Resonant spin-transfer torque in asymmetric double barrier magnetic tunnel junctions (MTJs)

Accepted Manuscript Resonant spin-transfer torque in asymmetric double barrier magnetic tunnel junctions (MTJs)

Reza Daqiq, Nader Ghobadi PII:

S0749-6036(16)31300-3

DOI:

10.1016/j.spmi.2017.01.004

Reference:

YSPMI 4767

To appear in:

Superlattices and Microstructures

Received Date:

23 October 2016

Revised Date:

03 January 2017

Accepted Date:

03 January 2017

Please cite this article as: Reza Daqiq, Nader Ghobadi, Resonant spin-transfer torque in asymmetric double barrier magnetic tunnel junctions (MTJs), Superlattices and Microstructures (2017), doi: 10.1016/j.spmi.2017.01.004

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ACCEPTED MANUSCRIPT

Spin torque (ST) is studied in asymmetric double barrier MTJs using NEGF. There are different electrodes and a middle non-magnetic metal (NM) layer. The results show oscillatory behavior due to quantum well states in the NM layer. The current and in-plane ST vs. bias increases in comparison with symmetric MTJs. The perpendicular ST decreases in comparison with symmetric MTJs.

ACCEPTED MANUSCRIPT

Resonant spin-transfer torque in asymmetric double barrier magnetic tunnel junctions (MTJs) Reza Daqiq* and Nader Ghobadi Department of Physics, Malayer University, Malayer, Iran

Abstract The substitution effect of a Ferro-magnet (FM) electrode by a half-metallic FM material La0.7Sr0.3MnO3 (LSMO) on charge current and spin-transfer torque (STT) components is studied in MgO-based double barrier magnetic tunnel junctions (DBMTJs) with a middle non-magnetic metal (NM) layer. Using nonequilibrium Green’s function (NEGF) formalism, it is observed that the current and STT components show oscillatory behavior due to quantum well states in the middle NM layer and resonant tunneling effect. We also study effect of difference in the thickness of the MgO insulators. Bias dependence demonstrate the magnitude enhancement of the current and in-plane STT in new asymmetric DBMTJs (A-DBMTJs) compared with symmetric DBMTJs (S-DBMTJs), however, perpendicular STT decreases in the A-DBMTJs. Results also show different behavior compared with conventional asymmetric MTJs and spin valves (SVs). Therefore, one can design new memory devices by means of suitable insulator and FM electrodes with proper thicknesses. Keywords: STT components; double-barrier MTJs; Resonant tunneling effect; LSMO;

1. Introduction Magnetic tunnel junctions (MTJs) are made of two ferromagnetic (FM) electrodes separated by a thin insulator barrier and they have attracted a lot of attention due to their application in memory technologies [1,2]. Spin-transfer torque (STT) effect - which is the magnetization switching of the free magnet due to a spin-polarized current - has a main role in nano- devices based on MTJs. This STT effect has been proposed theoretically [3,4] and subsequent has been observed in MTJs based on MgO [5,6] and AlO [7]. For low bias, theoretical studies [8-12] shown subsequent form for the STT components as 𝜏 ∥ = 𝑎0𝑉 + 𝑎1𝑉2 and 𝜏 ⊥ = 𝑏0 + 𝑏1𝑉 + 𝑏2𝑉2. The linear term of 𝜏 ⊥ emerges due to symmetry breaking [13] made from band filling difference of the electrodes [14,15], asymmetric barriers [16,17] and etc. *Corresponding author: [email protected]

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Symmetric Double barrier MTJs (S-DBMTJs) have been studied in nano-electronics due to the existence of the resonant states within the middle Ferro-magnet (FM) [18-21], semiconductor (SC) and non-magnetic metal (NM) layer [22,23]. Half-metallic FMs are appropriate materials because they supply full spin polarization at the Fermi level. Among these materials manganites such as La0.7Sr0.3MnO3 (LSMO) have been widely studied [24] due to its high Curie temperature 𝑇𝐶 = 350 𝐾 [25,26]. Half metals also present full symmetry polarization of current, so it allows investigating the symmetry filtering effect across MgO barriers [27]. Combination of perovskite manganites with MgO barriers may produce remarkable results due to the different lattice structure and interfacial effects. High field magneto-resistance (MR) values have been reported in the LSMO/MgO/Fe tunneling junctions [28]. The purpose of this work is to study the charge current and STT components in asymmetric DBMTJs (A-DBMTJs) with the structure CoFeB/MgO/NM/MgO/LSMO. However, the charge current and STT components in A-DBMTJs with a middle NM layer and different electrodes has not been studied before.

Figure1.Schematic illustration of asymmetric CoFeB/MgO/NM/MgO/LSMO junctions consisting of two semiinfinite CoFeB and LSMO electrodes surrounding the middle region of the left and right insulators and the NM layer. 𝑡𝐼 and 𝑡𝑁𝑀 indicate the thickness in the left (right) I and middle NM layer, respectively. The magnetizations of the fixed (left) CoFeB electrode is 𝑀 is along the z-axis and that of the free (right) LSMO electrode is 𝑚 which

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makes an angle 𝜃 with the 𝑀 direction. Difference in the bottom of the conduction band of the NM and CoFeB is 𝑈𝑊 and that of the LSMO and CoFeB is 𝑈𝑅.

Device is based on an NM layer as the quantum well between two MgO insulators and surrounded by two semi-infinite ferromagnetic CoFeB and LSMO electrodes (Figure 1). This paper is organized as follows. Sec. 2, describes the formalism for the charge current and STT components. Results and discussion are presented in Sec. 3. Conclusions are stated in Sec.4.

2. Formalism The non-equilibrium Green’s function (NEGF) technique with a single band effective mass Hamiltonian is used in current simulation [29- 31]. The Hamiltonian is given by: 𝐻 = 𝐻0𝐼 ‒ (𝜎.𝑚)

∆ 2

(1)

In eq. (1), 𝐻0 is the spin-independent part of the Hamiltonian, 𝑚 is the direction of the free electrode, 𝜎 is the Pauli spin vector, ∆ is the spin-splitting and 𝐼 is the 2x2 identity matrix. The 2x2 self-energy matrices of the left and right FM electrodes are given by: Σ𝐿,𝑅(𝑖,𝑖,𝑘 ∥ ) =

[

↑

- 𝑡𝐹𝑀exp (𝑖𝑘 𝑗 𝑎) 0

0 ↓ - 𝑡𝐹𝑀exp (𝑖𝑘 𝑗 𝑎)

]

(2)

2

⋆ ⋆ 2 where 𝑘 ∥ is the transverse wave vector, 𝑡𝐹𝑀 = ℏ 2𝑚𝐹𝑀 is 𝑎 is the coupling parameter, 𝑚𝐹𝑀

effective mass of electron inside the FM electrodes, ℏ is the reduced Planck constant, 𝑎 is the lattice spacing and 𝑘↑𝑗,↓ are the wave vectors of the spin up and the spin down electrons [31]. The DBMTJs are studied in the coherent regime and the periodic boundary conditions are also supposed in the transverse direction. Then, the correlation function 𝐺𝑛 is calculated from the NEGF equations [30]: 𝐺(𝐸) = [𝐸𝐼 - 𝐻 - Σ] -

1

(3)

𝐴(𝐸) = 𝑖[𝐺 - 𝐺 † ]

(4)

Γ𝐿,𝑅(𝐸) = 𝑖[Σ𝐿,𝑅 - Σ𝐿,𝑅] †

(5)

𝑖𝑛

Σ𝐿,𝑅(𝐸) = Γ𝐿,𝑅(𝐸)𝑓𝐿,𝑅(𝐸)

(6)

𝐺𝑛(𝐸) = 𝐺Σ𝑖𝑛𝐺 †

(7) 3

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where 𝑖𝑛 𝑖𝑛 𝑖𝑛 Σ = Σ𝐿 + Σ𝑅 , Σ = Σ 𝐿 + Σ 𝑅

(8)

In the NEGF equations, 𝐺(𝐸) is the Green’s function, 𝐸 is the energy and 𝐴 is the spectral function so that its diagonal elements give the local density of state (LDOS). The Fermi functions and the broadening matrices of the left and the right FM electrodes are 𝑓𝐿,𝑅, Γ𝐿,𝑅 𝑖𝑛 respectively. The in-scattering functions of the left and the right FM electrodes are Σ𝐿,𝑅 and they describe the rate at which electrons come into the device from the electrodes.

The current operator between two lattice points’ j and j ± 1 is given by [22, 23]: 𝐼𝑜𝑝 =

𝑖 𝑛 𝐻 𝐺 𝑛 -𝐺 † 𝐻 † ℏ 𝑗,𝑗 ± 1 𝑗 ± 1,𝑗 𝑗,𝑗 ± 1 𝑗 ± 1,𝑗

(

)

(9)

The charge currents 𝐼𝐶 and the spin currents 𝐼𝑆 are defined as: 𝐼𝐶 = 𝑞∫𝑑𝐸 𝑅𝑒𝑎𝑙 [𝑇𝑟𝑎𝑐𝑒(𝐼𝑜𝑝 )]

(10)

𝐼𝑆 = 𝑞∫𝑑𝐸𝑅𝑒𝑎𝑙 [𝑇𝑟𝑎𝑐𝑒 {𝜎 𝐼𝑜𝑝}]

(11)

The first 50 transverse modes are considered in the charge and spin currents equations. Therefore, the in-plane and perpendicular components of the STT are calculated as [31]: 𝜏 ∥ ,𝑚 =

𝐼𝑆 ∙ (𝑚 × 𝑀 × 𝑚)

𝜏 ⊥ ,𝑚 =

(12)

(1 ‒ (𝑚 ∙ 𝑀)2) 𝐼𝑆 ∙ (𝑀 × 𝑚)

(13)

(1 ‒ (𝑚 ∙ 𝑀)2)

3. Results and Discussion The parameters used here for the CoFeB and LSMO electrodes are the Fermi energy 𝐸𝐹 = 2.25 𝑒𝑉, the spin-splitting ∆𝐿 = 2.15 𝑒𝑉, the effective mass for electrons inside the CoFeB electrode * = 0.8 𝑚𝑒 [31] , ∆𝑅 = 0.7 𝑒𝑉, conduction band offset (CBO) 𝑈𝑅 = 1.90 𝑒𝑉 [32] and 𝑚𝐶𝑜𝐹𝑒𝐵 * * , respectively. = 𝑚𝐶𝑜𝐹𝑒𝐵 𝑚𝐿𝑆𝑀𝑂

The parameters used here for the insulators, the NM layer are the barrier height of the insulator 𝑈𝐼 = 0.77 𝑒𝑉, the effective mass for electrons inside the insulators 𝑚 *𝐼 = 0.18 𝑚𝑒 [31], the 4

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* effective mass for electrons inside the NM layer 𝑚𝑁𝑀 = 𝑚𝑒, ( 𝑚𝑒 is the mass of the free

electron), the CBO of the NM layer 𝑈𝑊 = 0.5 𝑒𝑉. The junction area is 70 × 160 𝑛𝑚2 [33]. The potentials drop linearly in the insulators while in the middle NM layer the potential is constant. It is regarded as ∆𝐿 ≠ ∆𝑅 ( ∆𝐿 = ∆𝑅) and the CBO of the LSMO (CoFeB) electrode is 𝑈𝑅 (zero) for A-DBMTJs (S-DBMTJs). It is assumed that the fixed (left) magnet 𝑀 is along 𝑧 and the free (right) magnet 𝑚 is along 𝑥 direction (𝜃 = 𝜋 2). Figure 2 (a)-(c) shows the charge current and STT components for different thicknesses of left and right insulators as a function of the NM layer thickness 𝑡𝑁𝑀. A constant bias of 𝑉 = 0.5 𝑉 is applied in Figure 2. The results show oscillatory behavior due to the resonant tunneling effect through double barrier structures and its physical origin is clarified by the quasi-bound states of the quantum well. A resonance condition is fulfilled when the energy of electrons concurs with the energy of an existing state in the quantum well and the transmission through A-DBMTJs strongly increases. However, the position of the quantum well states depends on the NM well thickness 𝑡𝑁𝑀. As a result, the position of the resonant states varies with different thicknesses 𝑡𝑁𝑀 and such oscillatory behavior appears. The sharp peaks in comparison with broad dips observe in the emerged oscillations, which relates to confinement of electrons to the NM layer. With increasing 𝑡𝑁𝑀, the quantum well levels cross the energy of electrons in the left MgO insulator, the current and STT components increase and the sharp peaks appear. On the contrary, the dips are broad due to the broad gaps between the discrete resonant levels in the middle NM layer. In order to attain the larger values of the current and STT components, effect of difference in the thickness of the MgO insulators is also investigated in A-DBMTJs. The results show a discrepancy for different thicknesses of left and right insulators. The reason for discrepancy is that the voltage drop within the MgO layer depends on the insulator thickness 𝑡𝐼 and hence the depth of quantum well in the NM layer depends on the position of the layer. Thus, the incident electrons see a deeper quantum well compared with the other cases as this affects the qualities of the quantum well states. As a result, the current and STT components are larger for thicker left insulator than the others at resonant positions.

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IC (mA)

6

(a)

4 2 0

(10 -19J)

20

(b)

||

10

0

(10 -19J)

2 1

(c)

0.5 nm/ tNM /0.5 nm

0.6 nm/ tNM /0.4 nm

0.4 nm/ tNM /0.6 nm

tI/ t NM/ t I

0 -1 -2 0.1

0.3

0.5

tNM(nm)

0.7

0.9

1.1

Figure 2. Charge current (a) and STT components (b),(c) as a function of middle NM layer in A-DBMTJs for different thicknesses of left and right insulators with 𝑉 = 0.5 𝑉and 𝜃 = 𝜋 2.

The bias dependence of the charge current and STT components for different thicknesses of left and right insulators is shown in Figure 3 (a)-(c) at a resonant position 𝑡𝑁𝑀 = 0.3 𝑛𝑚. For

(10 -19J)

||

(10 -19J)

IC (mA)

positive bias, the charge current and STT components are larger for thicker left insulator than the others. It is also observed that the negative bias results of the STT components differ from those of positive bias. 12 6 0 -6 -12

40

(a)

0.5 nm/0.3 nm/0.5 nm 0.6 nm/0.3 nm/0.4 nm 0.4 nm/0.3 nm/0.6 nm

(b)

20

tI/ t NM/ t I

0

1 0 -1 -2 -1

(c) -0.5

0

0.5

1

Voltage (V)

Figure 3. Bias dependence of charge current (a) and STT components (b),(c) in A-DBMTJs for different thicknesses of left and right insulators with 𝑡𝑁𝑀 = 0.3 𝑛𝑚 and 𝜃 = 𝜋 2.

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Figure 4 shows the bias dependence of the charge current for four thicknesses of the middle NM layer 𝑡𝑁𝑀, 𝐴 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚, 0.5 𝑛𝑚, 1.0 𝑛𝑚 and 𝑡𝑁𝑀,𝑆 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚. The thickness 0.3 𝑛𝑚 is corresponding to a resonant position of the quantum well as its current magnitude is larger than the others and that of 𝑡𝑁𝑀,𝑆 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚. The non-zero CBO in the NM layer and LSMO interface cause to increase of transmission through the A-DBMTJs. I-V characteristics of DBMTJs are asymmetric and parabolic at low bias, so indicating tunneling transport.

10 tNM,A-DBMTJ= 0.3 nm tNM,A-DBMTJ= 0.5 nm tNM,A-DBMTJ= 1.0 nm

0

10

IC(mA)

I C(mA)

5

-5

5 0 -5 -1

-10 -1

t NM,S-DBMTJ= 0.3 nm

-0.5

0

0.5

1

Voltage (V)

-0.5

0

0.5

1

Voltage (V)

Figure 4. Bias dependence of charge current for three thicknesses of the middle NM layer in A-DBMTJs 𝑡𝑁𝑀, 𝐴 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚, 0.5 𝑛𝑚, 1.0 𝑛𝑚 with 𝑡𝐼 = 0.5 𝑛𝑚 and 𝜃 = 𝜋 2 . Inset: Bias dependence of charge current for a thickness of the middle NM layer in S-DBMTJs 𝑡𝑁𝑀,𝑆 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚.

The bias dependence of the in-plane STT component for four thicknesses of the middle NM layer 𝑡𝑁𝑀, 𝐴 - 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚, 0.5 𝑛𝑚, 1.0 𝑛𝑚 and 𝑡𝑁𝑀,𝑆 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚 is shown in Figure 5. For 𝑡𝑁𝑀,

𝐴 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚,

the in-plane component is larger than the others at positive bias.

For negative bias, the in-plane STT is not as large as that at positive bias. The results also illustrate that the in-plane component of A-DBMTJs is larger than that of S-DBMTJs at the similar thickness of the NM quantum well (inset of Figure 4). Such results are achieved for A-DBMTJs due to the different spin-splitting in two electrodes. The mechanism of these properties is explained as follows. In general, the spin polarization of tunneling electrons increases with increase of spin-splitting which causes an increase of spin torque. Moreover, the in-plane component of the STT exerted on the LSMO electrode chiefly depends on the polarization of tunneling electrons in the CoFeB electrode. The spin-splitting of 7

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the CoFeB electrode (∆𝐿) is greater than that of the LSMO electrode (∆𝑅) and hence the in-plane component in A-DBMTJs is larger than that of S-DBMTJs. Using an applied bias to the ADBMTJs, polarization of the LSMO electrode decreases while polarization of the CoFeB electrode is constant.

30

||

(10

-19

J)

30

||

(10 -19J)

20

tNM,A-DBMTJ= 0.3 nm

t NM,S-DBMTJ= 0.3 nm

tNM,A-DBMTJ= 0.5 nm

20

tNM,A-DBMTJ= 1.0 nm

10 0 -1

-0.5

0

0.5

1

Voltage (V)

10

0

-1

-0.5

0

0.5

1

Voltage (V)

Figure 5. Bias dependence of in-plane STT component for three thicknesses of the middle NM layer in A-DBMTJs 𝑡𝑁𝑀, 𝐴 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚, 0.5 𝑛𝑚, 1.0 𝑛𝑚 with 𝑡𝐼 = 0.5 𝑛𝑚 and 𝜃 = 𝜋 2 . Inset: Bias dependence of in-plane STT component for a thickness of the middle NM layer in S-DBMTJs 𝑡𝑁𝑀,𝑆 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚.

Figure 6 shows the bias dependence of the perpendicular STT component for four thicknesses of the middle NM layer 𝑡𝑁𝑀, 𝐴 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚, 0.5 𝑛𝑚, 1.0 𝑛𝑚 and 𝑡𝑁𝑀,𝑆 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚. There are resonant peaks in 𝜏 ⊥ (𝑉) as its behavior differs from those of reported in asymmetric MTJs [13-17,31,34] due to the existence of the quantum well states in the middle NM layer. It is also found that for positive bias, the perpendicular component of the S-DBMTJs is about three times of magnitude larger than A-DBMTJs.

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1

(10 -19J)

0

-1

2

-2

(10

-19

J)

0 -2 -4

tNM,A-DBMTJ= 0.3 nm

-6 -8 -1

t NM,S-DBMTJ= 0.3 nm -0.5

0

0.5

tNM,A-DBMTJ= 0.5 nm 1

tNM,A-DBMTJ= 1.0 nm

Voltage (V)

-3 -1

-0.5

0

0.5

1

Voltage (V)

Figure 6. Bias dependence of perpendicular STT component for three thicknesses of the middle NM layer in ADBMTJs 𝑡𝑁𝑀, 𝐴 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚, 0.5 𝑛𝑚, 1.0 𝑛𝑚 with 𝑡𝐼 = 0.5 𝑛𝑚 and 𝜃 = 𝜋 2 . Inset: Bias dependence of perpendicular STT component for a thickness of the middle NM layer in S-DBMTJs 𝑡𝑁𝑀,𝑆 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚.

The STT components also show gradually increase behavior for positive bias unlike oscillatory behavior of conventional spin valves (SVs). For comparison of SVs and A-DBMTJs results, the bias dependence of the STT components in both structures is shown in Figure 7 (a), (b). The SVs parameters such as Fermi energy and spin-splitting are similar to those presented in ref. 35. For positive bias, A-DBMTJs show the magnitude enhancement of the STT components compared with those of SVs if suitable thicknesses are designed for an NM layer and insulators. 40

(10 -19J)

(a)

SV A-DBMTJ

20

||

0 -20

(10 -19J)

1

(b)

0 -1 -2 -1

-0.5

0

0.5

1

Voltage (V)

Figure 7. Bias dependence of STT components (a), (b) for spin valves (SVs) parameters [35] and for A-DBMTJs with 𝑡𝑁𝑀, 𝐴 ‒ 𝐷𝐵𝑀𝑇𝐽 = 0.3 𝑛𝑚, 𝑡𝐼 = 0.5 𝑛𝑚 and 𝜃 = 𝜋 2 .

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4. Conclusions The charge current and STT components is studied in resonant A-DBMTJs using NEGF formalism. The effect of difference in the thickness of insulators is also described. The results show oscillatory behavior due to the resonant states in the NM quantum well and resonant tunneling effect. It is observed that the magnitude of the charge current and in-plane STT in ADBMTJs enhances compared with S-DBMTJs due to different spin-splitting of electrodes and the non-zero CBO of the LSMO electrode. The bias dependence of the STT components also shows asymmetric behavior. The STT components are demonstrated different behavior compared with conventional asymmetric MTJs and SVs. Therefore, it would be possible to design memory devices by means of new A-DBMTJs.

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