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Abstract
Nanogranular films consisting of a complex of nanometer-sized magnetic granules and a dielectric insulator matrix exhibit a large Faraday rotation. In this study, the dielectric tensor of the nanogranular films with high refractive silicon nitride matrix are measured, and the effect of refractive index of the matrix and magnetic granules on the dielectric tensor is analyzed. Compared with the fluoride (low refractive index) matrix nanogranular films, the Faraday rotation angle is approximately two times higher in the nanogranular FeCo-SiN film, which exhibits a high refractive index effect on the Faraday rotation angle.
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1. Introduction
Magneto-optical materials exhibiting Faraday rotation (FR) are essential for optical communication technology [1–3], optical amplifiers [4,5], and photonic crystals [6,7]. An yttrium iron garnet (YIG) bulk crystal with a Bi or Ce dopant is the only material used for optical applications, because no material with FR higher than that of a (Bi or Ce)-YIG has been identified [8–20]. Recently, several studies have been reported on materials with high FR [21–27]. However, thin film materials exhibiting large FR angle are currently unavailable, hindering the progress of optical integrated circuits.
The magneto-optical effect is described using a dielectric tensor. In the case of isotropic magneto-optical materials with an applied magnetic field along the z-axis, the dielectric tensor of the magneto-optical materials is expressed as Eq. (1), owing to the immutability of rotation along the magnetic field (z-axis). The off-diagonal permittivity produces the difference between left circularly polarized light and right circularly polarized light, which is the origin of the magneto-optical effect. The FR angle is expressed as Eq. (2), using the diagonal and off-diagonal permittivity, wherein ω is the angular frequency, c is the velocity of light, and d is the thickness of the material. An off-diagonal element of the dielectric tensor is critical for achieving a large FR angle. The FR and Faraday ellipticity are expressed as Eq. (3) and (4) by dividing Eq. (2) into real and imaginary parts; the FR and Faraday ellipticity are linear combinations of the off-diagonal elements of the dielectric tensor. Therefore, the real and imaginary parts of the off-diagonal elements of the dielectric tensor are described as Eq. (5) and Eq. (6), respectively. wherein n is the refractive index, and κ is the extinction coefficient.
Here, we propose nanogranular films that exhibit large FR [28–31]. The structure of the nanogranular films comprises a complex of nanometer-sized ferromagnetic metal granules covered with a dielectric matrix [32]. The various functional properties of the nanogranular film are attributed to the ratio of the magnetic granules to the matrix, such as high permeability at gigahertz frequencies [33,34] at a high magnetic granule ratio, the tunneling magnetoresistance (TMR) effect [35,36] at a medium magnetic granule ratio, and the tunneling magnetodielectric (TMD) effect [37–39] at a low magnetic granule ratio. At low magnetic granule ratios, light transparency and FR appear in the nanogranular films [27–31]. The mechanism of considerably large FR in nanogranular films is associated with the interface between ferromagnetic granules and the insulator matrix, whereat the orbital magnetic moment of the 3d electron is enhanced [28]. The Maxwell-Garnett theory provides an effective dielectric tensor for an insulating matrix with dispersed spherical metal particles [40,41]. The effective dielectric tensor of the nanogranular films is then obtained using the volume fraction of the magnetic granules and the respective dielectric tensors, and refractive indices, of the matrix and magnetic granules. Accordingly, the FR angle is estimated by applying the effective dielectric tensor to Eq. (3). When a high refractive index material is used as the matrix of the nanogranular films, and the dielectric tensor of the magnetic granules is fixed, the enhancement in the FR angle is estimated from the change in the refractive index of the matrix based on the Maxwell-Garnett theory [28]. However, the dielectric tensor of the nanogranular films have not been analyzed in previous studies. Therefore, the effects of refractive indices of the matrix and magnetic granules on the dielectric tensor are not clear.
In this study, we investigated the magneto-optical effect in nanogranular films with a high refractive index of silicon nitride by measuring the dielectric tensor of the films. The FR in the FeCo-SiN films strongly depends on the magnetic metal content and is observed to be approximately ten times larger than that of a Ce-doped YIG at optical telecommunication wavelengths (1550 nm) [8]. A large imaginary part of the off-diagonal dielectric tensor results in a large FR in nanogranular films because of FeCo magnetic granules.
2. Experimental method
FeCo-SiN nanogranular films were prepared using an RF sputtering system (SPF-210B, Anelva) with Fe60Co40 alloy chips on a Si3N4 target. The films were deposited on 50 × 50 mm quartz substrates in an Ar + N2 atmosphere (N2 ratio: 20%) at a pressure of 1.0 Pa. The thickness of the films was 500–700 nm. To obtain a homogeneous granular structure, the quartz substrates were rotated on the composite target at a rotation speed of 1.0 rpm. The ratio of FeCo to silicon nitride was controlled by varying the number of FeCo chips on the target.
The compositions of the nanogranular films were evaluated through wavelength dispersive X-ray spectroscopy. The microstructure of the nanogranular film was observed using high-resolution transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDS) mapping. The crystal structures of the films were characterized via X-ray diffraction (XRD) analysis using Cu-Kα radiation. The optical constants of the nanogranular films were determined using spectroscopic ellipsometry (Uvisel Plus, Horiba) at wavelengths ranging from 200 to 2000 nm. Transmission and reflection spectra of the films were obtained using a spectrophotometer (UV-3600Plus, Shimadzu) over the wavelength range of 200–3000 nm. The magnetization curves were measured using a vibrating sample magnetometer (BHV-30, Riken) with a magnetic field of 0–800 kA/m. The FR angle and Faraday ellipticity were measured using the rotating-analyzer and polarization modulation methods (BH-501F, Neoark) over the wavelength range of 500–1700 nm, respectively. A magnetic field of 800 kA/m was applied perpendicular to the film surface during the FR and Faraday ellipticity measurements. All measurements were performed at room temperature.
3. Results
3.1 Film nanostructure
In this study, we prepared FeCo-SiN films with different FeCo content by changing the composite target. Table 1 lists the film contents. The FeCo contents of the films were 11–36 at.%. The N/Si ratio of the films was larger than 1.33, which is the stoichiometric composition of the silicon nitride (Si3N4) target. Figure 1(a) shows the XRD patterns of the FeCo-SiN films. A single broad peak corresponding to bcc-FeCo (110) at 2θ = 44.9°, approximately is observed for each sample, which indicates that the FeCo-SiN films consist of FeCo granules and amorphous silicon nitride. The bcc-FeCo (110) peaks become sharp with an increase in the FeCo content, which indicates the grain growth of the FeCo granules. The lattice parameter of the films, calculated using bcc-FeCo (110) diffraction line, is 0.285 nm, which is slightly smaller than that of bulk FeCo alloy (0.286 nm) [42], indicating the exitance of compressive stress in the films. The grain size of FeCo, calculated using Scherrer’s formula [43], is shown in Fig. 1(b), and it is almost proportional to the FeCo content of the films. It is assumed that the FeCo granules grow based on the ratio of FeCo particles through sputtering deposition.
Table 1. Atomic composition ratio of the FeCo-SiN films
Cross-sectional TEM image and EDS mapping of the FeCo-SiN film with the FeCo content of 19.9 at.% are presented in Figs. 2 and 3. The TEM images reveal a film structure in which nanometer-sized granules are distributed in the amorphous matrix. The dark and bright contrasts correspond to the FeCo granules and the SiN matrix, respectively. The EDS mapping results of the FeCo-SiN film with the FeCo content of 19.9 at.% (Fig. 3) indicate that the granules correspond to Fe and Co, and the matrix accords with Si and N, confirming the assumed structure of the films.
Fig. 2. Cross-sectional TEM image of the nanogranular FeCo-SiN film with an FeCo content of 19.9 at.%.
3.2 Magnetic properties of films
The magnetization curves of the FeCo-SiN films with different FeCo contents are shown in Fig. 4(a). The magnetization at an applied magnetic field of 800 kA/m increases with an increase in the FeCo content of the films (Fig. 4(b)). Superparamagnetic profiles are observed in the films with an FeCo content of ≤20 at.%, while ferromagnetic properties exhibiting considerably high coercivity are confirmed at the FeCo content of >20 at.% (Fig. 4(c)), which is attributed to the grain size of FeCo granules (Fig. 1(b)). In case of magnetic granules distributed in a non-magnetic matrix, the critical diameter of superparamagnetism is calculated to be 7.9 nm using the magnetic anisotropy energy of bulk FeCo alloy at 300 K (26 meV) [44–46]. According to Fig. 1(b), the size of FeCo granule increases with an increase in the FeCo content of the films, and exceeds the critical diameter for the films with high FeCo content. The presence of magnetic grains larger than the critical diameter in the films yields ferromagnetic magnetism, whereas the presence of small grains result in superparamagnetism. The magnetization of the FeCo-SiN films is almost equal to the value calculated using the magnetization of the bulk FeCo alloy (red line in Fig. 4(b)), which indicates that the FeCo granules in the FeCo-SiN nanogranular films consist of the metal FeCo alloy and the films exhibit magnetization similar to that of the FeCo alloy.
Fig. 4. (a) Magnetization curves of the FeCo-SiN films with different FeCo contents, (b) magnetization of the FeCo-SiN films with an applied field of 800 kA/m, (c) coercivity of the FeCo-SiN films.
Figure 5 depicts the wavelength dependence of the FR angle and Faraday ellipticity. All FeCo-SiN films show an inversion of the FR sign at wavelengths of 700–1000 nm. The Maxwell-Garnett theory reveals the sign inversion of FR and shows that its origin causes the film structure in which magnetic metal granules are dispersed in the insulator matrix. The effective dielectric tensor can be obtained using Maxwell-Garnett theory by approximating the local electric field acting on the magnetic metal granules and predicting the wavelength dependence of FR, assuming the magnetic granules calculated using the density functional theory [40,41]. The turnover wavelengths of the FR angle increased with the FeCo content, which may be attributed to the grain size of the FeCo granules. In particular, a large shift of the sign change wavelength was confirmed in the film with an FeCo content of 36 at.%, which indicates the strong influence of the granule size. The relationship between the FR sign change and magnetic granule size can be attributed to the effect of interface of the magnetic granules. The enhancement of the magnetic moment at the interface between magnetic granules and matrix is confirmed by the density functional theory calculation [28]. The increase in granule size reduces the ratio of the magnetic granule interface, which may result in the turnover shift of FR. The value of the FR angle at visible and infrared (IR) wavelengths increased with the FeCo content of the films. The magnitude of the FR angle at 1550 nm (optical telecommunication band) reached 8.7 deg./µm in the film with an FeCo content of 36 at.%; this value is approximately ten times higher than that of a Ce-added YIG [8], which implies the potential of the nanogranular films for optical telecommunication applications. In comparison to the FR angle of the nanogranular film with a low-refractive-index matrix (YF3: n = 1.5), the FR angle of the FeCo-SiN film (film thickness: 0.55 µm) with 36 at.% FeCo content is approximately two times higher than that of Fe60Co40-YF3 nanogranular films (film thickness: 0.30 µm) with 35.8 at.% FeCo content (−4.0 deg./µm at 1550 nm) [28]. Thus, the FeCo-SiN film exhibits a high refractive index matrix effect (Si3N4: n = 2.0) on the FR angle.
Fig. 5. (a) FR angle of the FeCo-SiN films with different FeCo contents, (b) Faraday ellipticity of the FeCo-SiN films.
The absolute value of Faraday ellipticity, which is proportional to the magnetic circular dichroism (MCD) per unit length of the FeCo-SiN films, reaches a maximum at wavelengths of 900–1000 nm. There is a similarity in the wavelength between the turnover of FR and the peak of Faraday ellipticity, which indicates that the FR profile is different from the Faraday ellipticity profile. A high Faraday ellipticity is confirmed at wavelengths of 700–1000 nm, which accords with the wavelengths of high change ratio of FR angle. The wavelength dependence of FR is partially similar to the differential of that of Faraday ellipticity. In the visible light and IR regions, the FR angle is dominant over MCD; in contrast, MCD is higher than the FR angle at near-IR wavelengths, which is mainly due to the off-diagonal element of the dielectric tensor.
3.3 Optical properties of films
The transmittance and reflectance of the FeCo-SiN films are shown in Fig. 6. The transmittance increases with wavelength, and the rate of increase in transmittance decreases with the FeCo content of the films, which originates from the absorption of magnetic metal granules. The reflectance increases with the FeCo content of the films, which implies an increase in the optical constant by FeCo granules [40,41].
Fig. 6. (a) Transmittance of the FeCo-SiN films with different FeCo contents, (b) reflectance of the FeCo-SiN films
Figure 7 shows the complex diagonal dielectric constants of the FeCo-SiN films. The real part of the diagonal dielectric constant (ɛxx’) is higher than that of silicon nitride at wavelengths of >500 nm. The ɛxx’ increases with the wavelength and FeCo content of the films, which is attributed to the magnetic metal grain distributed in the high refractive index SiN matrix [29], resulting in the reflectance increase (Fig. 6(b)). The imaginary part of the diagonal dielectric constant (ɛxx’’) increases with the FeCo content of the films. The wavelength at which ɛxx’’ reaches its maximum is shifted from 300 to 700 nm with an increase in the FeCo content of the films. The main cause of increase in ɛxx’’ is believed to be light absorption of a magnetic metal; therefore, ɛxx’’ increases with the FeCo content. The peak shift of ɛxx’’ maybe attributed to the FeCo grain size because the motion of the free electrons of the FeCo grains is limited inside the magnetic grain [47].
Fig. 7. Diagonal dielectric constant of the SiN and FeCo-SiN films with different FeCo contents: (a) real part, (b) imaginary part.
The complex off-diagonal dielectric constant of the FeCo-SiN films calculated using Eq. (5) and Eq. (6) are shown in Fig. 8. The real part of the off-diagonal dielectric constant (ɛxy’) increases with wavelength and causes the turnover of the sign at 600–900 nm. The imaginary part of the off-diagonal dielectric constant (ɛxy’’) decreases with increasing wavelength and turns over the sign at 700–1000 nm. The absolute value of the off-diagonal dielectric constant increases with the FeCo content of the films. The difference in the turnover wavelength between ɛxy’ and ɛxy’’ contributes to the MCD of the FeCo-SiN films. ɛxy’’, which is the origin of the FR angle, is attributed to the interface between the magnetic metal grains and the SiN matrix [28].
Fig. 8. Off-diagonal dielectric constant of the FeCo-SiN films with different FeCo contents: (a) real part, (b) imaginary part.
To evaluate the quality and usefulness of the magneto-optical material, a figure of merit (FoM) based on FR is defined as the ratio between FR angle and the absorbance of the films. Figure 9 shows the dependence of FoM on the FeCo content at the optical communication wavelength (1550 nm). The FR angle increases with the FeCo content because of the enhancement in the off-diagonal dielectric constant (Fig. 8(a)). On the contrary, the transmittance of the films decreases with FeCo content mainly because of the light absorbance by the magnetic metal granules (Fig. 6(a)). The change ratio of the transmittance is higher than that of FR angle; therefore, the FoM decreases with FeCo content, which indicates that the FeCo-SiN films with low FeCo content are suitable for device application. However, the FoM of the FeCo-SiN films is much smaller than that of the Ce-YIG films (943 deg./dB) [8–20], which strongly indicates the need to improve the absorbance of the films. The transmittance of the nanogranular films increases with the crystallinity of the matrix of the films [28], which implies that small transmittance of the FeCo-SiN films may result in the amorphous silicon nitride matrix.
4. Summary
The magneto-optical effect, magnetic properties, and nanostructure of the nanogranular FeCo-SiN films were investigated in this study. Structural analyses revealed a film structure in which nanometer-sized FeCo alloy granules were distributed in an amorphous silicon-nitride matrix. The FeCo granules in the FeCo-SiN nanogranular films consisted of a metal FeCo alloy and exhibited magnetization similar to that of the FeCo alloy. The absolute value of the off-diagonal dielectric constant increased with the FeCo content of the films. The magnitude of the FR angle at 1550 nm reached 8.7 deg./µm, because of the large imaginary part of the off-diagonal dielectric tensor caused by FeCo magnetic granules. Compared with a low refractive index matrix nanogranular films, the FR angle is approximately two times higher in the nanogranular FeCo-SiN film, which exhibits a high refractive index effect on the FR angle.
Funding
Japan Society for the Promotion of Science (19K21959, 20H02447, 20H02468, 20K03843); Core Research for Evolutional Science and Technology (JPMJCR19T1).
Acknowledgments
The authors would like to thank Prof. S. Iwamoto, Prof. Y. Ohta, and Dr. T. Liu for useful discussions. This work was supported by JST, CREST Grant Number JPMJCR19T1, Japan, and JSPS KAKENHI Grant Numbers 19K21959, 20K03843, 20H02468, 20H02447.
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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