The impact of vectorial magnetic field effects on electrical conductivity and nonlinear optical transmittance exhibited by multi-wall carbon nanotubes was studied. The samples were synthetized by an aerosol pyrolysis processing route in a thin film form. Optical signals in a two-wave mixing configuration allowed us to identify two orthogonal directions of propagation for a magnetic field travelling through the nanomaterials studied. A selective modification in optical absorption was considered to be induced by magnetic perturbations in the sample. Standard optical Kerr gate measurements were carried out for exploring the third order nonlinear optical behavior of the film. A capacitive effect influenced by optical and magnetic excitations was distinguished to be characteristic of the sample. Magneto-quantum conductivity sensitive to the direction of an external magnetic field interacting with the tubes was analyzed. Magnetically-induced changes in electronic band parameters seem to be the main responsible for the optical and electrical modulation observed in the nanostructures. Immediate applications for developing magneto-optical and magneto-electrical functions can be contemplated.
© 2016 Optical Society of America
Carbon nanotubes (CNTs) provide fascinating magnetic properties due to their two-dimensional morphology and energy band structure . The magnetic susceptibility related to CNTs has an important contribution to their optical , electronic , and mechanical  characteristics. These nanotructured materials can be described as graphite sheets shaped as hollow cylinders. But single-wall CNTs (SWCNTs) and multi-wall CNTs (MWCNTs) can be governed by dissimilar physical processes as a result to their differences in size, chirality, structure and morphology. The internal mechanisms exhibited by the walls conforming MWCNTs can determine certain optical parameters that concern to multi-photonic interactions. As a result, opposite nonlinearities in optical absorption have been found in SWCNTs  and MWCNTs . On the other hand, the valence band (π) and the conduction band (π*) corresponding to CNTs give rise to outstanding hierarchical architectures of tubes that promise ultrafast all-optical devices . Particularly, the electronic band parameters are affected by the presence of a magnetic field , and eventually, they produce a modification in the propagation of electromagnetic waves. In this direction, CNTs have proved to be useful as an active material in photo-actuators , optoelectronic systems , and polarization-selectable optical devices . Regarding to the vectorial dynamics of light in simultaneous propagation with magnetic fields, diverse low-dimensional magneto-optic and photo-magnetic systems are attractive to be proposed. With this motivation, this work was devoted to analyze magnetically-controlled nonlinear optical transmittance and conductivity in MWCNTs.
The preparation method and morphology characterization of the MWCNTs here studied, have been previously described . These aspects were confirmed in this research, and randomly distributed networks of MWCNTs conforming thin films were prepared. Transmission Electron Microscopy (TEM; JEOL system JEM 2100), Optical spectroscopy (Ocean Optics Spectrometer USB2000 + XR1-ES) and micro-Raman (Horiba Jobin Yvon LabRam HG System λ = 632.8 nm) measurements were carried out. The electrical properties of the samples were studied by a high power potentiostat/galvanostat (Autolab/PGSTAT302N). The electrical evaluations were acquired by using a 10 mV sinusoidal signal and an interval of frequencies between 500 and 105 Hz. Two carbon electrodes separated a 5 mm distance were incorporated to the film to carry out the electrical measurements. An iron cored coil emitting a static magnetic field of 0.3 Gauss was employed to explore the magneto-conductive response exhibited by the sample. This iron core electromagnet was separated from the film a linear distance of 2 mm. A class IV solid-state laser system at 532 nm was used to study the photo-conductive behavior of the film. An optical irradiation close to 3 W/cm2 was chosen to avoid the participation of any important photo-thermal process or the excitation of third order optical nonlinearities. Four different type of measurements were undertaken to inspect the impedance spectroscopy response of the samples: 1) in darkness, 2) with a magneto-conductive excitation, 3) with a photo-conductive excitation, and 4) with simultaneous photo-conductive and magneto-conductive interactions. Multi-photonic processes in the MWCNTs were investigated by using a Nd:YAG laser system (Continuum model SL-II) operated in an optical Kerr gate (OKE) configuration . The second harmonic at 532 nm with 4 ns pulse duration and linear polarization was employed. The angle between the planes of polarization of the interacting beams in the two-wave mixing was adjusted to 45°. A pump:probe irradiance relation 10:1 was used in a single-shot mode of the system. The geometrical angle between the interacting beams was about 30°. The beam waist in the sample was approximately 5 mm. A calcite analyzer was placed before a PIN photodetector to recover the cross-polarized transmittance of the probe beam after the interaction. For describing the propagation of the pump and probe beams, we used the finite-differences method to numerically solve the wave-equation .13]:
3. Results and discussions
In Fig. 1(a) is shown a typical TEM image were the nanostructured nature of the tubes can be observed. The diameter of the as-grown tubes was measured to be between 12 nm and 40 nm with an average of 26 nm. A modular spectrometer allowed us to estimate the homogeneity of the 120 nm thickness in the selected films with an error bar of about 20%. From Fig. 1(b) can be identified the characteristic G´ peak in the Raman shift at 2650 cm−1 in the spectrum of the sample. With this G´ peak can be associated an energy of 2.33 eV; besides, it represents a ratio to the C-C bond energy (γ0) . Figure 1(c) depicts the electrical frequency dependence of the MWCNTs excited by normal incidence of optical irradiation and magnetic field perpendicular to this field. It is considered that the plane XY was containing the film.
From Fig. 1(c) can be observed a monotonic decrease in the electrical impedance as a function of the electrical frequency in all the studied cases. This behavior corresponds to a capacitive phenomenon dominating the imaginary part of the electrical impedance exhibited by the film. Noticeable photo-conductive effects were observed for frequencies below a magnitude closer to 2 KHz; while magneto-conductivity seems to be present only below a magnitude close to 1 KHz. However, it is remarkable that the simultaneous propagation of optical and magnetic fields in the sample gives origin to stronger changes in conductivity in the whole range below 10 KHz. According to these results, it can be regarded that the contribution of the magnetic field is not only an influence for the magneto-conductivity, but also, for generating an enhancement in photo-conductive interactions. Considering that the photo-conductance can be described as a quantum process, it can be expected a significant influence of the magnetic field in the optical absorbance of the sample. The optical transmittance of a weak-field single-beam in propagation through a media can be expressed:15]. Also, the refractive index can be described by the intrinsic impedance in the medium η = η0/n, where η0 is the intrinsic impedance of the free space. On the other hand, η is a function of the magnetic permeability µ and the dielectric constant ε, such as η = (µ/ε)½ . Moreover, the magnetic permeability µ and susceptibility χm, are related by µ(B) = µ0(1 + χm(B)); where µ0 is the permeability of the free space. Consequently, it can be demonstrated that the transmittance of an electromagnetic wave in propagation through a susceptible magnetic material can be written:
In Fig. 2(a) was plotted the optical transmittance of a 532 nm beam with 3 W/cm2 as a function of an external magnetic field of 0.3 Gauss perpendicular to the surface of the sample (z-axis). The best fitting of the experimental data was accomplished by using Eq. (4), in which the magnetic susceptibility has a second order nonlinearity . Also it can be deduced that an important change in the optical interactions were taking place as a results of an external magnetic field. In Fig. 2(b) is exemplified the optical absorbance that concerns to the optical propagation of the 532 nm beam under the influence of a magnetic field (z-axis). These results were consistent with a constant value close to 0.09 for the reflectance exhibited by the sample and the relation between the transmittance T, reflectance R and absorbance A:
The absorbance curve shown in Fig. 2(b) seems to indicate a modification in the optical resonance exhibited by the sample when it is exposed to an external magnetic field. In order to predict the presence of a magneto-quantum effect in the MWCNTs, a variation in the induced magnetic field in the film was analyzed. The Aharonov-Bohm effect can be described as a magneto-quantum process where the electrons in motion through a magnetic potential modify their speed and trajectory. In a certain way, this effect could change electronic and optical interactions. The mathematical descriptions for these phenomena can be assisted by a tight binding model and effective-mass approximation , where the conductivity, σ, can be written:18]. The Fermi wavenumber influenced by a magnetic field in the axis direction can be denoted by k ± 0 = ((E/γ)2-k2B ± φe)½ in the K and K’ point; respectively. The band parameter γ is function of the C-C bond interaction, γ0, and the lattice constant, a, such as γ = √3/2aγ0. The functions kB ± φe are defined by 2π(Γ + AB/ϕ0 ± φe)/L in which the integer Γ corresponds to the discrete wave vector along the circumference direction, and E is the Fermy energy level defined by:
Figure 2(c) shows numerical and experimental results that correspond to two different orthogonal directions of propagation of the magnetic field through the sample. It is worth to mention that equivalent results can be obtained for experiments where the propagation of the magnetic field goes through the x-direction or y-direction. In the plot the marks represent the experimental data and solid lines correspond to numerical fitting by using Eq. (6). Following previous reports [18,19], the parameters in the fitting for the z-direction of the magnetic field were W = 1.35x10−15 Ω/atom and δ = 0.001; while for the y-direction W = 2.0x10−15 Ω/atom and δ = 0.001. The scattering strength is derived by the chirality of CNTs, which defines their unique electronic properties. This value has not been directly measured in view of distinct facts such as contact resistance issues, together to the difficulty of chirailty identification, and the uncertainty in the number of impurity atoms incorporated to CNTs .
Figure 3(a) illustrates the transmittance of the probe beam measured by the OKG system with the MWCNTs sample; the best fitting obtained corresponds to |χ(3)| = 2 × 10−9 esu. This parameter was in good agreement with comparative samples . It was corroborated by a high-irradiance single-beam transmittance experiment that no change in polarization was observed by the influence of a magnetic field in an interval from 0 to 0.3 Gauss. This result pointed out that in this case the magnetic field does not originate an important induced birefringence in the sample. However, we noticed modifications in the OKG transmittance under the influence of a magnetic field. Then, we systematically studied the transmittance in a two-wave mixing in two different configurations for the alignment of the magnetic field. In Fig. 3(b) is shown a scheme where it is possible to see two particular directions of the magnetic field and the optical beams in our two-wave mixing employed for the OKG configuration. The surface of the thin film sample was located in the XY plane according to the laboratory axes. From Fig. 3(c) can be deduced, a potential magnetically-controlled optical transmittance system assisted by third order optical nonlinearities in MWCNTs. Since the direction of the induced magnetic field has an impact in the nonlinear optical properties of the sample, it can be suggested that a two-wave mixing could be useful for ultrafast identification of vectorial magnetic field propagation in MWCNTs. Nevertheless, it is stated that the magnetic field applied in x-direction or y-direction present indistinguishable results. So, it can be easily engineered the magnetic fields only with parallel or orthogonal incidences in respect to the sample for a clear discernment. The optical anisotropies of MWCNTs obtained by the low magnetic field were observed at less than 10 mT, which seems to be due to the large magnetic polarization of the captured iron nanoparticles in the sample . The variation in the reactance parameters of the sample by magnetic and optical fields, seems to be a good candidate for implementing ultrafast nonlinear optical systems sensitive to magnetic signals.
The vectorial magneto-optic and magneto-conductive response exhibited by MWCNTs was analyzed. Drastic differences in the bandgap fluctuation and in the third order nonlinear optical behavior of the sample were studied taking into account the influence and direction of a magnetic field. The powerful electrical characteristics of the sample under optical and magnetic perturbations present the potential for developing nonlinear magneto-optic and magneto-conductive quantum applications. We emphasized the attractive promises of nonlinear nanostructures sensitive to the vectorial nature of light and magnetic fields.
Instituto Politécnico Nacional (SIP-2016), CONACyT (CB-2015-251201).
The authors kindly acknowledge the facilities of the CNMN del Instituto Politécnico Nacional.
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