyl semimetals (WSMs) with pointlike band crossings [2], while metallic systems are also capable of having band inversion. In momentum space around the SOC-induced band inversion, the electron spin is often correlated to its momentum, known as spin-momentum locking (SML). Moreover, the electron system acquires nontrivial band topology characterized by the Berry curvature, which serves as an effective magnetic field in momentum space. It is well understood that the band topology gives a substantial contribution to anomalous transport phenomena, such as the anomalous Hall effect (AHE) and the spin Hall effect (SHE), due to the anomalous velocity of electrons triggered by the Berry curvature. Recent experimental attempts have been successful in synthesizing materials having both nontrivial band topology and magnetism (magnetic TIs, WSMs, etc.), and it is an important question if their magnetic functionalities are also governed by their band topology. In this talk, I show from theoretical aspect that the current-induced spin torques in such magnetic topological materials are influenced and occasionally enhanced due to their band topology. After reviewing the current status of theoretical and experimental studies on magnetic topological materials, I will introduce some of my recent works. From the general point of view, I first propose that the momentum-space topology gives rise to an "intrinsic" contribution to the spin torques, which is robust against disorder and thermal fluctuation similarly to the intrinsic AHE and SHE [3]. This intrinsic torque originates from electron spin polarization converted from the anomalous velocity by SML, and is distinct from the conventional spin-transfer torque (STT) and the spin-orbit torque (SOT) driven by electron spins in transport current. In particular, I point out the intrinsic torque exerting on magnetic textures, such as domain walls (DWs), which we call the "topological Hall torque (THT)". The THT is induced by the cooperation of the real-space magnetic texture and the momentum-space Berry curvature, and can emerge dominantly in bulk crystals without building any complex heterostructures. As a typical example, I show our microscopic calculation result of current-induced torques with the low-energy effective model of magnetic WSM [4]. The band crossing points, called "Weyl points", serve as source and sink of the Berry curvature in momentum space, accompanied with SML of electrons around them (see Fig. 1). The Weyl electrons are therefore capable of generating a strong intrinsic torque. From the microscopic calculation in response to an externally applied electric field, we have derived the SOT, the STT, and the THT exerted by the Weyl electrons. The THT gets enhanced at a sharp magnetic DW, due to the localized states of Weyl electrons formed at the DW [5,6]. For more realistic situations, I also show the phenomenological calculation of the THT in a metallic ferromagnet with band inversion [3]. In response to an external electric field applied to a DW (see Fig. 2), we have obtained a large THT. The THT acts on a DW in the same form as the conventional nonadiabatic STT, but with the unusual size of the nonadiabaticity parameter β≈2, which will enable an efficient control of DW motion by electric field. Experimental measurability of the THT in the metallic ferromagnet SrRuO3, in connection with the temperature dependence in its AHE [7], will also be mentioned.

![](https://assets.underline.io/uploads/markdown_image/1/image/d0716b6a26c3c8035d704ada28777bbc.jpg)

Schematic image of Weyl points emerging from band inversion. The Berry curvature (magenta curves) emerges in the vicinity of the Weyl points.

![](https://assets.underline.io/uploads/markdown_image/1/image/9d1d264c88091f5f7c8512236cd257bf.jpg)

Schematic image of the setup of magnetic DW in our calculations [3]. We consider an external electric field Eext applied across the DW, and calculate the torque in response to Eext.

Theory of Spin Torques Emerging from Band Topology

The motion of domain walls by the use of the magnetic fields as well as spin polarized currents has been a major part of spintronics in the last two decades. The two mechanisms of current induced domain wall motion are Spin transfer torque(STT) and Spin orbit torques(SOT). In the recent years, compensated ferrimagnets have been in focus due to their ability to reach the magnetic and the angular momentum compensation points. At the angular mometum compensation point the precessional motion of the local magnetic moment becomes negligible which has shown to have massively increase the domain wall velocity[1,2]. Here we will focus on a rare-earth free ferrimagentic nitride called Manganese Nitride (Mn4N). We have previously shown epitaxially grown Mn4N has a very low magnetization (71 kA/m) and a very high perpedicular magnetic anisotropy (PMA) with mm sized domains[3]. This low magnetization is due to the two different Mn sub-lattices in the anti-perovskite crystal structure. With such a small magnetization and a high spin polarization led us to obtain a very high domain wall velocity of more than 900m/s at J=1.3*1012 A/m2 using pure STT[4]. In this work, we have have shown an even larger domain wall velocity approaching 3000 m/s at J=1.26*1012 A/m2 using pure STT near the magnetic and the angular compensation points in epitaxially grown Ni doped Mn4N[5]. The magnetic and angular momentum compensation points are obtained by the adjustment of Ni doping in this system at room temperature. These high domain wall velocities are comparable to the best velocities obtained by SOT. Also, in this system there is no requirement for an external in-plane field as shown in some other systems by SOT. Moreover, we also demonstrate a reversal of the domian wall motion direction after crossing the compensation points where the domain walls move in the same direction as the flow of electrons. This phenomenon will be explained with the help of ab-initio calculations.

![](https://assets.underline.io/uploads/markdown_image/1/image/c0c2ec29f2ef977b88dd4a5f908583e9.jpg)

Current density vs Velocity curves for Mn4-xNixN thin films. Filled symbols show samples before and the open symbols after the compensation point.


![](https://assets.underline.io/uploads/markdown_image/1/image/b73b2f498d533d34f95601fada6e88b3.jpg)

MS vs Velocity plot, measured for J=1*1012 A/m2(blacksquares) is compared with the best fit obtained using the q−φmodel.

Current driven domain wall dynamics across the angular momentum compensation point in epitaxially grown ferrimagnetic Ni-doped Mn4N thin films

Spin-torque oscillator (STO) is a class of emerging spintronic devices that can find applications in wireless communication systems in the form of radio frequency (rf) generator1,2 and rf detector3. The STO offers a compatibility with CMOS technology and high frequency tunability2. However, the single STO output is not sufficient for the rf applications. In order to overcome this, the mutual synchronization of STOs is critical for communication, energy harvesting and neuromorphic applications. The short range magnetic coupling-based synchronization has spatial restrictions (few μm), whereas the long-range electrical synchronization using vortex STOs has limited frequency responses in hundreds MHz (&lt; 500 MHz), restricting them for on-chip GHz-range applications. Here, we demonstrate electrical synchronization of four non-vortex uniformly-magnetized STOs at 2.4 GHz WiFi band4, resolving the frequency-area quandary for designing STO based on-chip systems. We use a single dc source to synchronize canted free layer STOs, thereby simplifying the synchronization scheme. Due to mutual synchronization, STOs show a power enhancement and linewidth reduction [Fig. 1a,b]. When injection-locked with an external rf source, the synchronised STOs show a wide locking range around 2.4 GHz [Fig. 1c,d], which can be useful for neuromorphic computing. Under injection locking, synchronized STOs demonstrate an excellent time-domain stability and improved phase noise performance [Fig. 1e,f]. Our results highlight the significance of electrical topology (series vs. parallel) while designing an on-chip STOs system.

![](https://assets.underline.io/uploads/markdown_image/1/image/5c47ef17602057fa745ff11bcef50d6b.jpg)

Fig. 1. a,b Oscillation power (P) and linewidth (△f) versus numbers of oscillators (N) in parallel (a) and series (b), respectively. Solid lines are linear fit and N−1 scaling for the power and linewidth, respectively. c,d STO frequency (f0) versus radio frequency (frf) response for a single oscillator (red) and four oscillators (blue) at Prf = −20 dBm for the parallel (c) and series (d) connection. The locking range defines the region where f0 ~ frf. e,f Phase noise for 1 ms time-domain trace in parallel (e) and series (f). The solid black and blue lines in (f) shows the 1/f2 and 1/f3 phase noise, respectively.

Electrically connected spin-torque oscillators array for 2.4 GHz WiFi band transmission

Understanding how spin currents flow across metal-semiconductor interfaces at femtosecond timescales has impacts on ultrafast spintronics, data processing and storage applications. However, the possibility to directly access the propagation of spin currents on these time scales has been hampered by the simultaneous lack of both ultrafast site selective magnetic sensitive probes and tailored metal-semiconductor interfaces. By means of FEL-based core-resonant Kerr spectroscopy, we report direct experimental evidence of spin currents across a Ni/Si interface in terms of different magnetodynamics at the Ni M2,3 and Si L2,3 absorption edges. This further allows us to extract the propagation velocity of the spin current in Si as 0.2 nm/fs.

![](https://assets.underline.io/uploads/markdown_image/1/image/ba4eb9360a1db64b8e33f4c491757403.jpg)

Fig. 1: a) The sample stack consists of a Si substrate (blue), a thin Si3N4 passivation layer (grey), 7 nm of Ni film (red) and 2 nm of Ag capping layer (yellow). The white arrow represents the in-plane magnetization of the Ni film. The FEL pulses at the Si L2,3 edge (blue arrow) and at the Ni M2,3 edge (red arrow) are also depicted. The IR laser pulses at 1.55 eV hit the sample at a time delay t-t0, before the FEL pulses arrival. The penetration depths of the pump and the probes are represented by the length of the arrows. The fraction of the IR laser energy absorbed by each layer is reported above the probe arrow. b) Scheme of the FEL RMOKE set-up at MagneDyn. RMOKE was probed in longitudinal configuration at an angle of incidence of 45°. The polarization ε of the incoming FEL pulses (blue arrow) is in the scattering plane, while the Kerr rotation of the polarization of the reflected pulse is indicated as θ.

![](https://assets.underline.io/uploads/markdown_image/1/image/388e11ba365f236752de3629d9784f15.jpg)

Fig. 2: RMOKE magnetic hysteresis in degrees of Kerr rotation at the Ni M2,3 edge (a) and at the Si L2,3 edge (b). Empty and filled circles curves represent the unpumped and pumped hysteresis after 0.5 ps (Ni) and 0.3 ps (Si) (colored star markers in c). c) relative change of the site resolved magnetization M (Ni - red and Si - blue dots) as a function of time delay measured in saturation at 550 mT. The solid lines represent the tting results, from which we extract the characteristic times for demagnetization and recovery. The difference (ΔM/M)js is also shown (gray pentagons).

All-Optical Spin Injection in Silicon Revealed by Element Specific Time-Resolved Kerr Effect

In the last decade, charge to spin conversion and spin-orbit torques have been extensively studied to manipulate the magnetization for efficient data storage devices functionalities. The charge-spin conversion is governed by spin-orbit interactions such as spin Hall effect in the bulk of heavy metals and Rashba effect at their interfaces[1]. Recently, substantial increase in the magnetic torques has been observed with Cu/CuOx or Cu/Al2O3 light element interfaces. The observation of magnetic torques in the absence of spin-orbit interaction can be explained in the framework of orbital currents at Cu/CuOx interface[2-3]. Furthermore, as the orbital effects are believed to be one order larger than the spin-orbital coupling effects, we expect larger torques efficiency by utilizing the orbital currents. To aim this, we have measured the damping-like (HDL) and field-like (HFL) effective fields in SiOx/Co(2)/Pt(x)/Cu/CuOx(3) and SiOx/Co2)Pt(x)/AlOx(1) samples (and where x=2-6 nm) using second harmonic Hall measurement technique. Here, all the samples possess an in-plane magnetic anisotropy. As the orbital current does not carry spin (S=0), it is important to convert them into spin-current to interact with magnetization via s-d exchange interactions to promote the torques. Therefore, Pt is used to convert the orbital current into the spin current. Although the HFL is found to be negligible in all the samples, one observes that the HDL increases linearly with the current density in Pt, like expected for the current induced torque. Fig. 1 shows HDL for 107 A/cm2 current density in Pt. However, we do not observe significant change for AlOx, a two-fold increase is observed in Co(2)/Pt(4)/Cu/CuOx(3) compared to our reference Co(2)/Pt(4) sample, and where the exact spin current profile has been analyzed. As proposed in the recent literature [2], we attribute this enhancement in torques to the generation of orbital current at Cu/CuOx interface.

![](https://assets.underline.io/uploads/markdown_image/1/image/919726e4cd4ba2cd060a27d54a1bd6b4.jpg)

Fig1. Comparison of HDL in various capping layers as a function of Pt thickness. The Blue (Black) arrow shows the increase in HDL in Co/Pt/Cu/CuOx (Co/Pt/Cu/AlOx) samples due to the orbital current at Cu/CuOx (Cu/AlOx) interface.

Enhanced Torques in Co/Pt Systems via Orbital Current Contribution

Gilbert damping remains among the foremost properties impacting the design of spintronic devices. There are many cases where the observed damping is larger than the predicted damping, which is usually based on considerations of electronic structure (such as the Kamberský torque-correlation model [1]). It is therefore of great importance to identify alternative damping mechanisms in order to obtain more accurate results. Two-magnon scattering is one such mechanism, but this can usually be distinguished from Gilbert damping due to its nonlinear dependence on frequency or by orienting the magnetization normal to the film plane [2]. In this talk we discuss how magnetoelastic coupling can cause a substantial enhancement of the overall Gilbert damping in a series of Fe0.7Ga0.3 thin films [3]. In our case, the effect is exaggerated due to the exceptionally high magnetostriction found in FeGa alloys (measured in these films as ~100 ppm at room temperature). The effect is based on a model of energy loss through phonon relaxation: Phonons are driven by magnetization dynamics through magnetoelastic coupling, and the relaxation of these phonons leads to a form of Gilbert damping (see Fig. 1) [4]. We show this by presenting the orientational and temperature dependence of the Gilbert damping in total of seven Fe0.7Ga0.3 thin films with thicknesses ranging from 17 to 70 nm. The orientation dependence of the Gilbert damping demonstrates that the magnetoelastic Gilbert damping is mitigated for out-of-plane magnetization due to confinement effects from the interfaces of the film, leading to a very large anisotropy (up to a factor of 10 at room temperature). The temperature dependence demonstrates both the effects of the magnetostriction and the phonon viscosity. The damping increases significantly at low temperatures due to the increasing magnetostriction. Importantly, however, we observe a nonmonotonic temperature dependence of the Gilbert damping. As the temperature decreases from ~75 K to 0, the damping decreases due to the reduction in the phonon relaxation rate (main panel of Fig. 2). This is attributed to the influence of the temperature dependence of the phonon viscosity, which increases linearly with temperature (inset of Fig. 2). It is thereby shown that the competing effects of magnetostriction, which decreases with increasing temperature, and phonon relaxation lead to the observed nonmonotonic temperature dependence. We conclude by emphasizing that, in general, the magnetoelastic damping may constitute a significant portion of the total Gilbert damping, particularly in materials with high magnetostriction. This work was supported by SMART, a center funded by nCORE, a Semiconductor Research Corporation program sponsored by NIST.

![](https://assets.underline.io/uploads/markdown_image/1/image/5c9a5677720ac744236b40def5e52359.jpg)

Fig. 1: Schematic diagram of the magnetoelastic damping process with magnetization M(t) lying in the film plane. The lattice displacement u(t) is driven by the magnetostriction λ, leading to energy loss due to the presence of phonon viscosity (represented by the wavy orange arrows).

![](https://assets.underline.io/uploads/markdown_image/1/image/cd4033452c06dedfa3fbed5997c11741.jpg)

Fig. 2: Main panel, left ordinate: Magneloelastic Gilbert damping as a function of temperature for the 21 nm (blue triangles), 57 nm (red circles), and 70 nm (black squares) Fe0.7Ga0.3 films. Main panel, right ordinate: The square of the magnetostriction λ as a function of temperature, interpolated from data given in Ref. [5]. Inset: Phonon viscosity, defined as the ratio of αme to λ2 shown as a function of temperature for the 21 nm (blue triangles), 57 nm (red circles), and 70 nm (black squares) Fe0.7Ga0.3 films.

Magnetoelastic Gilbert Damping in Magnetostrictive Fe0.7Ga0.3 Thin Films

The generation of phonons by ferromagnetic resonance in magnetic thin films and subsequent propagation of phonons into the substrate is an effect known as phonon pumping [1-2]. This effect can be utilized in spintronic devices that rely on magnetoelastic coupling for information transfer. The phonon pumping effect is most efficient in the perpendicular configuration, and can therefore be suitably integrated in devices composed of PMA materials. Here we demonstrate the pumping of phonons by ferromagnetic resonance in a series of [Co(0.8 nm)/Pd(1.5 nm)]n multilayers (n = 6, 11, 15, and 20) with large magnetostriction and perpendicular anisotropy. The effect is shown using broadband ferromagnetic resonance over a range of temperatures (10 to 300 K), where a resonant damping enhancement is observed at frequencies corresponding to standing wave phonons across the multilayer. The strength of this effect is strongly dependent on temperature—approximately a factor of 4 larger at 10 K compared to room temperature (see figure). Lastly, we demonstrate that the damping enhancement coincides with a shift in the ferromagnetic resonance field, and further that it is a complementary effect that can be predicted from the resonant damping enhancements. We emphasize that [Co/Pd]n multilayers are an ideal platform for studying this effect due to their large magnetostriction and perpendicular anisotropy. Importantly, the PMA does not show significant dependence on multilayer thickness, so devices can be engineered that have phonon pumping resonances at zero applied field. This work was supported by SMART, a center funded by nCORE, a Semiconductor Research Corporation program sponsored by NIST.
References [1] S. Streib, H. Keshtgar, and G. E. W. Bauer, Damping of Magnetization Dynamics by Phonon Pumping, Phys. Rev. Lett. 121, p.027202 (2018).
[2] K. An, A. N. Litvinenko, R. Kohno, A. A. Fuad, V. V. Naletov, L. Vila, U. Ebels, G. de Loubens, H. Hurdequint, N. Beaulieu, J. Ben Youssef, N. Vukadinovic, G. E. W. Bauer, A. N. Slavin, V. S. Tiberkevich, and O. Klein, Coherent long-range transfer of angular momentum between magnon Kittel modes by phonons, Phys. Rev. B 101, p.060407(R) (2020).

![](https://assets.underline.io/uploads/markdown_image/1/image/3704a35d4e1ee87bd33e2993e6fa34b3.jpg)

Ferromagnetic resonance linewidth enhancements due to phonon pumping at different temperatures for the [Co/Pd]11 multilayer. Linewidth contributions from Gilbert damping and inhomogeneous broadening are excluded. Vertical dashed lines at 23 and 46 GHz show positions of phonon pumping resonances.

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