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# Large Magnetic Susceptibility Anisotropy of Metallic Carbon Nanotubes 

T. A. Searles, 1 Y. Imanaka, 2 T. Takamasu, 2 H. Ajiki, 3 J. A. Fagan, 4 E. K. Hobbie, 4 and J. Kono 1, ∗ 

$^{1}$Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, USA 

$^{2}$National Institute for Materials Science, 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan 

$^{4}$National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA 

$^{3}$Photon Pioneers Center, Osaka University, Suita 565-0871, Japan 

(Dated: October 29, 2018) 

Through magnetic linear dichroism spectroscopy, the magnetic susceptibility anisotropy of metallic single-walled carbon nanotubes has been extracted and found to be 2-4 times greater than values for semiconducting single-walled carbon nanotubes. This large anisotropy is consistent with our calculations and can be understood in terms of large orbital paramagnetism of electrons in metallic nanotubes arising from the Aharonov-Bohm-phase-induced gap opening in a parallel field. We also compare our values with previous work for semiconducting nanotubes, which confirm a break from the prediction that the magnetic susceptibility anisotropy increases linearly with the diameter. 

Unusual magnetic properties of single-walled carbon nanotubes (SWNTs) have generated much theoretical in- terest during the last two decades [1–8]. The orbital mag- netic susceptibility χ of SWNTs is predicted to be large, two orders of magnitude larger than their spin magnetic susceptibility and comparable in magnitude to the well- known large diamagnetic susceptibility of graphite. In addition, the value of χ is predicted to be strongly de- pendent on the strength of the applied magnetic field, the Fermi energy, and the field orientation. Furthermore, the sign of χ can be either positive (paramagnetic) or nega- tive (diamagnetic), depending on the nanotube chirality as well as the orientation of the magnetic field relative to the nanotube axis. At the core of these properties is the Aharonov-Bohm effect [1, 9], which changes the elec- tronic band structure of the SWNTs via a tube-threading magnetic flux in a truly non-intuitive manner. 

The magnetic susceptibility anisotropy, Δ χ = $^{χ}$‖ − $^{χ}$⊥ , where $^{χ}$‖ ( $^{χ}$⊥ ) is the parallel (perpendicular) susceptibil- ity, of SWNTs has been calculated using different meth- ods [2, 4, 5, 8]. Metallic SWNTs are predicted to be paramagnetic along the tube axis and diamagnetic in the perpendicular direction ( χ M ‖ > 0 > χ M ⊥ ), whereas semi- conducting SWNTs are predicted to be diamagnetic in all directions but most strongly diamagnetic in the perpen- dicular direction ( χ S ⊥ < χ S ‖ < 0) [2, 4, 5]. See, e.g., Fig. 1 for our k · p calculations for (6,6) and (6,5) nanotubes at 300 K. Thus, all SWNTs are expected to have positive Δ χ , while metallic SWNTs are expected to have greater values of Δ χ than semiconducting SWNTs. A finite Δ χ results in the alignment of SWNTs in the magnetic field direction, which, combined with the anisotropic op- tical properties of SWNTs, allows for an estimation of Δ χ values for SWNTs through magneto-optical spec- troscopy. Previous magneto-optical studies found that Δ χ ∼ 1 . 5 × 10 − 5 emu/mol for semiconducting SWNTs with ∼ 1 nm diameters [9–14], while no information on Δ χ is currently available for metallic SWNTs. 

PACS numbers: 78.67.-n, 78.67.Ch 

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Here, we present the first experimental estimation of the Δ χ of metallic SWNTs through high-field magnetic linear dichroism spectroscopy of CoMoCAT nanotubes individually suspended in aqueous solution at room tem- perature. The sample had a much smaller diameter dis- tribution than the HiPco samples used in the previous studies [10, 11], which allowed us to clearly identify, and closely examine the magnetic field dependence of, ab- sorption peaks for metallic nanotubes. We made a de- tailed comparison of the Δ χ of metallic and semiconduct- ing nanotubes with similar diameters and lengths within 

