Giant Faraday Rotation in Metal-Fluoride Nanogranular Films

Magneto-optical Faraday effect is widely applied in optical devices and is indispensable for optical communications and advanced information technology. However, the bismuth garnet Bi-YIG is only the Faraday material since 1972. Here we introduce (Fe, FeCo)-(Al-,Y-fluoride) nanogranular films exhibiting giant Faraday effect, 40 times larger than Bi-YIG. These films have a nanocomposite structure, in which nanometer-sized Fe, FeCo ferromagnetic granules are dispersed in a Al,Y-fluoride matrix.


Results
Faraday effect and structure of (Fe,FeCo)-(Al-fluoride) films. Figure Figure 2c shows the relationship between wavelength and Faraday rotation angle. The angle changes from plus to minus around 1200 nm, and the value is 3.4 deg./μm at 405 nm and −0.53 deg./μm at 1550 nm. Figure 3a presents the high-resolution transmission electron microscope image obtained from the Fe 13 Co 10 Al 22 F 55 film deposited on the substrate at 600 °C. The film consists of FeCo magnetic alloy of nanometer-sized granules dispersed in an Al-fluoride matrix. The micrograph has many dark circles with diameters ranging from 10 to 15 nm. In addition, the bright section covers the whole area. The dark circles correspond to FeCo alloy granules, and the bright section indicates the Al-fluoride matrix. The schematic of the nanogranular structure is illustrated in Fig. 3b. When deposited on a heating substrate, the FeCo alloy granules become larger. FeCo granules with diameters 10-20 nm are single domain 19 and exhibit ferromagnetism because the granules are larger than the superparamagnetic critical diameter at room temperature 20 Fig. 4a, along with that of bulk Bi-YIG 8 for comparison. All the nanogranular films depicted in Fig. 4a have much larger absolute Faraday rotation angles than Bi-YIG. It is noteworthy that the value of the Faraday rotation angle of Bi-YIG decreases with increasing wavelength. The angle in the wavelength of 1310 to 1550 nm, which corresponds to the bands of optical communication, is small in Bi-YIG. In contrast, the nanogranular films exhibit large values in optical communication bands. Figure 4b indicates the Faraday rotation angles at wavelengths of 405 and 1550 nm as functions of the Fe + Co content in films deposited on substrates of different temperatures. The Faraday rotation angle increases with the Fe + Co content, indicating that the Faraday effect of the nanogranular films is due to the magnetic state of the FeCo granules. In this study, the substrates were heated to give ferromagnetism to the films by controlling the granular size. Depending on the substrate temperature, granular size may change; however, neither ferromagnetic properties nor Faraday rotation angle are affected.    Table 2. Calculated results of occupation number n d , spin moment S z , and orbital moment L z . For 3d orbitals of the Fe atom, density functional theory calculation results of occupation number n d , spin moment S z , and orbital moment L z in Fe-bcc bulk, Fe(001) surface, Fe-2ML with ML being the monolayer, and Fe/insulator interfaces with insulators being AlF 3 and YF 3 . In this calculation, we use GGA and include SO coupling. Table 1 lists the Faraday rotation angles in the visible light region (650 nm) and the optical communication band (1550 nm) of the nanogranular films, as well as that of Bi-YIG for comparison. At both wavelengths, the Faraday rotation angles of the nanogranular films are much larger than that of Bi-YIG; for example, the angle of the Fe 21 Co 14 Y 24 F 41 film is about 40 times larger than that of Bi-YIG at 1550 nm. This is a great practical advantage. In addition, the nanogranular materials are thin films (less than 1 μm thick). In contrast, Bi-YIG is a bulk material (1 mm thick). Optical devices can be miniaturized and integrated using the thin-film materials.

Mechanism of giant Faraday effects in nanogranular films. First, we calculated the electronic states
at Fe/insulator interfaces in density functional theory to clarify the mechanism of giant Faraday effect. In the density functional theory calculation with the WIEN2K package 21 , we obtain the occupation number n d of 3d orbitals of Fe atoms, spin moment S z , and orbital moment L z in Fe-bcc (body-centered cubic) bulk, Fe(001) surface, Fe-2ML with ML being the monolayer, and Fe/insulator interfaces with the insulators being MgO, AlF 3 and YF 3 .
Generalized gradient approximation (GGA) is used with spin-orbit (SO) coupling in the calculation. For bulk Fe and Fe(001) surface, our GGA + SO results are in good agreement with previous calculations 22,23 . It is clear that the orbital moment of the Fe atom is enhanced at the Fe(001) surface, Fe-2ML, and Fe/insulator interfaces compared with that of bulk.
Fe ( Table 2). The supercells of Fe/AlF 3 and Fe/YF 3 interfaces used in the calculation are depicted in Fig. 5. Enhancement of the orbital moment obtained on 3d transition metal surfaces is similar to that in previous studies 22,23 . It has been argued that the enhanced orbital moment comes from the reduced coordination of surface atoms, which causes narrower 3d electron bands and higher density of states at the Fermi level 23 . We use a similar argument for Fe-2ML and Fe/insulator interfaces: the Fe atoms at the interfaces have low-dimensional nature, which causes localized 3d electrons.
Our results suggest that the orbital moment is enhanced in various interfaces and is almost independent of the interfaces. Since the electronic states including the orbital moment are similar between interfaces, in the following Maxwell-Garnett theory the dielectric tensor  ( ) m λ of magnetic nanogranules is calculated using the density functional theory in the supercell of Fe-2ML as a function of light wavelength λ.
Next, we calculated Faraday rotation angle using the Maxwell-Garnett theory. The Faraday effect is a magneto-optical phenomenon caused by interaction between light and magnetic moment and gives rise to the rotation of light-polarization when a polarized light is transmitted through a magnetic film. The angle of rotation is the Faraday rotation angle given by 24 f xy xx where ϵ xx and ϵ xy are the diagonal and off-diagonal components of the dielectric tensor, d is the thickness of the magnetic film and λ is the light wavelength. The film thickness in Eq. (1) is fixed to d = 1 μm. In the Maxwell-Garnett theory 25 for magnetic nanogranular films with spherical nanogranules dispersed in an insulator matrix, the effective dielectric tensor is given by [26][27][28][29]  in Eq. (2) and obtain θ f . The result for p m = 0.5 is denoted by the blue line in Fig. 6. We find that the sign of θ f changes at long wavelengths λ of 2500 nm.
We also assume that  ( ) m λ is described by the dielectric tensor of Fe bcc bulk numerically obtained in density functional theory calculation with the Quantum-Espresso package 30 . The result for p m = 0.5 is denoted by the red line in Fig. 6. Sign change occurs at a long wavelength of λ of 1500 nm.
In Fig. 6, it is clear that the magnitude of the Faraday rotation angle θ f for Fe-2ML is larger than that for Fe-bcc in the whole wavelength range. This result indicates that the larger orbital moment in Fe-2ML gives rises to a larger magnitude of θ f . This result is in qualitative agreement with experimental results for nanogranular films. We note that the electronic states including orbital moment are similar between interfaces as discussed before.
As a result, we conclude that the enhancement of the Faraday effect in magnetic nanogranular films originates from the contribution of interfacial magnetic atoms.

Discussion
We analyzed the mechanism of the giant Faraday angle in nanogranular films. In each nanogranule, the surface/interface produces a main contribution to physical properties, where the orbital magnetic moments of 3d electrons are enhanced 31 . Orbital magnetic moments are of crucial importance for the Faraday effect, since the off-diagonal component of the dielectric tensor is given by spin-orbit coupling. Using the Maxwell-Garnett theory 25 , we examined the Faraday rotation angle as a function of the wavelength of light in nanogranular films with 50% volume fraction of Fe granules with dielectric tensors of bulk-Fe and 2 mono-layer-Fe. Here, in 2 mono-layer-Fe, all Fe atoms correspond to surface ones. We found that in nanogranular films with a dielectric tensor of 2-mono-layer-Fe, the Faraday rotation angle is enhanced in the short wavelength region and exhibits a sign change in the long wavelength region. These results explain the experimental data.
Giant Faraday materials were discovered for the first time in 45 years. These materials will contribute greatly to the miniaturization and integration of optical devices.

Methods
Preparation of thin film samples. Thin films were prepared using tandem deposition 32 with a conventional RF-sputtering apparatus. The films were 0.3 to 1.0 μm thick. Sputter deposition was performed on a 50 × 50 mm glass substrate (Corning Eagle 2000) at 500 to 700 °C in an argon atmosphere with 1.3 Pa pressure during deposition, using a 76 mm-diameter Fe or Fe 60 Co 40 alloy disk as the metal target and a 76 mm-diameter AlF 3 or YF 3 powder compacted disk as the insulator ceramics target.
Composition and structural analysis. The composition ratio of Fe,Fe-Co (granule) and Al-,Y-F (matrix) was controlled by changing the RF power applied to each target. The chemical composition of Fe, Co, Al, Y 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 magnetic properties, optical transmittance and Faraday angle. The magnetization curves were measured using an alternating gradient force magnetometer (AGM). Optical transmittance was measured using Fourier transform infrared spectroscopy (FTIR) with a measurement waveband of 400 to 2000 nm. The incident light is transmitted through the film samples or absorbed. The Faraday angle was measured using six laser light sources (405, 515, 650, 830, 1310 and 1550 nm). The magnetic field was applied from 0 to ± 800 kA/m perpendicular to the film surface of the samples in measurement of magnetization curves and Faraday angle. All measurements were carried out at room temperature.