4 TABLE I: Comparison of calculated and measured values of magnetic susceptibility anisotropy for seven types of SWNTs. For each chirality ( n , m ), the diameter d , the chiral index ν = mod 3 ( n − m ), and the chiral angle α are given, followed by theoretical (30 K and 300 K) and experimental (300 K) values of Δ χ . All values for Δ χ are × 10 − 5 emu/mol. ( n, m ) d (nm) ν α ( $^{◦}$) Δ χ 30K th Δ χ 300K th Δ χ 300K exp (6,6) 0.83 0 30 5.78 3.92 3.63 (5,5) 0.69 0 30 4.95 3.39 3.35 (7,4) 0.77 0 21 5.42 3.70 2.44 (8,3) 0.78 -1 15 1.49 1.46 2.13 (7,5) 0.83 -1 24 1.58 1.55 1.66 (6,5) 0.76 1 27 1.45 1.42 1.01 (6,4) 0.69 -1 23 1.33 1.29 1.24 and confirmed that they are much larger than those of semiconducting nanotubes. We also calculated the mag- netic field and temperature dependence of magnetic sus- ceptibilities of the SWNTs studied experimentally, which support the experimental findings. Lastly, we were able to confirm previous experimental results for the chiral- ity dependence of the magnetic susceptibility anisotropy in semiconducting nanotubes and found that this is also true for metallic nanotubes. This work was supported by DOE-BES (through Grant No. DEFG02-06ER46308), NSF (through Grant No. OISE-0530220), and the Robert A. Welch Founda- tion (through Grant No. C-1509). We thank Noe Alvarez for help with AFM length measurements and Ajit Srivas- tava for assistance with data analysis. Official contribu- tion of the National Institute of Standards and Technol- ogy; not subject to copyright in the United States. using this procedure, since the values of Δ χ are expected to depend on B and T , especially for metallic nanotubes. Thus, we calculated Δ χ as a function of B and T for all the seven SWNTs studied in this work. Figure 4(d) shows the B dependence of $^{χ}$‖ for the (6,6) nanotube for 30 K and 300 K. Although $^{χ}$‖ decreases by ∼ 27% at 30 K as the field increases from 0 T to 40 T, it stays constant within ∼ 0.7% at 300 K in the same field range, ensuring that the magnetic field dependence can be neglected for our room temperature measurements. Theoretical and experimental values of Δ χ obtained in the present work are summarized in Table I. The val- ues for the three metallic nanotubes, (7,4), (5,5), and (6,6), are all higher than those for the semiconducting nanotubes. In particular, the Δ χ of armchair, or ( n , n ), carbon nanotubes are 2-4 times larger than those in semi- conducting nanotubes, depending on the diameter. This large difference in magnetic susceptibility anisotropy is a direct consequence of the Aharonov-Bohm physics caus- ing the band structure to change in the form of bandgap opening in metallic nanotubes and bandgap shrinking for semiconducting nanotubes. 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