Increase of Gilbert damping in Permalloy thin films due to heat-induced structural changes

The emerging field of magnonics has attracted great attention due to the possibility of wave-based information processing, utilizing the amplitude, as well as the phase of spin waves, without the drawback of heat production caused by moving electrons.^1–4 This may give spin-wave based computing an edge over conventional CMOS technology for certain applications, such as neuromorphic computing and low energy consumption devices.^5,6

For the realization of those devices, materials with low Gilbert damping are required, allowing for spin waves to be transmitted coherently over distances that are comparable to the device size.

One common material that has been utilized for numerous magnonic devices is Permalloy, an alloy consisting of approximately 80% Ni and 20% Fe.^7–9 It can be grown on Si substrates using various techniques, such as magnetron and ion beam sputtering.^10,11

When combining magnonics with spintronics, which offers a large additional tool set for the control and manipulation of spin waves, the required current densities are usually very high, heating up the sample significantly.¹² This rise in temperature can lead to irreversible structural changes within the magnetic thin films rendering the device unusable, which will be discussed in detail in this work.

While the effects of vacuum annealing on magnonic devices have not received much attention in the literature, which this work attempts to address, the structure of Ni thin films grown on a Si substrate has previously been studied by Julies et al.¹³ They observed the formation of nickel silicides, with Ni–Si forming at approximately 350 $°$C, well below the eutectic temperature¹⁴ of the system. In their work, experimental evidence pointed to the fact that Ni was the major moving species during the growth of the silicides.

The effect of atomic composition on the magnetic properties of homogeneous 3$d$ transition-metal binary alloy thin films has been studied by Schoen et al.^15,16 However, the link between structural changes and changes of the magnonic properties in thin films has not been established yet, especially with regard to heat-induced structural phase transitions. In this article, we show how the Gilbert damping coefficient $α$ of Py thin films grown on Si is affected by annealing at different temperatures, up to 350 $°$C using ferromagnetic resonance (FMR) measurements. The same samples are also analyzed using high resolution transmission electron microscopy (HR-TEM), combined with energy dispersive x-ray (EDX) spectroscopy, in order to obtain information about their structural properties and the diffusion of different atomic species within the thin film system.

Although the observed effect seems undesirable at first glance, it has potential applications in magnonics to locally modify the damping of a device. This could be done using a focused laser spot or the tip of an atomic force microscope (AFM) probe to obtain structures on a nanometer length scale, opening up many possibilities for new magnonic devices that require alternating magnonic properties, such as magnonic crystals.¹⁷ 

A single $10×10$ mm$2$ sample has been prepared by depositing 36 nm of Ni$80$Fe$20$ on a Si substrate using ion beam sputtering with an Ar source. The process was carried out at room temperature, with a base pressure of $3.9×10−7$ mbar and a working pressure of $1.53×10−4$ mbar. The sample was then cut into four $5×5$ mm$2$ pieces, which were subsequently annealed separately for 60 min at $Ta=$ 100, 200, 300, and 350 $°$C in ultrahigh vacuum (⁠$<4×10−7$ mbar). The unannealed sample that was measured as deposited is labeled with $Ta=20$ $°$C.

The FMR measurements have been performed using a vector network analyzer (VNA-FMR) and sweeping the external magnetic field at fixed frequencies between 2 and 25 GHz. This was done for all four samples before and after annealing. The real and imaginary parts of S$12$ were then modeled using a single Lorentz function for both parts. The g-factor and effective magnetization $Meff$ have been extracted using the Kittel formula,¹⁸ while the damping parameter has been determined by a linear fit to the resonance linewidth over the frequency.^19,20

For the preparation of a TEM specimen, the dual beam focused ion beam (FIB) Nova 600 NanoLab by FEI was used to lift out thin lamellas and attach them to a copper grid using a Pt source.

TEM bright field images were recorded with a Philips CM-200 FEG TEM operated at 200 kV. Complementary EDX spectra were recorded using an ultra-thin window EDX spectroscopy system from EDAX to determine the samples’ composition. Elemental mappings were collected with a probe size of $≈3.5$ nm, a step size of $≈2$ nm, and a dwell time between 5 and 30 ms per pixel. Using these maps, elemental cross sections were generated by averaging the counts over several pixels. In addition, the maps were also utilized to quantify the elemental composition of different structural phases.

Figure 1 shows the FMR linewidth $ΔH$ as a function of resonance frequency $f$ for the unannealed sample, as well as the four different annealing temperatures. The plot shows the experimental data, which were acquired at certain fixed frequencies, as well as a fit using a function of the form $ΔH=(4πfα)/(γμ0)+ΔH0$⁠, with the Gilbert damping parameter $α$⁠, the gyromagnetic ratio $γ$⁠, and the vacuum permeability $μ0$⁠. The data set of the unannealed sample and the ones annealed at 100 and 200 $°C$ show no differences within the error margins, meaning that they are not discernible in the plot. From the slope of the curve, we can determine the damping of the sample, which is shown in Fig. 2. The measurements of the samples annealed at 300 and 350 $°C$ show a different slope, as well as clear deviations from the linear behavior. Such nonlinear behavior has been observed before in the context of extrinsic contributions to the FMR response of ultrathin films and the closely related two-magnon model of scattering.^21–24 

Figure 2 shows how the Gilbert damping coefficient changes when the thin films are annealed at different temperatures $Ta$ for 60 min.

The unannealed sample shows a low damping constant of 0.007 in accordance with literature values.¹⁶ The samples maintain this low damping up to an annealing temperature of 200 $°$C, indicating that their structure is unchanged. When annealed at 300 $°$C, $α$ increases drastically from 0.007 to 0.030. Higher annealing temperatures increase $α$ even further, yielding a value of 0.046 for $Ta=350$ $°$C. In addition to $α$⁠, the FMR measurements were used to determine the effective magnetization $μ0Meff$ of the samples, which is shown in Fig. 3. $μ0Meff$ shows a trend opposite to the one of $α$ at higher temperatures. While $μ0Meff$ also stays constant up to 200 $°$C, it is then reduced significantly for annealing temperatures of 300 and 350 $°$C, with a stronger decrease for higher temperatures.

Figure 4 shows bright field TEM images, together with the respective EDX elemental map and a cross section of atomic composition as derived from the EDX map for samples annealed at 100, 200, 300, and 350 $°$C. The unannealed sample, which was measured as deposited, looks identical to the one annealed at 100 $°$C and was omitted here. The spatial resolution of the EDX images is not sufficient to make individual grains visible, and the color distribution thus only indicates the presence of a certain species within the layers and does not yield any information on the grain size or inhomogeneities. The bright field image of the sample annealed at 100 $°$C in Fig. 4(a) shows three distinct phases with small transition regions in between. These regions are an artifact arising from the finite thickness of the sample, combined with a small tilt of the sample with respect to the cross-sectional plane. When looking at the samples in transmission, the different layers then seemingly overlap. From top to bottom, the three phases correspond to Pt, Ni–Fe, and Si, as can also be seen in the elemental map in the right part of the figure. The Pt layer has been deposited during the preparation of the TEM lamella as a protective layer. The respective cross section shows that the Ni–Fe layer consists of approximately 75% Ni and 20% Fe. For better quantification of the atomic composition, the EDX spectra were also averaged over each region individually, resulting in improved statistics. Using this method, the Ni–Fe layer was determined to contain 71% Ni, 22% Fe, 6% Si, and 1% Pt. The large Si signal is expected to come from the scattering of electrons into the large adjacent Si substrate.

Figure 4(b) shows the TEM image and EDX mappings for a sample annealed at 200 $°$C. The bright field image looks slightly different, which can be attributed to a change in the contrast, focus, as well as the lamella thickness. However, it does show the same kind of structure, which is also validated by the EDX mappings. The cross section shows a composition of the Ni–Fe layer very similar to the sample annealed at 100 $°$C. When averaging over the entire Ni–Fe layer, we obtain values of 69% Ni, 22% Fe, 8% Si, and 1% Pt for the atomic composition. Since all four samples were cut from a single large sample after ion beam sputtering, it can be expected that the composition of the interlayer should not vary too much aside from minor inhomogeneities over the sample area of $10×10$ mm$2$⁠.

In Fig. 4(c), we can see a drastic change in a sample structure. When annealed at 300 $°$C, a fourth phase forms between the Ni–Fe and Si layers. The EDX spectra reveal that this fourth phase consists of Ni and Si, confirming the results of a previous study¹³ that silicides form at these temperatures. It is evident that Ni is the moving species in this case, migrating from the Ni–Fe layer into the Si layer, leaving behind a Ni–Fe layer with a lowered fraction of Ni. Averaging over the Ni–Fe layer, we find that it now contains 52% Ni, 36% Fe, 11% Si, and 1% Pt. It remains unclear whether the increased amount of Si is an experimental artifact or an actual indication of Si moving into the Ni–Fe layer. When averaging over the newly formed Ni–Si layer, we obtain values of 47% Ni, 3% Fe, 50% Si, and 0% Pt.

Figure 4(d) shows the results for the sample annealed at 350 $°$C. Again, the bright field image looks quite different due to changed contrast, focus, and lamella thickness. However, the EDX mapping still shows the same trend as the one for the sample annealed at 300 $°$C. Once gain, Ni atoms have migrated from the Ni–Fe layer into the Si substrate, leaving behind a Ni–Fe layer with altered atomic composition. When averaging over the different regions, we find that the Ni–Fe layer contains 38% Ni, 38% Fe, 24% Si and 0% Pt. The newly formed Ni–Si layer yields values of 55% Ni, 1% Fe, 44% Si and 0% Pt. Although Ni is the species moving into the Si substrate, Fe atoms also move in the opposite direction. This can be seen by looking at the change in the thickness of the Ni–Fe layer when the sample is annealed at 300 or 350 $°$C. Without annealing and up to temperatures of 200 $°$C, the Ni–Fe layer was measured to be $36±1$ nm in thickness without showing any temperature dependence while also maintaining good homogeneity. At 300 $°$C, the thickness of the Ni–Fe layer was reduced to $24±2$ nm, and the newly formed Ni–Si layer has a thickness ranging from 29 to 53 nm. When annealed at 350 $°$C, the Ni–Fe layer shrinks to a size of $20±3$ nm, and the Ni–Si layer grows to thicknesses ranging from 35 to 61 nm. This means that not only do Ni atoms move into the Si layer, but Fe atoms are also moving away from the Si/Ni–Fe interface, resulting in an Ni–Fe layer with reduced thickness, which will inevitably change the crystallographic order of the Ni–Fe layer, which is also recognizable in the bright field images, where the samples annealed at 300 and 350 $°$C show less homogeneous Ni–Fe layers, indicating grain formation.

Figure 5 shows dark field images of the samples annealed at 100, 200, 300, and 350 $°$C. Individual grains are visible in each recorded picture. The decreasing size of the Ni–Fe layer, which was already observed in the bright field images, is also evident in the dark field images, with layer thicknesses of approximately 35, 35, 25, and 20 nm for annealing temperatures of 100, 200, 300, and 350 $°$C, respectively. The sample annealed at 100 $°$C shows grains that are significantly smaller than the thickness of the Ni–Fe layer, and the same thing is true for the sample annealed at 200 $°$C. When annealed at 300 $°$C, however, the grains slightly increase in size, and the Ni–Fe layer shrinks, resulting in grain sizes on the order of the layer thickness. This is even more pronounced in the dark field image of the sample annealed at 350 $°$C. The Ni–Si layer is not well discernible in the dark field images due to the relative alignment of the detector, the Ni–Si layer, and the electron beam.

The results of the FMR measurements demonstrate that devices with Ni$80$Fe$20$ thin films exposed to intense Joule heating may lose their desired magnonic properties, such as low damping and high effective magnetization. Combining the results from the FMR measurements and the TEM and EDX study, we can see that the increase in Gilbert damping as well as the decrease in $μ0Meff$ correlate with structural changes in the thin film system, namely, the migration of Ni atoms from the Ni–Fe layer into the Si substrate and Fe atoms moving away from the Si/Ni–Fe interface. The bright and dark field images both show that the Ni–Fe layer decreases in size significantly for higher annealing temperatures, while the grain size slightly increases.

Earlier works have shown that Ni readily diffuses into an adjacent Si layer at temperatures above 200 $°$C, forming nickel silicides in the process.¹³ Julies et al. find that Ni$2$Si is formed at temperatures above 200 $°$C, while increasing the temperature to 350 $°C$ causes Ni–Si to form, which the TEM pictures confirm. This newly formed Ni–Si could interact magnetically with the Ni–Fe, which in turn could affect the damping of the system; however, in previous studies, Ni–Si compounds have been found to be almost exclusively non-magnetic,^25,26 which makes this scenario highly unlikely. Another way in which the Ni–Si layer could increase the damping of the system is by means of spin pumping, where the precession of magnetization in the Ni–Fe layer is damped by the transfer of the magnetic moment and energy to the itinerant charge carriers of the Ni–Si layer.^27,28 Further studies have to be conducted in order to measure the magnitude of this effect.

Other works have investigated the effect of composition of 3$d$ transition-metal binary alloys on their magnetic properties and found that the effective magnetization of Ni–Fe alloys, also measured by FMR, decreases steadily as a function of Ni concentration in the fcc regime.¹⁵ This trend is opposite to the one we observed here. In a related work, the damping has been studied as a function of the composition of Ni–Fe alloys.¹⁶ They also obtained a value of 0.0073 for $α$ in an Ni$80$Fe$20$ alloy; however, their data showed an increase in $α$ for higher amounts of Ni. In our samples, the damping parameter increased drastically for higher annealing temperatures, where the EDX data indicated Ni atoms migrating out of the Ni–Fe layer into the Si substrate, leaving behind a Ni–Fe layer with significantly reduced Ni concentration. The opposite trends for $α$ most likely result from the fact that Schoen et al. studied homogeneous polycrystalline samples, while the present samples exhibit grain formation, as can be seen in the TEM pictures. The EDX measurements have indicated a migration of Ni atoms out of the Ni–Fe layer, which resulted in a layer with increased Fe content, and since the annealing temperatures are well below the eutectic temperature of the system, Ni and Fe will not form an alloy, resulting in the formation of Fe grains.²⁹ 

These inhomogeneities contribute to the increase of Gilbert damping as measured by FMR through a mechanism that can either be described by the two-magnon model or the local resonance model depending on the ratio of grain size and film thickness.^21–24,30 These effects arise due to the local variation of the anisotropy fields in inhomogeneous thin films with grains, and the non-linearity in the frequency dependence of the FMR linewidth that is associated with this effect is evident in the present FMR measurements. These mechanisms are not associated with the coupling of the magnons to a thermal bath, meaning that the scattering from the FMR mode (⁠$k=0$⁠) into higher order magnon modes (⁠$k≠0$⁠) is reversible. However, these higher order modes will still also dissipate to the lattice, contributing to the observed increase in damping.^24,31

In conclusion, a more than sixfold increase of the Gilbert damping has been observed in 36 nm thin Ni$80$Fe$20$ layers grown on Si when the samples are annealed above 300 $°$C, as well as a reduction of the effective magnetization by 28%. These findings have been linked to structural changes of the sample, studied by TEM and EDX measurements. These revealed that Ni atoms migrate from the Ni–Fe layer into the Si substrate, forming a Ni–Si layer of thicknesses up to 61 nm, while Fe atoms are pushed back from the Ni–Fe/Si interface. The changes of magnetic properties after annealing have been attributed to the formation of Fe grains at higher annealing temperatures due to the migration of Ni atoms into the Si layer. These structural changes could result in an increased damping parameter by means of two-magnon scattering induced viscous Gilbert damping. Thus, the results show that Py thin films can undergo irreversible changes that have fatal effects on their magnonic properties and on the limit of their applicability in magnonic devices, which should be taken into account when designing new devices. However, this seemingly unfavorable effect can potentially be exploited in the fabrication of magnonic devices to locally modify the damping of a device. This could be used, for example, to induce a damping gradient to avoid unwanted reflection of magnons in a magnon absorber.

The authors want to thank Ulrike Eigenthaler for the preparation of the TEM lamellas.

The data that support the findings of this study are available from the corresponding author upon reasonable request.