Introduction

Soft magnetic materials with isotropic high permeability (IHP) at working frequency are crucial components in modern information technology because of their extensive applications to improve the performance of magnetic devices such as micro-transformers, planar inductors and core materials of writing head1,2,3. Nowadays, data transfer rate is getting to GHz, but the classical Snoek’s law4 indicates that the IHP based on crystalline anisotropy in the traditional microwave soft magnetic materials can only be obtained in the MHz range. To find the desired materials with IHP in the GHz range is still a challenge. For instance, a variety of theoretical5,6,7 and experimental works focus on both high8,9,10 and isotropic11,12,13,14,15,16,17,18 permeability in the GHz range of granular films9 and multilayers10 of magnetic alloys, ferrites and their composites.

As Kittel predicted in 194719, magnetic thin film is a good candidate to achieve high permeability in the GHz range. The high permeability in the GHz range was measured experimentally in the CoZrNb magnetic thin films with an in-plane uniaxial magnetic anisotropy (IPUMA) in 199620. Subsequently, many film systems of alloys, ferrites and their composites have been investigated8,9,21,22,23. Therein, metallic magnetic thin films, which have higher saturation magnetization than ferrite films, are better to achieve higher permeability and resonance frequency. Besides the large saturation magnetization Ms, the large IPUMA is essential for high permeability in the GHz range24. As the frequency response of the permeability is almost flat up to a rolloff frequency, associated with ferromagnetic resonance, when a microwave magnetic field h is applied perpendicular to the IPUMA field HK, the resonance frequency fr and initial permeability μin of the magnetic thin films can be adjusted by HK as 19 with γ as the gyromagnetic ratio and 22, respectively. In fact, the IPUMA field HK has been modulated by many effective methods, such as composition gradient sputtering25,26, micro-stripe patterning27,28,29,30, annealing under magnetic fields31,32,33, inducing stress on substrates34,35,36, oblique deposition37,38, temperature39 and electric field control40,41, etc. The permeability higher than 100 was achieved in the 1–5 GHz range in (Fe, Co)-based magnetic thin films with the IPUMA24. However, the high permeability of magnetic thin films with the IPUMA is anisotropic, which depends on the relative direction of h with respect to HK.

Searching for the isotropic permeability in the GHz range is another important topic in magnetic thin films. For instance, magnetic thin films with rotatable stripe domain42,43,44,45,46, composite-anisotropy multilayer as well as crossed anisotropies multilayer11,12,13,14,15,16,17,18 are intensively investigated. The rotatable stripe domain was discovered firstly in Permalloy films in 196142, and then in many other magnetic thin films43,44,45,46. As the effective IPUMA is along the direction of the stripe domain, the in-plane omnidirectional equivalent permeability can be achieved46 by rotating the stripe domain. It is worth noting that this is a spurious isotropic performance, because an external saturated magnetic field needs to be applied to rotate the orientation of the stripe domains which may limit the application of the magnetic thin films in magnetic devices. Similar results are found in other magnetic thin films with rotatable anisotropy46. The composite-anisotropy multilayer11,12,13,14,15 is another idea to search for the isotropic permeability, in which many equivalent magnetic layers having the same IPUMA are piled up. Similar to a random particle composite, the overall anisotropy of the multilayer can be cancelled out by shifting sequentially the anisotropic axis of every layer from bottom to surface11. The isotropic permeability is then achieved. Furthermore, the crossed anisotropies multilayers16,17,18 were also investigated for the purpose of isotropic permeability. However, the resonance frequencies of those multilayers are normally lower than 2 GHz. Therefore, seeking for magnetic thin films with the IHP in higher frequency is still expected not only for fundamental research but also for the technological applications.

In this paper, we report the achievement of an in-plane IHP with resonance frequency higher than 5 GHz in a convenient FM1/NM/FM2 (FNF) film, in which two ferromagnetic layers (FMi, i = 1, 2) are decoupled by a non-ferromagnetic interlayer (NM). By theoretical analysis, FM1 and FM2 with the same magnetic moment and equivalent but mutually orthogonal IPUMA fields HK are proposed. The isotropic microwave performance with an in-plane IHP is found experimentally in a Co90Zr10/SiO2/Co90Zr10 FNF film. Moreover, it is indicated that the in-plane IHP characteristics of these FNF films can even be extended to higher working frequency by employing the oblique deposition technique.

Theoretical analysis

Figure 1 illustrates the FNF film designed to realize the in-plane IHP in the GHz range, in which the IPUMA fields are perpendicular to each other. Considering a microwave magnetic field h applied in the plane of the FNF film as shown in Fig. 1a, the complex susceptibility of the film comes from weighted average of complex susceptibility of FM1 and FM2, written as

Figure 1: Schematic diagram and the angular dependences of the susceptibility of FM1/NM/FM2 film.
figure 1

(a) HK1 and HK2 (HK1 ⊥ HK2, and HK1 = HK2) are the in-plane uniaxial magnetic anisotropy fields of the FM1 and FM2 ferromagnetic layers, NM is the non-ferromagnetic interlayer, and θ is the angle between HK1 and the microwave magnetic field h. (b) θ dependences of the susceptibility under h, where the left, middle and right polar diagrams are theoretical simulation results of FM1, FM2 and FM1/NM/FM2, respectively.

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where (i = 1, 2) is the volume ratio of the FMi layer to the two magnetic layers. The microwave susceptibility of each magnetic layer results from uniform precession of magnetization, which can be described by LLG equation47, so the susceptibility of FMi layer and can be derived from LLG equation, and given by

where γ is the gyromagnetic ratio, αi is damping parameter, ω is the angular frequency of h and θ is the angle between h and HK1, respectively. As and , the complex permeability is generally angular dependent. Combining Equation (1), (2), and Equation (3), (4) with the conditions of

an angular independent complex permeability of the FNF film can be derived as

Herein, and are the real and imaginary parts of the complex susceptibility of a single FM layer under the condition , as48

Consequently, the in-plane IHP can be realized in the FNF film as shown in Fig. 1(b).

Results and Discussion

In experiments, Co90Zr10(100 nm)/SiO2(10 nm)/Co90Zr10(100 nm) FNF films with in-plane IHP at GHz were fabricated by radio-frequency magnetron oblique sputtering (see Supplementary Fig. S1 online). Here Co90Zr10 (EDS and XRD data are shown in Supplementary Fig. S2 online) used as FM layer, which possesses a relative high saturation magnetization and a well-established IPUMA49,50, can result in the high permeability at GHz. Each Co90Zr10 layer was about 100 nm to ensure that Ms1 = Ms2 = Ms and p1 = p2 = 1/2. A 10 nm SiO2 interlayer was chosen to eliminate the exchange coupling between two FMs, and thus the IPUMA of each Co90Zr10 layer can be adjusted separately. The direction and strength of the IPUMA were induced by controlling the oblique deposition conditions to satisfy HK1 ⊥ HK2 and HK1 = HK2, α1 = α2 = α as the two Co90Zr10 layers are equivalent. The details are discussed in the supplementary information.

Static magnetic performance

Figure 2 depicts the in-plane magnetic hysteresis loops of the Co90Zr10 FNF film fabricated by 30° oblique deposition, as well as that of a Co90Zr10(100 nm) single layer as a comparison. Two significant characteristics of the loops shown in Fig. 2a indicate that the conditions for achieving IHP are met in the Co90Zr10 FNF film. Shape of the loops in Fig. 2a, which is different from that in Fig. 2b, can be explained as the superposition of loops along the easy and hard axis of FM, respectively. The loops parallel and perpendicular to the direction of HK1 are almost identical, which implies the saturation magnetization, as well as the anisotropies, of FM1 and FM2 are equivalent, i.e., Ms1 = Ms2 and HK1 = HK2. To clarify the results above, the remanence and the slope near H = 0 Oe are discussed further in the following. The remanence ratio of 0.53 shown in Fig. 2a is the weighted average of the remanence ratios 0.99 and 0.05 obtained from the easy and hard axis loops in Fig. 2b, that means HK1 ⊥ HK2. Moreover, the equal remanence Mri (i = 1, 2) ≈ Msi/2 along HKi, indicates Ms1 = Ms2. Meanwhile, the same slope at H = 0 Oe for both loops, which can be expressed as Ms/HK, reveals HK1 = HK2 as well. As the Co90Zr10 FNF film satisfies the conditions for achieving IHP very well, it is expected to have in-plane IHP as predicted by Equation (8)–(11), , , . It should be noted that the hysteresis loops of FNF trilayer are not fully isotropic even the permeability of the FNF is angular independent.

Figure 2: In-plane magnetic hysteresis loops of the films fabricated by 30° oblique deposition.
figure 2

(a) Loops of the Co90Zr10/SiO2/Co90Zr10 FNF film. The blue solid line and red dashed line represent the curves measured along and perpendicular to the anisotropy field HK1. The insert is an enlarged view of the loops near the remnant ratio 0.53. (b) Loops of the Co90Zr10 single layer. The blue solid line and red dashed line represent the curves measured along easy and hard axis, in which the remnant ratios are 0.99 and 0.05, respectively.

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Dynamic magnetic performance

The microwave performances of the Co90Zr10 FNF film and a Co90Zr10 single layer are shown in Fig. 3. Figure 3(a,b) displays a typical frequency dependence of the real (imaginary) part of the sample permeability μ′ (μ″) measured at θ = 90°. The real part μ′ higher than 50 is obtained from 1.0 to 2.5 GHz. The fitting results indicate both the Co90Zr10 FNF film and the single layer exhibit a resonance-type permeability spectra, i.e. the spectrum of the real (imaginary) part is a dispersive (Lorentzian) curve. In order to demonstrate the isotropic microwave properties, the angular dependence of the resonance frequency, the maximum value and the full width at half maximum (FWHM) of the imaginary parts are plotted in Fig. 3c–e, respectively. The angular independence of the three characteristic quantities of the Lorentzian curves indicates that the imaginary part of the Co90Zr10 FNF film is isotropic. Based on the Kramers-Kronig relation, the real part of the Co90Zr10 FNF film must be also isotropic, which is confirmed by the experimental data shown in Fig. 3f, where the angular dependence of the permeability μ′ at 1 GHz of the Co90Zr10 FNF film shows clearly a circular characteristic of the IHP instead of a spindle-like distribution for the Co90Zr10 single layer. By fitting the data in Fig. 3f, the IHP at 1 GHz is around 55 for the Co90Zr10 FNF film. Those results reveal that the isotropic microwave performance with the IHP is achieved in the Co90Zr10 FNF film rather than in the Co90Zr10 single layer.

Figure 3: GHz frequency characteristics of the Co90Zr10 FNF film (blue solid squares) and the Co90Zr10 single layer (grey open squares) fabricated by 30° oblique deposition.
figure 3

(a) Real and (b) imaginary parts of permeability spectra measured at θ = 90°. (c) Resonance frequency, (d) the FWHM, and (e) μ″ maximum as a function of θ. (f) Real part of permeability at 1 GHz as a function of θ. The red solid line is theoretical simulation result of Co90Zr10 FNF film.

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In order to extend experimentally the working frequency range of the Co90Zr10 FNF film with IHP and exploit the universality of the IHP of the FNF film, the Co90Zr10 FNF film with the same structure as previous but higher resonance frequency was fabricated by 40° oblique deposition. According to the self-shadow effect51,52,53, the larger angle of the oblique deposition leads to the larger IPUMA field HK of Co90Zr10 single layer and consequently the higher resonance frequency. The tunable high frequency properties of oblique deposited Co90Zr10 single layer can be found in Fig. S3 or in our previous works49,50. The isotropic microwave performances of this Co90Zr10 FNF film are displayed in Fig. 4, together with the corresponding data of 30° oblique deposition Co90Zr10 FNF film. Figure 4a shows typical frequency dependence of the real part of permeability for both Co90Zr10 FNF films. With the oblique deposition angle increasing from 30° to 40°, the fr of the Co90Zr10 FNF film increases from 3.1 to 5.3 GHz. Figure 4b shows fr vs θ plots, where the circular distribution implies the isotropic resonance frequency. The isotropic effective fields are calculated from the resonance frequency as about 299 Oe for Co90Zr10 FNF film fabricated by 40° oblique deposition and 102 Oe for the 30° oblique deposition sample. Figure 4c shows μ′ at 1 GHz vs θ plots of the two Co90Zr10 FNF films as well as the fitted curves with Equation (8). The high frequency permeability always keep isotropic even the resonance frequency has been pushed from 3.1 to 5.3 GHz. These results reveal that the working frequency range of the Co90Zr10 FNF film with in-plane IHP can be adjusted by tuning the oblique deposition angle.

Figure 4: GHz frequency characteristics of the Co90Zr10 FNF films fabricated by 40° (blue solid squares) and 30° (grey open squares) oblique deposition.
figure 4

(a) permeability spectra. (b) θ dependence of resonance frequency fr. (c) θ dependence of permeability (μ′) at 1 GHz. The red solid lines are theoretical simulation results.

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In conclusion, we have demonstrated that the Co90Zr10(100 nm)/SiO2(10 nm)/Co90Zr10(100 nm) sandwich-structured films fabricated by the oblique deposition exhibit an isotropic microwave performance, and especially an isotropic high permeability larger than 20 with resonance frequency up to 5.3 GHz. The valuable isotropic behavior comes from the superposition of two uncouple equivalent ferromagnetic layers in which the uniaxial anisotropic fields are mutually orthogonal. The finding of the in-plane isotropic high permeability with high working frequency of the universal FM/NM/FM sandwich-structured film may benefit in searching for new microwave materials and have important applications in magnetic devices desired in the information technology.

Methods

Sample fabrication

The Co90Zr10(100 nm)/SiO2(10 nm)/Co90Zr10(100 nm) sandwich-structured films and Co90Zr10(100 nm) single layer were deposited at room temperature onto Si (111) substrates by radio frequency magnetron sputtering, and the in-plane uniaxial magnetic anisotropy of each Co90Zr10 layer was induced by oblique deposition. The base vacuum is 8.5 × 10−5 Pa, the sputtering power is 50 W, the flow of Ar is 10 SCCM, and the sputtering pressure is 0.25 Pa. The component of Co90Zr10 layer is tuned by putting a few Zr chips on the Co target, and the thickness of each layer was controlled by deposition time and rate. The Co90Zr10 FNF film is deposited as follows: the Co90Zr10(100 nm) bottom layer on Si substrate is deposited firstly, after turning the sample by 90 degrees on the sample holder, SiO2(10 nm) interlayer and the Co90Zr10(100 nm) top layer were deposited, successively.

Measurement

The composition of the films was determined by energy dispersive X-ray spectroscope (EDS) and the structure of the films was characterized by an X-ray diffractometer. A vibrating sample magnetometer (VSM) was employed to measure the hysteresis loops of the samples at room temperature. The remanence depending on angle of the Co90Zr10 FNF film was used to determine firstly the directions of HK1 and HK2, and then in-plane magnetic hysteresis loops were measured along HK1 and HK2. The similar measurement procedure was used for the Co90Zr10 single layer film as well. In order to get permeability spectra at different θ, we used vector network analyzer (VNA) with shorted micro-strip method54. The isotropic effective field can be calculated from the resonance frequency with equation, but considering HK≪ Ms and for simplicity, was used to calculate the effective field in this paper.

Additional Information

How to cite this article: Pan, L. et al. In-plane Isotropic Microwave Performance of CoZr Trilayer in GHz Range. Sci. Rep. 6, 21327; doi: 10.1038/srep21327 (2016).