Oscillatory Tunnel Magnetoresistance in a Carbon Nanotube Based

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C: Physical Processes in Nanomaterials and Nanostructures

Oscillatory Tunnel Magnetoresistance in a Carbon Nanotube Based Three-Terminal Magnetic Tunnel Junction Meghnath Jaishi, and Ranjit Pati J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10458 • Publication Date (Web): 20 Nov 2018 Downloaded from http://pubs.acs.org on December 5, 2018

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The Journal of Physical Chemistry

Oscillatory Tunnel Magnetoresistance in a Carbon Nanotube Based ThreeTerminal Magnetic Tunnel Junction

Meghnath Jaishi and Ranjit Pati* Department of Physics and Henes Center for Quantum Phenomena, Michigan Technological University, Houghton, MI 49931

ABSTRACT Electrostatic control of tunnel magnetoresistance (TMR) in a carbon nanotube (CNT) based threeterminal magnetic tunnel junction (MTJ) is critical to the development of next generation nanospintronics. Using a quantum transport approach that explicitly considers the electronic structure of the junction including the exchange-interaction effects due to spin-alignments at the ferromagnetic electrodes, we have unraveled the origin behind the gate bias dependent modulation of the TMR in a single wall CNT based MTJ. Akin to the experimental observation, our calculation yields an oscillatory behavior in TMR with a strong variation in the amplitude and width of the magnetoresistance signal with gate bias. We attribute the gate-bias-driven non-linear change in the strength of spin-dependent-hybridization at the nanotube/contact interface as the main cause for the observed oscillatory feature in TMR.

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I. INTRODUCTION Tunneling magnetoresistance (MR)1-3 is a quantum phenomenon that involves a sizable change in resistance between the parallel and antiparallel spin configuration at the contacts in a magnetic tunnel junction (MTJ). This magneto-resistive effect, which serves as the basis behind modern high-density data storage technology, is intimately related to the spin-scattering length of the nonmetallic spacer that connects the ferromagnetic electrodes in an MTJ. The weak spin-orbit coupling and hyperfine interaction in carbon nanotube (CNT)4-7 as well as the observation of long spin-flip scattering lengths of at least 130 nm in multi-wall CNT4 and 1 m in single-wall (SW) CNTs8 have prompted researchers to use these low dimensional materials as the spacer in nextgeneration MTJs. Despite the challenges in fabricating reliable magnetic contacts with CNTs, several groups have been successful in demonstrating magneto-resistive effect in carbon nanotube based MTJs4,

9-26.

Measurements in two-terminal junctions reveal a considerable variation in

magnetoresistance4, 9-12, 20, 23, which could be ascribed to lack of chirality control in CNTs and difficulty in fabricating reproducible junctions. In the case of a three-terminal CNT-based MTJ, Sahoo et al,13 first observed an electric field modulation of MR; an oscillation with a strong variation in the amplitude and width of the MR signal with gate bias was reported13. A similar oscillatory feature in MR with gate bias was observed later by Man et al.16 in a carbon nanotube junction with transparent contacts. Despite these intriguing and robust experimental observations in three-terminal (3T) junctions13, 16, only a handful of theoretical efforts is made thus far to understand these results. In a pioneering work, Cottet and co-workers used the Anderson model to investigate the magnetoresistance in a CNT quantum dot coupled to ferromagnetic electrode 27-28. A one-orbital channel was used to model the CNT quantum dot and a parameterized approach was adopted to 2 ACS Paragon Plus Environment

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include the effective exchange interaction with the ferromagnetic contacts; gate bias effect was incorporated through a shift in chemical potential. Based on these studies, they concluded that the spin dependence of interfacial phase shift at the channel/lead boundary

27-28

is responsible for

splitting of eigen-channel into spin components, which is tunable by applied gate bias to yield oscillatory MR signal. A similar resonant tunneling behavior was suggested by Koller et al based on a reduced density matrix approach 29 to understand the single electron behavior in a CNT based spin-valve transistor coupled to a FM lead with arbitrary magnetization (in a low transparency regime); however, sign reversal of TMR was not reported. Though these investigations provided important insights into the magnetoresistance behavior in a weakly coupled 3T CNT junction, it does not confirm whether the observed aperiodic oscillation and sign reversal of TMR upon applied gate bias is universal to CNT irrespective of their junction transparency. Thus, it raises an important question. Are the oscillatory and sign reversal features in TMR observable in a transparent junction? An unswerving electronic structure level answer to these subtle questions requires a first-principles approach that does not make any assumption and explicitly considers the electronic structure of the CNT/lead interface, spin alignments at the contacts (parallel vs. antiparallel), magnetic proximity as well as electric field effects (both first and higher order). In this article, we present our quantum transport results that elucidate an oscillatory TMR feature with gate bias in a carbon nanotube based magnetic tunnel junction device. A single particle many-body Green’s function approach30-31 together with an explicit orbital-dependent, spin unrestricted density functional theory (DFT) is adopted to model a prototypical CNT-based MTJ device. We have used a semiconductor (8, 0) single wall CNT as the spacer between ferromagnetic Ni electrodes to build an MTJ. The choice of semiconducting CNT as a spacer in our model was prompted by the absence of gate-tunability in metallic CNT. Irrespective of applied bias, our 3 ACS Paragon Plus Environment


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calculations yield a strong variation in the amplitude and width of the MR signal with the gate bias as observed in the experiment. The origin of such an aperiodic behavior in TMR is attributed to the gate bias induced modification (nonlinear change) of the strength of spin-dependenthybridization at the CNT/Ni interface. The oppositely aligned dipole moments and the distinct spin-dependent polarizability are found to be responsible for the distinctive nonlinear response to gate bias from the parallel and anti-parallel spin configuration of the CNT-based MTJ. The rest of the article is organized as follows. We briefly describe our computational procedure in Section II. Results and Discussion are presented in Section III followed by a brief conclusion in section IV.

Figure 1. The prototypical CNT based three-terminal magnetic tunnel junction; PC and APC refer to the parallel and anti-parallel spin configuration.

II. COMPUTATIONAL METHODS The prototypical three-terminal MTJ used to calculate the TMR is shown in Fig. 1. To model the open junction, we have divided the MTJ into two regions. The first part is the active scattering


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region (AR), which is comprised of a fragment of the (8,0) semiconductor SWCNT contacted with a finite number of nickel atoms from the ferromagnetic nickel electrodes. The second part is the semi-infinite electrode (SE) part, which is assumed to be unperturbed and retain its bulk properties when the CNT is attached to the electrode. The AR is connected to the SE through the biasdependent spin-polarized self-energy functions30. The atomic structure for the CNT spacer used to build the MTJ is taken from the fully optimized geometry of (8,0) SWCNT (see Supporting Information), which is obtained using a periodic DFT32-33; the residual force on each atom is ≤ 0.01 eV/Å. To mimic the transparent contact in the experiment at the CNT/lead interface, the open end of the finite-CNT spacer was chemically bonded to Ni atoms of the lead; the perpendicular distance between the open end of the CNT and Ni lead is 0.73 Å, which is obtained by minimizing the repulsive interaction at the interface in the active scattering part. The channel length from source-electrode to drain-electrode is 17.12 Å. A real space spin-unrestricted orbital-dependent DFT technique that relies on an all-electron Gaussian basis function (6-311G*)34 is used to construct the retarded spin-dependent Green’s function (Gσ)35-36 of the MTJ. A posteriori hybrid DFT method (B3LYP)34,

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is used to include the exchange and correlation effects. The self-

consistently calculated Hamiltonian matrix (at each bias point) for the majority (or minority) spincomponent of dimension 2580×2580 is used to construct the Gσ. During the self-consistent calculation, a superfine grid is used for numerical integration and the convergence thresholds for the total energy, the root mean square and maximum density are set at 10-6,10-8, and 10-6 a.u., respectively. The gate field effect is incorporated through the inclusion of a dipole interaction term into the core-Hamiltonian during the self-consistent electronic structure calculation38, which allows us to include both linear and nonlinear electric field effects. A spin conserved tunneling approach formulated in Ref. 30 is used to calculate the spin-dependent current in the MTJ; the



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spin-orbit interaction effect is not included It is important to note that experimental measurements reveal the spin-orbit (SO) splitting in a CNT junction to be of the order of few meV39. This splitting may play an important role in a weakly coupled CNT junction. However, in a strongly coupled junction, which is considered here, we do not expect this small SO splitting to have any measurable effect on the spin-dependent current.

Figure 2. Tunnel magnetoresistance (TMR) in an (8, 0) SWCNT-Ni junction is plotted as a function of gate bias (Vg) for the fixed source-drain bias of (a) ~0.80 V and (b) ~1.55 V. III. RESULTS AND DISCUSSION A. Tunnel Magnetoresistance Fig. 2. shows the tunnel magnetoresistance (TMR) calculated for two different source-drain bias in a semiconductor single wall carbon nanotube (SWCNT) channel contacted with ferromagnetic Ni electrodes. The TMR is obtained using the expression ((IPC-IAPC)/IAPC) × 100 %)31; IPC refers to the current in the MTJ when the spin alignments between the ferromagnetic contacts are in a 6 ACS Paragon Plus Environment

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parallel configuration and IAPC is the current when the spin alignments are in an antiparallel configuration. Irrespective of different applied source-drain bias, we found oscillations and sign reversals of the TMR in a CNT junction with the increase of applied gate bias. It is important to note that a similar TMR behavior in ferromagnetically contacted single and multiwall carbon nanotube junctions have been reported experimentally13. To explain these intriguing TMR features, we examined a representative case with VDS ~ 0.80 V (Fig. 2a). The calculated TMR in the absence of gate bias (Vg) is found to be 22.32 %, which is in agreement with the reported magnetoresistance of 20% in a two-terminal CNT based spin-valve junction of similar dimension40. Upon increasing the gate bias from 0.0 V to 0.39 V, a rapid drop in TMR is noticed; a subsequent increase of Vg to 0.81 V results in an increase of TMR to 17.82 %. Thereafter, we found a steady drop in TMR value until it becomes 9.89 % following which it surges again to 10.78 % at Vg=1.56 V. This oscillatory TMR behavior persists as we go up to a higher gate bias; the sign reversal of TMR is seen at a higher gate bias. To ascertain the general nature of this observed non-linear TMR feature, we calculated TMR at a higher source-drain bias of ~1.55 V (Fig. 2b). Here, in the absence of gate bias, we found a negative TMR of -2.58 %, which is found to drop rapidly until it becomes -21.81 % at the Vg=0.39 V following which it increases to a positive value of 11.65 % at Vg=1.19 V; this value rapidly drops again upon increasing the gate bias. This confirms that the gate-bias-driven oscillatory and sign reversal behavior of TMR in CNT junctions observed here is independent of applied source-drain bias. Though we noticed a significant increase in amplitude along with multiple sign reversals in TMR in our calculations for the higher source-drain bias (Fig. 2b), the oscillations in both cases (VDS~0.80 V (Fig. 2a) and VDS ~1.55 V (Fig. 2b)) are found to be aperiodic in nature. This result is fully consistent with the aperiodic behavior of TMR observed in the experiment13. Though quantitative comparisons cannot



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be made between our results and the experiment13 because of different length scales, chirality conditions as well as the lack of atomic-level structural information of the CNT/lead interface in the fabricated device, reproducing the oscillatory feature with the TMR value of the same order as that of the experiment provides confidence on the robustness of our approach. B. Spin-Dependent Current-Voltage Characteristics To analyze the oscillations and sign reversals in TMR observed for the CNT junction, we have plotted the drain current (IDS) as a function of gate bias (Vg) for both the representative configurations shown in Fig. 2. The current-voltage characteristics for the PC and APC are summarized in Fig. 3. Regardless of applied source-drain bias, IDS vs. Vg plots (Fig 3a & b) show a nonlinear behavior. Examining the results from Fig. 3a, we found a higher current in PC (12.77 μA) than that of APC (10.44 μA) at Vg=0.00 V; this explains the positive value of TMR at zero applied gate bias (Fig. 2a). When we increase the gate bias to Vg=0.39 V, the current in the APC rapidly rises to 11.47 μA while a small drop in PC current to 12.45 μA is noticed; this results in a decrease in the difference between PC and APC current and hence a smaller TMR value is noted at Vg=0.39 V (Fig. 2a). A subsequent increase in gate bias to Vg=1.19 V results in a rapid decrease of current in APC and a gradual drop in current for PC leading to a higher TMR value. Following, an approximate in-phase behavior in PC and APC current is observed as we increase the gate bias to 2.65 V and 2.86 V respectively following which a crossover occurs at Vg= ~2.91V between the currents in PC and APC; this results in a negative TMR as shown in Fig. 2a. In the case of the higher source-drain bias (Fig. 3b), crossover between PC and APC currents are noted at several gate bias points resulting in multiple sign reversals and oscillatory behavior in TMR (Fig. 2b).


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Figure 3. Current-voltage characteristics in a semiconductor SWCNT channel contacted with Ni electrodes. Drain current (IDS) is plotted as a function of gate bias (Vg) for the fixed source-drain bias of (a) ~0.80 V and (b) ~1.55 V; PC and APC refer to parallel and antiparallel spin alignments between the electrodes.

C. Spin-Resolved Current Since the TMR effect is a spin-dependent phenomenon where both the majority and minority spin carriers have their contributions in PC as well as APC current, a detailed analysis of the role played by these carriers would help to gain a deeper understanding of the observed TMR and spin injection behavior in CNT junction. The contributions from the majority and minority carriers to drain current as a function of gate bias are depicted in Fig. 4. For the applied bias of ~0.80 V (Fig. 4a), minority spin states’ (Down) contribution is found to be appreciably larger than that of the majority states (Up) for parallel spin configuration between the contacts; the magnitude of spin injection factor, =(Up-Down)/(Up+Down), is found to be -0.22 at zero gate bias. While in the case of 9 ACS Paragon Plus Environment


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APC, the Up states’ contribution is higher than that of the Down states resulting in a  value of 0.20 at Vg=0 V. When we increase the source-drain bias from ~0.80 V to ~1.55 V, majority and minority spin states exchange their roles in PC; Up states’ contribution to current is found to be higher than that of the Down states (Fig. 4b). In the APC configuration, Up states’ contribution remains higher than that of the Down states’ over all the gate bias range considered here. In both PC and APC, majority and minority currents are found to be in phase (Fig. 4b). The  values in PC and APC decreased to 0.01 and 0.08 respectively upon increasing the applied source-drain bias from ~0.8 V to ~1.55 V at zero gate bias. This result is consistent with the general observation that the spin injection efficiency in CNT junction diminishes upon increasing bias voltage11, 16. The observed values of  in CNT/Ni junction are found to be much smaller than that in a boron nitride nanotube-nickel junction41, which suggests that an appropriate tunnel barrier (a thin Al2O3 or MgO layer)42-44 at the CNT/Ni junction is necessary to boost the spin injection efficiency and TMR. A high TMR value varying from -80% to 120% has been observed11, 15, 24, 26 in weakly coupled two terminal carbon nanotube based magnetic tunnel junctions.


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Figure 4. Spin-resolved current-voltage characteristics. Drain current (IDS) contribution is plotted as a function of gate bias for the fixed source-drain bias of (a) ~0.80 V and (b) ~1.55 V; Up and Down represent the respective drain current contributions from the spin up and spin down electrons.



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Figure 5. Spin-dependent transmission in a semiconductor SWCNT channel contacted with Ni electrodes. Transmission function is plotted at different gate bias for the fixed source-drain bias of ~0.80 V; (a) and (b) represent the majority (Up) and minority (Down) states’ contribution to transmission in PC and APC, respectively.

D. Multi-Channel Transmission To understand the origin of the observed asymmetry between the majority and minority spin states’ currents in PC (Fig. 4a) as well as APC (Fig. 4b), we analyzed multi-channel transmission function30, which is defined as the sum of transmission coefficients over all the eigen-channels; its integration within the chemical potential window gives us the drain current. For brevity, we have plotted the transmission function as a function of injection energy for VDS ~ 0.80 V at three different gate bias points; Fig. 5 shows the transmission plots within [-0.5 eV, 0.5 eV] energy window for the majority and minority carriers in PC and APC. In the case of PC (Fig. 5a), Downstates’ contribution to transmission is significantly higher than the Up-states in the vicinity of Fermi energy. This explains the higher observed spin-Down current in PC (Fig. 4a). When we 12 ACS Paragon Plus Environment

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increase the gate bias, the value of the transmission coefficient decreases in a non-linear way resulting in a non-monotonic decrease in Down-state current. However, in the case of APC (Fig. 5b), Up states’ contribution is higher than that of the Down states resulting in a higher Up-state current; upon increasing gate bias, Up states' contribution to transmission increases leading to an increase in the Up-state current. Comparing the transmission coefficients within the energy window [-0.5 eV, 0.5 eV] in PC and APC, we found a higher total transmission in PC than APC at Vg=0.0 V, which confirms the observed positive sign of TMR. In contrast, the total transmission within the same energy window is higher in APC than PC at a gate bias of Vg ~3 V resulting in a negative sign in TMR. The observed broadening in transmission in both cases is due to the metalinduced broadening caused by strong chemical bonding at the channel-lead interface between the Ni atoms of the lead and the C-atoms of the nanotube channel. Analysis of frontier spin orbitals in the active scattering part of the junction indicates a strong hybridization between the d as well as s states of Ni and the p as well as s sates of C at the interface. Upon a closer examination of the orbital coefficients, it is revealed that different Ni atoms at the interface contribute to spindependent hybridization at different gate bias (see Fig. 6); some Ni atoms are strongly coupled to the interfacial C-atoms than the others (Fig. 6).



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Figure 6. A schematic for the gate bias dependent nonlinear interfacial coupling change between the Ni and C atoms at the CNT-Ni interface of the MTJ; VG1, VG2, and VG3 are the three different gate bias points. The thickness of the lines joining the Ni and C atoms indicates the strength of the spin-dependent hybridization; thicker is the line – stronger is the strength of the hybridization.

Coupling change at the interface does not behave linearly with applied gate bias due to the strong non-linear Stark effect as evident from the calculated polarizability data (Table 1). The unique electron density with distinct dipole moment (oppositely aligned) and polarizability in PC and APC along the applied gate field direction (Y-axis) is responsible for the strong non-linear response to the gate bias, which leads to an aperiodic oscillatory behavior of TMR in CNT-Ni magnetic junction. We should note that even though the CNT spacer length considered in this study is much smaller than that used in experimental measurements, we expect the oscillatory and sign reversal feature of TMR with gate bias observed in this study to persist for longer channel length as the spin-dependent hybridization strength at the interface would not alter with the increase of spacer length.


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Table 1. Components of dipole moments (α) and polarizability (β) in a CNT-Ni magnetic tunnel junction. CNT Dipole moment (a.u.) tunnel αx αy αz junction PC 1.61 -0.05 0.09 APC

-0.43

0.04

-0.86

βxx

βyx

1046.00

-158.52

-618.24

-688.11

Polarizability (a.u) βyy βzx

βzy

βzz

1284.20 9.61

5.58

2932.18

935.61

156.96

2835.90

414.13

IV. CONCLUSIONS We have investigated the electrostatic control of spin injection and tunnel magnetoresistance in a three-terminal SWCNT based magnetic tunnel junction device. Our quantum transport calculation yields an aperiodic oscillation in TMR with gate bias as observed in the experiment. The nonlinear change in the strength of the spin-dependent hybridization at the CNT-Ni interface upon the application of gate bias is found to be responsible for the oscillatory TMR behavior. We expect a much better electric field control of the TMR in the CNT based MTJs can be achieved by engineering a suitable tunnel interface at the CNT- ferromagnetic contact. ASSOCIATED CONTENT Supporting Information Atomic coordinates of the CNT channel. This material is available free of charge via the Internet at http://pubs.acs.org AUTHOR INFORMATION Corresponding Author *E-mail:

[email protected] 15 ACS Paragon Plus Environment


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Notes There are no conflicts to declare. ACKNOWLEDGEMENTS This work is partially supported by the Henes Center for Quantum Phenomena. The computations performed in this work are carried out using the Superior, the high-performance computing clusters at the Michigan Technological University. REFERENCES 1.

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TOC Figure: Gate bias driven oscillatory tunnel magnetoresistance in a carbon nanotube based three terminal magnetic tunnel junction.


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TOC Caption: Gate bias driven oscillatory tunnel magnetoresistance in a carbon nanotube-based threeterminal magnetic tunnel junction. 189x76mm (150 x 150 DPI)

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Oscillatory Tunnel Magnetoresistance in a Carbon Nanotube Based

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