2 0.8 0.6 0.4 Absorbance (8,3) (7,5) (6,4) (6,5) (6,5) phonon (7,4) (6,6) (5,5) (a) A$_{//}$  @ 35 T A$_{GLYPH<s94>}$  @ 35 T  0 T &  A$_{0}$  Data A$_{0}$  = ( A$_{//}$  + 2 A )/3 0.6 0.5 0.4 LD r 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 Energy (eV) 35 T (b) (6,4) (6,5) (7,4) (6,6) (5,5) A$_{0}$ ≡ $^{A}$‖ + 2 $^{A}$⊥ 3 , (1) together with the fact that only the light-field component parallel to the tube axis is strongly absorbed in SWNTs. Namely, at 35 T there is a finite degree of alignment in the magnetic field direction within the nanotube ensem- ble, resulting in stronger (weaker) absorption for light polarized parallel (perpendicular) to the field. From the theory of linear dichroism for an ensemble of anisotropic molecules [15], the following quantity can be shown to be constant, independent of the degree of alignment: where $^{A}$‖ ( $^{A}$⊥ ) is the absorption for light polarized paral- lel (perpendicular) to the orientation axis, i.e., the mag- netic field direction. We calculated A$_{0}$ at 35 T using Eq. (1) and plotted it in Fig. 2(a) as a red dashed line. The agreement between the calculated A$_{0}$ and the zero- field absorbance spectrum confirms that A$_{0}$ is indepen- dent of alignment (or B ), because at 0 T $^{A}$‖ = $^{A}$⊥ = A$_{0}$ . We further confirmed that at any fields between 0 and 35 T the increase in $^{A}$‖ and decrease in $^{A}$⊥ are such that A$_{0}$ is preserved through Eq. (1). Linear dichroism, LD = $^{A}$‖ − $^{A}$⊥ , is a measure of the degree of alignment. However, since it directly depends on the absorbance, LD alone cannot be used for compar- ing different spectral features. To adjust for differences in relative absorbances due to the fact that our sample is enriched for (6,5), the LD was divided by A$_{0}$ , yield- ing the reduced linear dichroism, LD r = LD/A$_{0}$ [15, 16], which is plotted in Fig. 2(b) for 35 T. It is immediately evident from this plot that the spectral region where metallic peaks [(6,6) and (7,4)] exist has much larger LD r than the region where the most prominent semiconduct- ing peaks [(6,5) and (6,4)] exist. This is evidence that the (6,6) and (7,4) tubes are aligning more strongly than the (6,5) and (6,4) tubes. In order to quantitatively deter- mine the magnetic alignment properties of each chirality present in our sample, we performed detailed spectral analysis, as described below. Each absorption spectrum was fit by a superposition of multiple Lorentzian peaks plus a polynomial offset. The zero-field spectrum was fit first, as shown in Fig. 3(a), with each Lorentzian assigned to a specific chirality. The offset was included to account for the contributions from the π plasmon peaks, bundles, and light scattering [17– 19]. For each magnetic field, the parallel and perpendic- ular spectra were fit simultaneously with the constraint that each Lorentzian independently satisfy Eq. (1). Fig- ure 3(b) shows representative results for the (7,5), (6,5), (6,6), and (5,5) nanotubes at 0 and 35 T. Note that we required the width and position of each Lorentzian to be the same as the values obtained at 0 T, which ensured that the calculated LD r for each chirality is constant as a function of photon energy, as shown in Fig. 3(c) for 35 T. Here, each LD r line is a direct result of calculation from each Lorentzian of different chirality, while LD r in Figure 2(a) shows polarization-dependent optical ab- sorption spectra at 0 and 35 T. None of the spectra are intentionally offset, indicating an increase (decrease) in absorbance for light polarized parallel (perpendicular) to the field. This is a direct result of magnetic alignment, Polarized magneto-optical absorption measurements on length-sorted, (6,5)-enriched CoMoCAT SWNTs were performed using the 35 T hybrid magnet at the National Institute for Materials Science in Tsukuba, Japan. The SWNTs were suspended in 1% sodium deoxycholate and length-sorted by dense liquid ultracentrifugation to have an average length of ∼ 500 nm. A Xe lamp, fiber-coupled to a custom optical probe, allowed for broadband white- light excitation of the E$_{11}$ metallic, E$_{22}$ semiconductor, and E$_{33}$ semiconductor interband transitions of SWNTs. The sample was held in a cuvette with a film polarizer directly on the front face to ensure that the incident light was linearly polarized. The transmitted light was collimated by a lens, collected with another fiber, and dispersed through a monochromator equipped with a Si CCD. All measurements were done at ∼ 300 K. the same sample and found that the values of Δ χ are 2-4 times greater in metallic tubes. We also compared our values with previous work for semiconducting nan- otubes [13], which confirm a break from the prediction that Δ χ should increase linearly with the tube diameter. FIG. 2: (a) Absorption spectra (solid black) for 0 T and 35 T with all peaks assigned to specific chiralities. No trace is intentionally offset, indicating greater (smaller) absorption for parallel (perpendicular) polarization. The unpolarized isotropic absorbance (dashed red), calculated from the 35 T spectra via Eq. (1), agrees well with the 0 T data. (b) Re- duced linear dichroism versus energy from measured data. The largest peak is from metallic nanotubes (6,6) and (7,4).