Nano and Giga Abstract

In presence well known that d- and f-metals are able to carbon nanotubes infill, so the question about investigation of an interaction of d- and f- implants with nanotubes electrons is very interesting.
Our Hamiltonian is based on sd - model [1]:

$\begin{displaymath}H = H_0 + H_{int} \end{displaymath}$

$\begin{displaymath}H_0 = \sum_{k,\sigma} \varepsilon_k a^+_{k \sigma} a_{k \sigm... ...silon}_k b^+_{k \sigma} b_{k \sigma} + \omega_0 \sum_{R} S^Z_R \end{displaymath}$

$\begin{displaymath}H_{int} = \sum_{p p^\prime} J(\vec{q}) \sum_{\sigma \sigma^\p... ...sigma \sigma^\prime} b^+_{p \sigma} b_{p^\prime \sigma^\prime} \end{displaymath}$

where $\vec{S}_q = \sum_R exp(i \vec{q} \vec{R}) \vec{S}_R$ ; $\vec{q} = \vec{p} - \vec{p}\prime$ ; $J(\vec{q})$ - Fourier-images of the spin operator of implant and exchange operator; $\bf\sigma$ - Pauli matrix.
We calculated the indirect interaction by Frohlich method and have obtained following Hamiltonian:

$\begin{displaymath}H_{ss} = \sum_{R_1 R_2} M_1 (R_1, R_2)S^-_{R_1} S^-_{R_2} + h... ... M_1 (R_1, R_2)S^-_{R_1} S^+_{R_2} + h.c. + \sum_R M_2(R)S^Z_R \end{displaymath}$

where , , are a complex combination of Hamiltonian's parameters. Exchanged interaction effective radius is analyzed. Temperature dependencies are considered. The results have shown the possibility of antiferromagnetic ordering in carbon nanotubes.

Above-stated consideration gives a possibility to the serial microscopical construction of doped nanotubes magnetic property theory. Indirect interaction are able to influence on magnetic nanotubes properties and stimulating further research of this new solid body physics branch.

References:
1. M.B. Belonenko, N.G. Lebedev, A.A. Maigurov, Ukrainski fizicheski jurnal, 2000, v. 45, n. 10, p. 1229-1232.