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C: Physical Processes in Nanomaterials and Nanostructures

Manipulation of Giant Field-Like Spin Torque in Amine-Ended Single-Molecule Magnetic Junction Yu-Hui Tang, and Bao-Huei Huang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03772 • Publication Date (Web): 14 Aug 2018 Downloaded from http://pubs.acs.org on August 19, 2018

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The Journal of Physical Chemistry

Manipulation of Giant Field-Like Spin Torque in Amine-Ended Single-Molecule Magnetic Junction Y. -H. Tang∗ and B. -H. Huang Department of Physics, National Central University, Jung-Li 32001, Taiwan E-mail: [email protected]

Abstract We propose a comprehensive theoretical investigation for the angular, external bias, and mechanical strain dependence of giant field-like spin torque (FLST) effect for amine-ended Co/BDA/Co single-molecule magnetic junction in noncollinear magnetic configuration, by employing our newly developed non-equilibrium Green’s function method within the framework of density functional theory. In sharp contrast to the conventional Co/vacuum/Co magnetic tunnel junction, the hard-hard coupling between amine-linker and Co tip-atom plays an active role in interfacial spin filter to emerge the strong interlayer exchange coupling between two Co electrodes and the anomalous strain-enhanced FLST effect. These intriguing features may pave a novel way to engineer the magnetization switching either via external bias or mechanical strain to achieve the writing process in next-generation multifunctional organic FLST-MRAMs with lower power consumption.

Introduction Spintronics has emerged with the leading technology in the information process, data storage and magnetic sensor. Many of these new technologies rely on the magnetoresistance (MR) 1–3 and ∗ To

whom correspondence should be addressed

1

ACS Paragon Plus Environment

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spin torque effects. 4–7 There are two components of noncollinear spin torque effect, i.e. the spintransfer torque (STT, Tk ) and the field-like spin-torque (FLST, T⊥ ) components resulting from the interplays of spin current densities 8,9 and interlayer exchange couplings, 10 respectively, between parallel and antiparallel magnetic configurations. In the insulator (I)- and semiconductor-based magnetic tunnel junctions (MTJs), i.e. the MgO-based MTJ, the fact that Tk outweighs T⊥ renders the remarkable progress of STT writing technology in the so-called STT-MRAM, where the readout operation is reliably performed via the TMR effect. Although the STT-MRAMs provide the historical advantage of magnetic based memories, such as high speed and high density in a nonvolatile technology, a large current density typically required for STT switching becomes a primary source of power consumption. To achieve low-energy consumption in next-generation spintronics devices, much attention has shifted to the spin filter effect in ferromagnetic insulator europium chalcogenides, 11–13 GdN, 14,15 Sm1−x Srx MnO3 (0.1≤x≤0.3) 16,17 and organic metal phthalocyanine (MPc). 18–20 Recently, Tang et al. have employed the single-band tight-binding model to predict the dual control of giant FLST effect in FM/I/SF/I/FM MTJs, 21 where FM and SF denote the ferromagnetic electrode and spinfilter material, respectively. The underlying mechanism of SF-induced giant FLST effect can be understood by the strong interlayer exchange coupling (IEC) effect via the spin-polarized multireflection processes between noncollinear SF barrier and FM electrode, 22 resulting from the discriminative tunneling probabilities for spin-up and spin-down electrons through the central SF barrier. This agrees with previous theoretical works 23–25 to describe the IEC of FM/paramagnetic (PM) spacer/FM junction in terms of the quantum interferences due to the spin-dependent reflections at the FM/PM spinterfaces, which have been widely employed to explain the oscillatory coupling in magnetic multilayers and spin valves. 26,27 The spin-filter effect can be further adopted in the amine-ended Co/BDA/Co single-molecule magnetic junction (SMMJ) as shown in Fig. 1. Because the strong hard-hard coupling between amine-linker and Co tip-atom provides highly spin-polarized transmission channels near the Fermi energy via the hybridization between Co-d and N-Py orbitals, the amine-linker plays a significant

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role in the interfacial spin filter (ISF) layer and hence dominates the spin transport properties between Co NWs (FM) and central molecule (I). Except the anomalous bias-induced enhancement of MR value 28 and the strain-enhanced spin injection, 29 the ISF-induced spin-dependent reflections at the Co/N contacts may enhance the IEC and hence strength the FLST effect, which still remains unexplored thus far. For organic magnetic junctions, although the MR effect has been investigated extensively, 30–35 the noncollinear spin torque effect remains less studied by the first-principles calculation, due to the difficulties in self-consistent process of noncollinear magnetic configurations. In this study, our newly developed non-equilibrium Green’s function method within the framework of density functional theory is employed to investigate the noncollinear FLST and STT spin torque components for Co/BDA/Co SMMJ under an external bias and a mechanical strain. It is striking to discover that FLSTSTT, resulting from the significant role of amine-linker as an ISF layer to efficiently strengthen the IEC between two Co NWs. Moreover, the giant magnitude of FLST can be well preserved either under an external bias or via a stretching process. These intriguing features may expand the possibility to engineer the IEC from well-studied solid magnetoresistance devices 36–40 into organic spintronics devices with hard-hard coupling between amine-linker and ferromagnetic electrodes.

Computational Details A prototypical single-molecule magnetic junction, where a 1,4-Benzenediamine (BDA) with dissociated amine-linker is sandwiched between two semi-infinite hcp[0001] orientated Co tip-like nanowires (NWs), is presented in Fig. 1. The magnetization of left Co NW and N-linker, i.e. ML and MISF,L , are along the z direction, while those of right Co NW and N-linker, i.e. MR and MISF,R , are rotated by an angle θ around the z axis with respect to ML to form the noncollinear magnetic configuration. The calculated magnetic moments of Co, N, and C ions are about 1.62.1µB , 0.04-0.07µB , and 0.0-0.02µB , respectively. The strong hard-hard coupling between amine-

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Device Region

Left Electrode

Right Electrode H

… Co

C

N

Co

C

N FM (Co)

x

y

ML

z

ISF (N-linker)

…

N

N I

x

ISF (N-linker)

MISF,L

MISF,R

y

Qxz

MR

T⊥

θ

Qyz

T∥

FM (Co) Qzz

z

Figure 1: Junction geometry of the dissociated amine-ended Co/BDA/Co SMMJ at equilibrium (strain=0.0%) with θ =π/3 is expressed in an two-probe device. The central device region, including parts of left and right Co NWs and the cental BDA molecule, is sandwiched between two semiinfinite Co NWs. The red arrow represents the magnetic moment of each atom, and the calculated magnetic moment of Co ion is about two order larger than those of N and C ions. The net fieldlike, T⊥ , and spin-transfer, Tk , components of spin torque acting on the right Co NW are along ˆ L ×M ˆ R and M ˆ R × (M ˆ L ×M ˆ R ) directions, respectively. M

4


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linker and Co tip-atom can be treated as the interfacial spin filter (ISF) layer to mediate the spin transport between Co NWs (FM) and central molecule (I). The geometry of Co/BDA/Co SMMJ in parallel magnetic configuration (θ =0) under the stretching process is calculated the Quantum ESPRESSO package 41 based on the density functional theory (DFT) with the GGA-PBE form. Note that the bond angles 6 Co-N-C between left and right Co/N contacts may be slightly different in non-collinear magnetic configurations. The SMMJ is at equilibrium (strain=0.0%) and is gradually stretched until the breakdown of junction at the breaking point (BP, strain=13.1%). More details of structural relaxation can be found in Ref. [28]. To investigate the noncollinear spin torque effect, we first employed the two-probes model in the Nanodcal transport package 42–44 with density functional theory (DFT) and local density apˆ in noncollinear magnetic proximation (LDA) to obtain the self-consistent device Hamiltonian, H, configuration. Note that the device region (C) involves central BDA molecule and parts of left and right Co NWs. The double-ζ double-polarized basis sets of local numerical orbitals are applied to all ions, and the Sˆ is considered as the overlapping matrix for non-orthogonal linear combination of atomic orbitals (LCAO) basis. From our newly developed JunPy 45 package based on the nonequilibrium Green’s function (NEGF) method, the spin current density accumulated at site z with z1 < z < z2 can be defined by 1 Ql z = ∑∑ 4π i≥z 2 j≤z1

Z

ˆ ˆ ˜ l dE , Tr (E Sˆi, j − Hˆ i, j )Gˆ T⊥

and Tk , and their magnitudes satisfy the (V )

in conventional FM/I/FM MTJ. However, both T⊥ 7


and Tk in Co/BDA/Co


SMMJ exhibit odd parities with respect to angle θ . Surprisingly, their magnitudes are in the same (0)

order but two orders smaller than that of T⊥ . Thus, we can conclude the striking discovery in (0)

T⊥ ∼ T⊥ Tk for Co/BDA/Co SMMJ, where the amine linker plays an important role of ISF effect to creates the spin-polarized transmission channels near the Fermi energy as shown in Fig. 3 of Ref. [28] and hence further assists the strong IEC via quantum interferences due to the spindependent reflections at the Co/N contacts. (a) Co/BDA/Co =/6 =/2 =5/6

0.8

0.6 0.4

(c) Co/vacuum/Co with =/2 FLST Quadratic fitting STT General expression

0.003

0.6 0.4

0.04

0.02

0.002 0.00 0.001

0.2

0.2

0.0 -0.03

0.004

=/6 =/2 =5/6

1.0

T|| (meV)

T(V) (meV)

0.8

(b) Co/BDA/Co

1.2

T(V) (meV)

1.0

T|| (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-0.02

0.0 -0.02

-0.01

0.00

0.01

0.02

0.03

-0.03

0.000 -0.02

-0.01

Bias (V)

0.00

0.01

0.02

0.03

-0.03

-0.02

-0.01

Bias (V)

(V )

Figure 3: The bias dependence of (a) T⊥

0.00

0.01

0.02

-0.04 0.03

Bias (V)

and (b) Tk for noncollinear Co/BDA/Co SMMJ at equi(V )

librium (strain=0.0%) with various angles. (c) The bias dependence of T⊥ [left-hand coordinate] and Tk [right-hand coordinate] for noncollinear Co/vacuum/Co MTJ with θ =π/2. The dashed red (V )

line represents the quadratic fitting of T⊥ . The dashed blue line is calculated by the general ex (s) (s) (s) I (θ = 0) + I (θ = π) where Iz = h¯ (I ↑ − I ↓ )/2e is the calculated spin pression, Tk (θ ) = −sinθ z z 2 current densities along the z-direction. 22 (V )

The bias dependence of T⊥

and Tk for noncollinear Co/BDA/Co SMMJ with various angles

and Co/vacuum/Co MTJ with θ =π/2 are shown in Figs. 3(a)-(c). Similar to FM/I/FM 9,47 and FM/I/SF/I/FM 22 MTJs, the direct tunneling processes in symmetric Co/vacuum/Co MTJ gives (V )

with positive curvature, and the calculated Tk (V ) (s) (s) (s) I (θ = 0) + I (θ = π) where Iz = agrees well with the general expression, Tk (θ ) = −sinθ z z 2

rise to nearly quadratic bias dependence of T⊥

h¯ (I ↑ − I ↓ )/2e is the calculated spin current density along the z-direction. 22 When a BDA molecule (V )

is sandwiched between two Co NWs, T⊥

has an even parity with respect to external bias, i.e.

T⊥V (V ) ∼ T⊥V (−V ), due to the nearly symmetric geometry of Co/BDA/Co SMMJ. Moreover, the amine-linker assisted spin-polarized transmission channels near the Fermi energy, as shown in Fig. 3 of Ref. [28], strengthen the spin selective resonance tunneling processes to cause the failure in 8


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the general expression of Tk , resulting from the breakdown of sinusoidal angular dependence in Tk as shown in Fig. 2(b). This in turns renders the anomalous bias behavior of Tk with sign reversal without a corresponding sign reversal of bias.

FLST (meV)

(a) 20

0.8

BP

15 10

0.4

FLST STT

5

(b)

0

J1 (meV)

0

-5

0.6

0

5

0.2

STT (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.0 15

10

BP

-10 -15 -20

0

5

10

15

Mechanical strain (%)

Figure 4: The strain dependence of (a) net FLST [left-hand coordinate] and STT [right-hand coordinate] spin torque components with θ = π/2 and (b) fitted J1 for Co/BDA/Co SMMJ under an external bias of 0.02V. Note that the breaking point, BP, denotes the breakdown of SMMJ at strain = 13.1% Finally, we present in Figs. 4 (a) and (b) the mechanical strain effect on net FLST [left-hand coordinate] and STT [right-hand coordinate] spin torque components with θ = π/2 and the fitted J1 for Co/BDA/Co SMMJ with θ = π/2 and an external bias of 0.02V, respectively. It is striking to discover that both FLST and STT increase with the mechanical strain and then decline down to zero when junction breaks down at the breaking point (BP). Since the FLST component originate from IEC and Izs , the disconnection of hard-hard coupling between Co NW and central BDA at the BP gives rise to the strong deduction of J1 . The most intriguing finding is that the giant value of T⊥ can be preserved well under junction stretching process, which may provide a strain manipulation for the novel organic spintronics devices with hard-hard coupling between aminelinker and ferromagnetic electrodes.

9



Conclusions In conclusion, the newly developed NEGF method within the DFT framework is employed to comprehensively study the noncollinear FLST and STT spin torque components in amine-ended Co/BDA/Co SMMJ, including the rotation of magnetization in Co NW, the application of an external bias, and the mechanical strain to stretch the SMMJ. Similar to the conventional FM/I/FM MTJ, the Co/vacuum/Co MTJ exhibits the sinusoidal angle dependence of T⊥ and Tk , the purely quadratic bias dependence of T⊥ , and the validity of general expression of Tk . Once the BDA molecule is attached onto the Co NW via an amine-linker, it is intriguing to find T⊥ Tk for Co/BDA/Co SMMJ, resulting from the strong IEC via the hard-hard coupling between amine-linker and Co adatom. Such giant magnitude of T⊥ can be controlled either via the application of an external bias or by the junction stretching process, which may open a new avenue for multifunctional manipulation in next-generation organic FLST-MRAMs with lower power consumption.

Acknowledgement This work is supported by the Ministry of Science and Technology (NSC 102-2112-M-008-004MY3 and MOST 105-2112-M-008-010-) and the National Center for Theoretical Sciences, Republic of China.

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FM ISF I ISF (Co) (N) (N)

H Co

N

C

N Co

ML

0.8 0.6

13.6

0.4

13.4

0.2 0.0

13.2 -0.02

0.00

θ

y

STT BP

15

FLST STT

5 5

10

Mechanical strain (%)

16

z

0.6 0.4

10

0 0

0.02

Bias (V)

FM (Co)

MR

FLST

20 FLST (meV)

FLST >> STT

MISF

x


0.2 0.0 15

STT (meV)

FLST (meV)

1.0 13.8

STT (meV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Manipulation of Giant Field-Like Spin Torque in ... - ACS Publications

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