Seeking large thermoelectric effects in MgO-based tunnel junctions

There is much controversy concerning thermoelectric effects in the MgO-based magnetic tunnel junctions (MTJs) as reported in some recent publications. To clarify the problem, we give calculations from atomic first-principles systemically. Large Seebeck coefficient (S) and up-limit of figure of merit (ZT) are predicted in double- and multi-barrier MTJs, with those in single-barrier MTJs being relatively small. By restraining the phonon thermal conductance through the introduction of one vacuum barrier or numbers of MgO barriers, the up-limit of ZT can be obtained. Room temperature S ≈ − 220 μ V K − 1 and ZT ≈ 3.5 are predicted in an asymmetric Fe ∣ MgO ∣ Fe ∣ Vaccum ∣ Fe MTJs. The resonant quantum-well states are suggested to be responsible for the enhanced thermoelectric effects in the MTJs with double- and multi-barrier.


Introduction
Thermoelectric phenomena have recently been renovated by nanotechnology and spintronics [1][2][3][4]. Enhanced thermoelectric effects are found in nanostructures, which can be orders of magnitude larger than those in bulk systems. Therein, the localized states and phonon-scattering [5,6] are considered to be responsible for the enhancement. One most used parameter for thermoelectric element is the dimensionless figure of merit k = GS T ZT 2 0 with conductance G, Seebeck coefficient S, thermal conductance κ at ambient temperature T 0 . To seek large ZT, one should maximize S and G, and minimize κ. There are two sources for κ: electron (k e ) and phonon (k p ). Both k p and k e can be engineered by modulating the structure parameters, and the up-limit of ZT can be obtained in the absence of k p .
There are two kinds of localized states contributing to the thermoelectric effects in MTJs: interface states and quantum well (QW) states. The latter has been well-studied in double-barrier MTJs (DBMTJs) and superlattice structures. QW states can greatly improve the thermoelectric effects in Bi 2 Te 3 alloy-based superlattice structures [19]. Thermoelectric effects in ultrathin MgO-based MTJs is relatively small, where the free-electron-like tunneling states [8] around Γ ( = = k k 0, 0 x y ) point in the two-dimensional Brillouin zone (2D BZ) dominate electric and thermal transport. Resonant tunneling from the localized states [20][21][22] is the key to achieve large thermoelectric effects, which can be engineered by modulating the structure parameters such as barrier thickness and numbers, magnet type and thickness, defects concentration and position, and so on. If the Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.
Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. resonant states are shifted to the Fermi level (E F ), the energy dependence of the transmission would be strongly asymmetric, and the Seebeck coefficient would be large. In double-and multi-barrier MTJs, both interface states and QW states coexist [23][24][25], and the parameter space for thermoelectric effects is considerably larger than that in single-barrier MTJs. However, to the best of our knowledge, few works on this subject have been reported.
In this paper, we focus on the thermoelectric effects in the MgO-based MTJs in the presence of a nonequilibrium thermal distribution by applying the Landauer-Büttiker formalism with thermal bias [26]. At room temperature, we find » -S 220 μV K −1 and ZT ≈ 3.5 in a junction with 7 atomic layer (L) MgO and 5 L vacuum barriers. The resonant QW states are considered to be responsible for the large thermoelectric effects.
This paper is organized as follows. In section 2, we give the details of our first-principle calculations. In section 3, we present our results on the MgO-based MTJs with symmetric and asymmetric structures. Section 4 is our summary.

Electronic structure and transport calculations
The electric voltage DV and thermal flowQ in constrictions can be built by a current I and temperature bias D = -T T T R L passing across the structure with relation: [27,28] ( ) , 1 0 wherein the conductance G, Seebeck coefficient S and electron thermal conductance k e can be calculated from scatter matrix [ ] = S r t t r ; first-principle: Tr tt , and kernel of ( is ambient temperature. In figure 1, we give kernels used in the integrals above. When ( ) T E varys slowly around | . Generally, phonon thermal conductance dominates over electron one, and the former can be greatly restrained with the order of~10 8 W K −1 m −2 by interfaces [18,29]. When the lateral size of the thermoelectric element is shrunk to nanoscale, phonon thermal conductance decreases to one percent of that of the bulk as revealed in silicon nanowires by surface phonon scattering [30,31]. Unfortunately, there are few data on the relation between the phonon thermal conductance and lateral size of the MTJs. So, we introduce the up-limit of ZT, ZT(max) k = GS T e 2 , to assess the potential of the thermoelectric elements. In this study, we consider two-probe devices as Fe| MgO| Fe and Fe | MgO | Fe | MgO | Fe MTJs. We neglect small lattice mismatch at the Fe | MgO interface by fixing the interfacial atoms at their bulk positions, and assume the impurities existed at the first layer of MgO attached to Fe. In transport calculations, the electric current and thermal flow along the (001) direction, and a 800 × 800 k-mesh is used to sample the 2D BZ to ensure excellent numerical convergence. More numerical details of the electronic structure and transport calculations can be found elsewhere [26,32]. ]. As ( ) T E in MgO-based MTJs is sensitive to the resonant states, one can engineer the shape of ( ) T E by modulating the structure parameters to achieve large thermoelectric effects. In the following, we study the effects of the structure parameters on the thermoelectric effects in the MgO-based MTJs systematically. Firstly, we take a look at single-barrier MTJs. Secondly, we turn to DBMTJs with symmetric and asymmetric structures. Thirdly, we study MTJs with multi-barriers. Finally, we pay attention to a asymmetric DBMTJs with one MgO barrier and one vacuum barrier, where the up-limit of ZT would be achieved naturally in the absence of phonon thermal conductance. are from resonant tunneling carried by QW states, which produce a bright transmission ring with peak value around one unit in 2D BZ as shown in the insert of figure 3. As the barrier thickness increases, peaks in ( ) T E from the resonant QW states shift to left and decrease exponentially. At the same time, peaks from the resonant interfacial states shift less but decrease with ratio much faster than exponential form. As peaks in ( ) T E with energy below/above E F contribute to positive/negative S, we observe peaks above E F dominate the thermoelectric effects. At room temperature, the DBMTJs with 3 L and 7 L MgO barriers show S of −46.5 and m --210 V K 1 , respectively, and the latter is almost completely from the resonant QW states.

Single-barrier MTJs
By changing the thickness of the sandwiched Fe, the positions of the resonant peaks from the QW states in ( ) T E can be shift to E F , and larger thermoelectric effects may be achieved. In table 2

multi-barrier MTJs
Although the Seebeck coefficient in MgO-based MTJs with single or double barriers is comparable to the wellstudied thermoelectric materials, the optimistic room temperature ZT is around 10 −1 . The huge phonon thermal conductance would be responsible for the small ZT. By introducing more barriers (interfaces), the thermal conductance carried by phonon would be strongly restrained, and larger ZT is expected. , , e , and up-limit of ZT, while the introducing of more MgO barriers have a large effect on the room temperature ZT as shown in Table 2. Room temperature thermoelectric effect in ideal symmetric Fe | MgO(m)| Fe(l)| MgO(m)| Fe and asymmetric Fe | MgO(m)| Fe(l)| MgO(m)| Co (in bracket) DBMTJs.  The room temperature ZT almost increases linearly with the increase of the barrier number, leading to ZT 1 when barrier numbers are larger than 400. In the calculations, we suppose that the junction is infinite in lateral size, allowing the calculations simple but a little different from the real setups. As the phonon thermal conductance is sensitive to the size of lateral lattice, especially for the nanoscale devices, a MTJs with barrier numbers much less than 400 maybe possible to achieve ZT 1 in the experiment.

Asymmetric Fe | MgO | Fe | Vac | Fe DBMTJs
Although a up-limit of ZT 5 is found in a DBMTJ with 7 L MgO barrier as list in table 2, the real ZT is relatively small for the huge phonon thermal conductance. One simple way to restrain k p is introducing a vacuum barrier [33]. Substituting one MgO barrier by vacuum in the DBMTJ, the up-limit of ZT would be achieved by blocking phonon thermal constance. Two factors are responsible to the larger ZT in thicker barrier junction than that in the thinner one, one is the larger S and another is the larger electronic conductance to thermal conductance ratio k G e . Both factors are related to the sharper peak in ( ) T E in thick barrier junction, comparing with thinner one. From the evolvement of the shape of ( ) T E in Fe | MgO| Fe| Vac| Fe DBMTJs with respect to the barrier thickness as shown in figure 5(a), it is reasonable to deduce that the peaks in ( ) T E would be even sharper in junctions with MgO barrier thickness more than 7 L, and even larger room temperature thermoelectric effects are expected in such junction.
The most prevailing imperfection in MgO-based MTJs is oxygen vacancy (OV). When OV exists at the Fe| MgO interface, the peaks in ( ) T E are broadened and shift compared to clean junctions, leading to an enhanced k e , and weakened S G , , and ZT. Fore example, 5% OV in a Fe | MgO (7) 1 , leading to a reduction of 95% in ZT. So, to achieve large thermoelectricity, the MTJs should be as clean as possible.
The nature of enhanced thermoelectric effects in the MgO-based MTJs with double-and multi-barrier is the involvement of resonant QW states. Insulator | metal | insulator structure is the basis of QW states, and materials in the MTJs open a new parameter space for thermoelectric effects. So, enhanced thermoelectric effects in MTJs with double-and multi-barrier can be a general phenomena.
So far, we have discussed the effect of a group of structure parameters on the thermoelectric effects in the MgO-based MTJs, and give an example to achieve the up-limit of ZT. Besides the structure parameters discussed above, exterior parameters can also be used to modulate the thermoelectric effects such as texture (structure) engineering [34], electrons (holes) doping [35,36], electric bias [7,37,38], strain and stress [39,40], and so on. From the up-limit of ZT predicted first-principlely, one can see there are much space to improve the thermoelectric effects in the MgO-based MTJs.

Summary
Based on atomic first principles, we compute the thermoelectric effects in the MgO-based MTJs. The effects of the structure parameters on the thermoelectric effects are discussed systematically such as barrier thickness, barrier numbers, sandwiched Fe thickness, asymmetric barrier, and so on. We predict the large Seebeck coefficient and up-limit of ZT in double-and multi-barrier MTJs. In a multi-barrier MTJs, the linearly increased ZT with respect to the number of MgO barriers is predicted, where Seebeck coefficient is constant while thermal conductance (mainly from phonon) decreases linearly. By restraining the phonon thermal conductance by vacuum barrier, the up-limit of ZT can be obtained. At room temperature, Seebeck coefficient m » --S 220 V K 1 and ZT ≈ 3.5 are predicted in an asymmetric Fe | MgO(7)| Fe(24)| Vaccum(5)| Fe MTJs. The resonant QW states near Fermi energy are considered to be responsible for the enhanced thermoelectric effects in the double-and multi-barrier MTJs.