Maghemite nanoparticles were doped in optical poly phenyl methyl vinyl siloxane and oriented by externally applied electric fields before curing. Consequent change in the morphology of the nanocomposite was observed and characterized using small angle x-ray scattering (SAXS). After curing, Faraday rotation measurements were carried out at 632.8 nm. Electric field based alignment in addition to presence of the nanodopants enhanced the magneto-optic sensitivity by 14.3-48.6% for the polymer nanocomposites. A linear trend was observed between orienting electric fields and measured Faraday rotation angles. Limits on applicable electric fields for dopant concentrations were also ascertained from the magneto-optic response.
© 2012 OSA
Nanocomposite optical materials exhibiting very high Faraday rotation capabilities are employed in a multitude of applications ranging from current sensors, fiber optic current transformers, magneto-optic isolators, high powered lasers, data storage devices and magneto-optic imagery [1–4]. Investigations of glass and polymer based nanocomposites for the express purpose of developing highly magneto-optic Faraday rotators have been widely discussed with pertinence to aforementioned applications [5–7]. Those efforts have reported and substantiated the presence of Faraday effect leading to high magneto-optic sensitivities (Verdet constants) and have encouraged further study on such materials.
In the current study, Faraday effect related to electric field oriented maghemite (γ-Ferric Oxide) nanoparticles doped in poly-phenyl methyl vinyl siloxane is reported. Nanoparticle orientation related studies in polymers have been carried out by researchers but have seldom been explored for magneto-optical applications [8,9]. This paper describes the impact of nanoparticle orientation on the magneto-optic capabilities of a material. Optical grade phenyl methyl vinyl siloxane was chosen as a host due to its relative glass-like properties (refractive index 1.53). The theory behind nanoparticle orientation in the polymer was also explored in addition to the evaluation of Verdet constants based on the maghemite doping concentrations for possible magneto-optic enhancement, after electric field based nanoparticle alignment.
2. Experimental procedure
Ferric nitrate, glycine and ammonium nitrate were combusted at 650°C and yielded hematite nanocrystals (α-Fe2O3). The hematite thus obtained was then mixed with polyethylene glycol in a combustion reactor at 400°C to obtain the maghemite nanocrystals (γ-Fe2O3) . X-ray diffraction confirmed the material phase. The polymer nanocomposite samples were prepared by mixing phenyl methyl vinyl siloxane with dicumyl peroxide (99:1) and doping the mixture with maghemite at 0.03-wt % and 0.06-wt%. The dopant concentrations were chosen so as to observe possibilities of physical orientation even at extremely low concentrations. Following a 12 hour sonication process and filtering using 0.45 micron filters, the mixture was subjected to DC electric fields from 0.0 kV/cm to 7.5 kV/cm in a custom built electric field chamber capable of generating 10 kV/cm. Thermal cure was then carried out for 12 hours to get the nanocomposite (henceforth known as γ-PMVS). Characterization of the γ-PMVS was performed using a Rigaku Ultima IV x-ray diffractometer with the small angle x-ray scattering (SAXS) setup (CuKα-1.54Å) at an operating voltage of 40 kV/44 mA. The SAXS method was used as a diagnostic tool to observe occurrence of nanoparticle orientation and to get nanoparticle size distribution. The nanoparticles were also observed using a field emission scanning electron microscope (FESEM) and transmission electron microscope (TEM).
Measurement of Faraday rotation (FR) angle was carried out using a phase sensitive detection setup (Fig. 1 ) comprised of a 632.8nm Helium Neon Laser, a 1000:1 linear polarizer, a Wollaston prism, a Helmholtz coil and an SRS 830 lock in amplifier with two silicon photodetectors (0.3 A/W responsivity at 632.8nm). The Helmholtz coil was capable of generating magnetic fields upto 35 mT-rms at a frequency of 60 Hz. The sample was kept in the system such that the orientation of nanoparticles was orthogonal to the external magnetic field generated by the Helmholtz coil as well as to the direction of propagation of the laser light. Differential phase measurements and relative change in photodetector intensities measured with a lock-in amplifier were used to calculate the Faraday rotation angle with respect to change in magnetic field strength. Data acquisition was performed using a LabVIEW based virtual instrument (VI) to record and analyze data . The results were averaged over thousand data points acquired for every magnetic field and had an accuracy of < 1%. This was also established earlier and confirmed during the course of this work .
3. Faraday effect and theory for nanoparticle orientation
The Faraday effect describes the angle through which linearly polarized light rotates while propagating through a material under a parallel magnetic field. This angle is termed the Faraday rotation angle, θf (deg) and is directly proportional to the length of the material L (cm) and the applied magnetic field B = µH (T) .The proportionality constant is represented by V, called the Verdet constant (deg/T-cm) and is the magneto-optic sensitivity of the material. The FR angle is given by Eq. (1)
The maghemite nanoparticles are confocal ellipsoids with an aspect ratio of 3:1 (as shown in Figs. 2(a) and 2(b)). Application of external electric fields would result in induced dipole moments, causing a torque to orient the nanoparticles. For an electric field E0 applied in the ‘x’ direction (Fig. 2(c)), orientation occurs at an angle α, and the electric field at the nanoparticle-polymer interface, Enp, which is responsible for the orienting torque, can be written as follows :Fig. 2(c), the torque acting on the nanoparticle is given by ‘τ’. This torque was determined earlier as 
Equations (2) and (3) relate the electric field applied to the resulting torque that is responsible for the orientation. The term in the square brackets represents a shape function pertaining to the nanoparticle accounting for defects/irregularities, ‘ν’ is the volume of the nanoparticle in m3, α is the angle of orientation in degrees, E0 is the applied electric field in V/m, εp = 2.34ε0 is the permittivity of the polymer in F/m. An optimal torque results for an orientation angle of α = 45° corresponding to maximum electric field at the nanoparticle-polymer interface. For an orienting electric field of 5 kV/cm along the direction of x axis, the resultant torque was determined to be 8.01 × 10−14 N and based on a confocal ellipsoid nanoparticle of an average size of 100 nm, the orientation angle was determined to be α ~40.49°. In contrast, factors that could impede the orientation of the nanoparticle would be an opposing torque related to the viscosity of the polymer and a consequent anisotropic dispersion that is discussed by Brownian motion. The nanoparticle orientation reversal time for the nanoparticles is typically greater than 10 hours  and is partly so due to the high viscosity of the polymer itself. Hence, the thermosetting process for the nanocomposite results in the orientation being made permanent.
In the case of the Faraday effect, the propagation vector of the laser light is along the same direction as the magnetic flux density B and hence the sample magnetization vector. The magnetic flux density for a magneto-optic material can be related to the earlier applied electric field through the linear magneto-electric tensor Λ which is characteristic of the material [13,14]:Eq. (4) represents the change in actual magnetization of the sample because of the earlier applied electric field. Knowing the crystal structure for the dopant nanoparticle, this can be calculated and the amount of magnetization added to the sample by means of the orienting electric field can be determined. Using Eq. (4), the Faraday rotation angle is then calculated from Eq. (1). For the e-field oriented sample, the Faraday rotation angle is given by
This equation shows that with increase in the orienting electric field strength, the Faraday rotation angle changes its value while maintaining the same Verdet constant. This implies an improvement in the signal to noise ratio of the material, thus suggesting an improvement in sensitivity for applications in magneto-optic sensing.
4.1 SAXS characterization and electron microscopy
Small angle x-ray scattering was employed as a primary means of evaluating a change in orientation based on a change in the scattering intensities due to incident diffraction angles. The samples that were subjected to electric field orientations were characterized at incident angles of 2Theta from 0.1 degrees to 4 degrees. The resulting scattering intensity vs 2theta curves are shown in Fig. 3(a) . The measured scattering intensities increased for samples with orienting e-fields upto 5 kV/cm and showed a decrease in intensity for the sample oriented at 6.25 kV/cm. Based on the shift in scattering intensities and considering the cubic crystal structure of maghemite (diffraction peaks shown in Fig. 3(c)), the electric fields applied for orientation may have re-oriented the nanocrystal to its original state of anisotropy or a symmetrical position.
The nanoparticle size distribution for the electric field oriented γ-PMVS samples was determined via SAXS (Fig. 3(b)) and showed presence of nanoparticles ranging from sizes of 50 nm to 150 nm. It was observed that the distribution peaks shifted for the samples with increased orienting electric fields. This may be attributed to the electric fields possibly resulting in aggregation of the nanoparticles in addition to alignment during the orientation process. The sizes of the nanoparticles were also observed using transmission electron microscopy (accelerating voltage 120 kV). The TEM micrographs of sectioned γ-PMVS samples showing the anisotropic maghemite nanoparticles in PMVS and oriented maghemite nanoparticles in PMVS are furnished in Figs. 4(a) and 4(b). The sizes were found to be averaged at ~100 nm and were in agreement with nanoparticle size distribution obtained via SAXS.
4.2 Verdet constant measurements
Figures 5(a) and 5(b) show the plots of the measured Faraday rotation angle (in degrees) versus the applied AC magnetic fields (in mT-rms) for the 0.03 wt% and 0.06 wt% γ-PMVS samples. The corresponding Verdet constants were determined from the slopes of Figs. 4(a) and 4(b). Their values ranged from (3.5-4 °/T-cm) for 0.03 wt% doping and (2.1- 3.12 °/T-cm) for 0.06 wt% doping concentrations. The enhancement of Verdet constants due to the maghemite doping and e-field alignment was found to be about 14.3% and 48.6% for 0.03 wt% and 0.06 wt% doping respectively. The blank undoped polymer gave a Verdet constant of 1.419 °/T-cm. From the plots, a substantial increase in FR angle can be clearly observed for samples oriented at different electric fields. This increase in the numerical value of FR angle was found to be linear for the γ-PMVS. This variation of FR angle at an applied magnetic field of 34.1 mT-rms is shown in Fig. 6(a) . Such a response, from an application perspective, could signify an improved SNR in sensing.
Application of electric fields to the composite, causes an off-center charge displacement inside the maghemite nanoparticles. Consequently, the wavefunction overlap decreases between any weakly confined ions and so, the nanoparticles, under the influence of the dipole electric moment, alter their state of anisotropy from the resultant torque. To account for the decreased magneto-optic behavior for the 0.03 wt-% and the 0.06 wt-% γ-PMVS samples, application of high electric fields decreases the ionic exchange interaction in maghemite with increase in dopant concentration but magnetically induced Zeeman transition energies are still prevalent . This explains the observation of lower values of FR angle for the samples with increased maghemite concentration and gives a method for preferential tuning of the magneto-optics for this particular polymer-semiconductor nanocomposite via orienting electric fields.
Magneto-optic response of the material was also measured for orienting electric field durations of 1, 2, 5, 10 and 20 minutes. An e-field of 5 kV/cm appears to cause the optimal orientation based on observations from the SAXS plots. Therefore, the variation of FR angle for an e-field of 5 kV/cm at aforementioned durations is plotted in Fig. 6(b). This showed a non-linear change in FR angle as the orienting e-field duration increased. Interpolation of the data points for longer durations revealed that the FR angle may saturate beyond applied durations of 20 minutes. In general, physical orientation of the nanoparticles due to the applied e-fields also tunes the optical transmittance of the sample by affecting the birefringence of the sample in accordance with the Kerr effect. Since the Faraday rotation angle is also dependent on the birefringence of the sample to an extent, it is given by the equation
Electric fields were applied to orient maghemite nanoparticles doped in poly-phenyl methyl vinyl siloxane. Small angle x-ray scattering was employed to observe the orientation and change in morphology of the nanocomposite. After curing, Faraday rotation measurements of these e-field oriented polymer nanocomposites revealed a change in the numerical value of FR angles which could result in improving the signal to noise ratio for sensing applications. These observations could facilitate development of potential materials for applications in optical current sensing, magneto-optic isolators and modulators.
The authors wish to thank Dr. Jibao He of Tulane University for help with the transmission electron microscopy and the Center for Manufacturing Research, Tennessee Tech University for the use of SAXS instrumentation acquired through NSF grant DMR-0923042.
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