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A low-voltage magnetic nanorelay design

Calculated operating parameters for a novel design of a reed switch (based on cantilevered nanotubes filled with magnetic endofullerenes) show the feasibility of room-temperature operation at 100mV applied voltage.
19 November 2010, SPIE Newsroom. DOI: 10.1117/2.1201010.003091

The remarkable elastic properties and metallic conductivity of carbon nanotubes (CNTs) allow them to be used as parts of nanoelectromechanical systems1–5 and many different electromechanical nanorelays have already been constructed in a wide range of designs. These are based on the crossbar relative position of two carbon nanotubes,6 cantilevered7,8 and suspended9 nanotubes, telescopic extension of nanotubes,10,11 and a magnetic shuttle inside a carbon nanotube.12 These nanorelays are controlled by an electric field and require voltages between one and tens of volts for operation. These relatively high voltages have several disadvantages, including parasitic charging.

In the last few years, researchers have discovered how to obtain a variety of endofullerenes (a fullerene acting as a cage for an atom or cluster of atoms) and ‘nanotube peapods’ (nanotubes filled with fullerenes), including nanotube peapods filled with magnetic endofullerenes,13–16 even in macroscopic amounts.17 The magnetic moments Mef of many fullerenes with encapsulated magnetic atoms are known,13,18 and the largest belongs to the fullerene C80 filled with tri-holmium nitride, known as (Ho3N)@C80. For this endofullerene, Mef is equal to 21 Bohr magnetons (μB). This large magnetic moment and the metallic conductivity of CNTs make it possible to construct a magnetic-field-sensitive element by placing endofullerenes inside a CNT.

We propose a new type of nanorelay based on peapod CNTs with encapsulated magnetic endofullerenes. This allows us to disconnect control and controlled circuits, analogously to known19 macroscopic reed switches. We have calculated the operating parameters of such a novel nanorelay operated with a magnetic field, based on two (Ho3N)@C80@CNT(21,21) nanotube peapods (see Figure 1). The chirality indices (21,21) describe the way in which the nanotube is rolled up and correspond to an armchair metallic CNT. We found that it would operate at much lower voltage (c. 100mV) than existing nanorelays.

Figure 1. The scheme of the reed switch (magnetically operated nanorelay) based on two (21,21) CNTs filled with endofullerenes (Ho3N)@C80 with magnetic moments Mef=21μB. Here 1 is the controlled circuit, 2 is the electrode with the attached peapod nanotube, 3 is the wire passing the current I through it and used for inducing the magnetic field with the induction B, which brings tips of the nanotubes into contact with each other.

The proposed nanorelay has the following operational principles. When a magnetic field is applied, the majority of the magnetic moments of the endofullerenes line up in the direction of the magnetic field (see Figure 1a). As a result, the attraction between the CNTs rises. The condition for the nanorelay switching is determined by the balance of the magnetic and elastostatic forces.20 The amplitude of thermal vibrations of the tips of the CNTs has to be small enough to ensure that the nanorelay will close only when a magnetic field is present. It cannot operate at high temperatures, when the average thermal vibration amplitude is larger than xothxomin, where 2xomin = 2R + Δ R is the distance between the CNTs that corresponds to their contact, R is the nanotube radius, and ΔR=0.34nm is the thickness of nanotube wall, which is taken to be equal to the interlayer distance of graphite. For this condition, one can use an estimate k(xothxomin)22>kBT/2, where 2xoth is the minimal distance between the CNTs limited by thermal vibrations, k is the nanotube bending stiffness, kB is the Boltzmann constant, and T is temperature.

We calculated the operational characteristics of the nanorelay (see Figure 2). We assumed that the magnetic endofullerenes inside the nanotubes form a superparamagnetic phase. Thus, the magnetic moment corresponding to the magnetic saturation is NefMef, where Nef=3L/δef is the number of the endofullerenes in the fully filled (21,21) nanotube. Here δef ≈ (0.8 + 0.34)nm, where 0.8nm is the diameter of endofullerene (Ho3N)@C80, 0.34nm is the distance between the surfaces of adjacent endofullerenes, and Mef=21μB.

Figure 2. (a) Plot of the minimal magnetic field induction Bmin necessary for turning on the nanorelay versus the nanotube length L(left axis) at T=300K. The dependences of half of the minimal (2xoth) and maximal (2xomax) distances between the nanotubes for which the nanorelay operation is possible on the nanotube length L(right axis); xomin=1.594nm. (b) Plot of the induction B necessary for the nanorelay to turn on versus the distance 2xo between the nanotubes for nanotube length L=0.75μm. Arrows indicate the values of xoth, xomax and Bmin shown in (a). (c) A cross-section of the (21,21) nanotube (2Rin≈2.5nm, 2Rex≈3.19nm) filled with (Ho3N)@C80; δef≈1.14nm.

The switching time τ of the nanorelay cannot be considerably less than the period of free bending vibrations of the nanotube. We and others have estimated this for the (21,21) CNT of length L=0.75μm as:20,21

where β0≈1.8751 for the fundamental vibration mode, Rex = RR/2 = 1.594nm is the external radius of the nanotube, Y is Young's modulus, approximately equal to 1.2TPa,22,23 and ρ≈1.93g/cm3 is the density of the nanotube fully filled with (Ho3N)@C80. To turn on the nanorelay by applying the magnetic field with induction Bmin≈30mT (for the nanotube of 0.75μm length, and xoth≈9.1nm, see Figure 2) it is necessary to use current I=150mA passing through wire 3 (see Figure 1), which is positioned at distance d=1μm from the CNTs, for a time interval somewhat larger than τ≈50ns.

Our nanorelay is controlled by a magnetic field and not an electric field, as previous nanorelays were. This has the advantage that we exclude parasitic charging in the nanodevice. Another advantage is that the voltages necessary for the calculated current (150mA) are lower than in previously proposed nanorelays controlled by an electric field (about 100mV rather than between 1 and tens of volts.) Decoupling (isolation) of control and controlled circuits is another well known19 and obvious advantage.

In summary, we propose a reed switch based on cantilevered CNTs filled with magnetic endofullerenes. The nanorelay turns on as a result of bending of the CNTs by a magnetic force. Operational characteristics of the nanorelay based on the (21,21) CNTs fully filled with (Ho3N)@C80 endofullerenes are calculated. It is shown that this nanorelay can operate at room temperature. Realizing the proposed nanorelay requires two separate techniques to be combined: a nanorelay based on cantilevered nanotubes must be fabricated,7,8 and the nanotubes must be filled with magnetic endofullerenes.13–16 We hope that this will be possible within the next few years.

The authors are grateful for the support of the BFBR (Grants F10R-062 and F08VN-003) and RFBR (Grants 08-02-00685 and 10-02-90021-Bel).

Nikolai A. Poklonski, Eugene F. Kislyakov, Sergey A. Vyrko, Oleg N. Bubel', Andrei I. Siahlo
Belarusian State University
Minsk, Belarus

Nikolai A. Poklonski is a professor and the author of more than 170 journal papers. His current research interests include semiconductor physics and electronics, the radiospectroscopy of diamond, and the physics of carbon nanosystems. He received his DSc degree from Belarusian State University in 2001.

Nguyen N. Hieu
Institute of Physics and Electronics
Hanoi, Vietnam
Irina V. Lebedeva
Moscow Institute of Physics and Technology
Moscow, Russia
Andrey A. Knizhnik
Kintech Lab Ltd
Moscow, Russia
Russian Research Center, Kurchatov Institute
Moscow, Russia
Andrey M. Popov, Yurii E. Lozovik
Institute of Spectroscopy
Troitsk, Russia