Enhanced thermal spin transfer in MgO-based double-barrier tunnel junctions

Switching the magnetic order parameter thermally is the basis for spin caloritronic applications such as logic devices and memories [1]. As a easy, efficient, and 'green' method to manipulate the magnetic order parameter, thermal spin transfer (TST) torque has received much attention recently [1–14]. To achieve TST torque (also called thermal torque) comparable to that induced by an electric bias, a large temperature gradient across magnetic elements should be established. Marked TST effect is first reported in a MgO-based magnetic tunnel junctions (MTJs) with ultra-thin barrier [2, 3]. Therein, the skewed TST torque is more favorable to magnetic oscillation rather than switching, a temperature gradient ${\rm{\Delta }}T\approx 60\quad {\rm{K}}$ with ${\rm{\nabla }}T\approx 100$ K nm⁻¹ is predicted to be needed to switch the magnetic configurations circularly, which is beyond the current experimental capability. The steady-state temperature gradient in MTJs is relatively small, a temperature gradient ${\rm{\Delta }}T\approx 20\quad {\rm{K}}$ with ${\rm{\nabla }}T\approx 32\quad$K nm⁻¹ with order of ten picoseconds can be established by femtosecond laser pulses heating [4]. Thus, seeking materials with moderate switching temperature gradient is an urgent and important task in spin caloritronics.

It is resonant interfacial states, widely existed in high quality nanostructures, that to be responsible for the large TST in MgO-based MTJs [3]. Similar to interfacial states, quantum-well (QW) states can lead to resonant tunneling [15–18] and large spin transfer effects. QW states can be engineered easily by the structure parameters such as thickness and materials of barrier and spacer metal, crystal defects and so on [16–19]. Spin transfer torque created by bias voltage in double-barrier MTJs (DBMTJs) is well studied [20–27]. When the QW states calibrate to Fermi energy (E_F), thermoelectric effects, including TST, would be enhanced. In DBMTJs, both the resonant QW states and interfacial states can be coexistent. So, larger TST effect and a smaller temperature gradient for magnetic switching would be expected in DBMTJs than those in single-barrier MTJs (SBMTJs). However, as far as we know, few works on this subject have been reported both in experiments and theory.

In this work, we focus on the TST torque in MgO-based DBMTJs in the presence of a nonequilibrium thermal distribution by applying the Landauer–Büttiker formalism with thermal bias [3]. We consider an ultra-thin MgO barrier with thickness of three atomic layers (about 0.6 $\mathrm{nm}$) as spin transfer torque (STT) decrease exponentially as barrier thickness increases [3]. Our results show enhanced TST torque in DBMTJs owing to the coexistence of the resonant QW states and the resonant interfacial states. Based on Landau–Lifshitz–Gilbert (LLG) equation, [28] we estimate that a temperature gradient of 10 K nm⁻¹ across barriers would be sufficient to reverse the magnetic configurations circularly at room temperature.

This paper is organized as follows. In section 2, we give the details of our calculation based on first-principle scattering theory. In section 3, we present our results on Fe $|$ MgO $|$ Fe $|$ MgO $|$ Fe DBMTJs with clean and disordered interfaces. Section 4 is our summary.

Considering a DBMTJ as sketched in the inset of figure 1 with temperature and voltage bias across the barriers, the local thermal equilibrium can be depicted by Fermi–Dirac distribution function ${f}_{{\rm{L}}/{\rm{R}}}(\epsilon )\;=$ ${[{{\rm{e}}}^{(\epsilon -{\mu }_{{\rm{L}}/{\rm{R}}})/{k}_{B}{T}_{{\rm{L}}/{\rm{R}}}}+1]}^{-1}$ and local chemical potentials ${\mu }_{{\rm{L}}/{\rm{R}}}$ and temperatures ${T}_{{\rm{L}}/{\rm{R}}}$. TST torque transferred to the magnetization ${\bf{M}}$ can be estimated by the spin current pumped out of the precessing ${\bf{M}}$ based on scattering theory [30]

$$\begin{eqnarray}&&{{\bf{T}}}_{}^{T}=\displaystyle \frac{{\rm{\Delta }}{{TM}}_{{\rm{s}}}V}{{{eT}}_{0}}\displaystyle \sum _{k,l}\int {\rm{d}}{E}\displaystyle \frac{\partial f}{\partial E}[{{\bf{m}}}_{l}^{\prime }\times (\mathrm{Tr}[{\bf{Q}}(k,E)]\times {{\bf{m}}}_{l}^{\prime })],\end{eqnarray} \tag{ 1 }$$

where ${\bf{Q}}(k,E)={{\bf{Q}}}^{L}(k,E)-{{\bf{Q}}}^{R}(k,E)$ with ${{\bf{Q}}}_{i}^{{\rm{L}}/{\rm{R}}}=\tfrac{{i}{\rm{e}}}{4\pi {M}_{s}V}{\sum }_{{\rm{L}}/{\rm{R}}}{\bf{S}}{\partial }_{{m}_{i}}^{}{{\bf{S}}}^{\dagger }+{\rm{H.c}}$ sums all modes over left/right (L / R) lead and ${{\bf{S}}}_{{\bf{k}}}(E)$ is the scattering matrix that is evaluated at the energy E and k in the two-dimensional Brillouin zone (2D BZ), ${\bf{m}}$ and ${{\bf{m}}}_{{\rm{L}}/{\rm{R}}}^{\prime }$ are the unit vector along ${\bf{M}}$ and ${{\bf{M}}}_{{\rm{L}}/{\rm{R}}}$ with respect to saturation magnetization M_s in ferromagnetic region with volume V, ${T}_{0}=({T}_{{\rm{L}}}+{T}_{{\rm{R}}})/2$ is ambient temperature, and ${\rm{\Delta }}T={T}_{{\rm{R}}}-{T}_{{\rm{L}}}\$ is temperature bias. Therein, the magnetization dependent parameter ${\bf{Q}}$ is the key to equation (1), which is well-studied by spin pumping theory [31, 32]. By putting TST torque into the phenomenological LLG equation [2], one can estimate thermal induced magnetic dynamics.

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We consider two stable DBMTJs structures as shown in figure 1. Therein, S1/S2 has one/two magnetization fixed along z quantum axis and two/one free magnetizations, and the magnetic structure of S1 is similar to SBMTJs. In calculations, we neglect the minor lattice mismatch at Fe $|$ MgO interface and fix the interfacial atoms at their bulk positions. For disordered interface, we assume oxygen vacancies (OV) only exist at the first layer of MgO attached to Fe. In the transport calculations, an 800 × 800 k-mesh is used to sample the two-dimensional Brillouin zone (2D BZ) to ensure good numerical convergence. More numerical details of the electronic structure and transport calculations can be found elsewhere [3, 33]. To check the validity of equation (1), a wave-function-matching (WFM) method [34] is used to calculate STT in clean Fe $|$ MgO(3)$|$ Fe(8)$|$ MgO(3)$|$ Fe DBMTJs also, where the numbers in the bracket indicate the thickness in atomic layers. We find that the STT obtained by two methods give difference less than 2%, and equation (1) can save calculation cost greatly compared with WFM method.

Figure 1 shows the angular dependence of the in-plane TST torque (${T}_{| | }^{T}$) in clean Fe $|$ MgO(3)$|$ Fe(8)$|$ MgO(3)$|$ Fe DBMTJs. Therein, ${T}_{| | }^{T}$ in S2 is symmetric with parameter [35] ⁴ ${\rm{\Lambda }}=1.0$ with peak value of $-370\quad$nJ m⁻² K⁻¹ at $\theta =90^\circ$, while that in S1 is asymmetric (${\rm{\Lambda }}=1.5$) with peak value of $-230$ nJ m⁻² K⁻¹ at $\theta =120^\circ$. The former is nearly double larger than the latter. However, both ${T}_{| | }^{T}$ in S1 and S2 structures are larger than that ($-195$ nJ m⁻² K⁻¹ at $\theta =90^\circ$) in clean Fe $|$ MgO(3)$|$ Fe SBMTJs. At the same time, Λ in both S1 and S2 are smaller than that 3.5 in clean Fe $|$ MgO(3)$|$ Fe SBMTJs. It is rather interesting because the larger ${T}_{| | }^{T}$ companied with smaller Λ would favor the magnetization switching in DBMTJs than SBMTJs [2]. The out-of-plane part of TST torque (${T}_{\perp }^{T}$) is about 10% of ${T}_{| | }^{T}$, and we neglect ${T}_{\perp }^{T}$ in magnetic dynamic simulations. By putting TST torque into LLG equation [28], we get temperature gradient ${\rm{\Delta }}{T}_{{\rm{SW}}}$ = 19/9 ${\rm{K}}$ (${\rm{\Delta }}{T}_{{\rm{SW}}}={\rm{max}}$(${\rm{\Delta }}{T}_{{\rm{SW}}}^{{\rm{P}}\to {\rm{AP}}}$, ${\rm{\Delta }}{T}_{{\rm{SW}}}^{{\rm{AP}}\to {\rm{P}}}$)) and ${\rm{\nabla }}{T}_{{\rm{SW}}}\;=$ 16/7.5 K nm⁻¹ to switch between antiparallel (AP) and parallel (P) configurations in S1/S2 structure as shown in table 1, which is considerable smaller than that in SBMTJs with same barrier thickness.

Table 1.  Thermal torque in clean and dirty (in brackets) Fe $|$ MgO(3)$|$ Fe(8 )$|$ MgO(3)$|$ FM DBMTJs at $T=300\;{\rm{K}}$ and ${\rm{\Delta }}T=1\;{\rm{K}}$ for $\theta =90^\circ$. For dirty case, we consider 4% OV at Fe $|$ MgO interfaces of right side MgO barrier. ${\rm{\Delta }}{T}_{{\rm{SW}}}$ and ${\rm{\nabla }}{T}_{{\rm{SW}}}$ is calculated according to LLG equations [28] with saturation magnetization ${M}_{S}=1{\rm{T}}$, uniaxial anisotropy field ${\mu }_{0}{H}_{K}=15{\rm{mT}}$, dimensionless planar anisotropy ${h}_{{p}}={K}_{{\rm{P}}}/K=20$ is the ratio of easy-plane anisotropy energy K_P to uniaxial anisotropy energy $K=(1/2){M}_{S}{H}_{K}$, and magnetic damping coefficient $\alpha =0.01$. For comparison, we give thermal torque in Fe $|$ MgO(3)$|$ Fe SBMTJs, and we consider 4% OV at both Fe $|$ MgO interfaces and set thickness of the free magnetization d_f = 1.2 nm.

FM	Structure	TMR (%)	${T}_{| | }^{T}$ (nJ m−2 K−1)	Λ	${\rm{\Delta }}{T}_{{\rm{SW}}}$ (${\rm{K}}$)	${\rm{\nabla }}{T}_{{\rm{SW}}}$ (K nm−1)
Fe	S1	1540	−220	1.5	19	16
FeCo	S1	860	−125	1.0	25	21
Fe	S2	0(110)	−370(−270)	1.0(1.0)	9(12)	7.5(10)
FeCo	S2	110	−220	1.0	14	12
Fe $|$ MgO(3L)$|$ Fe		1300(200)	−195(−110)	3.5(1.5)	45(33)	75(55)
Fe $|$ MgO(3L)$|$ FeCo		420	−40	1.0	76	126

To check the parameters used in magnetic dynamics simulations, we estimate ${\rm{\Delta }}{T}_{{\rm{SW}}}\approx 16.4\quad {\rm{K}}$ in clean Fe $|$ MgO(3)$|$ Fe(8)$|$ MgO(3)$|$ Fe DBMTJs with S1 structure by taking experimental data, [36] ⁵ which shows minor difference ($\sim 10 \%$) from that obtained from LLG calculations. So, we conclude that the parameters in magnetic dynamic simulations are reasonable.

Huge ratio of the TST torque to thermocurrent ${{\bf{T}}}_{| | }^{T}/{{\bf{I}}}^{T}$ in S1 and S2 structures is found in a large energy range, as shown in the lower inset in figure 1. A saturated ${{\bf{T}}}_{| | }^{T}/{{\bf{I}}}^{T}\approx 300\quad {\rm{\hslash }}/2e$ is found at $\theta =75{(105)}^{\circ }$ in S2 structure. For S1 structure, ${{\bf{T}}}_{| | }^{T}/{{\bf{I}}}^{T}\to \infty$ at $\theta \approx 116^\circ$ as ${{\bf{I}}}^{T}\to 0$, this is a 'off' state produced thermally. The small thermocurrent ${{\bf{I}}}^{T}=\tfrac{e{\rm{\Delta }}T}{{{hT}}_{0}}\int {\rm{d}}{E}(E-{E}_{{F}})T(E)\tfrac{\partial f}{\partial E}$ is responsible to the huge ${{\bf{T}}}_{| | }^{T}/{{\bf{I}}}^{T}$ here, where $T(E)=\mathrm{Tr}[{{tt}}^{\dagger }]$ is electronic transmission and t is the transmission part of the scattering matrix. The small ${{\bf{I}}}^{T}$ can be understood from the small asymmetry in electronic transmission within thermal energy window ${k}_{B}{T}_{0}$ at room temperature, as shown in the upper inset of figure 2(a). The giant spin transfer efficiency in DBMTJs would favor the functional of devices. Furthermore, the 'off' state demonstrated here can be found logic device application.

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To check the source of the enhancement of TST torque in clean Fe $|$ MgO(3)$|$ Fe(8)$|$ MgO(3)$|$ Fe DBMTJs, we check the energy-dependent voltage torkance

$$\begin{eqnarray}&&{{\boldsymbol{\tau }}}_{}^{{\bf{v}}}(E)={M}_{s}V\displaystyle \sum _{k,l}{{\bf{m}}}_{l}^{\prime }\times (\mathrm{Tr}[{\bf{Q}}(k,E)]\times {{\bf{m}}}_{l}^{\prime })\end{eqnarray} \tag{ 2 }$$

with ${\bf{M}}$ and ${{\bf{M}}}_{{\rm{L}}/{\rm{R}}}$ perpendicular to each other. For S1 structure, ${{\bf{M}}}_{{\rm{L}}}$ is along the z axis while ${\bf{M}}$ and ${{\bf{M}}}_{{\rm{R}}}$ is parallel to the x axis. For S2 structure, ${{\bf{M}}}_{{\rm{L}}}/{{\bf{M}}}_{{\rm{R}}}$ and is along $z/-z$ while ${\bf{M}}$ is parallel to x. The processing ${\bf{M}}$ would pump spin current into both left and right leads, the left-going and right-going spin current are equal for S2 structure, while only left-going spin current existed in S1 structure. When ${\bf{M}}$ rotates towards the x/y direction, a in-plane/out-of-plane torkance (${{\boldsymbol{\tau }}}_{| | }^{{\bf{v}}}/{{\boldsymbol{\tau }}}_{\perp }^{{\bf{v}}}$) will be produced. We plot the results in figure 2(a) in the energy range [${E}_{{\rm{F}}}-0.4\quad \mathrm{eV}$, ${E}_{F}+0.4\quad \mathrm{eV}$]. Therein, ${{\boldsymbol{\tau }}}_{| | }^{{\bf{v}}}$ show a striking negative peak with value of $-120/-250\quad \times \quad$10 ${}^{14}\quad {\tau }_{0}$ (${\tau }_{0}\equiv \tfrac{{\rm{\hslash }}}{2e}k{{\rm{\Omega }}}^{-1}{{\rm{m}}}^{-2}$) at ${E}_{{\rm{F}}}-0.07\quad \mathrm{eV}$ and a broaden positive peak with value of $80/130\times {10}^{14}{\tau }_{0}$ at ${E}_{{\rm{F}}}+0.02/{E}_{{\rm{F}}}+0.06\quad \mathrm{eV}$ in S1/S2 structure. At both peaks, ${{\boldsymbol{\tau }}}_{| | }^{{\bf{v}}}$ in S2 structure is almost double larger than that in S1 structure due to the double spin transfer process existed in S2 structure, as expressed in equation (2). Both the two peaks contribute to room temperature TST torque. We take S1 structure as an example to analyze the k -resolved contribution to ${{\boldsymbol{\tau }}}_{| | }^{{\bf{v}}}$. Figure 2(b) plot the k-resolved ${{\boldsymbol{\tau }}}_{| | }^{{\bf{v}}}$ at ${E}_{{\rm{F}}}-0.07\quad \mathrm{eV}$ and ${E}_{{\rm{F}}}+0.07\quad \mathrm{eV}$. The former is dominated by several bright spots in $\downarrow$ spin, while the latter is dominated by a bright ring in $\uparrow$ spin.

The out-of-plane torkance ${{\boldsymbol{\tau }}}_{\perp }^{{\bf{v}}}$ in DBMTJs shows complicate energy dependency as shown in the lower inset of figure 2(a). Although the out-of-plane TST torques in both S1 and S2 structures are relatively small, the out-of-plane voltage torque are rather considerable. We observe large ratio ${{\boldsymbol{\tau }}}_{\perp }^{{\bf{v}}}/{{\boldsymbol{\tau }}}_{| | }^{{\bf{v}}}=3.0/0.9$ at E_F in S1/S2 structure, which is considerable larger than that (∼0.25 at E_F) in Fe $|$ MgO(3)$|$ Fe SBMTJs.

DBMTJ can be considered as two SBMTJs connected in series. The coupling between SBMTJs in DBMTJ can be estimated from the electron transmission. When the electron transmission in DBMTJ (T_d) and SBMTJs (T_s) follow /beyond the relation ${T}_{d}={T}_{s}\quad \ast \quad {T}_{s}$, the coupling of SMTJs in DBMTJs would be weak/strong. For clean Fe $|$ MgO(3)$|$ Fe(8)$|$ MgO(3)$|$ Fe DBMTJs with S1/S2 structure, T_d is 0.012/0.013 at E_F, which is close to that (${T}_{s}=0.02$) in Fe $|$ MgO(3)$|$ Fe MTJs, indicating strong coupling between SBMTJs. It is noted that the resonant interfacial states in $\downarrow$ spin and resonant QW states in $\uparrow$ spin that should be responsible to the strong coupling. From the value of T_d and T_s, we estimate that the resonant states would contribute to $\sim 50 \%$ of T_d in DBMTJs at E_F. Moreover, STT can be used to estimate the coupling of SBMTJs in DBMTJ also, which is related with electron transmission by a simple relation [37].

Due to the strong coupling between SBMTJs in DBMTJ, the energy-dependent torkances for ${k}_{x}{a}_{0}=1.03$ and ${k}_{y}{a}_{0}=1.67$ at ${E}_{{\rm{F}}}-0.07\quad \mathrm{eV}$ (point A in figure 2(b)) produce three resonant peaks as shown in figure 2(c), which is different from the double peaks scheme in SBMTJs. The energy-dependent torkance share the same shape as the electronic transmission, indicating that the resonant peaks are from interfacial states. Differently, the energy-dependent torkance for ${k}_{x}{a}_{0}=0.4$ and ${k}_{y}{a}_{0}=0.0$ at ${E}_{{\rm{F}}}+0.07\quad \mathrm{eV}$ (point B in figure 2(b)) give a large resonant peak and two ghost peaks, as shown in figure 2(d). The former is from the resonant QW states, and the latter is from the resonant interfacial states.

Both the resonant interfacial and QW states contribute to the TST torque in DBMTJs. The position of resonant QW states is sensitive to the thickness of sandwich metal, while the position of resonant interfacial states is stable. Figure 3 shows the contribution of resonant interfacial and QW states to the TST torque in clean Fe $|$ MgO(3)$|$ Fe $|$ MgO(3)$|$ Fe DBMTJs with respect to the thickness of the sandwiched Fe. Therein, the TST torque in junction with S1/S2 structure increases quickly as n increases, and reaches a saturation value $\sim -$ 210 $/-410$ nJ m⁻² K⁻¹ for n = 12. In addition, the contribution from resonant interfacial states saturate at a value ∼− 130 $/-260$ nJ m⁻² K⁻¹ for $n\;\geqslant$ 12, and the contribution from resonant QW states show a convex curve with peak value of ∼− 110 $/-190$ nJ m⁻² for n = 8.

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Owing to the presence of the double spin transfer process, DBMTJs with S2 structure show large TST torque with symmetric angular-dependency, which would favor thermal induced magnetic switching. However, symmetric DBMTJs with S2 structure show zero tunnel magnetoresistance (TMR $=\quad (G(0)-G(\pi ))/G(\pi )$ with conductance $G(E)=({e}^{2}/h)T(E)$. To achieve observable TMR and large TST at the same time, asymmetric DBMTJs with S2 structure can be devised. Here, we pay attention to the effects of asymmetric interfacial OV and asymmetric leads on ${{\boldsymbol{\tau }}}_{| | }^{{\bf{v}}}$ in DBMTJs with S2 structure, as show in figure 4 and table 1 . Firstly, we study the asymmetric interfacial OV, where the Fe $|$ MgO interfaces of left MgO barrier keep clean while that of right MgO barrier is dirty. We find that 4% OV at Fe $|$ MgO interfaces of right side MgO can produce TMR ∼110% at zero bias, simultaneously ${{\boldsymbol{\tau }}}_{| | }^{{\bf{v}}}$ decreases to −270 nJ m⁻² K⁻¹, as shown in table 1. Detail study shows interfacial OV would deteriorate both resonant interfacial and QW states. The resonant interfacial states are more sensitive to OV than the QW ones, as shown in figure 4. Quantitatively, ${{\boldsymbol{\tau }}}_{| | }^{{\bf{v}}}$ from resonant interfacial/QW states at energy ${E}_{{\rm{F}}}-0.07/{E}_{{\rm{F}}}+0.05\quad \mathrm{eV}$ is $-140/100\times {10}^{14}{\tau }_{0}$, show a reduction of 60/20 comparing with that in the clean structure. The asymmetric interfacial OV does not change the symmetry of the angular-dependency of the TST torque, and ${\rm{\Delta }}{T}_{{\rm{SW}}}\sim 12$ ${\rm{K}}$ with ${\rm{\nabla }}{T}_{{\rm{SW}}}\sim 10$ K nm⁻¹ are estimated according to the LLG simulation.

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When the bcc-Co_0.5Fe_0.5 alloy is used as the right lead, the resonant interfacial states would be quenched completely, while resonant QW states keep stable. The clean asymmetric Fe $|$ MgO(3)$|$ Fe(8)$|$ MgO(3)$|$ FeCo DBMTJs with S2 structure show TMR ∼110% at zero bias and symmetric angular-dependent TST torque with peak value of −220 nJ m⁻² K⁻¹ at $\theta =90^\circ$, and ${\rm{\Delta }}{T}_{{\rm{SW}}}\sim 14$ ${\rm{K}}$ with ${\rm{\nabla }}{T}_{{\rm{SW}}}\sim 12$ K nm⁻¹ are estimated from the magnetic dynamic simulation.

In table 1, we summarize the TST torque in Fe $|$ MgO(3L)$|$ Fe(8 L)$|$ MgO(3L)$|$ Fe DBMTJs. Therein, DBMTJs with SBMTJ-like magnetic structure (S1) show larger TMR, while those with S2 structure show larger TST torque. By introducing asymmetric OV or asymmetric leads, DBMTJs with S2 structure can give considerable TMR and larger TST torque. ${\rm{\Delta }}{T}_{{\rm{SW}}}\sim 10$ ${\rm{K}}$ with ${\rm{\nabla }}{T}_{{\rm{SW}}}\sim 10$ K nm⁻¹ is presented in an asymmetric DBMTJs with S2 structure, which is about one order smaller than that in SBMTJ with same barrier thickness. For same TST torque, the ratio of ${\rm{\Delta }}{T}_{{\rm{SW}}}$ and ${\rm{\nabla }}{T}_{{\rm{SW}}}$ in SBMTJs to those in DBMTJs is Λ and $2.0\quad \ast \quad {\rm{\Lambda }}$, respectively. Furthermore. when 4% OV is introduced in Fe $|$ MgO(3L)$|$ Fe SMTJs, the effect of the reduction in Λ cancel that of the reduction in TST torque, leading to smaller ${\rm{\Delta }}{T}_{{\rm{SW}}}$ and ${\rm{\nabla }}{T}_{{\rm{SW}}}$ comparing with clean junctions, as shown in table 1. It is suggested that, crystal defects such as interfacial OV, may be not always a deleterious factor to magnetic switching.

Owing to the involvement of resonant QW states, TST torque in DBMTJs is enhanced. At the same time, the angular-dependency of TST torque gets symmetric or close to symmetric. Both factors lead to considerable reduction in ${\rm{\Delta }}{T}_{{\rm{SW}}}$ and ${\rm{\nabla }}{T}_{{\rm{SW}}}$ comparing with the SBMTJs with the same barrier thickness. So, we predict that MgO-based DBMTJs is more promising in application for thermally induced magnetization switching.

We predict enhanced TST torque and small switching temperature gradient in Fe $|$ MgO $|$ Fe $|$ MgO $|$ Fe DBMTJs from atomic first principles. Temperature gradient ${\rm{\Delta }}{T}_{{\rm{SW}}}\sim 10$ ${\rm{K}}$ with ${\rm{\nabla }}{T}_{{\rm{SW}}}$ ∼ 10 ${\rm{K}}/\mathrm{nm}$ across MgO barriers is predicted to drive the magnetic configurations in a DBMTJs switch circularly at room temperature, which is about one order smaller than that in Fe $|$ MgO(3)$|$ Fe MTJs, and under the current experimental capacity. The coexistence of resonant QW states and resonant interfacial states is responsible to the enhancement. The introduction of asymmetry by interfacial OV and different leads would change TMR and TST torque including their angular dependency. Moreover, zero thermocurrent can present at a specific angle in a DBMTJ, indicates that we can produce a 'off' state in the material thermally. Based on these results, we predict that MgO-based DBMTJs is promising in application for heat-flow-induced magnetization switching and logic device.

JX thanks KX at BNU for his transport codes and valuable discussion, and we gratefully acknowledge financial support from National Natural Science Foundation of China (11274094 and 51332007). JX also acknowledge financial support from Henan Polytechnic University (B2012-021 and T2016-2).