Optically Transparent Ferromagnetic Nanogranular Films with Tunable Transmittance

Developing optically transparent magnets at room temperature is an important challenge. They would bring many innovations to various industries, not only for electronic and magnetic devices but also for optical applications. Here we introduce FeCo-(Al-fluoride) nanogranular films exhibiting ferromagnetic properties with high optical transparency in the visible light region. These films have a nanocomposite structure, in which nanometer-sized FeCo ferromagnetic granules are dispersed in an Al-fluoride crystallized matrix. The optical transmittance of these films is controlled by changing the magnetization. This is a new type of magneto-optical effect and is explained by spin-dependent charge oscillation between ferromagnetic granules due to quantum-mechanical tunneling.

shows a high-resolution transmission electron microscope image obtained from the Fe 9 Co 5 Al 19 F 67 film depicted in Fig. 1. This film consists of FeCo magnetic alloy of nanometer-sized granules dispersed in an Al-fluoride matrix. This micrograph has many dark circles with diameters ranging from 10 to 15 nm. In addition, a bright section covers the whole area. The dark circles are FeCo alloy granules, and the bright section with a lattice pattern indicates the Al-fluoride matrix with AlF 3 crystal structure.
Fluoride crystals (e.q., MgF 2 and BaF 2 ) have good transmittance and are widely used as optical materials. AlF 3 crystals also exhibit good transmittance from the short-wavelength region (200 nm) to near-infrared (2000 nm). On the other hand, FeCo is a ferromagnetic alloy with the largest known magnetization 21 . FeCo alloy granules with diameters exceeding 10 nm exhibit ferromagnetism because the granules are larger than the superparamagnetic critical diameter 22 at room temperature. However, since the diameter of the granules is very small compared to the light wavelength, light can pass through the film (to be discussed later). If the density of the FeCo granules in the film increases, transmittance decreases (Fig. 2b). This behavior can be explained simply since the FeCo granules are of the origin of the ferromagnetic properties while the Al-fluoride matrix allows optical transparency. Figure 3a depicts the change in the transmittance (Δ T/T 0 ) of light with wavelength of a 1500 nm, Fig. 3b presents the magnetization curve of the Fe 13 Co 10 Al 22 F 55 film. Transmittance decreases with an increase of magnetic field. The hysteresis of the transmittance is caused by the magnetization, as seen in Fig. 3.
where T M is the transmittance with the magnetization M, and T 0 is that with zero magnetization. Table 1 lists ΔT/T 0 , the magnetization and the transmittance in Fe 9 Co 5 Al 19 F 67 (Fe + Co = 14 at.%) and Fe 13 Co 10 Al 22 F 55 (Fe + Co = 23 at.%) films. Δ T/T 0 is observed in both films. It is noteworthy that optical transmittance changes with the magnetic field (Δ T/T 0 = 0.03% and 0.05%). As indicated in Fig. 3a, the magnetic fields at which two of the maxima in the transmittance appear are consistent with the coercivity. This result clearly confirms that the change in the transmittance corresponds to magnetization. The DC resistivity of the films shown in Fig. 3 and Table 1 is larger than 10 11 μ Ω m and the magnetoresistance was not observed. The result in Fig. 3 and Table 1 demonstrate a new magneto-optical effect in transparent nanogranular films.

Mechanism of optical transmission responses in nanogranular films.
Optical transmission responses to magnetization in nanogranular films may be explained by the TMD effect. Figure 4 illustrates a nanogranular structure with the image of optical transmittance and a model of a granular pair. The magneto-optical response is due to transition of electric charges between neighboring ferromagnetic granules through an insulating barrier via quantum-mechanical electron tunneling 23,24 , which depends strongly on the relative orientation of magnetization of the granules. When optical light is incident on the film, electric charge carriers in granules are subject to the oscillating electric field of the light that causes tunneling of the charge carriers back and   forth between neighboring granules through the thin insulator barrier (Fig. 4). The oscillation of charging states between granules is spin-dependent and contributes to additional magneto-dielectric and optical responses of nanogranular films 24 .
Incorporating the TMD constant 12 with a broad distribution of dielectric relaxation around the characteristic relaxation time 24,25 , where P T is the tunneling spin polarization, m = (M/M s ) is the normalized magnetization and M s is the saturation magnetization, we have the total magneto-dielectric constant of granular films where ε r (ω) is the effective dielectric constant of the media in the absence of tunneling effect between granules, Δ ε m (ω) is the tunneling contribution 12 , Δ ε is the dielectric strength, and β is the Cole-Cole's exponent (0 < β ≤ 1) representing a measure of the distribution of relaxation time 26 . In magnetic nanogranular films, β = 0.7 to 0.8 was found in a previous study 12 .
Using the dielectric constant (1) in the formula of transmission for a normal-incident optical light through a film 27 , we obtain the magneto-optical transmittance of a granular film as , where Δ α 0 is the magneto-optical absorption coefficient and d is the film thickness (see Methods for details). In Fig. 3a, we fit the magnetic field dependence of Δ T/T 0 using the experiment data of the magnetization curve in Fig. 3b for the optical light of wave-length λ = 1500 nm and frequency ω = 10 8 s −1 , refractive index n r = 3, and film thickness d = 1000 nm. Using the values of P T = 0.5, β = 0.7 (P T and β values are a little different from the previous results 12 . This is because of the increase of the granule size and the granule size distribution as seen in Fig. 2), Δ ε = 300 and τ 0 = 10 −8 s, appropriate for the Fe+ Co of 23 at.% granular film 12 and Δ α 0 d = (2πd/n r λ) (ωτ 0 ) −β Δ εsin(β π/2) = 2.3× 10 −3 we find a good agreement between the experiment and theoretical data (Fig. 3a), in particular for the hysteretic behavior of the transmittance reflecting the magnetization process in Fig. 3b. The magnetic fields, at which the transmittance is greatest, coincide with the coercive fields where there is a change of sign in the magnetization curves.
The values of Δ T/T 0 can be enhanced if one uses a half-metal with full spin polarization (P F = 1) for ferromagnetic nanogranules; makes the granule density higher, which shortens relaxation time due to the reduced distance  between granules; and designs broader size distribution, which makes β smaller. Nanogranular structures can be controlled by changing the film composition, the deposition conditions, and the annealing. For instance, when the values of P F = 1 and τ 0 = 10 −9 s are used, large magneto-optical transmittances of Δ T/T 0 (~5% for β = 0.6 and ~10% for β = 0.5 are expected in half-metallic nanogranular films.

Discussion
We have reported that nanogranular FeCo-(Al-fluoride) films are optically transparent ferromagnetic materials. These films have transmittance even for short wavelengths of light (less than 400 nm), exhibit 90% transmittance at a wavelength of 1500 nm, and are ferromagnetic with magnetization exceeding 18 kA/m at room temperature. Furthermore, these films have magneto-transmittance response Δ T/T 0 of 0.05% at a wavelength of 1500 nm. This new magneto-optical phenomenon is explained by the TMD effect due to the spin-dependent quantum effect in the nanogranular structure. A large value of Δ T/T 0 (more than 10%) is expected theoretically in nanogranular films by optimizing material and structural conditions. Magnetic materials in electric devices are not optically transparent. With the realization of a transparent magnet, more complete display devices will be constructed. For example, speed and fuel meters and a map can be displayed directly on the front glass of a car or an airplane.

Methods
Preparation of thin film samples. Thin films were prepared by a tandem deposition method 28 using a conventional RF-sputtering apparatus. Sputter deposition was performed on a 50 × 50 mm glass (Corning Eagle 2000) substrate at 600 to 700 °C in argon atmosphere with 1.3 Pa pressure during deposition, using a 76 mm-diameter Fe 60 Co 40 alloy disk target and an AlF 3 powder target compacted in the form of a 76 mm-diameter disk.
Composition and structural analysis. The composition ratio of Fe-Co (granule) and Al-F (matrix) was controlled by changing the RF power applied to each target. The chemical composition of Fe, Co, Al, and F in the thin films was analyzed using wavelength dispersion spectroscopy (WDS). For structural analysis, transmission electron microscopy (TEM) was performed on several selected thin films.

Measurements of optical and magnetic properties. Optical transmittance was measured using
Fourier transform infrared spectroscopy (FTIR) with a measurement waveband of 400 to 2000 nm. Change in the transmittance was measured using an optical spectrometer with a measurement waveband of 900 to 2000 nm and a magnetic field of 0 to 480 kA/m. The magnetization curves were measured using a vibrating sample magnetometer (VSM). In the magnetization and magneto-optical measurements, a magnetic field was applied parallel to the films surface. All the measurements reported in this paper were carried out at room temperature.  where E i is the incident electric field, E t is the transmitted electric field, ω ε ω = k c ( / ) ( ) is the complex wave number, ε ω ( ) = n + iκ is the complex refractive index, α = 4πκd/λ is the absorption coefficient, θ = 2πnd/λ, ϕ = − tan −1 [2κ/(n 2 + κ 2 − 1)], λ is the wave length, and R 0 = [(n− 1) 2 + κ 2 ]/[(n + 1) 2 + κ 2 ].
The interference is weak (Fig. 1b), due to modulation of film thickness and/or refractive index, which allows us to average T M over (θ− ϕ) from 0 to 2π, yielding 25 The effective dielectric constant of granular films may be separated into the two contributions where ε r (ω) is the effective dielectric constant in the absence of the tunneling effect between granules and Δ ε m (ω) is the tunneling contribution of the form 12 , where P T is the tunneling spin polarization, M is the magnetization and M s is the saturation magnetization; and β is an exponent representing a measure of the distribution of relaxation time 26 (β ~ 0.7 to 0.8 in the granular films 12 ). In the optical region, the light frequency (~10 15 s −1 ) is much higher than the tunneling rate (~10 4 s −1 to 10 9 s −1 ) depending on the ferromagnetic composition 12 (ω τ m ≫ 1) so that the tunneling contribution is approximated as Δ ε m (ω) ≈ Δ εe −iβπ/2 (ωτ m ) −β .