# Effect of Twisting and Stretching on Magneto Resistance and Spin Filtration in CNTs

^{*}

## Abstract

**:**

## 1. Introduction

_{2}is essentially the only material that has been experimentally shown to definitively be a half-metal [4]. Magnetic tunnel junctions were experimentally fabricated using thin films of the half-metallic ferromagnet CrO

_{2}, employing SnO

_{2}tunnel barriers in [5].

## 2. Simulation Method and Setup

_{2}HMF electrodes. Figure 3 shows comparison among all the three structures.

_{2}electrodes. The mesh cutoff and electron temperature are assumed to be 150 Ry and 1800 K, respectively. The k point sampling in x, y, and z directions are assumed to be 3, 3, 100, respectively, as in [13]. In the simulations, magnetization of the electrodes can be simply changed to either up or down by assuming 1 or −1 spin polarization values. We have done simulation-based studies by assuming parallel magnetization and antiparallel magnetization of the electrodes. The relative spin in a parallel configuration of both electrodes and carbon atoms of twisted or stretched CNT are assumed to be 1, 0, 1. Whereas, in an antiparallel configuration, the right electrode atom spin is assumed to be −1, so the spin sequence will be 1, 0, −1. The direction of spin polarization—parallel or antiparallel—is in relation to the electron’s velocity.

_{B}) represents the Transmission coefficient, E as Energy, F as Fermi-Dirac distribution function, μ

_{R}and μ

_{L}are the chemical potential for right and left electrodes.

## 3. Results and Discussion

_{0}, 0.59G

_{0}and 0.58G

_{0}, respectively, where G

_{0}represents conductance quanta, G

_{0}= 2e

^{2}/h [1].

_{0}, 2.64G

_{0}and 7.0G

_{0,}respectively.

_{PC}− I

_{APC})/I

_{PC}[25], where I

_{PC}and I

_{APC}are the total currents in parallel configuration and antiparallel configuration. From the current-voltage curve, it can be seen that at zero volts, total current in all three structures is zero, and MR is calculated by utilizing equilibrium conductance. The MR obtained at zero bias is ~100%. At low bias, I

_{APC}is negligible for all three structures; however, at high bias voltages, I

_{APC}marginally increases in the case of pristine and twisted CNTs, and is greater in pristine CNT (see Figure 5). For stretched CNT, I

_{APC}remains negligible even at high bias voltages. This results in higher MR in stretched CNT than in twisted and pristine CNTs (see Figure 8). The physical phenomenon behind the higher MR in stretched and twisted CNTs can be directly associated with the number of electronic states available near Fermi level.

_{APC}(see Figure 5).

## 4. Conclusions

## Author Contributions

## Conflicts of Interest

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**Figure 4.**Comparison of current-voltage curves in PC for all three structures. The total spin current of twisted CNT is greater than that of stretched CNT, and the total spin current of stretched CNT is greater than that of pristine CNT.

**Figure 5.**Comparison of I-V curves in APC for all three structures. The total spin current for all three structures is zero for low biases, but for higher biases, spin-down current remains zero, and spin-up current of pristine CNT is greater than that of twisted CNT and the spin-up current of stretched CNT is greater than that of pristine CNT.

**Figure 6.**Transmission spectrum T (E, V

_{b}) with respect to energy ranging from −0.3 eV to +0.3 eV for different applied voltages for PC. At zero volts, the comparative transmission probability for all three structures, shown separately for spin-up (

**a**) and spin-down (

**b**).

**Figure 7.**Transmission spectrum T (E, V

_{b}) with respect to energy ranging from −0.3 eV to +0.3 eV for different applied voltages for APC. At zero volts, the comparative transmission probability for all three structures, shown separately for spin-up (

**a**) and spin-down (

**b**).

**Figure 8.**Comparative plots for magneto resistance with respect to applied voltages. For high bias voltage, MR of stretched CNT is higher than that of twisted CNT, and MR of twisted CNT is higher than that of pristine CNT.

**Figure 9.**Spin injection factor with respect to applied voltages for all three structures in parallel configuration and antiparallel configuration.

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**MDPI and ACS Style**

Singh, A.K.; Choudhary, S.
Effect of Twisting and Stretching on Magneto Resistance and Spin Filtration in CNTs. *Magnetochemistry* **2017**, *3*, 27.
https://doi.org/10.3390/magnetochemistry3030027

**AMA Style**

Singh AK, Choudhary S.
Effect of Twisting and Stretching on Magneto Resistance and Spin Filtration in CNTs. *Magnetochemistry*. 2017; 3(3):27.
https://doi.org/10.3390/magnetochemistry3030027

**Chicago/Turabian Style**

Singh, Anil Kumar, and Sudhanshu Choudhary.
2017. "Effect of Twisting and Stretching on Magneto Resistance and Spin Filtration in CNTs" *Magnetochemistry* 3, no. 3: 27.
https://doi.org/10.3390/magnetochemistry3030027